Core Content Connectors by Common Core State Standards: Mathematics 3rd Grade

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='''Grade 4 Overview'''=
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='''Grade 3 Overview'''=
  
 
=='''Operations and Algebraic Thinking'''==
 
=='''Operations and Algebraic Thinking'''==
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*'''Use the four operations with whole numbers to solve problems.'''
+
*'''Represent and solve problems involving multiplication and division.'''
−
*'''Gain familiarity with factors and multiples.'''
+
*'''Understand properties of multiplication and the relationship between multiplication and division.'''
−
*'''Generate and analyze patterns.'''
+
*'''Multiply and divide within 100.'''
 +
*'''Solve problems involving the four operations, and identify and explain patterns in arithmetic.'''
  
 
=='''Number and Operations in Base Ten'''==
 
=='''Number and Operations in Base Ten'''==
−
*'''Generalize place value understanding for multi-digit whole numbers.'''
 
 
*'''Use place value understanding and properties of operations to perform multi-digit arithmetic.'''
 
*'''Use place value understanding and properties of operations to perform multi-digit arithmetic.'''
  
−
=='''Numbers and Operations – Fractions'''==
+
=='''Numbers and Operations—Fractions'''==
−
*'''Extend understanding of fraction equivalence and ordering.'''
+
*'''Develop understanding of fractions as numbers.'''
−
*'''Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.'''
+
−
*'''Understand decimal notation for fractions, and compare decimal fractions.'''
+
  
 
=='''Measurement and Data'''==
 
=='''Measurement and Data'''==
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*'''Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.'''
+
*'''Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.'''
 
*'''Represent and interpret data.'''
 
*'''Represent and interpret data.'''
−
*'''Geometric measurement: understand concepts of angle and measure angles.'''
+
*'''Geometric measurement: understand concepts of area and relate area to multiplication and to addition.'''
 +
*'''Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.'''
  
 
=='''Geometry'''==
 
=='''Geometry'''==
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*'''Draw and identify lines and angles, and classify shapes by properties of their lines and angles.'''
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*'''Reason with shapes and their attributes.'''
  
  
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|width = "625" style="background-color:#D9D9D9;"|'''Operations and Algebraic Thinking'''
 
|width = "625" style="background-color:#D9D9D9;"|'''Operations and Algebraic Thinking'''
  
−
|width = "1875" style="background-color:#D9D9D9;"|'''4.OA'''
+
|width = "1875" style="background-color:#D9D9D9;"|'''3.OA'''
  
 
|-
 
|-
−
| colspan=2|'''Use the four operations with whole numbers to solve problems.'''
+
| colspan=2|'''Represent and solve problems involving multiplication and division.'''
  
 
|-
 
|-
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| colspan=2|1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
+
| colspan=2|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.
  
 
|-
 
|-
−
||'''''CCCs linked to 4.OA.A.1'''''
+
| rowspan=7|'''''CCCs linked to 3.OA.A.1'''''
  
−
||4.PRF.1d2 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.
+
||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.
  
 
|-
 
|-
−
| colspan=2|2. Multiply or divide to solve word problems 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.NO.2d2 Find the total number inside an array with neither number in the columns or rows larger than 5.
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.OA.A.2'''''
+
||3.NO.2d3 Solve multiplication problems with neither number greater than 5.
−
 
+
−
||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.
+
  
 
|-
 
|-
−
||4.PRF.1e3 Solve multiplicative comparisons with an unknown using up to 2-digit numbers with information presented in a graph or word problem (e.g., an orange hat cost $3. A purple hat cost 2 times as much. How much does the purple hat cost? [3 x 2 = p]).
+
||3.PRF.1d1 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.  
  
 
|-
 
|-
−
| colspan=2|3. Solve multi-step 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.
+
||4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10.
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.0A.A.3'''''
+
||4.NO.2d8 Match an accurate addition and multiplication equation to a representation.
−
 
+
−
||4.NO.2e2 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100.
+
  
 
|-
 
|-
−
||5.NO.2a1 Solve problems or word problems using up to three digit numbers and addition or subtraction or multiplication.
+
||4.PRF.1d2 Use objects to model multiplication and division situations involving up to 10 groups with up to 5 objects in each group and interpret the results.
  
 
|-
 
|-
−
| colspan=2|'''Gain familiarity with factors and multiples.'''
+
| colspan=2|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.
  
