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(K-4) Elementary School Learning Targets	(5-8) Middle School Learning Targets	(9-12) High School Learning Targets
E.NO-2 Build an understanding of computational strategies and algorithms: Fluently add, subtract, multiply, divide, and estimate; Perform and represent operations with whole numbers, fractions, and mixed numbers; Identify multiples and factors of whole numbers.	M.NO-2 Expand use of computational strategies and algorithms to rational numbers: Perform operations fluently with rational numbers, including fractions, decimals, and percents; Identify equivalence of indicated division and fractional parts.	H.NO-2 Build an understanding of computational strategies and algorithms including matrices and irrational and complex numbers: Use matrix operations and complex and irrational number operations; Apply exponential expressions (laws and properties).

Number and Operations: Whole numbers, Ratios, Exponents
Grades K-2	Grades 3-4	Grades 5-6	Grades 7-8	HS
K.NO.2a1 Count 2 sets to find sums up to 10	3.NO.2b1 Use the relationships between addition and subtraction to solve problems	5.NO.2a1 Solve problems or word problems using up to three digit numbers and addition or subtraction	7.NO.2i1 Solve multiplication problems with positive/negative numbers	H.NO.2a1 Solve simple equations using rational numbers with one or more variables
K.NO.2a2 Decompose a set of up to 10 objects into a group; count the quantity in each group	3.NO.2c1 Solve multi-step addition and subtraction problems up to 100	5.NO.2a2 Separate a group of objects into equal sets when given the number of sets to find the total in each set with the total number less than 50	7.NO.2i2 Solve division problems with positive / negative numbers	H.NO.2b1 Explain the pattern for the sum or product for combinations of rational and irrational numbers
K.NO.2a3 Solve word problems within 10	3.NO.2d1 Find the total number of objects when given the number of identical groups and the number of objects in each group neither number larger than 5	5.NO.2a3 Find whole number quotients up to two divendends and two divisors		H.NO.2c1 Simplify expressions that include exponents
1.NO.2a4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record or select the answer	3.NO.2d2 Find total number inside an array with neither number in the columns or rows larger than 5	5.NO.2a4 Find whole number quotients up to four divendends and two divisors		H.NO.2c2 Rewrite expressions that include rational exponents
1.NO.2a5 Count 2 sets to find sums up to 10	3.NO.2d3 Solve multiplication problems with neither number greater than 5	5.NO.2a5 Solve word problems that require multiplication or division
1.NO.2a6 Count 2 sets to find sums up to 20	3.NO.2d4 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 5	6.NO.2a6 Solve problems or word problems using up to three digit numbers and any of the four operations
1.NO.2a7 Decompose a set of up to 10 objects into a group; count the quantity in each group	3.NO.2d5 Determine the number of groups given the total number of objects and the number of objects in each group where the number in each group and the number of groups is not greater than 5	6.NO.2e1 Determine the difference between two integers using a number line
1.NO.2a8 Decompose a set of up to 20 objects into a group; count the quantity in each group	3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100	6.NO.2e2 Compare two numbers on a number line (e.g., -2 > -9)
1.NO.2a9 Use manipulatives or representations to write simple addition or subtraction equations within 20 based upon a word problem	4.NO.2c2 Solve multi digit addition and subtraction problems up to 1000
1.NO.2a10 Use data presented in graphs (i.e., pictoral, object) to solve one step "how many more" or "how many less" word problems	4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10
1.NO.2a11 Solve word problems within 20	4.NO.2d7 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 10
1.NO.2c1 Identify and apply addition and equal signs	4.NO.2d8 Match an accurate addition and multiplication equation to a representation
2.NO.2a12 Model addition and subtraction with base 10 blocks within 20	4.NO.2e2 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100
2.NO.2a13 Model addition and subtraction with base 10 blocks within 50	4.NO.2f1 Identify multiples for a whole number (e.g., 2= 2, 4, 6, 8, 10)
2.NO.2a14 Model addition and subtraction with base 10 blocks within 100	4.NO.2f2 Solve multiplication problems up to two digits by one digit
2.NO.2a15 Remove objects from a set in a subtraction situation to find the amount remaining up to a minend of 20
2.NO.2a16 Solve word problems within 20
2.NO.2a17 Solve word problems within 100
2.NO.2a18 Use diagrams and number lines to solve addition or subtraction problems
2.NO.2a19 Combine up to 3 sets of 20 or less
2.NO.2b1 Use commutative properties to solve addition problems with sums up to 20 (e.g., 3+8=11 therefore 8+3=__)
2.NO.2b2 Use associative property to solve addition problems with sums up to 20
2.NO.2c2 Identify and apply addition, subtraction, and equal signs
2.NO.2c3 Compose ones into tens and/or tens into hundreds in addition situation
2.NO.2c4 Decompose tens into ones and/or hundreds into tens in subtraction situations

Number and Operations: Fractions and Decimals
	4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ )	5.NO.2b1 Add and subtract fractions with unlike denominators by replacing fractions with equivalent fractions (identical denominators)	7.NO.2f1 Identify the proportional relationship between two quantities
	4.NO.2h1 Add and subtract fractions with like denominators of (2,3,4, or 8)	5.NO.2b2 Add or subtract fractions with unlike denominators	7.NO.2f2 Determine if two quantities are in a proportional relationship using a table of equivalent ratios or points graphed on a coordinate plane
	4.NO.2h2 Add and subtract fractions with like denominators (2,3,4, or 8) using representations	5.NO.2b3 Multiply or divide fractions	7.NO.2f3 Find unit rates given a ratio
	4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8)	5.NO.2c1 Solve 1 step problems using decimals	7.NO.2f4 Use a rate of change or proportional relationship to determine the points on a coordinate plane
		5.NO.2c2 Solve word problems involving the addition, subtraction, multiplication or division of fractions	7.NO.2f5 Use proportions to solve ratio problems
		6.NO.2c3 Solve one step, addition, subtraction, multiplcation, or division problems with fractions or decimals	7.NO.2f6 Solve word problems involving ratios
		6.NO.2c4 Solve word problems involving the addition, subtraction, multiplication or division of fractions	7.NO.2h2 Solve one step percentage increase and decrease problems
			8.NO.2i3 Solve one step addition, subtraction, multiplication, division problems with fractions, decimals, and positive/negative numbers
			8.NO.2i4 Solve two step addition, subtraction, multiplication, and division problems with fractions, decimals, or positive/negative numbers

Number and Operations: Application
			7.NO.2h1 Find percents in real world contexts

