Element Cards Number Operations Real Numbers
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+ | {{BACK TO|[[Element Cards]]}} | ||
=Teaching Number Operations= | =Teaching Number Operations= | ||
All of the CCCs in this document relate to teaching Number Operations. Below are some additional resources that may be helpful: | All of the CCCs in this document relate to teaching Number Operations. Below are some additional resources that may be helpful: | ||
− | NCSC Curriculum Resource Guide: Equations | + | |
− | NCSC Curriculum Resource Guide: Ratio and Proportions | + | NCSC Curriculum Resource Guide: [[Equations]] |
− | NCSC Content Module: Radicals and Exponents | + | |
− | NCSC Content Module: Expressions | + | NCSC Curriculum Resource Guide: [[Curriculum Resource Guide: Ratio and Proportions]] |
+ | |||
+ | NCSC Content Module: [[Radicals and Exponents Content Module]] | ||
+ | |||
+ | NCSC Content Module: [[Expressions Content Module]] | ||
==Websites== | ==Websites== | ||
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[http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] | [http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] | ||
− | =CCC Mathematics | + | =CCC Mathematics: Number Operations (Real Numbers)= |
{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' K.CC.1 Count to 100 by ones and by tens. | | colspan=3|'''CCSS:''' K.CC.1 Count to 100 by ones and by tens. | ||
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|- | |- | ||
− | | colspan=3|'''Progress Indicator:''''' E.NO.1a Showing mastery of the prerequisite core skills of cardinality, constancy, and 1:1 correspondence'' | + | | colspan=3|'''Progress Indicator:'''''E.NO.1a Showing mastery of the prerequisite core skills of cardinality, constancy, and 1:1 correspondence'' |
|- | |- | ||
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{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality. | | colspan=3|'''CCSS:''' K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality. | ||
− | + | <ol type=lower-alpha><li> When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.</li></ol> | |
|- | |- | ||
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* A number line with a raised dots paired with each number, and/or Braille | * A number line with a raised dots paired with each number, and/or Braille | ||
* Provide a number line composed of raised cells | * Provide a number line composed of raised cells | ||
− | 1 | + | {|border=1px solid black style="border-collapse:collapse; background-color:#D9D9D9; text-align:center;" |
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− | + | |} | |
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{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | | colspan=3|'''CCSS:''' 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | ||
− | + | <ol type=lower-alpha><li> 10 can be thought of as a bundle of ten ones – called a "ten".</li> | |
− | + | <li> The numbers from 11 to 19 are composed of a ten and one, two, three four, five, six seven, eight, or nine ones.</li></ol> | |
|- | |- | ||
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|} | |} | ||
− | [[File: | + | [[File:Element Cards Numbers Operations Real Numbers1.PNG| stack of 6 blocks next to stack of 10 blocks]] |
{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' K.NBT.1 Compose and decompose numbers from 11 to 19 into tens ones and some further ones, e.g., by using objects or drawings, and record each compositions or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | | colspan=3|'''CCSS:''' K.NBT.1 Compose and decompose numbers from 11 to 19 into tens ones and some further ones, e.g., by using objects or drawings, and record each compositions or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | ||
+ | |||
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | ||
− | + | <ol type=lower-alpha><li> The numbers from 11 to 19 are composed of a ten and one, two, three four, five, six seven, eight, or nine ones.</li></ol> | |
|- | |- | ||
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* Interactive whiteboards | * Interactive whiteboards | ||
− | |||
|} | |} | ||
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{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones: e.g. 706 equals 7 hundreds 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | | colspan=3|'''CCSS:''' 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones: e.g. 706 equals 7 hundreds 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | ||
− | + | <ol type=lower-alpha><li> 100 can be thought of as a bundle of ten tens – called a "hundred." </li> | |
− | + | <li> The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).</li></ol> | |
|- | |- | ||
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|} | |} | ||
− | [[File: | + | [[File:Element Cards Numbers Operations Real Numbers2.PNG|10 by 10 grid of blocks]] |
{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | | colspan=3|'''CCSS:''' 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||
