Common Core State Standards for Mathematics Standards for Mathematical Practice [K-12] Make sense of problems and persevere in solving them. [K-12] Reason abstractly and quantitatively. [K-12] Construct viable arguments and critique the reasoning of others. [K-12] Model with mathematics. [K-12] Operations and Algebraic Thinking [K - 5] Represent and solve problems involving multiplication and division.  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.  Use the four operations with whole numbers to solve problems.  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.  Gain familiarity with factors and multiples.  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.  Number and Operations in Base Ten [K - 5] Understand the place value system.  4. Use place value understanding to round decimals to any place.  Perform operations with multi-digit whole numbers and with decimals to hundredths.  5. Fluently multiply multi-digit whole numbers using the standard algorithm.  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.  Measurement and Data [K - 5] Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.  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 twocolumn 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), ...  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.  Number and Operations—Fractions [3 - 5] Develop understanding of fractions as numbers.  3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.  a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.  Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.  3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.  a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.  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.  4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.  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?  Apply and extend previous understandings of multiplication and division to multiply and divide fractions.  7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.  c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?