Grade Differentiation

Elementary School Progress Indicators

Progress Indicator: E.NO.2a representing addition and subtraction in multiple ways (composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping
Core Content Connectors: K	CCSS Domain/Cluster	Common Core State Standard
K.NO.2a1 Count 2 sets to find sums up to 10	Operations and Algebraic Thinking K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.	K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
K.NO.2a2 Decompose a set of up to 10 objects into a group; count the quantity in each group	Operations and Algebraic Thinking K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.	K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.NO.2a3 Solve word problems within 10	Operations and Algebraic Thinking K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.	K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Progress Indicator: E.NO.2a representing addition and subtraction in multiple ways (composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.NO.2a4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record or select the answer	Operations and Algebraic Thinking K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.	K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation
1.NO.2a5 Count 2 sets to find sums up to 10	Operations and Algebraic Thinking K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.	K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.A.5 Fluently add and subtract within 5.
1.NO.2a6 Count 2 sets to find sums up to 20	Operations and Algebraic Thinking 1 OA Add and subtract within 20.	1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.NO.2a7 Decompose a set of up to 10 objects into a group; count the quantity in each group	Operations and Algebraic Thinking K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.	K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.A.5 Fluently add and subtract within 5.
1.NO.2a8 Decompose a set of up to 20 objects into a group; count the quantity in each group	Operations and Algebraic Thinking 1 OA Add and subtract within 20.	1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.NO.2a9 Use manipulatives or representations to write simple addition or subtraction equations within 20 based upon a word problem	Operations and Algebraic Thinking 1 OA Represent and solve problems involving addition and subtraction.	1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.NO.2a10 Use data presented in graphs (i.e., pictorial, object) to solve one step "how many more" or "how many less" word problems	Operations and Algebraic Thinking 1 OA Represent and solve problems involving addition and subtraction.	1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.NO.2a11 Solve word problems within 20	Operations and Algebraic Thinking 1 OA Represent and solve problems involving addition and subtraction.	1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.NO.2c1 Identify and apply addition and equal signs	Operations and Algebraic Thinking 1 OA Work with addition and subtraction equations.	1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Progress Indicator: E.NO.2a representing addition and subtraction in multiple ways (composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.NO.2a12 Model addition and subtraction with base 10 blocks within 20	Number and Operations in Base Ten 2 NBT Use place value understanding and properties of operations to add and subtract.	2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
2.NO.2a13 Model addition and subtraction with base 10 blocks within 50	Number and Operations in Base Ten 2 NBT Use place value understanding and properties of operations to add and subtract.	2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
2.NO.2a14 Model addition and subtraction with base 10 blocks within 100	Number and Operations in Base Ten 2 NBT Use place value understanding and properties of operations to add and subtract.	2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
2.NO.2a15 Remove objects from a set in a subtraction situation to find the amount remaining up to a minuend of 20	Operations and Algebraic Thinking 1 OA Represent and solve problems involving addition and subtraction.	1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.B.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.
2.NO.2a16 Solve word problems within 20	Number and Operations in Base Ten 2 OA Represent and solve problems involving addition and subtraction.	2.OA.A.1 Use addition and subtraction within 100 to solve one-and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions
2.NO.2a17 Solve word problems within 100	Operations and Algebraic Thinking 2 OA Represent and solve problems involving addition and subtraction.	2.OA.A.1 Use addition and subtraction within 100 to solve one-and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions
2.NO.2a18 Use diagrams and number lines to solve addition or subtraction problems	Number and Operations in Base Ten 2 NBT Use place value understanding and properties of operations to add and subtract.	2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.MD.B.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
2.NO.2a19 Combine up to 3 sets of 20 or less	Number and Operations in Base Ten 2 NBT Use place value understanding and properties of operations to add and subtract.	2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
Progress Indicator: E.NO.2b explaining or modeling the relationship between addition and subtraction
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.NO.2b1 Use commutative properties to solve addition problems with sums up to 20 (e.g., 3+8=11 therefore 8+3=__)	Operations and Algebraic Thinking 1 OA Understand and apply properties of operations and the relationship between addition and subtraction.	1.OA.B.3 Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
2.NO.2b2 Use associative property to solve addition problems with sums up to 20	Operations and Algebraic Thinking 1 OA Understand and apply properties of operations and the relationship between addition and subtraction.	1.OA.B.3 Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.NO.2c2 Identify and apply addition, subtraction, and equal signs	Number and Operations in Base Ten 1 OA Work with addition and subtraction equations.	1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
2.NO.2c3 Compose ones into tens and/or tens into hundreds in addition situation	Number and Operations in Base Ten 1 NBT;2 NBT Use place value understanding and properties of operations to add and subtract.	1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NO.2c4 Decompose tens into ones and/or hundreds into tens in subtraction situations	Number and Operations in Base Ten 1 NBT; 2 NBT Use place value understanding and properties of operations to add and subtract.	1.NBT.C.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Progress Indicator: E.NO.2b explaining or modeling the relationship between addition and subtraction
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.NO.2b1 Use the relationships between addition and subtraction to solve problems	Number and Operations in Base Ten 3 NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.	3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.NO.2c1 Solve multi-step addition and subtraction problems up to 100	Number and Operations in Base Ten 3 NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.	3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Progress Indicator: E.NO.2d modeling multiplication (equal-sized groups, arrays, area models, equal-sized jumps on number lines, multiplicative comparisons) and division (successive subtraction, partitioning, sharing) of whole numbers
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.NO.2d1 Find the total number of objects when given the number of identical groups and the number of objects in each group neither number larger than 5	Operations and Algebraic Thinking 2 OA Work with equal groups of objects to gain foundations for multiplication. 3 OA Represent and solve problems involving multiplication and division.	2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. 2.G.A.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
3.NO.2d2 Find total number inside an array with neither number in the columns or rows larger than 5	Operations and Algebraic Thinking 2 OA Work with equal groups of objects to gain foundations for multiplication. 3 OA Represent and solve problems involving multiplication and division.	2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7
3.NO.2d3 Solve multiplication problems with neither number greater than 5	Operations and Algebraic Thinking 3 OA Represent and solve problems involving multiplication and division.	3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7
3.NO.2d4 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 5	Operations and Algebraic Thinking 3 OA Represent and solve problems involving multiplication and division.	3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8
3.NO.2d5 Determine the number of groups given the total number of objects and the number of objects in each group where the number in each group and the number of groups is not greater than 5	Operations and Algebraic Thinking 3 OA Represent and solve problems involving multiplication and division.	3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Progress Indicator: E.NO.2e describing relationships between addition-multiplication; multiplication-division; addition-subtraction; why commutative property does not apply to subtraction or division
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100	Operations and Algebraic Thinking 3 OA Solve problems involving the four operations, and identify and explain patterns in arithmetic.	3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.NO.2c2 Solve multi digit addition and subtraction problems up to 1000	Number and Operations in Base Ten 3 NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.	3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Progress Indicator: E.NO.2d modeling multiplication (equal-sized groups, arrays, area models, equal-sized jumps on number lines, multiplicative comparisons) and division (successive subtraction, partitioning, sharing) of whole numbers
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10	Operations and Algebraic Thinking 3 OA Represent and solve problems involving multiplication and division.	3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
4.NO.2d7 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 10	Operations and Algebraic Thinking 4 OA Use the four operations with whole numbers to solve problems.	4.OA.A.2 Multiply or divide to solve word problem involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem distinguishing multiplicative comparison from additive comparison. 3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
4.NO.2d8 Match an accurate addition and multiplication equation to a representation	Operations and Algebraic Thinking 3 OA Represent and solve problems involving multiplication and division.	3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Progress Indicator: E.NO.2e describing relationships between addition-multiplication; multiplication-division; addition-subtraction; why commutative property does not apply to subtraction or division
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.NO.2e2 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100	Operations and Algebraic Thinking 4 OA Use the four operations with whole numbers to solve problems.	4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Progress Indicator: E.NO.2f identifying factors and multiples of numbers
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.NO.2f1 Identify multiples for a whole number (e.g., 2= 2, 4, 6, 8, 10)	Operations and Algebraic Thinking 4 OA Gain familiarity with factors and multiples.	4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
4.NO.2f2 Solve multiplication problems up to two digits by one digit	Number and Operations in Base Ten 4 NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.	4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
Progress Indicator: E.NO.2g recognizing fractions as one number/one quantity, rather than two numbers (numerator and denominator) and using number lines to represent magnitude of fractions
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ )	Numbers and Operations – Fractions 3 NF Develop understanding of fractions as numbers. Numbers and Operations – Fractions 4 NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.	3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Progress Indicator: E.NO.2h adding, subtracting, and multiplying fractions, including mixed numbers
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.NO.2h1 Add and subtract fractions with like denominators of (2,3,4, or 8)	Numbers and Operations – Fractions 4 NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.	4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
4.NO.2h2 Add and subtract fractions with like denominators (2,3,4, or 8) using representations	Numbers and Operations – Fractions 4 NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.	4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8)	Numbers and Operations – Fractions 3 NF Develop understanding of fractions as numbers. 4 NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.	3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Progress Indicator: M.NO.2a working flexibility with common addition, subtraction, multiplication, and division situations
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.NO.2a1 Solve problems or word problems using up to three digit numbers and addition or subtraction or multiplication	Operations and Algebraic Thinking 4 OA Use the four operations with whole numbers to solve problems.	4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
5.NO.2a2 Separate a group of objects into equal sets when given the number of sets to find the total in each set with the total number less than 50	Number and Operations in Base Ten 4 NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.	4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NO.2a3 Find whole number quotients up to two dividends and two divisors	Number and Operations in Base Ten 5 NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.	5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NO.2a4 Find whole number quotients up to four dividends and two divisors	Number and Operations in Base Ten 5 NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.	5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NO.2a5 Solve word problems that require multiplication or division	Number and Operations in Base Ten 5 NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.	5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Progress Indicator: M.NO.2b recognizing fractions as one number/one quantity, rather than two numbers (numerator and denominator) and using number lines to represent magnitude of fractions and equivalent /non-equivalent fractions
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.NO.2b1 Add and subtract fractions with unlike denominators by replacing fractions with equivalent fractions (identical denominators)	Numbers and Operations – Fractions 5 NF Use equivalent fractions as a strategy to add and subtract fractions.	5.NF.A.1 Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd).
5.NO.2b2 Add or subtract fractions with unlike denominators	Numbers and Operations – Fractions 5 NF Use equivalent fractions as a strategy to add and subtract fractions.	5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd). 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
5.NO.2b3 Multiply a fraction by a whole or mixed number.	Numbers and Operations – Fractions 5 NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions.	5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5.NF.B.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins?
Progress Indicator: M.NO.2c using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.NO.2c1 Solve 1 step problems using decimals	Number and Operations in Base Ten 5 NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.	5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
5.NO.2c2 Solve word problems involving the addition, subtraction, multiplication or division of fractions	Numbers and Operations – Fractions 5 NF Use equivalent fractions as a strategy to add and subtract fractions.	5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Explanations and clarifications: Not included: M.NO.2d contrasting situations as additive or multiplicative

Middle School Progress Indicators

Progress Indicator: M.NO.2a working flexibility with common addition, subtraction, multiplication, and division situations
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.NO.2a6 Solve problems or word problems using up to three digit numbers and any of the four operations	Expressions and Equations 6 EE Reason about and solve one-variable equations and inequalities.	6.EE.B.7 Solve real world and mathematical problems by writing and solving equations of the form x = p = q and px = q for cases in which p, q, and x are all non negative rational numbers.
Progress Indicator: M.NO.2c using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.NO.2c3 Solve one step, addition, subtraction, multiplication, or division problems with fractions or decimals	The Number System 6 NS Apply and extend previous understandings of multiplications and division to divide fractions by fractions.	6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc). How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi.? Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NO.2c4 Solve word problems involving the addition, subtraction, multiplication or division of fractions	Numbers and Operations – Fractions 5 NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions. The Number System 6 NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions.	5.NF.B.7c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc). How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples.
Progress Indicator: M.NO.2e ordering/comparing integers and representing them on the number line
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.NO.2e1 Determine the difference between two integers using a number line	The Number System 6 NS Apply and extend previous understandings of numbers to the system of rational numbers.	6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
6.NO.2e2 Compare two numbers on a number line (e.g., -2 > -9)	The Number System 6 NS Apply and extend previous understandings of numbers to the system of rational numbers.	6.NS.C.7 Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

Progress Indicator: M.NO.2f describing proportional relationships and solving related problems
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.NO.2f1 Identify the proportional relationship between two quantities	Ratios and Proportional Relationships 7 RP Analyze proportional relationships and use them to solve real-world and mathematical problems.	7.RP.A.2 Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7.NO.2f2 Determine if two quantities are in a proportional relationship using a table of equivalent ratios or points graphed on a coordinate plane	Ratios and Proportional Relationships 7 RP Analyze proportional relationships and use them to solve real-world and mathematical problems.	7.RP.A.2 Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.NO.2f3 Find unit rates given a ratio	Ratios and Proportional Relationships 7 RP Analyze proportional relationships and use them to solve real-world and mathematical problems.	7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units
7.NO.2f4 Use a rate of change or proportional relationship to determine the points on a coordinate plane	Ratios and Proportional Relationships 7 RP Analyze proportional relationships and use them to solve real-world and mathematical problems.	7.RP.A.2 Recognize and represent proportional relationships between quantities. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7.NO.2f5 Use proportions to solve ratio problems	Ratios and Proportional Relationships 7 RP Analyze proportional relationships and use them to solve real-world and mathematical problems.	7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
7.NO2.f6 Solve word problems involving ratios	Ratios and Proportional Relationships 6 RP Understand ratio concepts and use ratio reasoning to solve problems.	7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Progress Indicator: M.NO.2h using operations involving percents and percent increase/decrease
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.NO.2h1 Find percents in real world contexts	Ratios and Proportional Relationships 7 RP Analyze proportional relationships and use them to solve real-world and mathematical problems.	7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
7.NO.2h2 Solve one step percentage increase and decrease problems	Ratios and Proportional Relationships 7 RP Analyze proportional relationships and use them to solve real-world and mathematical problems.	7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Progress Indicator: M.NO.2i using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.NO.2i1 Solve multiplication problems with positive/negative numbers	The Number System 7 NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.	7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NO.2i2 Solve division problems with positive/negative numbers	The Number System 7 NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.	7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Explanations and clarifications: Not included: M.NO.2g using operations with complex fractions

