Divide and Conquer

AZ Math Standards Performance Objectives (samples):

Strand 1: Number Sense and Operation Concept 2: Numerical Operations

  • Grade 3 PO8: Demonstrate the process of division with one-digit divisors (separating elements of a set into smaller equal sets, sharing equally, or repeatedly subtracting the same number).
  • Grade 4 PO6: Divide with one-digit divisors.
  • Grade 5 PO4: Divide with whole numbers.

Measurement/Repeated Subtraction Model: How Many Groups?

  • For this model we are considering a question such as the following: A group of 8 students breaks into teams of 4. How many teams are there?
  • Look at the Set Model (Circle groups of 4. How many groups are there?)

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  • Look at the Base Ten Block Model for (Circle groups of 12. How many groups are there?)

Partitioning/Sharing Model: How Many per Group?

  • For this model we are considering a question such as the following: A teacher has 4 computers for her 8 students to share. If the students are put into equal sized groups, how many students are there for each computer?
  • Look at the Set Model for (Put evenly into 4 groups. How many per group?)

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  • Look at the Base Ten Block Model for (Put evenly into 3 groups. How many per group?)
  1. Write a number sentence for each of the following scenarios.

(a)At the bakery, a batch of one dozen sugar cookies is put into packets of three. How many packets of the sugar cookies can be made?

Division Problem:______

(b)At the same bakery, a batch of one dozen chocolate chip cookies is divided evenly into three boxes. How many chocolate chip cookies are there in each box?

Division Problem:______

  1. What do you notice about your two number sentences?
  1. The situation in part (a) is an example of the ______model.
  1. The situation in part (b) is an example of the ______model.
  1. Use the colored counters to physically represent the situation in (a). Draw a diagram of your representation below.
  1. Use the colored counters to physically represent the situation in (b). Draw a diagram of your representation below.
  1. Use the base ten blocks to represent the division problem using the “How Many Groups” approach.
  1. Use the base ten blocks to represent the division problem using the “How Many per Group” approach.
  1. Write a division problem to describe the situation represented by the diagram below. Write a word problem represented by the diagram.
  1. Write a division problem to describe the situation represented by the diagram below. Write a word problem represented by the diagram.

Whole Number Division 1