 
|-
 
|-
−
| colspan=2|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.
+
| rowspan=3|'''''CCCs linked to 3.OA.A.2'''''
 +
 
 +
||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.  
  
 
|-
 
|-
−
||'''''CCCs linked to 4.0A.B.4'''''
+
||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.
−
 
+
−
||4.NO.2f1 Identify multiples for a whole number (e.g., 2= 2, 4, 6, 8, 10).
+
  
 
|-
 
|-
−
| colspan=2|'''Generate and analyze patterns.'''
+
||3.PRF.1d1 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.  
  
 
|-
 
|-
−
| colspan=2|5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
+
| colspan=2|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.
  
 
|-
 
|-
−
| rowspan=4|'''''CCCs linked to 4.OA.C.5'''''
+
||'''''CCCs linked to 3.0A.A.3'''''
  
−
||4.PRF.2d3 Generate a pattern when given a rule and word problem<br/> (I run 3 miles every day, how many miles have I run in 3 days).
+
||3.NO.2e1 Solve or solve and check one- or two-step word problems requiring addition, subtraction or multiplication with answers up to 100.
  
 
|-
 
|-
−
||4.PRF.2e1 Extend a numerical pattern when the rule is provided.
+
| colspan=2|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 = ?.
  
 
|-
 
|-
−
||5.PRF.2a1 Generate a pattern that follows the provided rule.
+
||'''''CCCs linked to 3.0A.A.4'''''
  
−
|}
+
||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 = "625" style="background-color:#D9D9D9;"|'''Numbers and Operations in Base Ten'''
+
−
 
+
−
|width = "1875" style="background-color:#D9D9D9;"|'''4.NBT'''
+
  
 
|-
 
|-
−
| colspan=2|'''Generalize place value understanding for multi-digit whole numbers.'''
+
| colspan=2|'''Understand properties of multiplication and the relationship between multiplication and division.'''
  
 
|-
 
|-
−
| colspan=2|1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
+
| colspan=2|5. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication). 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30 (Associative property of multiplication). Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (Distributive property).
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.NBT.A.1'''''
+
||'''''CCCs linked to 3.OA.B.5'''''
  
−
||4.NO.1k1 Compare the value of a number when it is represented in different place values of two 3 digit numbers.
+
||3.PRF.2d2 Apply properties of operations as strategies to multiply and divide.
  
 
|-
 
|-
−
||4.NO.1k1 Compare the value of a number when it is represented in different place values of two 3 digit numbers.
+
| colspan=2|6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
  
 
|-
 
|-
−
| colspan=2|2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
+
| rowspan=2|'''''CCCs linked to 3.OA.B.6'''''
 +
 
 +
||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.
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.NBT.A.2'''''
+
||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.
−
 
+
−
||4.NO.1j6 Compare multi-digit numbers using representations and numbers.  
+
  
 
|-
 
|-
−
||4.NO.1j7 Write or select the expanded form for a multi-digit number.
+
| colspan=2|'''Multiply and divide within 100.'''
  
 
|-
 
|-
−
| colspan=2|3. Use place value understanding to round multi-digit whole numbers to any place.
+
| colspan=2|7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.
  
 
|-
 
|-
−
||'''''CCCs linked to 4.NBT.A.3'''''
+
||'''''CCCs linked to 3.OA.C.7'''''
  
−
||4.NO.1j5 Use place value to round to any place (i.e., ones, tens, hundreds, thousands).
+
||None
  
 
|-
 
|-
−
| colspan=2|'''Use place value understanding and properties of operations to perform multi-digit arithmetic.'''
+
| colspan=2|'''Solve problems involving the four operations, and identify and explain problems in arithmetic.'''
  
 
|-
 
|-
−
| colspan=2|4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.
+
| colspan=2|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.
  
 
|-
 
|-
−
||'''''CCCs linked to 4.NBT.B.4'''''
+
||'''''CCCs linked to 3.OA.D.8'''''
  
−
||4.NO.2c2 Solve multi-digit addition and subtraction problems up to 1000.
+
||3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100.
  
 
|-
 
|-
−
| colspan=2|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.
+
| colspan=2|9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that four times a number is always even, and explain why four times a number can be decomposed into two equal addends.
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.NBT.B.5'''''
+
| rowspan=3|'''''CCCs linked to 3.OA.D.9'''''
  
−
||4.NO.2f2 Solve multiplication problems up to two digits by one digit.
+
||3.PRF.1e1 Describe the rule for a numerical pattern (e.g., increase by 2, 5 or 10).
  
 
|-
 
|-
−
||4.PRF.1f4 Solve a 2-digit by 1-digit multiplication problem using 2 different strategies.
+
||3.PRF.1e2 Select or name the three next terms in a numerical pattern where numbers increase by 2, 5 or 10.
  
 
|-
 
|-
−
| colspan=2|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.
+
||3.PRF.2d1 Identify multiplication patterns in a real word setting.
  