Progress Indicator: M.NO.2i using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.NO.2i3 Solve one step addition, subtraction, multiplication, division problems with fractions, decimals, and positive/negative numbers	The Number System 7 NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.	7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
8.NO.2i4 Solve two step addition, subtraction, multiplication, and division problems with fractions, decimals, or positive/negative numbers	The Number System 7 NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.	7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

High School Progress Indicators

Progress Indicator: H.NO.2a using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.NO.2a1 Solve simple equations using rational numbers with one or more variables	Reasoning with Equations and Inequalities A REI Understand solving equations as a process of reasoning and explain the reasoning.	HSA-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Progress Indicator: H.NO.2b operating with irrational and complex numbers
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.NO.2b1 Explain the pattern for the sum or product for combinations of rational and irrational numbers	The Real Number System N RN Use properties of rational irrational numbers.	HSN-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational.
Progress Indicator: H.NO.2c identifying exponential situations and applying the laws and properties of exponents in simplifying expressions and solving equations
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.NO.2c1 Simplify expressions that include exponents	Seeing Structure in Expressions A SSE Interpret the structures of expressions.	HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
H.NO.2c2 Rewrite expressions that include rational exponents	The Real Number System N RN Extend the properties of exponents to rational exponents. Seeing Structure in Expressions A SSE Interpret the structures of expressions.	HSN-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
'Explanations and clarifications: Not included: H.PRF.1d recognizing that there limitations in mathematics models A.CE-3 S.IC-2'

Geometry

Revision as of 10:51, 7 July 2014

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Elementary School Progress Indicators

