Minds On

The word on problem solving

Explore the following MathXplosion segment entitled "The Word on Problem Solving" to learn some tips from Eric on how to solve word problems.

What is Eric’s top tip when working with word problems?

Let’s use Eric’s tip to solve the following problem.

Friend #1 owns 5 pairs of sunglasses. Friend #2 owns 2 times as many sunglasses as Friend #1. How many sunglasses does Friend #2 own?

Student Success

Think-Pair-Share

  • Create your own word problem that involves multiplying or dividing.

Record your thinking digitally, orally or in print.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Action

Let's multiply!

In this lesson, we will explore multiplication and division to solve problems.

We can add to find the sum of two or more numbers.

We can group to find the total.

25 chickens organized in 5 groups of 5.

5 + 5 + 5 + 5 + 5 = 25

5 groups of 5 = 25

5 × 5 = 25

The “×” is a sign that means “a group of.”

Practice

Find the total.

5 groups of 2 is the same as (Blank)

4 groups of 5 is the same as (Blank)

1 groups of 9 is the same as (Blank)

6 groups of 3 is the same as (Blank)

Student Success

Think-Pair-Share

Solve the following word problem. Use counters, tools or drawings to help you solve it.

Question:

Friend #1 and their friends bought tickets to a fundraiser for the school. Friend #2 bought 3 packs, Friend #3 bought 2 packs and Friend #4 bought 5 packs. Each pack has 5 tickets.

Use multiplication to show the number of tickets each person bought. Use a variety of representations to show your thinking.

Share your ideas in your notebook.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Multiplication properties

It is important to know different strategies when solving problems.

Let's examine each property in more detail.

Strategy 1 (Identity Property)

Let’s count by 1’s to 10.

When multiplying a number by 1, there is only 1 group of that number, so the total is always that number.

A number × 1 = the number

1 × a number = the number

Example:

1 × 8 = 8

32 × 1 = 32

1 × 92 = 92

Multiplying by 1.1 times 4 equals 4. 1 times 7 equals 7. 1 times 16 equals 16. 1 times 19 equals 19. 1 times 84 equals 84. 1 times 99 equals 99.

Strategy 2 (Zero Property)

Now, let’s count by 0’s to 10.

What do you notice? Is it hard to count to 10 by 0’s? Why?

The value of 0 represents nothing. When you have nothing, you cannot count at all.

When multiplying a number by 0, there is no group of that number, so the total is always 0.

Any number multiplied by 0 is 0.

Example:

0 × 5 = 0

7 × 0 = 0

0 × 22 = 0

Multiplying by 0. 0 times 1 equals 0. 0 times 3 equals 0. 0 times 9 equals 0. 0 times 15 equals 0. 0 times 60 equals 0.

Strategy 3 (Associative Property)

When we multiply 3 or more numbers, it doesn't matter how we group the numbers. The total remains the same.

Student Success

Think-Pair-Share

Use 3 number cubes for this game.

Roll the number cubes and record the numbers. Record a multiplication sentence using the 3 numbers. Group any 2 of the 3 numbers. Solve. Then, change the group and solve again.

Take 2 turns. What do you notice about the totals each time?

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Strategy 4 (Commutative Property)

When multiplying 2 numbers, the order of the numbers does not matter when we multiply. The total remains the same.

Practice

Record 2 related multiplication facts for the following arrays.

Commutative property. Image A. 18 chickens grouped in 3 rows with 6 chickens each. Image B. 12 chickens grouped in 6 rows with 3 chickens each.

  1. 3 × 4 = 12 or 4 × 3 = 12
  2. 3 × 6 = 18 or 6 × 3 = 18

Strategy 5 (Distributive Property)

Large numbers can be broken apart into smaller groups so that they are easier to work with. For example, consider 2 × 6. We can take the number 6 and break it into 2 groups of 3: 3 + 3 (= 6).

So, 2 × 6 is the same as 2 × 3 + 2 × 3.

Practice

Let’s use the strategy to solve 4 × 8. (Hint: You can break up 8 into smaller numbers to solve this problem.)

4 × 8 = 4 × (5 + 3)

= (4 × 5) + (4 × 3)

= 20 + 12

= 32

Multiplication and division

Multiplication and division are opposite operations (or inverse operations).

Brainstorm

Brainstorming

Choose any two numbers from 1 to 10.

Use your two numbers to create a multiplication statement.

Rearrange the numbers to make two division statements.

Example:

I chose the numbers 2 and 3.

2 × 3 ≡ 6

6 ÷ 3 ≡ 2

6 ÷ 2 ≡ 3

Consolidation

Problem solving

Part 1: Use the strategies from the Action section to complete the following problem.

Question:

Author #1 wrote a book with 6 chapters. Each chapter has 8 pages. Author #2 wrote a book with 3 chapters. Each chapter has 4 pages. Whose book has more pages?

Use a variety of representations to show your thinking.

Record your thinking using a method of your choice.

Part 2: Reflect on your learning.

Which of the multiplcation properties learned help you decide on your solution?

Reflection

How do you feel about what you have learned in this activity?  Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel...

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.