−
|-
+
|}
−
||'''''CCCs linked to 4.NBT.B.6'''''
+
  
−
||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.
 
  
−
|-
 
−
| style="background-color:#D9D9D9;"|'''Numbers and Operations--Fractions'''
 
  
−
| style="background-color:#D9D9D9;"|'''4.NF'''
 
  
−
|-
+
{|border=1
−
| colspan=2|'''Extend understanding of fraction equivalence and ordering.'''
+
|width = "625" style="background-color:#D9D9D9;"|'''Numbers and Operations in Base Ten'''
  
−
|-
+
|width = "1875" style="background-color:#D9D9D9;"|'''3.NBT'''
−
| colspan=2|1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
+
  
 
|-
 
|-
−
||'''''CCCs linked to 4.NF.A.1'''''
+
| colspan=2|'''Use place value understanding and properties of operations to perform multi-digit arithmetic.'''
−
 
+
−
||4.NO.1m1 Determine equivalent fractions.
+
  
 
|-
 
|-
−
| colspan=2|2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
+
| colspan=2|1. Use place value understanding to round whole numbers to the nearest 10 or 100.
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.NF.A.2'''''
+
| rowspan=2|'''''CCCs linked to 3.NBT.A.1'''''
  
−
||4.SE.1g2 Use =, <, or > to compare 2 fractions (fractions with a denominator or 10 or less).
+
||3.NO.1j3 Use place value to round to the nearest 10 or 100.
  
 
|-
 
|-
−
||4.NO.1n2 Compare up to 2 given fractions that have different denominators.  
+
||3.NO.1j4 Use rounding to solve word problems.
  
 
|-
 
|-
−
| colspan=2|'''Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.'''
+
| colspan=2|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=2|3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
+
| rowspan=3|'''''CCCs linked to 3.NBT.A.2'''''
  
−
|-
+
||3.NO.2c1 Solve multi-step addition and subtraction problems up to 100.
−
| colspan=2|1. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
+
  
 
|-
 
|-
−
| colspan=2|b. 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.''
+
||3.NO.2b1 Use the relationships between addition and subtraction to solve problems.
  
 
|-
 
|-
−
| colspan=2|c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
+
||4.NO.2c2 Solve multi-digit addition and subtraction problems up to 1000.
  
 
|-
 
|-
−
| colspan=2|d. 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.
+
| colspan=2|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.
  
 
|-
 
|-
−
| rowspan=4|'''''CCCs linked to 4.NF.B.3'''''
+
||'''''CCCs linked to 3.NBT.A.3'''''
  
−
||4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ ).
+
||4.NO.2f2 Solve multiplication problems up to two digits by one digit.
  
−
|-
+
|}
−
||4.NO.2h1 Add and subtract fractions with like denominators of (2, 3, 4, or 8.)
+
  
−
|-
 
−
||4.NO.2h2 Add and subtract fractions with like denominators (2, 3, 4, or 8) using representations.
 
  
−
|-
 
−
||4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8).
 
  
−
|-
+
 
−
| colspan=2|4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
+
{|border=1
 +
|width = "625" style="background-color:#D9D9D9;"|'''Numbers and Operations – Fractions'''
 +
 
 +
|width = "1875" style="background-color:#D9D9D9;"|'''3.NF'''
  
 
|-
 
|-
−
| colspan=2|a. Understand a fraction ''a''/''b'' as a multiple of 1/''b''. ''For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).''
+
| colspan=2|'''Develop an understanding of fractions as numbers.'''
  
 
|-
 
|-
−
| colspan=2|b. Understand a multiple of ''a''/''b'' as a multiple of 1/''b'', and use this understanding to multiply a fraction by a whole number. ''For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)''
+
| colspan=2|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.
  