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* Start with color coded templates as they relate to tens and ones and remove for generalization | * Start with color coded templates as they relate to tens and ones and remove for generalization | ||
* Expanded form template (e.g., _____ + _____ ) | * Expanded form template (e.g., _____ + _____ ) | ||
+ | |} | ||
− | |||
− | |||
− | |||
{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | | colspan=3|'''CCSS:''' 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||
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* Computer software | * Computer software | ||
* Place value mat with a column for hundreds, tens and ones | * Place value mat with a column for hundreds, tens and ones | ||
− | + | {|border=1px solid black style="border-collapse:collapse; font-family:arial;" | |
− | * Graphic organizer that provides the correct number of "0s" | + | ||Hundreds |
− | + | ||Tens | |
− | + | ||Ones | |
+ | |- | ||
+ | |style="border-bottom:none;" height=50px| | ||
+ | |height=50px| | ||
+ | |height=50px| | ||
+ | |} | ||
+ | * Graphic organizer that provides the correct number of "0s" ie <math>549=\_00+\_0+</math> | ||
* Computer software | * Computer software | ||
− | |||
|- | |- | ||
|} | |} | ||
− | + | ||
{|border=1 | {|border=1 | ||
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* Place value mat or other graphic organizer | * Place value mat or other graphic organizer | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
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{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS''': 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones: e.g. 706 equals 7 hundreds 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | | colspan=3|'''CCSS''': 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones: e.g. 706 equals 7 hundreds 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | ||
− | + | <ol type=lower-alpha><li> 100 can be thought of as a bundle of ten tens – called a "hundred." </li> | |
− | + | <li> The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).</li></ol> | |
|- | |- | ||
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|- | |- | ||
|} | |} | ||
− | + | [[File:Element Cards Numbers Operations Real Numbers2.PNG|10 by 10 grid of blocks]] | |
{|border=1 | {|border=1 | ||
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|- | |- | ||
|} | |} | ||
+ | [[File:Element Cards Numbers Operations Real Numbers4.png|400px]] | ||
{|border=1 | {|border=1 | ||
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{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' 6.NS.7c Understand ordering and absolute value of rational numbers. | | colspan=3|'''CCSS:''' 6.NS.7c Understand ordering and absolute value of rational numbers. | ||
− | + | <ol type=lower-alpha><li> Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. ''For example, for an account balance of -30 dollars write \|-30\| = 30 to describe the size of the debt in dollars.''</li> | |
|- | |- | ||
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{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | | colspan=3|'''CCSS:''' 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | ||
+ | |||
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. | 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. | ||
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{|border=1 | {|border=1 | ||
− | || | + | |colspan=3|'''CCSS:''' N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. |
− | + | ||
|- | |- | ||
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|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
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||''One millionth'' | ||''One millionth'' | ||
− | || | + | ||<math>0.000001</math> |
− | || | + | ||<math>10^{-6}</math> |
− | || | + | ||<math>1*10^{-6}</math> |
|- | |- | ||
||''One thousandth'' | ||''One thousandth'' | ||
− | || | + | ||<math>0.001</math> |
− | || | + | ||<math>10^{-3}</math> |
− | || | + | ||<math>1*10^{-3}</math> |
|- | |- | ||
||''One hundredth'' | ||''One hundredth'' | ||
− | || | + | ||<math>0.01</math> |
− | || | + | ||<math>10^{-2}</math> |
− | || | + | ||<math>1*10^{-2}</math> |
|- | |- | ||
||''One tenth'' | ||''One tenth'' | ||
− | || | + | ||<math>0.1</math> |
− | || | + | ||<math>10^{-1}</math> |
− | + | ||
− | + | ||
+ | ||<math>1*10^{-1}</math> | ||
|- | |- | ||
||''One'' | ||''One'' | ||
− | || | + | ||<math>1</math> |
− | || | + | ||<math>10^{0}</math> |
− | || | + | ||<math>1*10^{0}</math> |
|- | |- | ||
||''Ten'' | ||''Ten'' | ||
− | || | + | ||<math>10</math> |
− | || | + | ||<math>10^{1}</math> |
− | || | + | ||<math>1*10^{1}</math> |
|- | |- | ||
||''One hundred'' | ||''One hundred'' | ||
− | || | + | ||<math>100</math> |
− | || | + | ||<math>10^{2}</math> |
− | || | + | ||<math>1*10^{2}</math> |
|- | |- | ||
||''One thousand'' | ||''One thousand'' | ||
− | || | + | ||<math>1,000</math> |
− | || | + | ||<math>10^{3}</math> |
− | || | + | ||<math>1*10^{3}</math> |
|- | |- | ||
||''One million'' | ||''One million'' | ||
− | || | + | ||<math>1,000,000</math> |
− | || | + | ||<math>10^{6}</math> |
− | || | + | ||<math>1*10^{6}</math> |
