#### 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.**

- Bar diagram
- 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:**

- Bar diagram
- Distributive property
- Array Model
- 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:

- 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.
- 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.
- Ben saved $5 a week for 8 weeks. How much did he save altogether? Use a bar diagram to solve.
- Mrs. Flu baked 6 cakes. She put 10 cherries on each cake. How many cherries did she use altogether?
- 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?
- Hassan weighs 36kg. He is 4 times as heavy as his brother. How heavy is his brother?
- 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?
- 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?
- 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?
- 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.

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