 
|-
 
|-
−
| colspan=2|c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. ''For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?''
+
| rowspan=5|'''''CCCs linked to 3.NF.A.1'''''
 +
 
 +
||3.NO.1l1 Identify the number of highlighted parts (numerator) of a given representation (rectangles and circles).
  
 
|-
 
|-
−
||'''''CCCs linked to 4.NF.B.4'''''
 
  
−
||5.NO.2b3 Multiply a fraction by a whole or mixed number  
+
||3.NO.1l2 Identify the total number of parts (denominator) of a given representation (rectangles and circles).
  
 
|-
 
|-
−
| colspan=2|'''Understand decimal notation for fractions, and compare decimal fractions.'''
+
||3.NO.1l3 Identify the fraction that matches the representation (rectangles and circles; halves, fourths, thirds, eighths).
  
 
|-
 
|-
−
| colspan=2|5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
+
||4.NO.1n1 Select a model of a given fraction (halves, thirds, fourths, sixths, eighths).
  
 
|-
 
|-
−
||'''''CCCs linked to 4.NF.C.5'''''
+
||4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ ).
  
−
||4.NO.1o2 Find the equivalent decimal for a given fraction.
+
|-
 +
| colspan=2|2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  
 
|-
 
|-
−
| colspan=2|'''Generate and analyze patterns.'''
+
| colspan=2|a. Represent a fraction 1/''b'' on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into ''b'' equal parts. Recognize that each part has size 1/''b'' and that the endpoint of the part based at 0 locates the number 1/''b'' on the number line.
  
 
|-
 
|-
−
| colspan=2|6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
+
| colspan=2|b. Represent a fraction ''a''/''b'' on a number line diagram by marking off ''a'' lengths 1/''b'' from 0. Recognize that the resulting interval has size ''a''/''b'' and that its endpoint locates the number ''a''/''b'' on the number line.
  
 
|-
 
|-
−
| rowspan=6|'''''CCCs linked to 4.NF.C.6'''''
+
| rowspan=4|'''''CCCs linked to 3.NF.A.2'''''
  
−
||4.SE.1h2 Identify the equivalent decimal for a fraction
+
||3.NO.1l4 Identify that a part of a rectangle can be represented as a fraction that has a value between 0 and 1.
  
 
|-
 
|-
−
||4.NO.1o1 Match a fraction with a denominator of 10 or 100 as a decimal (5/10 = .5).  
+
||3.NO.1l5 Locate given common unit fractions (i.e., ½, ¼, 1/8,) on a number line or ruler.
  
 
|-
 
|-
−
||4.NO.1p1 Read, write or select decimals to the tenths place.  
+
||4.NO.1l6 Locate fractions on a number line.
  
 
|-
 
|-
−
||4.NO.1p2 Read, write or select decimals to the hundredths place.
+
||4.NO.1l7 Order fractions on a number line.
  
 
|-
 
|-
−
||5.NO.1c1 Rewrite a fraction as a decimal.
+
| colspan=2|3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
  
 
|-
 
|-
−
||5.NO.1c2 Rewrite a decimal as a fraction.
+
| colspan=2|4. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.
  
 
|-
 
|-
−
| colspan=2|'''Generate and analyze patterns.'''
+
| colspan=2|5. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
  
 
|-
 
|-
−
| colspan=2|7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
+
| colspan=2|6. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. ''Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.''
  
 
|-
 
|-
−
| rowspan=3|'''''CCCs linked to 4.NF.C.7'''''
+
| colspan=2|7. 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.SE.1g3 Use =, <, or > to compare 2 decimals (decimals in multiples of 10).
+
|-
 +
| rowspan=4|'''''CCCs linked to 3.NF.A.3'''''
 +
 
 +
||3.SE.1g1 Use =, <, or > to compare two fractions with the same numerator or denominator.
  
 
|-
 
|-
−
||4.NO.1q1 Compare two decimals to the tenths place with a value of less than 1.  
+
||4.SE.1h1 Express whole numbers as fractions.
  
 
|-
 
|-
−
||4.NO.1q2 Compare two decimals to the hundredths place with a value of less than 1.
+
||4.NO.1m1 Determine equivalent fractions.
 +
 
 +
|-
 +
||4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8).
  
 
|}
 
|}
Line 306: Line 290:
 
|width = "625" style="background-color:#D9D9D9;"|'''Measurement and Data'''
 
|width = "625" style="background-color:#D9D9D9;"|'''Measurement and Data'''
  
