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Grade 3 Math Unit 1

Understanding Multiplication and Division

Students will develop an understanding of multiplication and division and their relationship. Students will develop strategies to solve single digit multiplication number sentences. Students will develop strategies to solve division number sentences. Students will relate multiplication and division to equal groups story problems.

Download the complete Grade 3 Math Unit 1 framework to customize for your own planning.

Essential Outcomes

Operations and Algebraic Thinking

  • NY-3.OA.3 – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. e.g., using drawings and equations with a symbol for the unknown number to represent the problem.
  • NY-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. Describe a context in which a total number of objects can be expressed as 5 × 7.
  • NY-3.OA.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. Describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
  • NY-3.OA.4 – Determine the unknown whole number in a multiplication or division equation relating three whole numbers. e.g., Determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.
  • NY-3.OA.5 – Apply properties of operations as strategies to multiply and divide. E.g.,
    • 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)
      Note: Students need not use formal terms for these properties.
      Note: A variety of representations can be used when applying the properties of operations, which may or may not include parentheses.
  • NY-3.OA.6 – Understand division as an unknown-factor problem. e.g., Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
  • NY-3.OA.7a – Fluently solve single-digit multiplication and related divisions, using strategies such as the relationship between multiplication and division or properties of operations. e.g., Knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8.
  • NY-3.OA.7b – Know from memory all products of two one-digit numbers.
  • NY-3.OA.9 – Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).

Number and Operations in Base Ten

  • NY-3.NBT.3 – Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations. e.g., 9 × 80, 5 × 60

Essential Questions and Big Ideas

  • What is multiplication?
    • Multiplication represents finding a total made from equal groups.
    • A x B represents A groups of the number B.
  • What is division?
    • Division represents splitting a total into equal groups.
    • B ÷ A can represents a total B split into A groups or a total B split into groups of size A.
  • How are multiplication and division related?
    • Multiplication and division are inverse operations.
    • Factors are multiplied to create a product.
    • An unknown factor can be found through division.
    • A dividend is divided by a divisor to find a quotient.
    • An unknown dividend can be found through multiplication.
  • What are strategies that can be used to efficiently multiply or divide?
    • Skip counting can be used to solve multiplication and division problems.
    • Known multiplication facts can be used to solve division problems.
    • Factors can be rearranged to solve multiplication problems.
    • A factor can be broken up into smaller pieces to find known products.
    • Memorizing multiplication facts can support more fluent solving.
    • Multiplying by multiples of 10 can be thought of as by multiplying a digit and 10, ex. 3 x 20 = 3 x 2 x 10.

Download the complete Grade 3 Math Unit 1 framework to customize for your own planning.