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Subtraction by counting back

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visibility 14update 4 days agobookmarkshare

🎯 In this topic you will

Subtract numbers by counting back using a number line.
Split numbers into smaller parts to make subtraction easier.
Use complements to 10 to help solve subtraction problems.

🧠 Key Words

compose

Show Definitions

compose: To combine smaller numbers or parts to make a larger number.

🧮 Finding What’s Left

Sometimes we need to find how many objects are left.

🍪 Biscuit Subtraction Check

If there are 14 biscuits and 9 are eaten, are there enough left for 6 people to have 1 each?

🛒 Shopping Decisions

You can work out if you need to buy more biscuits when you are shopping.

📘 Worked example

$11 - 6 = \square$

Answer:

$11 - 6 = 5$

Method 1: Count back one step at a time.
Starting at $11$, count back six jumps: $10, 9, 8, 7, 6, 5$. So $11 - 6 = 5$.

Method 2: Make one jump of $6$ on the number line.
Moving back $6$ from $11$ lands on $5$. Both methods give the same answer.

❓ EXERCISES

1. Count back. Draw your jumps.

👀 Show answer

a. $13 - 4 = 9$

b. $9 - 6 = 3$

2. This is Sammy’s number line. What calculation is he solving?

👀 Show answer

$17 - 6 = 11$

3. This is Erin’s number line. What calculation is she solving?

👀 Show answer

$15 - 4 = 11$

📘 Worked example

$18 - 13 = \square$

Answer:

$18 - 13 = 5$

Method 1: Split $13$ into $10$ and $3$. Count back $3$ first, then $10$.
Starting at $18$, jump back $3$ to get $15$, then jump back $10$ to reach $5$.

Method 2: Think of $18$ as $10 + 8$. Jump back $10$ to $8$, then subtract $3$.
Both methods show that $18 - 13 = 5$.

❓ EXERCISES

4. Draw your jumps.

👀 Show answer

a. $19 - 14 = 5$

📘 Worked example

$14 - 8 = \square$

Answer:

$14 - 8 = 6$

Split $8$ into $4$ and $4$. First count back $4$ from $14$ to reach $10$.

Then use complements to $10$ and count back another $4$ to reach $6$.

So, $14 - 8 = 6$.

❓ EXERCISES

5. Draw your jumps.

a. $13 - 7 =$

👀 Show answer

a. $13 - 7 = 6$

🧠 Think like a Mathematician

Question: What happens when you subtract $0$ from a number? How could you show subtracting $0$ on a number line?

Method:

Choose any number, for example $8$ or $14$.
Write a subtraction such as $14 - 0$.
Mark the starting number on a number line.
Try to count back $0$ jumps and observe what happens.
Record your result and describe the pattern you notice.

Follow-up Questions:

1. What is the result of subtracting $0$ from any number?

2. How does this appear on a number line?

3. Write a general rule for subtracting $0$.

Show Answers

1: Subtracting $0$ from any number gives the same number.
2: On a number line, there is no movement because counting back $0$ means staying on the starting number.
3: For any number $a$, $a - 0 = a$.

❓ EXERCISES

6. Choose a number from each circle. Subtract the smaller number from the larger number. Do this twice. Choose which method to use. Write your number sentence.

👀 Show answer

Example answers:
$13 - 7 = 6$
$15 - 8 = 7$
(Answers may vary.)

7. Find the difference.

a. $18 - 14 =$

b. $9 - 4 =$

c. The difference between $8$ and $11$ is ______.

d. The difference between $3$ and $9$ is ______.

👀 Show answer

a. $18 - 14 = 4$

b. $9 - 4 = 5$

c. $3$

d. $6$

📘 What we've learned

We learned to subtract by counting back on a number line.
We practiced splitting numbers into smaller parts to make subtraction easier.
We used complements to $10$ to help solve subtraction calculations.
We understood that subtracting $0$ leaves the number unchanged: $a - 0 = a$.

Subtraction by counting back

🎯 In this topic you will

🧠 Key Words

🧮 Finding What’s Left

🍪 Biscuit Subtraction Check

🛒 Shopping Decisions

❓ EXERCISES

❓ EXERCISES

❓ EXERCISES

🧠 Think like a Mathematician

❓ EXERCISES

📘 What we've learned

Related Past Papers

Related Tutorials

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