Middle School Progress Indicators

High School Progress Indicators

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@@ Line 3: / Line 3: @@
 {| border=1
-||'''(K-4) Elementary School Learning Targets'''
-||'''(5-8) Middle School Learning Targets'''
+|width = "833" style="background-color:#FFFFFF;"|'''(K-4) Elementary School Learning Targets'''
-||'''(9-12) High School Learning Targets'''
+|width = "833" style="background-color:#FFFFFF;"|'''(5-8) Middle School Learning Targets'''
+|width = "834" style="background-color:#FFFFFF;"|'''(9-12) High School Learning Targets'''
 |-
-||'''''E.GM-1''' Recognize that two-and three-dimensional shapes have particular attributes:''
-''Describe and compare objects and figures based on reasoning and the properties and attributes of the shapes;''
-''Compose, decompose, and draw figures based on spatial reasoning and the properties and attributes of the shapes;''
-''Apply concepts of symmetry.''
-||'''''GM-1 '''Apply reasoning using properties of two- and three-dimensional shapes to analyze, represent, and model geometric relationships:''
+|width = "417" style="background-color:#FFFFFF;"|'''''E.NO-2 '''Build an understanding of computational strategies and algorithms:''
-''Classify objects based on attributes and properties and solve problems using geometric relationships and properties;''
+*''Fluently add, subtract, multiply, divide, and estimate;''
-''Decompose figures into new figures and construct figures with given conditions;''
+*''Perform and represent operations with whole numbers, fractions, and mixed numbers;''
-''Apply concepts of parallel and perpendicular.''
+*''Identify multiples and factors of whole numbers.''
+|width = "417" style="background-color:#FFFFFF;"|'''''M.NO-2 '''Expand use of computational strategies and algorithms to rational numbers:''
+*''Perform operations fluently with rational numbers, including fractions, decimals, and percents;''
+*''Identify equivalence of indicated division and fractional parts.''
-||'''''H.GM-1 '''Explain solutions using geometric attributes and relationships in diverse contexts:''
+|width = "417" style="background-color:#FFFFFF;"|'''''H.NO-2 '''Build an understanding of computational strategies and algorithms including matrices and irrational and complex numbers:''
-''Extend understanding of congruence and similarity working with complex figures and situations;''
+*''Use matrix operations and complex and irrational number operations;''
-''Solve problems involving quadrilaterals and triangles;''
+*''Apply exponential expressions (laws and properties).''
-''Perform geometric constructions and use informal proofs to describe relationships and transformations''
 |}
@@ Line 31: / Line 31: @@
 {| border=1
-| colspan= "5" align= "center" |'''Properties and attributes of shapes and figures and their corresponding parts'''
+|width = "417" colspan= "5" align= "center" style="background-color:#FFFFFF;"|'''Number and Operations: Whole numbers, Ratios, Exponents'''
 |-
-|width = "500" align=center|'''Grades K-2'''
-|width = "500" align=center|'''Grades 3-4'''
+|width = "417" style="background-color:#FFFFFF;"|'''Grades K-2'''
+|width = "417" style="background-color:#FFFFFF;"|'''Grades 3-4'''
-|width = "500" align=center|'''Grades 5-6'''
+|width = "417" style="background-color:#FFFFFF;"|'''Grades 5-6'''
-|width = "500" align=center|'''Grades 7-8'''
+|width = "417" style="background-color:#FFFFFF;"|'''Grades 7-8'''
-|width = "500" align=center|'''HS'''
+|width = "415" style="background-color:#FFFFFF;"|'''HS'''
 |-
-||'''K.GM.1a1'''
-'''Recognize two- dimensional shapes (e.g., circle, square, triangle, rectangle) regardless of orientation of size'''
-||'''3.GM.1h1 Identify shared attributes of shapes'''
-||'''5.GM.1a1'''
+|width = "417" style="background-color:#FFFFFF;"|'''K.NO.2a1 Count 2 sets to find sums up to 10'''
-'''Recognize properties of simple plane figures'''
-||'''7.GM.1e1'''
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2b1 Use the relationships between addition and subtraction to solve problems'''
-'''Construct or draw plane figures using properties'''
-||'''H.GM.1e1 Make formal geometric constructions with a variety of tools and methods'''
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2a1 Solve problems or word problems using up to three digit numbers and addition or subtraction'''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2i1 Solve multiplication problems with positive/negative numbers'''
+|width = "415" style="background-color:#FFFFFF;"|'''H.NO.2a1 Solve simple equations using rational numbers with one or more variables'''
 |-
-||'''K.GM.1a2'''
-'''Recognize two-dimensional shapes in environment regardless of orientation of size'''
-||'''4.GM.1h2 Classify two-dimensional shapes based on attributes (# of angles)'''
+|width = "417" style="background-color:#FFFFFF;"|'''K.NO.2a2 Decompose a set of up to 10 objects into a group; count the quantity in each group'''
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2c1 Solve multi-step addition and subtraction problems up to 100'''
-||'''5.GM.1b1'''
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2a2 Separate a group of objects into equal sets when given the number of sets to find the total in each set with the total number less than 50'''
-'''Distinguish plane figures by their properties'''
-||'''8.GM.1g1'''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2i2 Solve division problems with positive / negative numbers'''
-'''Recognize congruent and similar figures '''
-||'''H.GM.1b1 Use definitions to determine congruency and similarity of figures'''
+|width = "415" style="background-color:#FFFFFF;"|'''H.NO.2b1 Explain the pattern for the sum or product for combinations of rational and irrational numbers'''
 |-
-||'''K.GM.1a3'''
-'''Use spatial language (e.g., above, below, etc.) to describe two-dimensional shapes'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''K.NO.2a3 Solve word problems within 10 '''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2d1 Find the total number of objects when given the number of identical groups and the number of objects in each group neither number larger than 5 '''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2a3 Find whole number quotients up to two divendends and two divisors'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|'''H.NO.2c1 Simplify expressions that include exponents'''
 |-
-||'''2.GM.1a4 Identify two-dimensional shapes such as rhombus, pentagons, hexagons, octagon, ovals, equilateral, isosceles, and scalene triangles'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record or select the answer'''
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2d2 Find total number inside an array with neither number in the columns or rows larger than 5'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2a4 Find whole number quotients up to four divendends and two divisors'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "415" style="background-color:#FFFFFF;"|'''H.NO.2c2 Rewrite expressions that include rational exponents'''
 |-
-||'''1.GM.1b1 Identify shapes as two-dimensional (lying flat) or three-dimensional (solid)'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a5 Count 2 sets to find sums up to 10'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2d3 Solve multiplication problems with neither number greater than 5'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2a5 Solve word problems that require multiplication or division'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''1.GM.1b2'''
-'''Distinguish two-dimensional shapes based upon their attributes (i.e., size, corners, and points)'''
-||'''4.GM.1j1 Recognize a point, line and line segment, rays in two-dimensional figures'''
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a6 Count 2 sets to find sums up to 20'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2d4 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 5 '''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''6.NO.2a6 Solve problems or word problems using up to three digit numbers and any of the four operations'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''2.GM.1b3'''
-'''Distinguish two- or three-dimensional shapes based upon their attributes (i.e., # of sides, even or different lengths, # of faces, # of corners)'''
-||'''4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures'''
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a7 Decompose a set of up to 10 objects into a group; count the quantity in each group'''
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2d5 Determine the number of groups given the total number of objects and the number of objects in each group where the number in each group and the number of groups is not greater than 5'''
-||'''5.GM.1j1'''
+|width = "417" style="background-color:#FFFFFF;"|'''6.NO.2e1	 Determine the difference between two integers using a number line'''
-'''Recognize parallel and perpendicular lines within the context of figures'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''K.GM.1c1 '''
-'''Compose a larger shape from smaller shapes'''
-||'''4.GM.1j3 Recognize an angle in two-dimensional figures'''
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a8 Decompose a set of up to 20 objects into a group; count the quantity in each group'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''6.NO.2e2 Compare two numbers on a number line (e.g., -2 > -9)'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''1.GM.1c 2'''
-'''Compose or recognize two-and three-dimensional shapes'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a9 Use manipulatives or representations to write simple addition or subtraction equations within 20 based upon a word problem '''
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2c2 Solve multi digit addition and subtraction problems up to 1000'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''2.GM.1d1'''
-'''Compose three-dimensional shapes'''
-||'''4.GM.1j4 Categorize angles as right, acute, or obtuse'''
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a10 Use data presented in graphs (i.e., pictoral, object) to solve one step "how many more" or "how many less" word problems'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
-|}
+|width = "415" style="background-color:#FFFFFF;"|
+|-
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2a11 Solve word problems within 20'''
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2d7 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 10'''
-{| border=1
+|width = "417" style="background-color:#FFFFFF;"|
-| colspan= "5" align= "center" |'''Transformation in the Coordinate Plane'''
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-|width = "500" align=center|'''Grades K-2'''
-|width = "500" align=center|'''Grades 3-4'''
+|width = "417" style="background-color:#FFFFFF;"|'''1.NO.2c1 Identify and apply addition and equal signs '''
-|width = "500" align=center|'''Grades 5-6'''
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2d8 Match an accurate addition and multiplication equation to a representation'''
-|width = "500" align=center|'''Grades 7-8'''
+|width = "417" style="background-color:#FFFFFF;"|
-|width = "500" align=center|'''HS'''
+|width = "417" style="background-color:#FFFFFF;"|
-|-
+|width = "415" style="background-color:#FFFFFF;"|
-||'''2.GM.1e1'''
-'''Draw two-dimensional shapes with specific attributes'''
+|-
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a12 Model addition and subtraction with base 10 blocks within 20'''
-||'''4.GM.1k1'''
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2e2 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100'''
-'''Recognize a line of symmetry in a figure'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a13 Model addition and subtraction with base 10 blocks within 50'''
-||'''5.GM.1c1 Locate the x and y axis on a graph'''
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2f1 Identify multiples for a whole number (e.g., 2= 2, 4, 6, 8, 10)'''
-||'''8.GM.1i1 Identify supplementary angles'''
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a14 Model addition and subtraction with base 10 blocks within 100'''
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2f2 Solve multiplication problems up to two digits by one digit'''
-||'''5.GM.1c2 Locate points on a graph'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''8.GM.1i2 Identify complimentary angles'''
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a15 Remove objects from a set in a subtraction situation to find the amount remaining up to a minend of 20'''
-||'''5.GM.1c3 Use order pairs to graph given points'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''8.GM.1i3 Identify adjacent angles'''
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a16 Solve word problems within 20'''
-||'''6.GM.1c4 Locate points on a graph'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''8.GM.1i4 '''
+|width = "417" style="background-color:#FFFFFF;"|
-'''Use angle relationships to find the value of a missing angle'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a17 Solve word problems within 100'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''6.GM.1c5 Use order pairs to graph given points'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''8.GM.1f1 Recognize a rotation, reflection, or translation of a figure'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''H.GM.1c 1 Construct, draw or recognize a figure after its rotation, reflection, or translation'''
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a18 Use diagrams and number lines to solve addition or subtraction problems'''
-||'''6.GM.1c6 Find coordinate values of points in the context of a situation'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''H.GM.1d1Use the translations, reflections, rotations and dilations in the coordinate plane to solve problems with right angles'''
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2a19 Combine up to 3 sets of 20 or less'''
+|width = "417" style="background-color:#FFFFFF;"|
-||'''6.GM.1c7 Use coordinate points to draw polygons'''
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2b1 Use commutative properties to solve addition problems with sums up to 20 (e.g., 3+8=11 therefore 8+3=__)'''
-||'''6.GM.1c8 Use coordinate points to find the side lengths of polygons that are horizontal or vertical '''
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
-|}
+|width = "415" style="background-color:#FFFFFF;"|
+|-
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2b2 Use associative property to solve addition problems with sums up to 20'''
+|width = "417" style="background-color:#FFFFFF;"|
-{| border=1
+|width = "417" style="background-color:#FFFFFF;"|
-| colspan= "5" align= "center" |'''Mathematical operations using shapes and figures'''
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-|width = "500" align=center|'''Grades K-2'''
-|width = "500" align=center|'''Grades 3-4'''
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2c2 Identify and apply addition, subtraction, and equal signs'''
+|width = "417" style="background-color:#FFFFFF;"|
-|width = "500" align=center|'''Grades 5-6'''
+|width = "417" style="background-color:#FFFFFF;"|
-|width = "500" align=center|'''Grades 7-8'''
+|width = "417" style="background-color:#FFFFFF;"|
-|width = "500" align=center|'''HS'''
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''1.GM.1f1'''
-'''Partition circles and rectangles into two equal parts'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2c3 Compose ones into tens and/or tens into hundreds in addition situation'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||'''7.GM.1h1 Add the area of each face of a prism to find surface area of three-dimensional objects'''
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''2.GM.1f2'''
-'''Partition circles and rectangles into 2 and 4 equal parts'''
-||'''3.GM.1i 1'''
+|width = "417" style="background-color:#FFFFFF;"|'''2.NO.2c4 Decompose tens into ones and/or hundreds into tens in subtraction situations'''
-'''Partition shapes into equal parts with equal area'''
-||'''6.GM.1d1 '''
+|width = "417" style="background-color:#FFFFFF;"|
-'''Find area of quadrilaterals'''
-||'''7.GM.1h2 Find the surface area of three-dimensional figures using nets of rectangles or triangles'''
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "415" style="background-color:#FFFFFF;"|
+|}
+{| border=1
+|width = "417" colspan= "5" align= "center" style="background-color:#FFFFFF;"|'''Number and Operations: Fractions and Decimals'''
 |-
-||'''2. GM.1f3 Label a partitioned shape (e.g., one whole rectangle was separated into 2 halves, one whole circle was separated into three thirds)'''
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||'''6.GM.1d2 Find area of triangles'''
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ )'''
-||'''7.GM.1h3 Find area of plane figures and surface area of solid figures (quadrilaterals)'''
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2b1 Add and subtract fractions with unlike denominators by replacing fractions with equivalent fractions (identical denominators)'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2f1 Identify the proportional relationship between two quantities'''