−
|width = "1875" style="background-color:#D9D9D9;"|'''4.MD'''
+
|width = "1875" style="background-color:#D9D9D9;"|'''3.MD'''
  
 
|-
 
|-
−
| colspan=2|'''Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.'''
+
| colspan=2|'''Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.'''
  
 
|-
 
|-
−
| colspan=2|1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
+
| colspan=2|1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.MD.A.1'''''
+
| rowspan=3|'''''CCCs linked to 3.MD.A.1'''''
  
−
||4.ME.2f1 Complete a conversion table for length and mass within a single system.
+
||3.ME.1a2 Solve word problems involving the addition and subtraction of time intervals of whole hours or within an hour (whole hours: 5:00 to 8:00, within hours: 7:15 to 7:45).
  
 
|-
 
|-
−
||5.ME.1a1 Identify the appropriate units of measurement for different purposes in a real life context (e.g., measure a wall using feet, not inches).
+
||3.PRF.1f1 Determine the equivalence between number of minutes and the fraction of the hour (e.g., 30 minutes = ½ hour).  
  
 
|-
 
|-
−
| colspan=2|2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
+
||3.PRF.1f 2 Determine the equivalence between the number of minutes and the number of hours (e.g., 60 minutes = 1 hour).
  
 
|-
 
|-
−
||'''''CCCs linked to 4.MD.A.2'''''
+
| colspan=2|2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
  
−
||4.ME.1g2 Solve word problems using perimeter and area where changes occur to the dimensions of a figure.
+
|-
 +
| rowspan=5|'''''CCCs linked to 3.MD.A.2'''''
 +
 
 +
||3.ME.1f1 Select appropriate units for measurement (liquid volume, area, time, money).
  
 
|-
 
|-
−
| colspan=2|3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
+
||3.ME.1f2 Add to solve one-step word problems.
  
 
|-
 
|-
−
||'''''CCCs linked to 4.MD.3'''''
+
||3.ME.2e1 Select appropriate tool for measurement: liquid volume, area, time, money.
  
−
||4.ME.1g2 Solve word problems using perimeter and area where changes occur to the dimensions of a figure.
+
|-
 +
||3.ME.2i1 Estimate liquid volume.
 +
 
 +
|-
 +
||4.ME.2g1 Determine whether a situation calls for a precise measurement or an estimation (distance, volume, mass, time, money).
  
 
|-
 
|-
Line 342: Line 333:
  
 
|-
 
|-
−
| colspan=2|4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
+
| colspan=2|3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent five pets.
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.MD.B.4'''''
+
| rowspan=6|'''''CCCs linked to 3.MD.B.3'''''
  
−
||4.ME.2e7 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
+
||3.DPS.1g1 Collect data, organize into picture or bar graph.
  
 
|-
 
|-
−
||4.ME.2e8 Solve problems involving addition and subtraction of fractions with like denominators by using information presented in line plots.
+
||3.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots).
  
 
|-
 
|-
−
| colspan=2|'''Geometric measurement: Understand concepts of angle and measure angles.'''
+
||4.DPS.1g3 Collect data, organize in graph (e.g. picture graph, line plot, bar graph).
  
 
|-
 
|-
−
| colspan=2|5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.
+
||4.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots).
  
 
|-
 
|-
−
| colspan=2|a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.
+
||4.DPS.1j1 Select an appropriate statement that describes the most frequent or the least frequent data point using a line plot, picture graph, or bar graph.
  
 
|-
 
|-
−
| colspan=2|b. An angle that turns through ''n'' one-degree angles is said to have an angle measure of ''n'' degrees.
+
||5.DPS.1c1 Collect and graph data: bar graph, line plots, picture graph (e.g., average height among three classrooms, # of boys and girls).
  
 
|-
 
|-
−
||'''''CCCs linked to 4.MD.C.5'''''
+
| colspan=2|4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
  
−
||4.GM.1j3 Recognize an angle in two-dimensional figures.
+
|-
 +
| rowspan=4|'''''CCCs linked to 3.MD.B.4'''''
 +
 
 +
||3.ME.2e2 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
  
 
|-
 
|-
−
| colspan=2|6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
+
||3.ME.2e3 Measure to solve problems using number lines and ruler to 1 inch, ½ inch, or ¼ of an inch.  
  
 
|-
 
|-
−
| rowspan=3|'''''CCCs linked to 4.MD.C.6'''''
+
||3.DPS.1g2 Organize measurement data into a line plot.
  