|- | |- | ||
||''One billion'' | ||''One billion'' | ||
− | || | + | ||<math>1,000,000,000</math> |
− | || | + | ||<math>10^{9}</math> |
− | || | + | ||<math>1*10^{9}</math> |
|- | |- | ||
||''One trillion'' | ||''One trillion'' | ||
− | || | + | ||<math>1,000,000,000,000</math> |
− | || | + | ||<math>10^{12}</math> |
− | || | + | ||<math>1*10^{12}</math> |
|- | |- | ||
|} | |} | ||
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|- | |- | ||
| colspan=3|'''Supports and Scaffolds:''' | | colspan=3|'''Supports and Scaffolds:''' | ||
− | * Manipulatives to place in sets to compare numbers | + | * Manipulatives to place in sets to compare numbers [[File:Element Cards Numbers Operations Real Numbers3.PNG|right|chart for comparing numbers. Numbers smaller than the selected number are placed to the left, numbers that are greater are placed to the right.]] |
* Interactive whiteboards | * Interactive whiteboards | ||
* Assistive Technology | * Assistive Technology | ||
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|} | |} | ||
− | + | ||
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|- | |- | ||
|} | |} | ||
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{|border=1 | {|border=1 | ||
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|- | |- | ||
|} | |} | ||
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{|border=1 | {|border=1 | ||
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|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
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{|border=1 | {|border=1 | ||
− | | colspan=3|'''CCSS:''' N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. | + | |colspan=3|'''CCSS:''' N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. |
A.SSE.3c Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | A.SSE.3c Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | ||
− | + | <ol type=lower-alpha><li> Use the properties of exponents to transform expressions for exponential functions. ''For example: <math>\sqrt{2}*\sqrt{2} | |
+ | =2^{\frac{1}{2}} * 2^{\frac{1}{2}} | ||
+ | =2^{\frac{1}{2}+\frac{1}{2}} | ||
+ | =2</math></li></ol> | ||
|- | |- | ||
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||'''Strand: '''Number Operations (Real Numbers) | ||'''Strand: '''Number Operations (Real Numbers) | ||
− | | colspan=2|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | + | | colspan=2 style="background-color:#365F91;"|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers |
|- | |- | ||
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{|border=1 | {|border=1 | ||
| colspan=3|'''CCSS:''' 3.OA.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=3|'''CCSS:''' 3.OA.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.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 = ?. | 3.OA.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 = ?. | ||
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||'''Strand:''' Number Operations (Real Numbers) | ||'''Strand:''' Number Operations (Real Numbers) | ||
− | | colspan=2|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | + | | colspan=2 style="background-color:#365F91;"|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers |
|- | |- | ||
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|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
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||'''Strand:''' Number Operations (Real Numbers) | ||'''Strand:''' Number Operations (Real Numbers) | ||
− | | colspan=2|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | + | | colspan=2 style="background-color:#365F91;"|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers |
|- | |- | ||
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||'''Strand:''' Number Operations (Real Numbers) | ||'''Strand:''' Number Operations (Real Numbers) | ||
− | | colspan=2|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | + | | colspan=2 style="background-color:#365F91;"|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers |
|- | |- | ||
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|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
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||'''Strand:''' Number Operations (Real Numbers) | ||'''Strand:''' Number Operations (Real Numbers) | ||
− | | colspan=2|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | + | | colspan=2 style="background-color:#365F91;"|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers |
|- | |- | ||
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|- | |- | ||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
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||'''Strand: '''Symbolic Expression | ||'''Strand: '''Symbolic Expression | ||
− | | colspan=2|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | + | | colspan=2 style="background-color:#365F91;"|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers |
|- | |- | ||
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||'''Strand:''' Number Operations (Real Numbers) | ||'''Strand:''' Number Operations (Real Numbers) | ||
