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Division

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visibility 75update 2 months agobookmarkshare

In this topic you will

Explain division as repeated subtraction.
Describe division as grouping and as sharing.
Decide whether to add or subtract to solve a word problem.

Key Words

division, divide
division as grouping
division as sharing
repeated subtraction

Show Definitions

division, divide: An operation that splits a number into equal parts or equal groups to find how many in each part or how many groups.
division as grouping: A way to divide by counting how many equal groups of a given size can be made from a total.
division as sharing: A way to divide by sharing a total equally between a given number of groups to find how many in each group.
repeated subtraction: Subtracting the same number again and again to find how many times it can be taken away, which models division.

Division as grouping and sharing

When we know the whole, we use division to find out how many equal groups we can make or how to share equally.

$Sharing $6$ buns equally between $2$ plates, showing $6\div 2=3$ (sharing)$

EXERCISES

Exercise $1.7$

$1.$Use repeated subtraction on the number line to help you solve each division.

a. $45\div 5=$ ________

b. $14\div 2=$ ________

$Two number lines for repeated subtraction: one from $0$ to $100$ for $45\div 5$, and one from $0$ to $20$ for $14\div 2$$

👀 Show answer

a.$45\div 5=9$

b.$14\div 2=7$

$2.$Use the arrays to help you solve each division.

a. $35\div 5=$ ________

b. $12\div 2=$ ________

Tip

Use the groups of $5$ and groups of $2$ to help you.

$Arrays for division: an array showing $35$ items in groups of $5$ for $35\div 5$, and cupcakes arranged in pairs for $12\div 2$, with a tip box$

👀 Show answer

a.$35\div 5=7$

b.$12\div 2=6$

📘 Worked example

$10\div 2=$ ________

$Sharing $10$ biscuits between $2$ plates to show $10\div 2$$

Answer:

$10\div 2=5$

There are $2$ plates, so we share $10$ biscuits equally between them.

Put $1$ biscuit on each plate again and again until there are none left.

Each plate ends up with $5$ biscuits, so $10\div 2=5$.

❓ EXERCISES

3. Share the flowers between two vases.

$20\div 2=$ ________

$Flowers to share between $2$ vases for $20\div 2$$

👀 Show answer

$20\div 2=10$

4. Share the strawberries between $5$ children.

$30\div 5=$ ________

$Strawberries to share between $5$ children for $30\div 5$$

👀 Show answer

$30\div 5=6$

5. Write a division number sentence for each array.

💡 Quick Math Tip

Group Before You Divide: Arrange the frogs and the wheels into equal groups first. Seeing the objects in clear groups makes it easier to write the correct division number sentence.

Arrays of frogs and wheels with a tip to put them into groups

👀 Show answer

Frogs:$16\div 2=8$

Wheels:$40\div 10=4$

6. Choose a method to use and find the answers.

a. $80\div 10=$ ________

b. $25\div 5=$ ________

c. $18\div 2=$ ________

Number lines from $0$ to $20$ and from $0$ to $100$ to help solve the divisions

👀 Show answer

a.$80\div 10=8$

b.$25\div 5=5$

c.$18\div 2=9$

7. $30$ children are playing some games.

The first game needs teams of $2$.

The second game needs teams of $5$.

The third game needs teams of $10$.

How many teams play in each game?

👀 Show answer

Teams of $2$: $30\div 2=15$

Teams of $5$: $30\div 5=6$

Teams of $10$: $30\div 10=3$

Think like a Mathematician

Task: Look at your answers when you divide by $5$.

Follow-up Questions:

1. When do you get an odd number answer?

2. When do you get an even number answer?

3. Explain why. Write your ideas clearly.

👀 show answer

1: You get an odd answer when the number you are dividing is an odd multiple of$5$, such as $5$, $15$, $25$, $35$, … because $5\div 5=1$, $15\div 5=3$, $25\div 5=5$, $35\div 5=7$.
2: You get an even answer when the number you are dividing is an even multiple of$5$, such as $10$, $20$, $30$, $40$, … because $10\div 5=2$, $20\div 5=4$, $30\div 5=6$, $40\div 5=8$.
3: Any number that divides exactly by $5$ can be written as $5\times n$. When you do $5\times n\div 5$, the $5$ cancels and the answer is $n$. So the answer is odd if $n$ is odd, and even if $n$ is even.

❓ EXERCISES

8. Write and solve the number sentences. Do you need to multiply or divide?

a. $5$ children can sit on a bench. How many benches are needed for $30$ children?

b. $10$ children have $5$ marbles each. How many marbles do they have altogether?

Children sitting on a bench and a hand holding marbles to support the word problems

👀 Show answer

a. Divide because we are making equal groups of $5$: $30\div 5=6$. So $6$ benches are needed.

b. Multiply because each child has the same number of marbles: $10\times 5=50$. So they have $50$ marbles altogether.

📘 What we've learned

We learned that division can be understood as repeated subtraction, such as subtracting $5$ again and again to solve $45\div 5$.
We used grouping and sharing models to solve division problems, for example $20\div 2=10$.
We practiced writing division number sentences from arrays and pictures.
We chose whether to multiply or divide when solving word problems, such as using $30\div 5=6$ or $10\times 5=50$.
We applied division facts involving $2$, $5$, and $10$, including problems like $80\div 10=8$ and $30\div 10=3$.

Division

In this topic you will

Key Words

Division as grouping and sharing

EXERCISES

❓ EXERCISES

💡 Quick Math Tip

Think like a Mathematician

❓ EXERCISES

📘 What we've learned

Related Past Papers

Related Tutorials

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