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2h1 Add and subtract fractions with like denominators of (2,3,4, or 8)'''
-||
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2b2 Add or subtract fractions with unlike denominators'''
-||'''7.GM.1h4 Find area of an equilateral, isosceles, and scalene triangle '''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2f2 Determine if two quantities are in a proportional relationship using a table of equivalent ratios or points graphed on a coordinate plane'''
-||
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2h2 Add and subtract fractions with like denominators (2,3,4, or 8) using representations '''
-||'''8.GM.1j1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2b3 Multiply or divide fractions '''
-||'''H.GM.1a1 Find hypotenuse of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2f3 Find unit rates given a ratio'''
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||
-||
+|width = "417" style="background-color:#FFFFFF;"|
-||
+|width = "417" style="background-color:#FFFFFF;"|'''4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8)'''
-||'''8.GM.1j2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2c1 Solve 1 step problems using decimals '''
-||'''H.GM.1a2 Find any missing side lengths of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2f4 Use a rate of change or proportional relationship to determine the points on a coordinate plane'''
-|}
+|width = "415" style="background-color:#FFFFFF;"|
+|-
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|
-=Grade Differentiation=
+|width = "417" style="background-color:#FFFFFF;"|'''5.NO.2c2 Solve word problems involving the addition, subtraction, multiplication or division of fractions '''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2f5 Use proportions to solve ratio problems'''
-==Elementary School Progress Indicators==
+|width = "415" style="background-color:#FFFFFF;"|
+|-
-{| border=1
+|width = "417" style="background-color:#FFFFFF;"|
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1a recognizing, describing (using spatial language) and naming shapes regardless of orientation or size and locating shapes in the environment'''
-|-
+|width = "417" style="background-color:#FFFFFF;"|
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: K'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "417" style="background-color:#FFFFFF;"|'''6.NO.2c3 Solve one step, addition, subtraction, multiplcation, or division problems with fractions or decimals'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2f6 Solve word problems involving ratios'''
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''K.GM.1a1'''
-'''Recognize two-dimensional shapes (e.g., circle, square, triangle, rectangle) regardless of orientation or size'''
-||'''Geometry'''
+|width = "417" style="background-color:#FFFFFF;"|
-K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|'''6.NO.2c4 Solve word problems involving the addition, subtraction, multiplication or division of fractions'''
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2h2 Solve one step percentage increase and decrease problems'''
+|width = "415" style="background-color:#FFFFFF;"|
+|-
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|'''8.NO.2i3 Solve one step addition, subtraction, multiplication, division problems with fractions, decimals, and positive/negative numbers'''
-||K.G.A.2 Correctly name shapes regardless of their orientations or overall size.
+|width = "415" style="background-color:#FFFFFF;"|
 |-
-||'''K.GM.1a2'''
-'''Recognize two-dimensional shapes in environment regardless of orientation or size'''
-||'''Geometry'''
+|width = "417" style="background-color:#FFFFFF;"|
-K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)
-||K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as ''above, below, beside, in front of, behind, and next to.''
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|'''8.NO.2i4 Solve two step addition, subtraction, multiplication, and division problems with fractions, decimals, or positive/negative numbers'''
+|width = "415" style="background-color:#FFFFFF;"|
+|}
+{| border=1
+|width = "417" colspan= "5" align= "center" style="background-color:#FFFFFF;"|'''Number and Operations: Application'''
 |-
-||'''K.GM.1a3'''
-'''Use spatial language (e.g., above, below, etc.) to describe two-dimensional shapes'''
-||'''Geometry'''
+|width = "417" style="background-color:#FFFFFF;"|
-K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)
-||K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as ''above, below, beside, in front of, behind, and next to.''
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|
+|width = "417" style="background-color:#FFFFFF;"|'''7.NO.2h1 Find percents in real world contexts'''
+|width = "415" style="background-color:#FFFFFF;"|
+|}
+==Grade Differentiation==
+=Elementary School Progress Indicators=
+{| border=1
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2a representing addition and subtraction in multiple ways (composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping'''
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1c'' ''composing two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter circles)'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: K'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: K'''
+|width = "833" style="background-color:#FFFFFF;"|'''K.NO.2a1 Count 2 sets to find sums up to 10'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
 |-
-||'''K.GM.1c 1'''
+|width = "833" style="background-color:#FFFFFF;"|'''K.NO.2a2 Decompose a set of up to 10 objects into a group; count the quantity in each group'''
-'''Compose a larger shape from smaller shapes'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-K G Analyze, compare, create, and compose shapes.
+K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
-||K.G.B.6 Compose simple shapes to form larger shapes. ''For example, "Can you join these two triangles with full sides touching to make a rectangle?"''
+|width = "834" style="background-color:#FFFFFF;"|K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
 |-
-|width = "833" colspan= "3" |'''Explanations and clarifications: '''CCSS not addressed:
+|width = "833" style="background-color:#FFFFFF;"|'''K.NO.2a3 Solve word problems within 10 '''
-K.G.B.4 Analyze and compare two and three dimensional shapes in different sizes and orientations, using information language to describe their similarities, differences, parts, and other attributes
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
-K.G.B.5 Model shapes in the world by building shapes from components and drawing shapes
+|width = "834" style="background-color:#FFFFFF;"|K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
+|-
 |}
@@ Line 457: / Line 532: @@
 {| border=1
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1b'' ''analyzing and comparing two- (and later) three-dimensional shapes using informal language (e.g., flat, solid, corners) to describe their differences and similarities, as well as their component parts (number of sides, vertices) and other attributes (e.g., sides of equal length)'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2a representing addition and subtraction in multiple ways (composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping '''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 1'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 1'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''1.GM.1b1 Identify shapes as two-dimensional (lying flat) or three dimensional (solid) '''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record or select the answer'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-K G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)
+K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
-||K.G.A.3 Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").
+|width = "834" style="background-color:#FFFFFF;"|K.OA.A.4''' '''For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation
 |-
-||'''1.GM.1b2 Distinguish two-dimensional shapes based upon their defining attributes (i.e., size, corners, and points)'''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a5 Count 2 sets to find sums up to 10'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Reason with shapes and their attributes.
+K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
-||1.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
+|width = "834" style="background-color:#FFFFFF;"|K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
+K.OA.A.5 Fluently add and subtract within 5.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1c''''' '''''composing two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter-circles)'''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a6 Count 2 sets to find sums up to 20'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Add and subtract within 20.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
+.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 1'''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a7 Decompose a set of up to 10 objects into a group; count the quantity in each group'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+K OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
+K.OA.A.5 Fluently add and subtract within 5.
 |-
-||'''1.GM.1c 2 Compose two- and three-dimensional shapes'''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a8 Decompose a set of up to 20 objects into a group; count the quantity in each group'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Reason with shapes and their attributes.
+OA Add and subtract within 20.
-||1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter circles)  or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
+.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1f'' ''partitioning shapes into 2, 3, or 4 equal parts and describing the parts (halves, quarters, fourths, thirds)'''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a9 Use manipulatives or representations to write simple addition or subtraction equations within 20 based upon a word problem '''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Represent and solve problems involving addition and subtraction.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 1'''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a10 Use data presented in graphs (i.e., pictorial, object) to solve one step "how many more" or "how many less" word problems'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Represent and solve problems involving addition and subtraction.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
 |-
-||'''1.GM.1f1'''
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2a11 Solve word problems within 20'''
-'''Partition circles and rectangles into two equal parts'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Reason with shapes and their attributes.
+OA Represent and solve problems involving addition and subtraction.
-||1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases ''half of, fourth of,'' and ''quarter of''. Describe the whole as two of or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares
+|width = "834" style="background-color:#FFFFFF;"|1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
+.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
 |-
-| colspan=3 |'''Explanations and clarifications: '''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations'''
+|-
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 1'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
+|-
+|width = "833" style="background-color:#FFFFFF;"|'''1.NO.2c1 Identify and apply addition and equal signs '''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Work with addition and subtraction equations.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
 |}
@@ Line 528: / Line 635: @@
 {| border=1
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1a recognizing, describing (using spatial language) and naming shapes regardless of orientation or size and locating shapes in the environment'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2a representing addition and subtraction in multiple ways (composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping'''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 2'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 2'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''2.GM.1a4 Identify two-dimensional shapes such as rhombus, pentagons, hexagons, octagon, ovals, equilateral, isosceles, and scalene triangles'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a12 Model addition and subtraction with base 10 blocks within 20'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Reason with shapes and their attributes.
+NBT Use place value understanding and properties of operations to add and subtract.
-||2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
+|width = "834" style="background-color:#FFFFFF;"|2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
 |-
-|width = "833" colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1b'''''  '''''analyzing and comparing two- (and later) three-dimensional shapes using informal language (e.g., flat, solid, corners) to describe their differences and similarities, as well as their component parts (number of sides, vertices) and other attributes (e.g., sides of equal length)'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a13 Model addition and subtraction with base 10 blocks within 50'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
+NBT Use place value understanding and properties of operations to add and subtract.
+|width = "834" style="background-color:#FFFFFF;"|2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 2'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a14 Model addition and subtraction with base 10 blocks within 100'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
+NBT Use place value understanding and properties of operations to add and subtract.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
 |-
-||'''2.GM.1b3 Distinguish two- or three- dimensional shapes based upon their attributes (i.e., # of sides, equal or different lengths of sides, # of faces, # of corners)'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a15 Remove objects from a set in a subtraction situation to find the amount remaining up to a minuend of 20'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Reason with shapes and their attributes.
+OA Represent and solve problems involving addition and subtraction.
-||2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
+.OA.B.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1d composing three-dimensional shapes, using concrete models/materials (cubes, prisms, cones, and cylinders)'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a16 Solve word problems within 20'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
+OA Represent and solve problems involving addition and subtraction.
+|width = "834" style="background-color:#FFFFFF;"|2.OA.A.1 Use addition and subtraction within 100 to solve one-and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 2'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a17 Solve word problems within 100'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Represent and solve problems involving addition and subtraction.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|2.OA.A.1 Use addition and subtraction within 100 to solve one-and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions
 |-
-||'''2.GM.1d1 Compose three- dimensional shapes'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a18 Use diagrams and number lines to solve addition or subtraction problems'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Reason with shapes and their attributes.
+NBT Use place value understanding and properties of operations to add and subtract.
-||1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half circles, and quarter circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
+|width = "834" style="background-color:#FFFFFF;"|2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
+.MD.B.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1e''''' '''''drawing and identifying shapes with specific attributes (e.g., number of sides or equal angles) not determined by direct measuring'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2a19 Combine up to 3 sets of 20 or less'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
+NBT Use place value understanding and properties of operations to add and subtract.
+|width = "834" style="background-color:#FFFFFF;"|2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
+|-
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2b explaining or modeling the relationship between addition and subtraction'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 2'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 2'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''2.GM.1e1 Draw two- dimensional shapes with specific attributes'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2b1 Use commutative properties to solve addition problems with sums up to 20 (e.g., 3+8=11 therefore 8+3=__)'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Reason with shapes and their attributes.
