Connecting Division to Multiplication

Primary Standards:

MAFS.3.OA.2.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

MAFS.3.OA.1.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = [] ÷ 3, 6 × 6 = ?.

MAFS.3.OA.1.2: 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.

Connecting Standards:

MAFS.3.OA.3.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 • 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Content Knowledge:

In prior Units, students developed a conceptual understanding about the operations of multiplication and division.  Students also worked on developing their fluency with basic multiplication facts.  Giving students the time to gain fluency with a set of multiplication facts allows them to use those skills as they explore division facts.

In this Unit, students will explore further the relationship between multiplication and division, and use that relation to solve division facts using known multiplication facts.  Many children find it easier to solve division facts by thinking about multiplication.  For example, if posed with 54 ÷ 9, their first thought could be “9 times what is 54?”

Students need experience using concrete materials and drawing pictures to solve problem situations that involve finding a missing factor.  Students should be given the opportunity to make connections between models, written missing factor multiplication equations and the related division equation.

GCG 1 – Learning Goal:  As a mathematician, I will be able to build fact families and explain the relationship among the facts

  • Step 1: Use models to demonstrate that the divisor and quotient of a division problem are both factors of the dividend (for example, 24÷8=3 and 8X3= 24)
  • Step 2: Build fact families and explain the relationship among the facts

GCG 2 – Learning Goal:  As a mathematician, I will be able to use multiplication to solve division problems

  • Step 1:  Determine the unknown whole number in a multiplication or division equation relating three whole numbers
  • Step 2: Write and solve missing factor multiplication equations to represent division situations (i.e., think: how many groups of 7 are needed to make 28?)
  • Step 3: Use known multiplication facts to solve division problems & equations

GCG 3 – Learning Goal:  As a mathematician, I will be able to model and solve division problems using multiplication

  • Step 1: Model and solve problems involving division
  • Step 2: Apply patterns and relationships between math facts to build towards division fluency through ongoing games & centers
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