Usage of Different Strategies of Multiplication

Introduction:

A scientist on a boat is studying hammerhead sharks. The length of 6 hammerhead sharks lined up nose to tail without gaps is equal to the length of the boat. How long is the boat?

To find the length of the boat, we have two ways/strategies.

1. Bar diagram
2. Distributive property

We solve the problem by using each method.

1. Bar Diagram:

A bar diagram can be defined as a pictorial representation of a number in the form of bars or boxes.​​

​​A bar diagram helps to understand the problem easily.​​

Length of one hammerhead shark = 5 yards

Length of 6 hammerheads sharks = ?

So, we must find 6 × 5.

6 × 5 means 6 groups of 5.

Skip count by 5s.

So, 6 × 5= 30.

The boat is 30 yards long.

2. Distributive Property:

The distributive property says that when you multiply a factor by two addends, you can first multiply the factor with each addend, and then add the sum.

To find the length of the boat, we must find 6 × 5.

Use 2s facts and 4s facts to help. that is (2 + 4) × 5.

2 × 5 = 10

4 × 5 = 20

Then add the two products:10 + 20 = 30.

The boat is 30 yards long.

To multiply any two numbers, the following are the different strategies:

1. Bar diagram
2. Distributive property
3. Array Model
4. Counters

1. Bar Diagram:

Example 1:

7 children shared the cost of a gift equally. Each of them paid $5. What was the cost of the gift?

1 unit = $5

7 units = 7 × $5

So, the cost of the gift was $35.

Example 2:

Roberta is planting flowers in her garden. She plants 9 rows of flowers. There are 7 flowers in each row. How many flowers does she plant in all?

Solution:

She plants 9 rows of flowers.

There are 7 flowers in each row.

So, if we find 9 × 7, we get the total number of flowers she planted. Skip count by 7s.

So, the total number of flowers she planted was 63.

2. Distributive Property:

Example 3:

Solve 12 × 7 by using the distributive property.

Solution:

The distributive property says you can break the problem into smaller parts and then add.

So, 12 × 7 = (7 + 5) × 7

12 × 7 = (7 + 5) × 7

            = (7 × 7) + (5 × 7)

            = (49 + 35)

            = 84

12 × 7 = 84.

Example 4:

A soccer team traveled to a game in 11 vans. Each van has 7 players. Three of the total number of players are goalkeepers. How many players are not goalkeepers?

Solution:

Total number of players= 11 × 7

By using distributive property, we break the problem into smaller parts and then add.

11 × 7 = (5 + 6) × 7

            = (5 × 7) +(6 × 7)

            = 35 + 42

            = 77

Total number of players = 77

The number of players that are not goalkeepers is 77 – 3 = 74.

3. Array Model:

Array model of multiplication
uses the number of rows and
number of columns in an array
to illustrate the product of two
numbers.

Product:

2 × 3 = 6

3 × 2 = 6

4. Counters:

Counters are an excellent tool that children can use in their attempts to master math skills, including counting, adding, subtracting, making patterns, and comparing numbers.​

Example 5:​

Share 4 counters between 2 groups.​

Solution:

There are 4 altogether​.

There are 2 groups in total​.

There are 2 in each group​.

Try it!

Example 6:

A farmer has 7 ducks. He has 5 times as many chickens as ducks. How many more chickens than ducks does he have?

Solution:

7 × 5 = 35

He has 35 chickens.

35 – 7 = 28

He has 28 chickens more than ducks.

Example 7:

Mr. Marks is studying 3 blacktip sharks and 4 tiger sharks. What is the total length of the 7 sharks? Show your strategy.

Solution:

Length of blacktip shark = 2 yards

Length of tiger shark = 4 yards

The number of blacktip sharks = 3

The number of tiger sharks = 4

Total length of the 7 sharks = (3 × 2) + (4 × 4) = 6 + 16 = 22 yards

So, the total length of the 7 sharks is 22 yards.

Exercise:

1. Mrs. Flu bought 3 packets of strawberries. There were 8 strawberries in each packet. How many strawberries did she buy altogether? Use the distributive property to solve.
2. Albert arranged 24 toy soldiers in 4 rows. There were an equal number of toy soldiers in each row. How many toy soldiers were there in each row? Use the counters method to solve.
3. Ben saved $5 a week for 8 weeks. How much did he save altogether? Use a bar diagram to solve.
4. Mrs. Flu baked 6 cakes. She put 10 cherries on each cake. How many cherries did she use altogether?
5. A toy car costs $6. A train set costs 5 times as much as the toy car. What is the cost of the train set?
6. Hassan weighs 36kg.  He is 4 times as heavy as his brother. How heavy is his brother?
7. Mrs. Bob bought 4 boxes of pencils. There were 5 blue pencils and 3 red pencils in each box. How many pencils did Mrs. Bob buy?
8. Miss Li marked 5 sets of 8 books in the morning. She marked 30 books in the afternoon. How many books did she mark altogether?
9. Raj bought 18 pencils. He bought twice as many pencils as pens. How much did he pay for the pens if each pen cost $3?
10. Minffa has 6 goldfish. He has 5 times as many guppies as goldfish. If he puts his guppies equally into 3 tanks, how many guppies are there in each tank?

Concept Summary:

What We Have Learned:

• Understand bar diagram.
• Understand distributive property.
• Understand counters and array model.
• Use different strategies to solve problems.