− | | colspan=2|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | + | | colspan=2 style="background-color:#365F91;"|'''Family:''' Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers |
|- | |- | ||
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|- | |- | ||
− | |||
− | |||
| colspan=3|'''Supports and Scaffolds:''' | | colspan=3|'''Supports and Scaffolds:''' | ||
* Operation template to fill in the steps of the word problem (___ x ____ = ____; (___ + ____ = ____; a horizontal structure with boxes for carrying/regrouping) | * Operation template to fill in the steps of the word problem (___ x ____ = ____; (___ + ____ = ____; a horizontal structure with boxes for carrying/regrouping) | ||
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* Highlight text that provides important information/vocabulary | * Highlight text that provides important information/vocabulary | ||
− | |||
|} | |} | ||
+ | |||
+ | |||
+ | |||
+ | [[Category:Math]] [[Category:Elementary]] [[Category:Middle]] [[Category:High]] [[Category:Element Cards]] |
Latest revision as of 11:03, 3 September 2014
BACK TO Element Cards
Contents |
[edit] Teaching Number Operations
All of the CCCs in this document relate to teaching Number Operations. Below are some additional resources that may be helpful:
NCSC Curriculum Resource Guide: Equations
NCSC Curriculum Resource Guide: Curriculum Resource Guide: Ratio and Proportions
NCSC Content Module: Radicals and Exponents Content Module
NCSC Content Module: Expressions Content Module
[edit] Websites
http://www.mathmammoth.com/lessons/multiplication_tables.php
http://www.mathplayground.com/
[edit] Other Resources
http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf
http://www.ncpublicschools.org/acre/standards/common-core-tools/
[edit] CCC Mathematics: Number Operations (Real Numbers)
CCSS: K.CC.1 Count to 100 by ones and by tens. | ||
CCC: | K.NO.1a2 | Rote count up to 31. |
Strand: Number Operations (Real Numbers) | Family: Counting and Representing Numbers | |
Progress Indicator:E.NO.1a Showing mastery of the prerequisite core skills of cardinality, constancy, and 1:1 correspondence | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | ||
CCC: | 1.NO.1a7 | Count forward beginning from any given number below 10. |
Strand: Number Operations (Real Numbers) | Family: Counting and Representing Numbers | |
Progress Indicator: E.NO.1a Showing mastery of the prerequisite core skills of cardinality, constancy, and 1:1 correspondence | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
| ||||||||||||||
CCC: | 1.NO.1c1 | Use a number line to count up to 31 objects by matching 1 object per number. | ||||||||||||
Strand: Number Operations (Real Numbers) | Family: Counting and Representing Numbers | |||||||||||||
Progress Indicator: E.NO.1c Developing number line skills (linear representations) using 0 to 20, and later 0 to 100 | ||||||||||||||
Essential Understandings | Concrete Understandings:
|
Representation:
| ||||||||||||
Suggested Instructional Strategies:
| ||||||||||||||
Supports and Scaffolds:
|
CCSS: 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
| ||
CCC: | 1.NO.1h2 | Identify the value of the numbers in the tens and ones place within a given number up to 31. |
Strand: Number Operations (Real Numbers) | Family: Understanding the Base Ten Number System | |
Progress Indicator: E.NO.1h Applying place value understanding to compare and order numbers, express number relationships (<, >, =), and express numbers in expanded form | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: K.NBT.1 Compose and decompose numbers from 11 to 19 into tens ones and some further ones, e.g., by using objects or drawings, and record each compositions or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
| ||
CCC: | 1.NO.1h1 | Build representations of numbers up to 19 by creating a group of 10 and some 1s (e.g., 13 = one 10 and three 1s). |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1h Applying place value understanding to compare and order numbers, express number relationships (<, >, =), and express numbers in expanded form | ||
Essential Understandings | Concrete Understandings:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | ||
CCC: | 1.NO.1i1 | Recognize zero as representing none or no objects. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1i Recognizing zero as an additive identify, origin for the number line, and representing no units as a quantity or in place value | ||
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CCSS: 1.OA.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 = 2 + 10 = 12. (Associative property of addition.) | ||
CCC: | 1.NO.1i2 | Recognize zero as an additive identity. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1i Recognizing zero as an additive identify, origin for the number line, and representing no units as a quantity or in place value | ||
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CCSS: 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||
CCC: | 2.NO.1e3 | Write or select the numerals 0-100. |
Strand: Number Operations (Real Numbers) | Family: Counting and Representing Numbers | |
