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?
![The length of 6 hammerhead sharks](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/The-length-of-6-hammerhead-sharks.png)
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.
![Skip count by 5s](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Skip-count-by-5s.png)
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 units = 7 × $5](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/7-units-7-×-5.png)
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.
![Skip count by 7s](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Skip-count-by-7s-1024x186.png)
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
![Array Model](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Array-Model.png)
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](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/4-counters.png)
Share 4 counters between 2 groups.
Solution:
![Share 4 counters between 2 groups](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/2-groups.png)
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:
![Ducks and Chickens](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Ducks-and-Chickens.png)
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.
![Blacktip sharks and tiger sharks](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/blacktip-sharks-and-tiger-sharks-1024x343.png)
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:
![Concept Summary](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Concept-Summary-8-1024x598.png)
What We Have Learned:
- Understand bar diagram.
- Understand distributive property.
- Understand counters and array model.
- Use different strategies to solve problems.
![Strategies of Multiplication](/_next/image?url=https%3A%2F%2Fwww.turito.com%2Flearn-internal%2Fwp-content%2Fuploads%2F2023%2F07%2FStrategies-of-Multiplication.png&w=1920&q=50)
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