E.NO-2 Build an understanding of computational strategies and algorithms: Fluently add, subtract, multiply, divide, and estimate; Perform and represent operations with whole numbers, fractions, and mixed numbers; Identify multiples and factors of whole numbers. M.NO-2 Expand use of computational strategies and algorithms to rational numbers: Perform operations fluently with rational numbers, including fractions, decimals, and percents; Identify equivalence of indicated division and fractional parts. H.NO-2 Build an understanding of computational strategies and algorithms including matrices and irrational and complex numbers: Use matrix operations and complex and irrational number operations; Apply exponential expressions (laws and properties). Grades K-2 Grades 3-4 Grades 5-6 Grades 7-8 HS Number and Operations: Whole numbers, Ratios, Exponents K.NO.2a1 Count 2 sets to find sums up to 10 3.NO.2b1 Use the relationships between addition and subtraction to solve problems 5.NO.2a1 Solve problems or word problems using up to three digit numbers and addition or subtraction 7.NO.2i1 Solve multiplication problems with positive/negative numbers H.NO.2a1 Solve simple equations using rational numbers with one or more variables K.NO.2a2 Decompose a set of up to 10 objects into a group; count the quantity in each group 3.NO.2c1 Solve multi-step addition and subtraction problems up to 100 5.NO.2a2 Separate a group of objects into equal sets when given the number of sets to find the total in each set with the total number less than 50 7.NO.2i2 Solve division problems with positive/ negative numbers H.NO.2b1 Explain the pattern for the sum or product for combinations of rational and irrational numbers K.NO.2a3 Solve word problems within 10 3.NO.2d1 Find the total number of objects when given the number of identical groups and the number of objects in each group neither number larger than 5 5.NO.2a3 Find whole number quotients up to two divendends and two divisors H.NO.2c1 Simplify expressions that include exponents
groups is not greater than 5 1.NO.2a8 Decompose a set of up to 20 objects into a group; count the quantity in each group 3.NO.2e1 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100 6.NO.2e2 Compare two numbers on a number line (e.g., -2 > -9) 1.NO.2a9 Use manipulatives or representations to simple addition or subtraction equations within 20 based upon a word problem 4.NO.2c2 Solve multi digit addition and subtraction problems up to 1000 1.NO.2a10 Use data presented in graphs (i.e., pictoral, object) to solve one step “how many more” or “how many less” word problems 4.NO.2d6 Find total number inside an array with neither number in the columns or rows larger than 10
2.NO.2c2 Identify and apply addition, subtraction, and equal signs 2.NO.2c3 Compose ones into tens and/or tens into hundreds in addition situation 2.NO.2c4 Decompose tens into ones and/or hundreds into tens in subtraction situations Number and Operations: Fractions and Decimals 4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ ) 5.NO.2b1 Add and subtract fractions with unlike denominators by replacing fractions with equivalent fractions (identical denominators) 7.NO.2f1 Identify the proportional relationship between two quantities 4.NO.2h1 Add and subtract fractions with like denominators of (2,3,4, or 8) 5.NO.2b2 Add or subtract fractions with unlike denominators 7.NO.2f2 Determine if two quantities are in a proportional relationship using a table of equivalent ratios or points graphed on a coordinate plane 4.NO.2h2 Add and subtract fractions with like denominators 5.NO.2b3 Multiply or divide fractions 7.NO.2f3 Find unit rates given a ratio
(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) 5.NO.2c1 Solve 1 step problems using decimals 7.NO.2f4 Use a rate of change or proportional relationship to determine the points on a coordinate plane 5.NO.2c2 Solve word problems involving the addition, subtraction, multiplication or division of fractions 7.NO.2f5 Use proportions to solve ratio problems 6.NO.2c3 Solve one step, addition, subtraction, multiplcation, or division problems with fractions or decimals 7.NO.2f6 Solve word problems involving ratios 6.NO.2c4 Solve word problems involving the addition, subtraction, multiplication or division of fractions 7.NO.2h2 Solve one step percentage increase and decrease problems 8.NO.2i3 Solve one step addition, subtraction, multiplication, division problems with fractions,
decimals, and positive/negative numbers 8.NO.2i4 Solve two step addition, subtraction, multiplication, and division problems with fractions, decimals, or positive/negative numbers Number and Operations: Application 7.NO.2h1 Find percents in real world contexts Number and Operations 2 Differentiation Progress Indicator: E.NO.2a representing addition and subtraction in multiple ways (composing/ decomposing numbers, diagrams, using objects, arrays, equations, number lines), including regrouping Core Content Connectors: K CCSS Domain/Cluster Common Core State Standard K.NO.2a1 Count 2 sets to find sums up to 10 Operations and Algebraic Thinking K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
numbers with one or more variables A REI Understand solving equations as a process of reasoning and explain the reasoning. Progress Indicator: H.NO.2b operating with irrational and complex numbers Core Content Connectors: 9-12 CCSS Domain/Cluster Common Core State Standard H.NO.2b1 Explain the pattern for the sum or product for combinations of rational and irrational numbers The Real Number System N RN Use properties of rational irrational numbers. N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational. Progress Indicator: H.NO.2c identifying exponential situations and applying the laws and properties of exponents in simplifying expressions and solving equations Core Content Connectors: 9-12 CCSS Domain/Cluster Common Core State Standard H.NO.2c1 Simplify expressions that include exponents Seeing Structure in Expressions A SSE Interpret the structures of expressions. A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). H.NO.2c2 Rewrite expressions that include rational exponents The Real Number System N RN Extend the properties of exponents to rational exponents. Seeing Structure in Expressions A SSE Interpret the structures of expressions. N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Explanations and clarifications: Not included: H.PRF.1d recognizing that there limitations in mathematics models A.CE-3 S.IC-2