Progress Indicator: E.NO.1e Reading and writing numbers; counting and estimating (e.g., how many?; skip counting by 2s, 5s, 10s; even/odd) | ||
Essential Understandings | Concrete Understandings:
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CCSS: 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones: e.g. 706 equals 7 hundreds 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
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CCC: | 2.NO.1h5 | Build representations of 3 digit numbers using hundreds, tens and ones. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1h Applying place value understanding to compare and order numbers, express number relationships (<, >, =), and express numbers in expanded form | ||
Essential Understandings | Concrete Understandings:
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CCSS: 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||
CCC: | 2.NO.1h8 | Write or select expanded form for any 2 digit number. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1h Applying place value understanding to compare and order numbers, express number relationships (<, >, =), and express numbers in expanded form | ||
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CCSS: 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||||||||
CCC: | 2.NO.1h9 | Write or select expanded form for any 3 digit number. | ||||||
Strand: Number Operations (Real Numbers) | Family: Understanding Base Ten Number System | |||||||
Progress Indicator: E.NO.1h Applying place value understanding to compare and order numbers, express number relationships (<, >, =), and express numbers in expanded form | ||||||||
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CCSS: 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||
CCC: | 2.NO.1i3 | Explain what the zero represents in place value (hundreds, tens, ones) in a number. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1i Recognizing zero as an additive identify, origin for the number line, and representing no units as a quantity or in place value | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||
CCC: | 3.NO.1j2 | Write or select the expanded form for up to 3 digit number. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1j Applying place value concepts to: read, write, and compare whole numbers up to 100,000; use expanded form; and round numbers to a given place | ||
Essential Understandings | Concrete Understandings:
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CCSS: 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones: e.g. 706 equals 7 hundreds 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
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CCC: | 3.NO.1j1 | Build representations of numbers using hundreds, tens, and ones. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1j Applying place value concepts to: read, write, and compare whole numbers up to 100,000; use expanded form; and round numbers to a given place | ||
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CCSS: 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | ||
CCC: | 3.NO.1j3 | Use place value to round to the nearest 10 or 100. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1j Applying place value concepts to: read, write, and compare whole numbers up to 100,000; use expanded form; and round numbers to a given place | ||
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CCSS: 2.NBT.4 Compare two three-digit numbers based on meanings if the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | ||
CCC: | 3.NO.1h1 | Compare 3-digit numbers using representations and numbers (e.g., identify more hundreds, less hundreds, more tens, less tens, more ones, less ones, larger number, smaller number). |
Strand: Number Operations (Real Numbers) | Family: Determine Relative Position of Whole Numbers | |
Progress Indicator: E.NO.1h Applying place value understanding to compare and order numbers, express number relationships (<, >, =), and express numbers in expanded form | ||
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CCSS: 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. | ||
CCC: | 4.NO.1j5 | Use place value to round to any place (i.e., ones, tens, hundreds, thousands). |
Strand: Number Operations (Real Numbers) | Family: Understanding Base Ten Number System | |
Progress Indicator: E.NO.1j Applying place value concepts to: read, write, and compare whole numbers up to 100,000; use expanded form; and round numbers to a given place | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 4.NBT.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. | ||
CCC: | 4.NO.1j7 | Write or select the expanded form for a multi-digit number. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: E.NO.1j Applying place value concepts to: read, write, and compare whole numbers up to 100,000; use expanded form; and round numbers to a given place | ||
Essential Understandings | Concrete Understandings:
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CCSS: 6.NS.7c Understand ordering and absolute value of rational numbers.
