Lesson plan

9. Use inverse operations to find unknowns in multiplication & division problems (FP)

teaches Common Core State Standards CCSS.Math.Content.3.OA.A.1 http://corestandards.org/Math/Content/3/OA/A/1
teaches Common Core State Standards CCSS.Math.Content.3.OA.A.2 http://corestandards.org/Math/Content/3/OA/A/2
teaches Common Core State Standards CCSS.Math.Content.3.OA.A.3 http://corestandards.org/Math/Content/3/OA/A/3
teaches Common Core State Standards CCSS.Math.Content.3.OA.B.6 http://corestandards.org/Math/Content/3/OA/B/6
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
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Lesson objective: Divide using the relationship between multiplication and division.

This lesson helps to build fluency with division. Arrays are used here because they support student understanding of how to write an equation from a model using multiplication and division. This work develops students' understanding that multiplication and division are inverse operations and using properties of the operations can be applied to multiply within 100.

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them) as they understand they are finding an unknown factor.  Using manipulatives to represent the situation, students will see the connection between the inverse operations. 

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they understand that they are finding an unknown factor. They draw pictures or arrays, equal groups or number lines and write equations to represent the situation.  Giving students a multiplication equation to represent the problem can help them start to make sense of how they can find the unknown factor.  Doubling and halving factors, breaking apart numbers and sharing into equal groups are strategies that will help them to solve these problems.   Be sure to ask if there is a better way to solve the problem if you see students still using additive reasoning to count multiple tally marks or share larger numbers into groups.  Using number sense and multiplicative reasoning, they can be more efficient in finding answers to division situations.  

Key vocabulary:

  • array
  • double
  • equal groups
  • equation
  • half
  • inverse operations
  • product
  • quotient
  • unknown factor

Special materials needed:

  • base ten blocks to reason with, such as breaking apart numbers
  • manipulatives such as square tiles, counters or cubes