Third Grade (Operations & Algebraic Thinking (Represent and solve…
Operations & Algebraic Thinking
Represent and solve problems involving multiplication and division.
Interpret products of whole numbers, For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Interpret whole-number quotients of whole numbers. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
Understand properties of multiplication and the relationship between multiplication and division.
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.)
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8
Multiply and divide within 100.
Multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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.
Identify arithmetic patterns and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Numbers and Operations: Fractions
Develop understanding of fractions as numbers.
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts. Ex: 1/4 is 1 split into 4 equal parts. Understand a fraction a/b as the quantity formed by a parts of size 1/b.
Understand a fraction as a number on the number line. Be able to represent fractions on a number line diagram.
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.
Represent a fraction 1/b ( b representing a whole number) 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.
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
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 show how the conclusion was found
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Ex.: 3 = 3/1; 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram
Recognize and create simple equivalent fractions. Explain why the fractions are equivalent.
Numbers and Operations Base 10
Use place value understanding and properties of operations to perform multi-digit arithmetic.
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.
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 by using strategies based on place value and properties of operations.
Use place value understanding to round whole numbers to the nearest 10 or 100