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CCC: | 6.NO.1e1 | Determine the meaning of absolute value. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: M.NO.1e Describing, representing, and comparing absolute value relationships | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. | ||
CCC: | 6.NO.1i1 | Identify what an exponent represents (e.g., 8³= 8X8X8). |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: M.NO.1i Using exponents and scientific notation to express very large or very small quantities | ||
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CCSS: 8.EE.3 Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger. | ||
CCC: | 8.NO.1i1 | Convert a number expressed in scientific notation up to 10,000. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: M.NO.1i Using exponents and scientific notation to express very large or very small quantities | ||
Essential Understandings | Concrete Understandings:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | ||
CCC: | 8.NO.1k1 | Identify π as an irrational number (e.g., not necessary for counting, computation, etc). |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: M.NO.1k Distinguishing rational numbers (terminating and repeating) from irrational numbers (non-terminating and non-repeating), and recognizing that together they form the real number system and that both can be represented on the number line | ||
Essential Understandings | Concrete Understandings:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. | ||
CCC: | 8.NO.1k2 | Round irrational numbers to the hundredths place. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: M.NO.1k Distinguishing rational numbers (terminating and repeating) from irrational numbers (non-terminating and non-repeating), and recognizing that together they form the real number system and that both can be represented on the number line | ||
Essential Understandings | Concrete Understandings:
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CCSS: N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. | ||
CCC: | H.NO.1a3 | Convert a number expressed in scientific notation. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: H.NO.1a Using exponents and scientific notation to represent quantities and expressions | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. | ||
CCC: | H.NO.1a2 | Explain the influence of an exponent on the location of a decimal point in a given number. |
Strand: Number Operations (Real Numbers) | Family: Understanding base Ten Number System | |
Progress Indicator: H.NO.1a Using exponents and scientific notation to represent quantities and expressions | ||
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Common name | Decimal form | Power of 10 | Scientific Notation |
One millionth | |||
One thousandth | |||
One hundredth | |||
One tenth | |||
One | |||
Ten | |||
One hundred | |||
One thousand | |||
One million | |||
One billion | |||
One trillion |
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
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CCC: | K.NO.1b2 | Identify the set that has more. |
Strand: Number Operations (Real Numbers) | Family: Determine Relative Position of Whole Numbers | |
Progress Indicator: E.NO.1b Developing an understanding of number and principles of quantity (e.g., hold up 5 fingers at once to show 5, locate things in 2s without counting; using number words to indicate small exact numbers or relative change in quantity - more, small) | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 6.NS.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.
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. | ||
CCC: | 6.NO.1d2 | Locate positive and negative numbers on a number line. |
Strand: Number Operations (Real Numbers) | Family: Determine Relative Position of Whole Number | |
Progress Indicator: M.NO.1d Representing integers (positive/negative numbers) and locating them on a number line | ||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | ||
CCC: | 6.NO.1d4 | Select the appropriate meaning of a negative number in a real-world situation. |
Strand: Number Operations (Real Numbers) | Family: Determine Relative Position of Whole Numbers | |
Progress Indicator: M.NO.1d Representing integers (positive/negative numbers) and locating them on a number line | ||
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CCSS: 2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations. | ||
CCC: | 2.NO.2a19 | Combine up to 3 sets of 20 or less. |
Strand: Number and Operations; (Whole numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator: E.NO.2a Representing addition and subtraction in multiple ways composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping | ||
Essential Understandings | Concrete Understandings:
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CCSS: 1.OA.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.) | ||
CCC: | 2.NO.2b1 | Use commutative properties to solve addition problems with sums up to 20 (e.g., 3+8=11 therefore 8+3=__). |
Strand: Number and Operations; (Whole numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator:E.NO.2b Explaining or modeling the relationship between addition and subtraction | ||
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CCSS: 1.OA.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.) | ||
CCC: | 2.NO.2b2 | Use associative property to solve addition problems with sums up to 20. |
Strand: Number and Operations; (Whole numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator: E.NO.2b Explaining or modeling the relationship between addition and subtraction | ||
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CCSS: 3.NBT.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. | ||
CCC: | 3.NO.2b1 | Use the relationships between addition and subtraction to solve problems. |
