Minds On
Word Problems
When exploring a word problem, it is important to think about what details we need to solve the problem.
Explore the following word problem. What details do you need to answer the questions and solve the problem?
How many sunglasses?
Two friends are going to head to the beach to meet a group of people. They are bringing extra sunglasses for everyone to wear. How many sunglasses are there altogether?
Friend #1 has 5 pairs of sunglasses and a hat.
Friend #2 has 2 times as many sunglasses as Friend #1.
Press ‘Possible Answer’ to access one way to solve the problem.
The main information I need is that Friend #2 has double the number of sunglasses than Friend #1.
I can use multiplication to figure out how many sunglasses Friend #2 has.
5 x 2 = 10
Friend #2 has 10 pairs of sunglasses.
In order to find out how many sunglasses there are altogether, I can add the total sunglasses from Friend#1 and Friend#2.
5 + 10 = 15
There are 15 pairs of sunglasses altogether.
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.
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
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
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.
First multiplication sentence reads: 3 times bracket 2 times 4 end bracket equals 24 with an image of 24 chickens organized in 3 groups of 8 chickens. Second multiplication sentence reads: bracket 3 times 2 end bracket times 4 equals 24 with an image of 24 chickens organized in 4 rows of 6 chickens.
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.
- 3 × 4 = 12 or 4 × 3 = 12
- 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.