Operations & Algebraic Thinking

3rd Grade students will be able to:

• Interpret and/or describe products of whole numbers (up to and including 10 × 10). 

  • Example 1: Interpret 35 as the total number of objects in 5 groups, each containing 7 objects. 

  • Example 2: Describe a context in which a total number of objects can be expressed as 5 × 7. 

• Interpret and/or describe whole-number quotients of whole numbers (limit dividends through 50 and limit divisors and quotients through 10). 

  • Example 1: Interpret 48 ÷ 8 as the number of objects in each share when 48 objects are partitioned equally into 8 shares, or as a number of shares when 48 objects are partitioned into equal shares of 8 objects each. 

  • Example 2: Describe a context in which a number of shares or a number of groups can be expressed as 48 ÷ 8.

• Use multiplication (up to and including 10 × 10) and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities. 

• Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers. 

  • Example: Determine the unknown number that makes an equation true.

• Apply the commutative property of multiplication (not identification or definition of the property). 

• Apply the associative property of multiplication (not identification or definition of the property).

• Interpret and/or model division as a multiplication equation with an unknown factor. 

  • Example: Find 32 ÷ 8 by solving 8 × ? = 32.

• Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers. 

• Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers. 

• Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers. 

• Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols). 

• Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. 

  • Example 1: Observe that 4 times a number is always even. 

  • Example 2: Explain why 6 times a number can be decomposed into three equal addends. 

• Create or match a story to a given combination of symbols (+, –, ×, ÷, <, >, and =) and numbers. 

• Identify the missing symbol (+, –, ×, ÷, <, >, and =) that makes a number sentence true.