+OA Understand and apply properties of operations and the relationship between addition and subtraction.
-||2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.B.3 Apply properties of operations as strategies to add and subtract. ''Examples: If 8 + 3 = 11 is'' ''known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6'' ''+ 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.'' ''(Associative property of addition.)''
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1f partitioning shapes into 2, 3, or 4 equal parts and describing the parts (halves, quarters, fourths, thirds)'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2b2 Use associative property to solve addition problems with sums up to 20'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Understand and apply properties of operations and the relationship between addition and subtraction.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.B.3 Apply properties of operations as strategies to add and subtract. ''Examples: If 8 + 3 = 11 is'' ''known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6'' ''+ 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.'' ''(Associative property of addition.)''
+|-
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 2'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 2'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''2.GM.1f2 Partition circles and rectangles into 2 and 4 equal parts'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2c2 Identify and apply addition, subtraction, and equal signs'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Reason with shapes and their attributes.
+OA Work with addition and subtraction equations.
-||2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words ''halves, thirds, half of, a third of'', etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
+|width = "834" style="background-color:#FFFFFF;"|1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
 |-
-||'''2.GM.1f3 Label a partitioned shape (e.g., one whole rectangle was separated into 2 halves, one whole circle was separated into three thirds)'''
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2c3 Compose ones into tens and/or tens into hundreds in addition situation'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Reason with shapes and their attributes.
+NBT;2 NBT Use place value understanding and properties of operations to add and subtract.
-||2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words ''halves, thirds, half of, a third of'', etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
+|width = "834" style="background-color:#FFFFFF;"|1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
+.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
 |-
-| colspan= "3" |'''Explanations and clarifications:''' The following Progress Indicator was '''not included''' due to complexity, no CCSS are linked to this Progress Indicator: '''E.GM.1g '''using spatial language to describe and name more complex or atypical shapes based on their defining characteristics.
+|width = "833" style="background-color:#FFFFFF;"|'''2.NO.2c4 Decompose tens into ones and/or hundreds into tens in subtraction situations'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
+NBT; 2 NBT Use place value understanding and properties of operations to add and subtract.
+|width = "834" style="background-color:#FFFFFF;"|1.NBT.C.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
+.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
 |}
@@ Line 634: / Line 778: @@
 {| border=1
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1h describing, analyzing, comparing, and classifying two-dimensional figures (triangles, quadrilaterals) using shared attributes'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2b explaining or modeling the relationship between addition and subtraction'''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 3'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 3'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''3.GM.1h1 Identify shared attributes of shapes'''
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2b1 Use the relationships between addition and subtraction to solve problems'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Reason with shapes and their attributes.
+NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.
-||3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having 4 sides) and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals that do not belong to any of these subcategories.
+|width = "834" style="background-color:#FFFFFF;"|3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1i partitioning shapes into equal parts with equal areas and recognizing that each part is a unit fraction of the whole'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 3'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 3'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''3.GM.1i1 Partition rectangles into equal parts with equal area'''
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2c1 Solve multi-step addition and subtraction problems up to 100'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Reason with shapes and their attributes.
+NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.
-||3.G.A.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. ''For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape.''
+|width = "834" style="background-color:#FFFFFF;"|3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
 |-
-| colspan=3 |'''Explanations and clarifications: '''CCSS not addressed
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2d modeling multiplication (equal-sized groups, arrays, area models, equal-sized jumps on number lines, multiplicative comparisons) and division (successive subtraction, partitioning, sharing) of whole numbers'''
-|}
+|-
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 3'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
+|-
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2d1 Find the total number of objects when given the number of identical groups and the number of objects in each group neither number larger than 5 '''
-{| border=1
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1h describing, analyzing, comparing, and classifying two-dimensional figures (triangles, quadrilaterals) using shared attributes'''
+OA Work with equal groups of objects to gain foundations for multiplication.
+OA Represent and solve problems involving multiplication and division.
+|width = "834" style="background-color:#FFFFFF;"|2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
+.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. ''For example, describe a'' ''context in which a total number of objects can be expressed as 5 × 7. 2.G.A.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. ''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 4'''
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2d2 Find total number inside an array with neither number in the columns or rows larger than 5'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Work with equal groups of objects to gain foundations for multiplication.
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+OA Represent and solve problems involving multiplication and division.
+|width = "834" style="background-color:#FFFFFF;"|2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
+.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. ''For example, describe a'' ''context in which a total number of objects can be expressed as 5 × 7''
 |-
-||'''4.GM.1h2 Classify two-dimensional shapes based on attributes (# of angles)'''
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2d3 Solve multiplication problems with neither number greater than 5'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
+OA Represent and solve problems involving multiplication and division.
-||4.G.A.2 Classify two dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right angles as a category, and identify right angles.
+|width = "834" style="background-color:#FFFFFF;"|3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. ''For example, describe a'' ''context in which a total number of objects can be expressed as 5 × 7''
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1j recognizing and drawing points, lines, line segments, rays, angles, and perpendicular and parallel lines and identifying these in plane figures'''
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2d4 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 5 '''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Represent and solve problems involving multiplication and division.
+|width = "834" style="background-color:#FFFFFF;"|3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. ''For example,'' ''describe a context in which a number of shares or a number of groups'' ''can be expressed as 56 ÷ 8.
+.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 4'''
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2d5 Determine the number of groups given the total number of objects and the number of objects in each group where the number in each group and the number of groups is not greater than 5'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Represent and solve problems involving multiplication and division.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. ''For example,'' ''describe a context in which a number of shares or a number of groups'' ''can be expressed as 56 ÷ 8.
+.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.''
 |-
-||'''4.GM.1j1 Recognize a point, line and line segment, rays in two-dimensional figures'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2e describing relationships between addition-multiplication; multiplication-division; addition-subtraction; why commutative property does not apply to subtraction or division'''
-||'''Geometry'''
+|-
-G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 3'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-||4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figures'''
+|width = "833" style="background-color:#FFFFFF;"|'''3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
+OA Solve problems involving the four operations, and identify and explain patterns in arithmetic.
-||4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
+|width = "834" style="background-color:#FFFFFF;"|3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
+.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. '''
+|}
+{| border=1
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2c working flexibly with common addition and subtraction situations'''
 |-
-||'''4.GM.1j3 Recognize an angle in two-dimensional figures'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 4'''
-||'''Geometry'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
-||4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''4.GM.1j4 Categorize angles as right, acute, or obtuse'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2c2 Solve multi digit addition and subtraction problems up to 1000'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
+NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.
-||4.G.A.2 Classify two dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right angles as a category, and identify right triangles.
+|width = "834" style="background-color:#FFFFFF;"|3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
+.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1k'' ''recognizing and drawing lines of symmetry in a variety of figures'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2d modeling multiplication (equal-sized groups, arrays, area models, equal-sized jumps on number lines, multiplicative comparisons) and division (successive subtraction, partitioning, sharing) of whole numbers'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 4'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 4'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''4.GM.1k1 Recognize a line of symmetry in a figure'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
+OA Represent and solve problems involving multiplication and division.
-||4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts, identify line-symmetric figures and draw lines of symmetry.
+|width = "834" style="background-color:#FFFFFF;"|3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. ''For example, describe a'' ''context in which a total number of objects can be expressed as 5 × 7.''
 |-
-| colspan=3 |'''Explanations and clarifications: '''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2d7 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 10'''
-|}
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
+OA Use the four operations with whole numbers to solve problems.
+|width = "834" style="background-color:#FFFFFF;"|4.OA.A.2 Multiply or divide to solve word problem involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem distinguishing multiplicative comparison from additive comparison.
+.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
+|-
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2d8 Match an accurate addition and multiplication equation to a representation'''
-{| border=1
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: E.GM.1j recognizing and drawing points, lines, line segments, rays, angles, and perpendicular and parallel lines and identifying these in plane figures'''
+OA Represent and solve problems involving multiplication and division.
+|width = "834" style="background-color:#FFFFFF;"|3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. ''For example, describe a'' ''context in which a total number of objects can be expressed as 5 × 7.''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 5'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2e describing relationships between addition-multiplication; multiplication-division; addition-subtraction; why commutative property does not apply to subtraction or division'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|-
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 4'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures '''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2e2 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
+OA Use the four operations with whole numbers to solve problems.
-||4.G.A.1 Draw points, lines, line segments, rays, angles, perpendicular, and parallel lines. Identify these in two-dimensional figures.
+|width = "834" style="background-color:#FFFFFF;"|4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1a describing and classifying plane figures based on their properties'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2f identifying factors and multiples of numbers'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 5'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 4'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''5.GM.1a1 Recognize properties of simple plane figures'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2f1 Identify multiples for a whole number (e.g., 2= 2, 4, 6, 8, 10)'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Classify two-dimensional figures into categories based on their properties.
+OA Gain familiarity with factors and multiples.
-||5.G.B.3 Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category . ''For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.''
+|width = "834" style="background-color:#FFFFFF;"|4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1b recognizing and using properties belonging to categories and subcategories of plane figures (e.g., all rectangles have four right angles, so all squares are rectangles and have four right angles)'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2f2 Solve multiplication problems up to two digits by one digit'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
+NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.
+|width = "834" style="background-color:#FFFFFF;"|4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
+.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 5'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2g recognizing fractions as one number/one quantity, rather than two numbers (numerator and denominator) and using number lines to represent magnitude of fractions'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|-
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 4'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''5.GM.1b1 Distinguish plane figures by their properties'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ )'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
-G Classify two-dimensional figures into categories based on their properties.
+NF Develop understanding of fractions as numbers.
+'''Numbers and Operations – Fractions'''
+NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
-||5.G.B.4 Classify two dimensional figures in a hierarchy based on properties.
+|width = "834" style="background-color:#FFFFFF;"|3.NF.A.1 Understand a fraction 1/''b ''as the quantity formed by 1 part when ''a ''whole is partitioned into ''b ''equal parts; understand a fraction ''a''/''b ''as the'' ''quantity formed by a parts of size 1/''b''
+.NF.B.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''.
+# Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
+# Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. ''Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2'' ''1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.''
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1c demonstrating the use of a coordinate system by locating/graphing a given point or polygon using ordered pairs'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: E.NO.2h adding, subtracting, and multiplying fractions, including mixed numbers'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 5'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 4'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''5.GM.1c1 Locate the x and y axis on a graph'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2h1 Add and subtract fractions with like denominators of (2,3,4, or 8)'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
-G Graph points on the coordinate plane to solve real-world and mathematical problems.
+NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
-||5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
+|width = "834" style="background-color:#FFFFFF;"|4.NF.B.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''.
+# Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
+# Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. ''Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2'' ''1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.''
 |-
-||'''5.GM.1c2 Locate points on a graph'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2h2 Add and subtract fractions with like denominators (2,3,4, or 8) using representations '''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
-G Graph points on the coordinate plane to solve real-world and mathematical problems.
+NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
-||5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
+|width = "834" style="background-color:#FFFFFF;"|4.NF.B.3 Understand a fraction ''a''/''b ''with ''a ''> 1 as a sum of fractions 1/''b''.
+# Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
+# Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. ''Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2'' ''1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.''
 |-
-||'''5.GM.1c3 Use order pairs to graph given points'''
+|width = "833" style="background-color:#FFFFFF;"|'''4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8)'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
-G Graph points on the coordinate plane to solve real-world and mathematical problems.
+NF Develop understanding of fractions as numbers.
-||5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
+NF Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
-|-
+|width = "834" style="background-color:#FFFFFF;"|3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
-| colspan=3 |'''Explanations and Clarifications: '''CCSS not addressed
+## Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
+.NF.B.3 Understand a fraction ''a''/''b'' with ''a'' > 1 as a sum of fractions 1/''b''.
+# Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
 |}
-==Middle School Progress Indicators==
 {| border=1
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1c demonstrating the use of a coordinate system by locating/graphing a given point or polygon using ordered pairs'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2a working flexibility with common addition, subtraction, multiplication, and division situations'''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 6'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 5'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''6.GM.1c4 Locate points on a graph'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2a1 Solve problems or word problems using up to three digit numbers and addition or subtraction or multiplication'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Operations and Algebraic Thinking'''
-G Graph points on the coordinate plane to solve real-world and mathematical problems.
+OA Use the four operations with whole numbers to solve problems.
-||5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
+|width = "834" style="background-color:#FFFFFF;"|4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
 |-
-||'''6.GM.1c5 Use order pairs to graph given points'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2a2 Separate a group of objects into equal sets when given the number of sets to find the total in each set with the total number less than 50'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Graph points on the coordinate plane to solve real-world and mathematical problems.
+NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.
-||5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the – on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
+|width = "834" style="background-color:#FFFFFF;"|4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 |-
-||'''6.GM.1c6 Find coordinate values of points in the context of a situation'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2a3 Find whole number quotients up to two dividends and two divisors'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Graph points on the coordinate plane to solve real-world and mathematical problems.
+NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.
-||5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
+|width = "834" style="background-color:#FFFFFF;"|5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 |-
-||'''6.GM.1c7 Use coordinate points to draw polygons '''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2a4 Find whole number quotients up to four dividends and two divisors'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Solve real-world and mathematical problems involving area, surface area, and volume.
+NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.
-||6.G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
+|width = "834" style="background-color:#FFFFFF;"|5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 |-
-||'''6.GM.1c8 Use coordinate points to find the side lengths of polygons that are horizontal or vertical'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2a5 Solve word problems that require multiplication or division'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Solve real-world and mathematical problems involving area, surface area, and volume.
+NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.
-||6.G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
+|width = "834" style="background-color:#FFFFFF;"|5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1d  solving area, surface area, and volume problems by composing and decomposing figures'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2b recognizing fractions as one number/one quantity, rather than two numbers (numerator and denominator) and using number lines to represent magnitude of fractions and equivalent /non-equivalent fractions'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 6'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 5'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''6.GM.1d1 Find area of quadrilaterals'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2b1 Add and subtract fractions with unlike denominators by replacing fractions with equivalent fractions (identical denominators)'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
-G Solve real-world and mathematical problems involving area, surface area, and volumes.
+NF Use equivalent fractions as a strategy to add and subtract fractions.
-||6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
+|width = "834" style="background-color:#FFFFFF;"|5.NF.A.1 Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce equivalent sum or difference of fractions with like denominators. ''For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd).''
 |-
-||'''6.GM.1d2 Find area of triangles'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2b2 Add or subtract fractions with unlike denominators'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
-G Solve real-world and mathematical problems involving area, surface area, and volumes.
+NF Use equivalent fractions as a strategy to add and subtract fractions.
-||6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems
+|width = "834" style="background-color:#FFFFFF;"|5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. ''For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd).
+.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.''
 |-
-|colspan=3 |'''Explanations and clarifications: '''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2b3 Multiply a fraction by a whole or mixed number.'''
-|}
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
+NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
+|width = "834" style="background-color:#FFFFFF;"|5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
+# Interpret the product (''a''/''b'') × ''q ''as a parts of a partition of ''q ''into ''b ''equal parts; equivalently, as the result of a sequence of operations ''a ''× ''q ''÷ ''b''. ''For example,'' ''use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context'' ''for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)''
+# Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
+.NF.B.7.''' '''Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
+# Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. ''For example, create a story context for (1/3) ÷ 4,'' ''and use a visual fraction model to show the quotient. Use the relationship'' ''between multiplication and division to explain that (1/3) ÷ 4 = 1/12'' ''because (1/12) × 4 = 1/3.''
+# Interpret division of a whole number by a unit fraction, and compute such quotients. ''For example, create a story context for 4 ÷ (1/5), and use a'' ''visual fraction model to show the quotient. Use the relationship between'' ''multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 ×'' ''(1/5) = 4.''
+# Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. ''For'' ''example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins?''
+|-
-{| border=1
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2c using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)'''
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1e constructing or drawing geometric shapes from given conditions (e.g., draw triangles given three angle or side measures; change scale)'''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 7'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 5'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''7.GM.1e1 Construct or draw plane figures using properties'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2c1 Solve 1 step problems using decimals '''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Number and Operations in Base Ten'''
-G Draw, construct, and describe geometrical figures and describe the relationships between them.
+NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.
-||7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
+|width = "834" style="background-color:#FFFFFF;"|5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1h solving real-world area, surface area, and volume problems using different strategies (formulas and decomposing figures)'''
+|width = "833" style="background-color:#FFFFFF;"|'''5.NO.2c2 Solve word problems involving the addition, subtraction, multiplication or division of fractions '''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
+NF Use equivalent fractions as a strategy to add and subtract fractions.
+|width = "834" style="background-color:#FFFFFF;"|5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. ''For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 7'''
+|width = "833" colspan= "3" style="background-color:#FFFFFF;"|'''Explanations and clarifications: Not included: M.NO.2d contrasting situations as additive or multiplicative'''
+|}
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+=Middle School Progress Indicators=
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+{| border=1
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2a working flexibility with common addition, subtraction, multiplication, and division situations'''
 |-
-||'''7.GM.1h1 Add the area of each face of a prism to find surface area of three-dimensional objects'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 6'''
-||'''Geometry'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
-||7.G.B.6 Solve real-world and mathematical problems involving area, volume, and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''7.GM.1h2 Find the surface area of three-dimensional figures using nets of rectangles or triangles'''
+|width = "833" style="background-color:#FFFFFF;"|'''6.NO.2a6 Solve problems or word problems using up to three digit numbers and any of the four operations'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Expressions and Equations'''
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
+EE Reason about and solve one-variable equations and inequalities.
-||7.G.B.6 Solve real-world and mathematical problems involving area, volume, and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
+|width = "834" style="background-color:#FFFFFF;"|6.EE.B.7 Solve real world and mathematical problems by writing and solving equations of the form x = p = q and px = q for cases in which p, q, and x are all non negative rational numbers.
 |-
-||'''7.GM.1h3 Find area of plane figures and surface area of solid figures (quadrilaterals)'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2c using operations and standard algorithms with whole numbers, fractions (unlike denominators), and decimals (to hundredths)'''
-||'''Geometry'''
+|-
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 6'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-||7.G.B.6 Solve real-world and mathematical problems involving area, volume, and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''7.GM.1h4 Find area of an equilateral, isosceles, and scalene triangle '''
+|width = "833" style="background-color:#FFFFFF;"|'''6.NO.2c3 Solve one step, addition, subtraction, multiplication, or division problems with fractions or decimals'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Number System'''
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
+NS Apply and extend previous understandings of multiplications and division to divide fractions by fractions.
-||7.G.B.6 Solve real-world and mathematical problems involving area, volume, and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
+|width = "834" style="background-color:#FFFFFF;"|6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. ''For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc). How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi.? Compute fluently with multi-digit numbers and find common factors and multiples.
+.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
 |-
-|width = "833"|'''7.GH.1h5  Describe the two dimentional figures that result from a decomposed three dimentional figure.'''
+|width = "833" style="background-color:#FFFFFF;"|'''6.NO.2c4 Solve word problems involving the addition, subtraction, multiplication or division of fractions'''
-|width = "833"|'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Numbers and Operations – Fractions'''
-G Draw, construct, and describe geometrical figures and describe the relationships between them.
+NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
+'''The Number System'''
+NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
-|width = "834"|7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
+|width = "834" style="background-color:#FFFFFF;"|5.NF.B.7c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
+## Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. ''For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?''
+.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. ''For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc). How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Compute fluently with multi-digit numbers and find common factors and multiples.''
 |-
-| colspan=3 |'''Explanations and clarifications:'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2e ordering/comparing integers and representing them on the number line'''
-|}
+|-
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 6'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
-{| border=1
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1f recognizing and demonstrating rotations, reflections, and translations using multiple contexts (e.g., using coordinates, models, drawings, technology)'' '''''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 8'''
+|width = "833" style="background-color:#FFFFFF;"|'''6.NO.2e1	 Determine the difference between two integers using a number line'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Number System'''
+NS Apply and extend previous understandings of numbers to the system of rational numbers.
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
+# Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
 |-
-||'''8.GM.1f1 Recognize a rotation, reflection, or translation of a figure'''
+|width = "833" style="background-color:#FFFFFF;"|'''6.NO.2e2 Compare two numbers on a number line (e.g., -2 > -9)'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Number System'''