−
||4.ME.2e4 Select appropriate tool for measurement: mass, length, angles.
+
|-
 +
||4.DPS.1k2 Apply results of data to a real world situation.
  
 
|-
 
|-
−
||4.ME.2e5 Construct a given angle
+
| colspan=2|'''Geometric measurement: understand concepts of area and relate area to multiplication and to addition.'''
  
 
|-
 
|-
−
||4.ME.2e6 Measure right angles using a tool (e.g., angle ruler, protractor).
+
| colspan=2|5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
  
 
|-
 
|-
−
| colspan=2|7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
+
| colspan=2|a. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
  
 
|-
 
|-
−
||'''''CCCs linked to 4.MD.C.7'''''
+
| colspan=2|b. A plane figure which can be covered without gaps or overlaps by ''n'' unit squares is said to have an area of ''n'' square units.
  
−
||None
+
|-
 +
||'''''CCCs linked to 3.MD.C.5'''''
  
−
|}
+
||3.ME.1d1 Use tiling and multiplication to determine area.
  
 +
|-
 +
| colspan=2|6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
  
 +
|-
 +
||'''''CCCs linked to 3.MD.C.6'''''
  
 +
||3.ME1d2 Measure area of rectangles by counting squares.
  
−
{|border=1
+
|-
−
|width = "625" style="background-color:#D9D9D9;"|'''Geometry'''
+
| colspan=2|7. Relate area to the operations of multiplication and addition.
  
−
|width = "1875" style="background-color:#D9D9D9;"|'''4.G'''
+
|-
 +
| colspan=2|a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
  
 
|-
 
|-
−
| colspan=2|'''Draw and identify lines and angles, and classify shapes by properties of their lines and angles.'''
+
| colspan=2|b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
  
 
|-
 
|-
−
| colspan=2|1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
+
| colspan=2|c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths ''a'' and ''b'' + ''c'' is the sum of ''a'' × ''b'' and ''a'' × ''c''. Use area models to represent the distributive property in mathematical reasoning.
  
 
|-
 
|-
−
| rowspan=4|'''''CCCs linked to 4.G.A.1'''''
+
| colspan=2|d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
  
−
||4.GM.1j1 Recognize a point, line and line segment, rays in two-dimensional figures.
+
|-
 +
| rowspan=4|'''''CCCs linked to 3.MD.C.7'''''
 +
 
 +
||3.ME.1d1 Use tiling and addition to determine area.
  
 
|-
 
|-
  
−
||4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figure.
+
||4.ME.1d3 Use tiling and multiplication to determine area.
  
 
|-
 
|-
−
||4.GM.1j3 Recognize an angle in two-dimensional figures.
+
 
 +
||4.ME.2h1 Apply the formulas for area and perimeter to solve real world problems.
  
 
|-
 
|-
−
||5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures.  
+
 
 +
||4.PRF.1f3 Apply the distributive property to solve problems with models.
  
 
|-
 
|-
−
| colspan=2|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 triangles as a category, and identify right triangles.
+
| colspan=2|'''Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.'''
  
 
|-
 
|-
−
| rowspan=2|'''''CCCs linked to 4.G.A.2'''''
+
| colspan=2|8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
  
−
||4.GM.1h2 Classify two-dimensional shapes based on attributes (# of angles).
+
|-
 +
| rowspan=3|'''''CCCs linked to 3.MD.D.8'''''
 +
 
 +
||3.ME.1g1 Identify a figure as getting larger or smaller when the dimensions of the figure change.
  
 
|-
 
|-
−
||4.GM.1j4 Categorize angles as right, acute, or obtuse.
+
||3.ME.2h1 Use addition to find the perimeter of a rectangle.
  
 
|-
 
|-
−
| colspan=2|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.
+
||4.ME.2h1 Apply the formulas for area and perimeter to solve real world problems.
 +
 
 +
|}
 +
 
 +
 
 +
 
 +
 
 +
{|border=1
 +
|width = "625" style="background-color:#D9D9D9;"|'''Geometry'''
 +
 
 +
|width = "1875" style="background-color:#D9D9D9;"|'''3.G'''
  
 
|-
 
|-
−
||'''''CCCs linked to 4.G.A.3'''''
+
| colspan=2|'''Reason with shapes and their attributes.'''
  
−
| rowspan=2|4.GM.1k1 Recognize a line of symmetry in a figure.
+
|-
 +
| colspan=2|1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
 +
 
 +
|-
 +
||'''''CCCs linked to 3.G.A.1'''''
 +
 
 +
||3.GM.1h1 Identify shared attributes of shapes.
 +
 
 +
|-
 +
| colspan=2|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 four parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
 +
 
 +
|-
 +
||'''''CCCs linked to 3.G.A.2'''''
 +
 
 +
| rowspan=2|3.GM.1i1 Partition rectangles into equal parts with equal area.
  
 
|}
 
|}
  
  
−
[[Category:Math]]
 
 
[[Category: CCCs]]
 
[[Category: CCCs]]
 
[[Category: CCSS]]
 
[[Category: CCSS]]
 +
[[Category:Math]]
 +
[[Category:Elementary]]

Latest revision as of 13:52, 23 July 2014

BACK TO Core Content Connectors


Contents

[edit] Grade 3 Overview

[edit] Operations and Algebraic Thinking

  • Represent and solve problems involving multiplication and division.
  • Understand properties of multiplication and the relationship between multiplication and division.
  • Multiply and divide within 100.
  • Solve problems involving the four operations, and identify and explain patterns in arithmetic.

[edit] Number and Operations in Base Ten

  • Use place value understanding and properties of operations to perform multi-digit arithmetic.

[edit] Numbers and Operations—Fractions

  • Develop understanding of fractions as numbers.

[edit] Measurement and Data

  • Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
  • Represent and interpret data.
  • Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
  • Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

[edit] Geometry

  • Reason with shapes and their attributes.



Operations and Algebraic Thinking 3.OA
Represent and solve problems involving multiplication and division.
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.
CCCs linked to 3.OA.A.1 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.
3.NO.2d2 Find the total number inside an array with neither number in the columns or rows larger than 5.
3.NO.2d3 Solve multiplication problems with neither number greater than 5.
3.PRF.1d1 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.
4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10.
4.NO.2d8 Match an accurate addition and multiplication equation to a representation.
4.PRF.1d2 Use objects to model multiplication and division situations involving up to 10 groups with up to 5 objects in each group and interpret the results.
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.
CCCs linked to 3.OA.A.2 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.
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.
3.PRF.1d1 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.
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.
CCCs linked to 3.0A.A.3 3.NO.2e1 Solve or solve and check one- or two-step word problems requiring addition, subtraction or multiplication with answers up to 100.
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 = ?.
CCCs linked to 3.0A.A.4 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.
Understand properties of multiplication and the relationship between multiplication and division.
5. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication). 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30 (Associative property of multiplication). Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (Distributive property).
CCCs linked to 3.OA.B.5 3.PRF.2d2 Apply properties of operations as strategies to multiply and divide.
6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
CCCs linked to 3.OA.B.6 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.
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.
Multiply and divide within 100.
7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers.
CCCs linked to 3.OA.C.7 None
Solve problems involving the four operations, and identify and explain problems in arithmetic.
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.
CCCs linked to 3.OA.D.8 3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100.
9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that four times a number is always even, and explain why four times a number can be decomposed into two equal addends.
CCCs linked to 3.OA.D.9 3.PRF.1e1 Describe the rule for a numerical pattern (e.g., increase by 2, 5 or 10).
3.PRF.1e2 Select or name the three next terms in a numerical pattern where numbers increase by 2, 5 or 10.
3.PRF.2d1 Identify multiplication patterns in a real word setting.



Numbers and Operations in Base Ten 3.NBT
Use place value understanding and properties of operations to perform multi-digit arithmetic.
1. Use place value understanding to round whole numbers to the nearest 10 or 100.
CCCs linked to 3.NBT.A.1 3.NO.1j3 Use place value to round to the nearest 10 or 100.
3.NO.1j4 Use rounding to solve word problems.
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.
CCCs linked to 3.NBT.A.2 3.NO.2c1 Solve multi-step addition and subtraction problems up to 100.
3.NO.2b1 Use the relationships between addition and subtraction to solve problems.
4.NO.2c2 Solve multi-digit addition and subtraction problems up to 1000.
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.
CCCs linked to 3.NBT.A.3 4.NO.2f2 Solve multiplication problems up to two digits by one digit.