Strand: Number and Operations; (Whole numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator: E.NO.2b Explaining or modeling the relationship between addition and subtraction | ||
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CCSS: 3.OA.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. | ||
CCC: | 3.NO.2d3 | Solve multiplication problems with neither number greater than 5. |
Strand: Number Operations (Real Numbers) | Family: Perform Operations with Whole Numbers | |
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 | ||
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CCSS: 4.OA.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.OA.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. | ||
CCC: | 4.NO.2f1 | Identify multiples for a whole number (e.g., 2= 2, 4, 6, 8, 10). |
Strand: Number and Operations; (Whole numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator: E.NO.2f Identifying factors and multiples of numbers | ||
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CCSS: 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
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CCC: | 7.NO.2i1 | Solve multiplication problems with positive/negative numbers. |
Strand: Number Operations (Real Numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator: M.NO.2i Using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line | ||
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CCSS: 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions 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. | ||
CCC: | 7.NO.2i2 | Solve division problems with positive/negative numbers. |
Strand: Number Operations (Real Numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator: M.NO.2i Using operations with rational numbers; representing rational numbers and approximations of irrational numbers on a number line | ||
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CCSS: N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
A.SSE.3c Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
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CCC: | H.NO.1a1 | Simplify expressions that include exponents. |
Strand: Number Operations (Real Numbers) | Family: Perform Operations with Whole Numbers | |
Progress Indicator: H.NO.1a Using exponents and scientific notation to represent quantities and expressions | ||
Essential Understandings | Concrete Understandings:
a7 = a × a × a × a × a × a × a = aaaaaaa
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 3.OA.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.
3.OA.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. | ||
CCC: | 3.NO.2e1 | Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100. |
Strand: Number Operations (Real Numbers) | Family: Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | |
Progress Indicator: E.NO.2e Describing relationships between addition-multiplication; multiplication-division; addition-subtraction; why commutative property does not apply to subtraction or division | ||
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CCSS: 3.OA.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.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 = ?. | ||
CCC: | 4.NO.2d7 | Determine how many objects go into each group when given the total number of objects and groups where the number in each group or number of groups is not > 10. |
Strand: Number Operations (Real Numbers) | Family: Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | |
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 | ||
Essential Understandings | Concrete Understandings:
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CCSS: 3.OA.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 | ||
CCC: | 4.NO.2d8 | Match an accurate addition and multiplication equation to a representation. |
Strand: Number Operations (Real Numbers) | Family: Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | |
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 | ||
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CCSS: 4.OA.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.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. | ||
CCC: | 5.NO.2a1 | Solve problems or word problems using up to three digit numbers and addition or subtraction or multiplication. |
Strand: Number Operations (Real Numbers) | Family: Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | |
Progress Indicator: M.NO.2a working flexibility with common addition, subtraction, multiplication, and division situations | ||
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CCSS: 5.NBT.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 | ||
CCC: | 5.NO.2a5 | Solve word problems that require multiplication or division. |
Strand: Number Operations (Real Numbers) | Family: Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | |
Progress Indicator: M.NO.2a Working flexibility with common addition, subtraction, multiplication, and division situations | ||
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CCSS: 6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for | ||
CCC: | 5.SE.1b1 | Evaluate whether or not both sides of an equation are equal. |
Strand: Symbolic Expression | Family: Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | |
Progress Indicator: M.SE.1b Writing, interpreting, and using expressions, equations, and inequalities (including using brackets, parentheses, or braces) | ||
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CCSS: 6.EE.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 | ||
CCC: | 6.NO.2a6 | Solve problems or word problems using up to three digit numbers and any of the four operations |
Strand: Number Operations (Real Numbers) | Family: Modeling/Symbolizing Operations (Problem Solving) with Whole Numbers | |
Progress Indicator: M.NO.2a Working flexibility with common addition, subtraction, multiplication, and division situations | ||
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