Counting And Cardinality 
K.CC: Compare Numbers. 
K.CC.6  Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1 

K.CC.7  Compare two numbers between 1 and 10 presented as written numerals. 
Number And Operations In Base Ten 
1.NBT: Understand Place Value. 
1.NBT.2  Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases: 

1.NBT.3  Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 
2.NBT: Use Place Value Understanding And Properties Of Operations To Add And Subtract. 
2.NBT.5  Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 
3.NBT: Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.4 
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. 
5.NBT: Perform Operations With MultiDigit Whole Numbers And With Decimals To Hundredths. 
5.NBT.5  Fluently multiply multidigit whole numbers using the standard algorithm. 
Number And Operations—Fractions 
5.NF: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions. 
5.NF.4  Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 

5.NF.7  Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 
Use Equivalent Fractions As A Strategy To Add And Subtract Fractions. 
5.NF.1  Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 

5.NF.2  Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions 
4.NF: Build Fractions From Unit Fractions By Applying And Extending Previous Understandings Of Operations On Whole Numbers. 
4.NF.3  Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. 

4.NF.4  Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 
Extend Understanding Of Fraction Equivalence And Ordering. 
4.NF.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. 

4.NF.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. 
Understand Decimal Notation For Fractions, And Compare Decimal Fractions. 
4.NF.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 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 

4.NF.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. 
3.NF: Develop Understanding Of Fractions As Numbers. 
3.NF.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. 

3.NF.2  Understand a fraction as a number on the number line; represent fractions on a number line diagram. 

3.NF.3  Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 
Operations And Algebraic Thinking 
1.OA: Represent And Solve Problems Involving Addition And Subtraction. 
1.OA.1  Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 
2.OA: Represent And Solve Problems Involving Addition And Subtraction. 
2.OA.1  Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 
3.OA: Multiply And Divide Within 100. 
3.OA.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 onedigit numbers. 
Represent And Solve Problems Involving Multiplication And Division. 
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. 

3.OA.2  Interpret wholenumber 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. 
Ratios And Proportional Relationships 
6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. 
6.RP.3.c  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 