# Multiplying and Dividing Whole Numbers

**Strand:** Number

**Outcomes:** 5, 6

## Step 3: Plan for Instruction

### Guiding Questions

- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?

### A. Assessing Prior Knowledge and Skills

Before introducing new material, consider ways to assess and build on students' knowledge and skills related to multiplication and division. For example:

- Write a number sentence and describe a personal strategy to solve the following problem. Write the answer to the problem in a complete sentence.

You have 5 cans of nuts that each weigh 360 g. What is the total weight of these cans of nuts?
- You read 4 times as long this week as you read last week. If you read for 72 minutes this week, how long did you read last week? Show your work and write your answer in a complete sentence.
- Write all the possible number sentences that are represented in the following array. Explain how each number sentence relates to the array.

********** ********** * * *

********** ********** * * *

********** ********** * * *

- Sarah has 96 apples to put into bags and can put 6 apples in each bag. How many bags does she need? Explain your thinking. Write your answer in a complete sentence.
- You saved 3 times as much money this year as you saved last year. If you saved $128 last year, how much money did you save this year? Show your work and write your answer in a complete sentence. Explain why the following solution makes sense or not.

3 × 128 = (3 × 100) + (3 × 20) + (3 × 5) = 600 + 12 + 30 = 642

Answer: I saved $642 this year.
- Create a problem that can be represented by the following number sentence:

72 ÷ 3 = . Explain how you know your problem matches the number sentence.

Sample Structured Interview: Assessing Prior Knowledge and Skills

### B. Choosing Instructional Strategies

Consider the following guidelines for teaching multiplication and division:

- Teach in a problem-solving context. Research shows that by solving problems using multiplication and division, students create personal strategies for computing and develop understanding about the relationship between the operations and their properties (NCTM 2000, p. 153).
- Choose problems that relate to the students' own lives (Van de Walle 2001).
- Provide a variety of problems representing the different multiplication and division situations with varying degrees of difficulty to differentiate instruction.
- Work with the whole group initially and have the students paraphrase the problem to enhance understanding (Willis et al. 2006) and to recognize whether the numbers in the problem refer the whole, the number of groups or the quantity in each group. Discuss whether the unknown refers to the whole, the number of groups or the quantity in each group, thereby facilitating thinking about which operation to use in solving the problem.
- Have the students estimate the answer to the problem before calculating so that they are better able to determine the reasonableness of their answers.
- Make base ten materials available for the students to use as needed.
- Provide time for the students to create their personal strategies to solve the problem and share these strategies with members of their groups or with the entire class.
- Guide the discussion by asking questions to encourage thinking about number relationships, the connections among the operations and their personal strategies.
- Have the students compare their answers to the estimates they made before solving the problems.
- Challenge the students to solve the problem another way, do a similar problem without models or clarify the explanation of their personal strategies.
- Have the students critique their personal strategies as well as those of their classmates to decide which strategy works best for them and why.
- Have the students create problems for a variety of number sentences illustrating multiplication and division, including examples of equal sharing, equal grouping, comparison problems and combination problems.

### C. Choosing Learning Activities

Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.

Multiplying Two 2-digit Numbers Using Personal Strategies, Concrete Materials Connected to Diagrams and Symbolic Representations, Arrays and the Distributive Property |
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Multiplying Two 2-digit Numbers Using Personal Strategies without Concrete Materials |
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Dividing 3-digit Numbers by 1-digit Numbers with and without Remainders Using Personal Strategies, Concrete Materials Connected to Diagrams and Symbolic Representations, and Connections to Multiplication |
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Dividing 3-digit Numbers by 1-digit Numbers Using Personal Strategies without Concrete Materials |
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