-G Understand congruence and similarity using physical models, transparencies, or geometry software.
+NS Apply and extend previous understandings of numbers to the system of rational numbers.
-||8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations:
+|width = "834" style="background-color:#FFFFFF;"|6.NS.C.7 Understand ordering and absolute value of rational numbers.
-a)  Lines are taken to lines, and line segments to line segments of the same length.
+# Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. ''For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.''
+|}
-b)  Angles are taken to angles of the same measure.
-c)  Parallel lines are taken to parallel lines.
-|-
-||'''8.GM.1f2 Identify a rotation, reflection, or translation of a plane figure when given coordinates'''
-||'''Geometry'''
-G Understand congruence and similarity using physical models, transparencies, or geometry software.
-||8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
+{| border=1
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2f describing proportional relationships and solving related problems'''
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1g demonstrating congruence and similarity using a variety of two-dimensional figures''''' ''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 7'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 8'''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2f1 Identify the proportional relationship between two quantities'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
+RP Analyze proportional relationships and use them to solve real-world and mathematical problems.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.2 Recognize and represent proportional relationships between quantities.
+# Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
+# Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
+# Represent proportional relationships by equations. ''For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.''
+# Explain what a point (''x'', ''y'') on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, ''r'') where r is the unit rate.
 |-
-||'''8.GM.1g1 Recognize congruent and similar figures '''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2f2 Determine if two quantities are in a proportional relationship using a table of equivalent ratios or points graphed on a coordinate plane'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
-G Understand congruence and similarity using physical models, transparencies, or geometry software.
+RP Analyze proportional relationships and use them to solve real-world and mathematical problems.
-||8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.2 Recognize and represent proportional relationships between quantities.
+# Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
+# Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator: M.GM.1i exploring and explaining angle relationships (e.g., pairs of parallel lines cut by a transversal, including perpendicular lines) '''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2f3 Find unit rates given a ratio'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
+RP Analyze proportional relationships and use them to solve real-world and mathematical problems.
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 8'''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2f4 Use a rate of change or proportional relationship to determine the points on a coordinate plane'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
+RP Analyze proportional relationships and use them to solve real-world and mathematical problems.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.2 Recognize and represent proportional relationships between quantities.
+# Explain what a point (''x'', ''y'') on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, ''r'') where r is the unit rate.
 |-
-||'''8.GM.1i1 Identify supplementary angles'''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2f5 Use proportions to solve ratio problems'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
+RP Analyze proportional relationships and use them to solve real-world and mathematical problems.
-||7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
 |-
-||'''8.GM.1i2 Identify complimentary angles'''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO2.f6 Solve word problems involving ratios'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
+RP Understand ratio concepts and use ratio reasoning to solve problems.
-||7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
 |-
-||'''8.GM.1i3 Identify adjacent angles'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2h using operations involving percents and percent increase/decrease'''
-||'''Geometry'''
+|-
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 7'''
-||7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''8.GM.1i4 Use angle relationships to find the value of a missing angle'''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2h1 Find percents in real world contexts'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
-G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
+RP Analyze proportional relationships and use them to solve real-world and mathematical problems.
-G Understand congruence and similarity using physical models, transparencies, or geometry software.
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
-||7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
+|-
-.G.5 Use informal arguments to establish facts about the angle sum and exterior angle for triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. ''For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and given an argument in terms of transversals why this is so.''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2h2 Solve one step percentage increase and decrease problems'''
+|width = "833" style="background-color:#FFFFFF;"|'''Ratios and Proportional Relationships'''
+RP Analyze proportional relationships and use them to solve real-world and mathematical problems.
+|width = "834" style="background-color:#FFFFFF;"|7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator:'' ''M.GM.1j applying the Pythagorean Theorem'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2i using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 8'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 7'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''8.GM.1j1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2i1 Solve multiplication problems with positive/negative numbers'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Number System'''
-G Understand and apply the Pythagorean Theorem.
+NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
-||8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
+|width = "834" style="background-color:#FFFFFF;"|7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
+# Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
+# Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If ''p'' and ''q'' are integers, then –(''p''/''q'') = (–''p'')/''q'' = ''p''/(–''q''). Interpret quotients of rational numbers by describing real-world contexts.
+# Apply properties of operations as strategies to multiply and divide rational numbers.
+# Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
 |-
-||'''8.GM.1j2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "833" style="background-color:#FFFFFF;"|'''7.NO.2i2 Solve division problems with positive/negative numbers'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Number System'''
-G Understand and apply the Pythagorean Theorem.
+NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
-||8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
+|width = "834" style="background-color:#FFFFFF;"|7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
+# Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
+# Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If ''p'' and ''q'' are integers, then –(''p''/''q'') = (–''p'')/''q'' = ''p''/(–''q''). Interpret quotients of rational numbers by describing real-world contexts.
+# Apply properties of operations as strategies to multiply and divide rational numbers.
+# Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
 |-
-| colspan=3 |'''Explanations and clarifications:'''
+|width = "833" colspan= "3" style="background-color:#FFFFFF;"|'''Explanations and clarifications: Not included: M.NO.2g using operations with complex fractions'''
 |}
@@ Line 1,149: / Line 1,408: @@
-==High School Progress Indicators==
 {| border=1
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator:''''' '''''H.GM.1a applying the Pythagorean Theorem'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: M.NO.2i using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line'''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 9-12'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 8'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''H.GM.1a1 Find the hypotenuse of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "833" style="background-color:#FFFFFF;"|'''8.NO.2i3 Solve one step addition, subtraction, multiplication, division problems with fractions, decimals, and positive/negative numbers'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Number System'''
-G Understand and apply the Pythagorean Theorem.
+NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
-||8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
+|width = "834" style="background-color:#FFFFFF;"|7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
+# Apply properties of operations as strategies to add and subtract rational numbers.
+.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
 |-
-||'''H.GM.1a2 Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem)'''
+|width = "833" style="background-color:#FFFFFF;"|'''8.NO.2i4 Solve two step addition, subtraction, multiplication, and division problems with fractions, decimals, or positive/negative numbers'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Number System'''
-G Understand and apply the Pythagorean Theorem.
+NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
-||8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
+|width = "834" style="background-color:#FFFFFF;"|7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
+# Apply properties of operations as strategies to add and subtract rational numbers.
+.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
-|-
-|width = "833"|'''H.GM.1a3 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.'''
-|width = "833"|'''Geometry'''
-G Understand and apply the Pythagorean Theorem.
-|width = "834"|8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
 |}
+=High School Progress Indicators=
 {| border=1
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator:'' ''H.GM.1b using congruence and similarity relationships to solve problems, including triangle congruence relationships''''' ''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: H.NO.2a using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line'''
 |-
-|width = "833" style="background-color:#D9D9D9;"|'''Core Content Connectors: 9-12'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 9-12'''
-|width = "833" style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-|width = "834" style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''H.GM.1b1 Use definitions to demonstrate congruency and similarity in figures'''
+|width = "833" style="background-color:#FFFFFF;"|'''H.NO.2a1 Solve simple equations using rational numbers with one or more variables'''
-||'''Congruence'''
+|width = "833" style="background-color:#FFFFFF;"|'''Reasoning with Equations and Inequalities'''
-G CO Understand congruence in terms of rigid motions.
+A REI Understand solving equations as a process of reasoning and explain the reasoning.
-'''Similarity, Right Triangles, and Trigonometry'''
+|width = "834" style="background-color:#FFFFFF;"|HSA-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
-G.SRT Understand similarity in terms of similarity transformations.
-||HSG-CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
-HSG-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator:'' ''H.GM.1c applying understanding of rotations, reflections, and translations to construct figures (e.g., using coordinates, models, drawings, transparencies, dynamic geometry software)''''' ''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: H.NO.2b operating with irrational and complex numbers'''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 9-12'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 9-12'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''H.GM.1c1 Construct, draw or recognize a figure after its rotation, reflection, or translation'''
+|width = "833" style="background-color:#FFFFFF;"|'''H.NO.2b1 Explain the pattern for the sum or product for combinations of rational and irrational numbers'''
-||'''Congruence'''
+|width = "833" style="background-color:#FFFFFF;"|'''The Real Number System'''
-G CO Experiment with transformations in the plane.
+N RN Use properties of rational irrational numbers.
-||HSG-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformation that will carry a given figure onto another.
+|width = "834" style="background-color:#FFFFFF;"|HSN-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational.
-HSG-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry onto itself.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator:'' ''H.GM.1d  applying scale factors in solving multiple similarity problems, including transformations in the coordinate plane and similarity relationships with right triangles'''
+|width = "833" colspan= "3" style="background-color:lightgray;"|'''Progress Indicator: H.NO.2c identifying exponential situations and applying the laws and properties of exponents in simplifying expressions and solving equations '''
 |-
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 9-12'''
+|width = "833" style="background-color:lightgray;"|'''Core Content Connectors: 9-12'''
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+|width = "833" style="background-color:lightgray;"|'''CCSS Domain/Cluster'''
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:lightgray;"|'''Common Core State Standard'''
 |-
-||'''H.GM.1d1 Use the reflections,  rotations, or translations in the coordinate plane to solve problems with right angles'''
+|width = "833" style="background-color:#FFFFFF;"|'''H.NO.2c1 Simplify expressions that include exponents'''
-||'''Geometry'''
+|width = "833" style="background-color:#FFFFFF;"|'''Seeing Structure in Expressions'''
-G Understand congruence and similarity using physical models, transparencies, or geometry software.
+A SSE Interpret the structures of expressions.
-'''Similarity, Right Triangles, and Trigonometry'''
+|width = "834" style="background-color:#FFFFFF;"|HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. ''For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).''
-G SRT Understand similarity in terms of similarity transformations.
-||8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations
-a)  Lines are taken to lines, and line segments to line segments of the same length.
-b)  Angles are taken to angles of the same measure.
-c)  Parallel lines are taken to parallel lines.
-HSG-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformation the meaning of similarity for triangles and the equality of all corresponding pairs and angles and the proportionality of all corresponding pairs of sides.
 |-
-| colspan= "3" style="background-color:#D9D9D9;"|'''Progress Indicator:''''''' '''''''H.GM.1e making various geometric constructions, including use of dynamic geometry software, and creating informal proofs of relationships (lines and angles, circles, polygons)'''
+|width = "833" style="background-color:#FFFFFF;"|'''H.NO.2c2 Rewrite expressions that include rational exponents'''
-|-
+|width = "833" style="background-color:#FFFFFF;"|'''The Real Number System'''
-| style="background-color:#D9D9D9;"|'''Core Content Connectors: 9-12'''
+N RN Extend the properties of exponents to rational exponents.
-| style="background-color:#D9D9D9;"|'''CCSS Domain/Cluster'''
+'''Seeing Structure in Expressions'''
+A SSE Interpret the structures of expressions.
-| style="background-color:#D9D9D9;"|'''Common Core State Standard'''
+|width = "834" style="background-color:#FFFFFF;"|HSN-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
+HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. ''For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).''
 |-
-||'''H.GM.1e1  Make formal geometric constructions with a variety of tools and methods'''
+|width = "833" colspan= "3" style="background-color:#FFFFFF;"|''''''Explanations and clarifications: Not included: H.PRF.1d recognizing that there limitations in mathematics models A.CE-3 S.IC-2''''''
-||'''Congruence'''
-G CO Make Geometric constructions.
-||HSG-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straight edge, string, reflective devices, paper folding dynamic geometric software, etc.) Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
 |-
-| colspan= "3" |'''Explanations and clarifications:''' High school standards not addressed; will be in a separate document
 |}
-[[Category: Math]]
 [[Category:CCCs]]
+[[Category:Math]]