Lesson plan

3. Choose efficient strategies to solve division problems (A)

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.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: Connect finding quotients to real-world situations and apply use of equal groups and sharing to both multiplication and division situations.  

This lesson provides an opportunity for students to apply their knowledge and understanding of quotients to a real-life situation. Students are asked to help complete a field journal by finding the number of eggs per nest, which will supply information linking to what kinds of birds the student is finding in her backyard.  They will then use the situation and what Gwen alreay knows to put clues together to label each type and number of eggs to a bird.  

Key Concept students will use: 

  • Interpreting quotients of whole numbers as a number of shares.

Skills students will use:

  • Using drawings and equations to represent and solve multiplication and division situational problems involving equal groups and arrays (Grade 3, Unit 1)
  • Interpreting quotients of whole numbers as a number of shares (partitive or distribution division) and a number of groups (quotative or measurement division); (Grade 3, Unit 1)
  • Interpreting products of whole numbers as a number of groups or a number of objects (Grade 3, Unit 1)
  • Using skip-counting or repeated addition to find the total number of objects in an array because there is the same number of objects in every row or column (Grade 2, Unit 13)

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them as they practice dividing and sharing manipulatives into different equal groups or rows.  Using doubling and halving, breaking apart numbers, and skip counting, they will be able to explore easily with even and odd numbers. 

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they form distinguishable groups, rows, or jumps to distribute total eggs in parts, shares, or groups in many different combinations.  They should be aware of equal groups and make use of structure by keeping the rows or groups equal.  Using manipulatives, they can rearrange total numbers of eggs into multiple equal groups to find all possibilities.  Recounting or double checking their groups or rows after they are finished sharing will help them be efficient in finding the answers.  Questions such as "Are all of your rows equal?" or "How could your rearrange those to make them equal?" or "Do you have any clues right away whether you can make equal groups or not?" will help students make better sense of the structures they are forming.  

Key vocabulary:

  • array
  • divide
  • equal groups
  • quotient
  • share
  • unknown factor

Special materials needed:

  • base ten blocks to help break numbers apart
  • manipulatives such as square tiles, counters or cubes