Numbers and Operations – Fractions 3.NF
Develop an understanding of fractions as numbers.
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.
CCCs linked to 3.NF.A.1 3.NO.1l1 Identify the number of highlighted parts (numerator) of a given representation (rectangles and circles).
3.NO.1l2 Identify the total number of parts (denominator) of a given representation (rectangles and circles).
3.NO.1l3 Identify the fraction that matches the representation (rectangles and circles; halves, fourths, thirds, eighths).
4.NO.1n1 Select a model of a given fraction (halves, thirds, fourths, sixths, eighths).
4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ ).
2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
CCCs linked to 3.NF.A.2 3.NO.1l4 Identify that a part of a rectangle can be represented as a fraction that has a value between 0 and 1.
3.NO.1l5 Locate given common unit fractions (i.e., ½, ¼, 1/8,) on a number line or ruler.
4.NO.1l6 Locate fractions on a number line.
4.NO.1l7 Order fractions on a number line.
3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
4. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.
5. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
6. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
7. 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.
CCCs linked to 3.NF.A.3 3.SE.1g1 Use =, <, or > to compare two fractions with the same numerator or denominator.
4.SE.1h1 Express whole numbers as fractions.
4.NO.1m1 Determine equivalent fractions.
4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8).



Measurement and Data 3.MD
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
CCCs linked to 3.MD.A.1 3.ME.1a2 Solve word problems involving the addition and subtraction of time intervals of whole hours or within an hour (whole hours: 5:00 to 8:00, within hours: 7:15 to 7:45).
3.PRF.1f1 Determine the equivalence between number of minutes and the fraction of the hour (e.g., 30 minutes = ½ hour).
3.PRF.1f 2 Determine the equivalence between the number of minutes and the number of hours (e.g., 60 minutes = 1 hour).
2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
CCCs linked to 3.MD.A.2 3.ME.1f1 Select appropriate units for measurement (liquid volume, area, time, money).
3.ME.1f2 Add to solve one-step word problems.
3.ME.2e1 Select appropriate tool for measurement: liquid volume, area, time, money.
3.ME.2i1 Estimate liquid volume.
4.ME.2g1 Determine whether a situation calls for a precise measurement or an estimation (distance, volume, mass, time, money).
Represent and interpret data.
3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent five pets.
CCCs linked to 3.MD.B.3 3.DPS.1g1 Collect data, organize into picture or bar graph.
3.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots).
4.DPS.1g3 Collect data, organize in graph (e.g. picture graph, line plot, bar graph).
4.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots).
4.DPS.1j1 Select an appropriate statement that describes the most frequent or the least frequent data point using a line plot, picture graph, or bar graph.
5.DPS.1c1 Collect and graph data: bar graph, line plots, picture graph (e.g., average height among three classrooms, # of boys and girls).
4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
CCCs linked to 3.MD.B.4 3.ME.2e2 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
3.ME.2e3 Measure to solve problems using number lines and ruler to 1 inch, ½ inch, or ¼ of an inch.
3.DPS.1g2 Organize measurement data into a line plot.
4.DPS.1k2 Apply results of data to a real world situation.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
5. Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
CCCs linked to 3.MD.C.5 3.ME.1d1 Use tiling and multiplication to determine area.
6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
CCCs linked to 3.MD.C.6 3.ME1d2 Measure area of rectangles by counting squares.
7. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
CCCs linked to 3.MD.C.7 3.ME.1d1 Use tiling and addition to determine area.
4.ME.1d3 Use tiling and multiplication to determine area.
4.ME.2h1 Apply the formulas for area and perimeter to solve real world problems.
4.PRF.1f3 Apply the distributive property to solve problems with models.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
CCCs linked to 3.MD.D.8 3.ME.1g1 Identify a figure as getting larger or smaller when the dimensions of the figure change.
3.ME.2h1 Use addition to find the perimeter of a rectangle.
4.ME.2h1 Apply the formulas for area and perimeter to solve real world problems.



Geometry 3.G
Reason with shapes and their attributes.
1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
CCCs linked to 3.G.A.1 3.GM.1h1 Identify shared attributes of shapes.
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 four parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
CCCs linked to 3.G.A.2 3.GM.1i1 Partition rectangles into equal parts with equal area.
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