T: What does 4 represent? S: The size of each group. T: Write a number sentence to represent Diana’s stickers where the answer represents the size of the group. S: (Write 12 ÷ 3 = 4.) T: (Write 12 ÷ 3 = 4 and 12 ÷ 4 = 3 on the board, even if students have written the correct number sentence.) What is the difference between these division sentences? S: In the first one, the answer represents the size of each group. In the second one, the answer represents the number of groups. T: If we’re writing a division sentence where the answer represents the size of the group, then which number sentence should we use? S: 12 ÷ 3 = 4. Abstract to pictorial: Analyze equations for the meaning of the solution and represent the equation with a drawing. Write 8 ÷ 4 = ___. T: If 8 is the total and 4 is the number of groups, then what does the unknown factor represent? S: The size of the groups! T: Draw a picture on your personal white board to go with my division equation. Use your picture to help you find the unknown factor, then write the complete equation. S: (Draw various pictures that show 8 ÷ 4, then write 8 ÷ 4 = 2.) Repeat the process with 10 ÷ 2. As you design examples, keep in mind that Lesson 5 introduces students to division where the unknown factor represents the number of groups. Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students should solve these problems using the RDW approach used for Application Problems. Student Debrief (10 minutes) Lesson Objective: Understand the meaning of the unknown as the size of the group in division. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson.
T: What does 4 represent? S: The size of each group. T: Write a number sentence to represent Diana’s stickers where the answer represents the size of the group. S: (Write 12 ÷ 3 = 4.) T: (Write 12 ÷ 3 = 4 and 12 ÷ 4 = 3 on the board, even if students have written the correct number sentence.) What is the difference between these division sentences? S: In the first one, the answer represents the size of each group. In the second one, the answer represents the number of groups. T: If we’re writing a division sentence where the answer represents the size of the group, then which number sentence should we use? S: 12 ÷ 3 = 4. Abstract to pictorial: Analyze equations for the meaning of the solution and represent the equation with a drawing. Write 8 ÷ 4 = ___. T: If 8 is the total and 4 is the number of groups, then what does the unknown factor represent? S: The size of the groups! T: Draw a picture on your personal white board to go with my division equation. Use your picture to help you find the unknown factor, then write the complete equation. S: (Draw various pictures that show 8 ÷ 4, then write 8 ÷ 4 = 2.) Repeat the process with 10 ÷ 2. As you design examples, keep in mind that Lesson 5 introduces students to division where the unknown factor represents the number of groups. Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students should solve these problems using the RDW approach used for Application Problems. Student Debrief (10 minutes) Lesson Objective: Understand the meaning of the unknown as the size of the group in division. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson.