Basic Subtraction

Let’s Start with a Question! 🤔

Imagine you have 7 chocolates and you share 3 with your best friend. How many do you have left? Or, if there are 10 birds on a fence and 4 fly away, how many birds remain? The answer to both questions involves subtraction - the mathematical skill of finding what’s left after taking something away!

What is Subtraction?

Subtraction is the process of taking away, removing, or finding the difference between two numbers. It answers questions like “How many are left?” or “How much more/less?”

Think of it like this:

• If you have 8 crayons and you lose 3, subtraction tells you that you now have 5 crayons left.
• The symbol we use for subtraction is - (called “minus” or “take away”)
• The answer we get is called the difference

Why is Subtraction Important?

Subtraction is everywhere in daily life! You use it when you:

• Figure out how many sweets are left after eating some
• Calculate how much change you should get at a shop
• Work out how many more goals your team needs to win
• Count down days until something exciting happens

Subtraction is also the foundation for division and helps you understand relationships between numbers better!

Understanding Subtraction Through Pictures

Imagine you have 6 strawberries 🍓🍓🍓🍓🍓🍓 and you eat 2 of them 🍓🍓.

Now you have: 🍓🍓🍓🍓

Count what’s left: 1, 2, 3, 4 - that’s 4 strawberries!

So 6 - 2 = 4

Teacher’s Insight 👨‍🏫

Here’s what I’ve learned from teaching thousands of students: Many children find subtraction trickier than addition at first, and that’s completely normal! The key is understanding that subtraction is just “the opposite of addition” - if you know that 3 + 2 = 5, then you automatically know that 5 - 2 = 3!

My top tip: Practice using real objects (toys, blocks, fruit) so subtraction becomes visual and concrete, not just abstract numbers on paper. When children can “see” what’s being taken away, subtraction makes perfect sense!

The Connection Between Addition and Subtraction

Here’s a powerful secret: Addition and subtraction are opposites! They’re like best friends who do opposite things.

If you know: 4 + 3 = 7

Then you automatically know:

• 7 - 3 = 4
• 7 - 4 = 3

This relationship is called a fact family, and it’s your secret weapon for mastering both addition AND subtraction!

Strategies for Subtraction

Strategy 1: Counting Back

Start at the bigger number and count backward!

Example: For 8 - 3, start at 8 and count back 3: “7, 6, 5” - the answer is 5!

This works brilliantly for subtracting small numbers.

Strategy 2: Using Your Fingers

Your fingers are perfect for subtraction! For 7 - 2:

1. Hold up 7 fingers
2. Put down 2 fingers
3. Count how many are still up: 5!

Strategy 3: Number Line Jumps

Imagine jumping backward on a number line:

0---1---2---3---4---5---6---7---8---9---10

For 9 - 4, start at 9 and make 4 jumps backward: 8, 7, 6, 5 - you land on 5!

Strategy 4: Think Addition (Counting Up)

Sometimes it’s easier to count UP from the smaller number!

Example: For 10 - 7, think “What do I add to 7 to make 10?”

• 7 + ? = 10
• 7 + 3 = 10
• So 10 - 7 = 3!

This is especially helpful for subtraction facts you find tricky.

Strategy 5: Using Number Bonds to 10

If you know your number bonds to 10, subtraction from 10 is easy!

10 - 1 = 9, 10 - 2 = 8, 10 - 3 = 7, and so on!

Key Vocabulary

• Minus (-): The symbol that tells us to subtract
• Difference: The answer in subtraction
• Take away: Another way to say subtract
• Minuend: The number you start with (in 8 - 3, the 8 is the minuend)
• Subtrahend: The number being taken away (in 8 - 3, the 3 is the subtrahend)
• Fact family: Related addition and subtraction facts (e.g., 3+4=7, 4+3=7, 7-3=4, 7-4=3)

Worked Examples

Example 1: Starting Simple

Problem: 5 - 2

Solution: 3

Detailed Explanation:

• Start with 5 objects: ⚫⚫⚫⚫⚫
• Take away 2 objects: ⚫⚫⚫
• Count what’s left: 3

Think about it: If you had 5 pencils and gave 2 to your friend, you’d have 3 pencils remaining!

Example 2: Counting Back Strategy

Problem: 7 - 3

Solution: 4

Detailed Explanation:

• Start at 7
• Count back 3: “6, 5, 4”
• Answer: 4

Think about it: You’re moving backward on a number line, like walking backwards 3 steps from position 7!

Example 3: Subtracting from 10

Problem: 10 - 6

Solution: 4

Detailed Explanation:

• This is a number bond to 10
• If 6 + 4 = 10, then 10 - 6 = 4
• Think: “What goes with 6 to make 10? It’s 4!”

Think about it: Number bonds to 10 are super helpful - memorise them!

Example 4: Subtracting Zero

Problem: 8 - 0

Solution: 8

Detailed Explanation:

• When you subtract zero, nothing is taken away
• 8 - 0 = 8 (you started with 8, took away nothing, still have 8)

Think about it: Zero means “nothing” - if you take away nothing, everything stays the same!

Example 5: Subtracting to Get Zero

Problem: 6 - 6

Solution: 0

Detailed Explanation:

• When you subtract a number from itself, nothing is left
• 6 - 6 = 0 (you had 6, took away all 6, now you have 0)

Think about it: If you eat all your cookies, you have zero cookies left!

Example 6: Real-Life Subtraction

Problem: You have 9 toy cars. You give 4 to your cousin. How many toy cars do you have left?

Solution: 5 toy cars

Detailed Explanation:

• Start with 9 toy cars
• Take away 4: 9 - 4
• Count back from 9: “8, 7, 6, 5”
• You have 5 toy cars left

Think about it: Subtraction helps you solve real problems about what remains!

Example 7: Using Fact Families

Problem: 4 - 1

Solution: 3

Detailed Explanation:

• Think of the fact family: 1 + 3 = 4, 3 + 1 = 4, 4 - 1 = 3, 4 - 3 = 1
• If you know 1 + 3 = 4, then you know 4 - 1 = 3

Think about it: Knowing your addition facts makes subtraction much easier!

Common Misconceptions & How to Avoid Them

Misconception 1: “Subtraction and addition are the same thing”

The Truth: They’re opposites! Addition puts together (makes bigger), subtraction takes away (makes smaller, unless you’re subtracting zero).

How to think about it correctly: Plus (+) means combine or join. Minus (-) means separate or take away.

Misconception 2: “Order doesn’t matter in subtraction”

The Truth: Unlike addition, order DOES matter in subtraction!

• 5 - 3 = 2, but 3 - 5 is very different (you can’t take away more than you have when learning basic subtraction)
• Always start with the larger number and subtract the smaller one

How to think about it correctly: You can’t take 5 apples away from 3 apples - you only have 3!

Misconception 3: “Subtraction always makes numbers smaller”

The Truth: Mostly yes, BUT subtracting zero keeps the number the same (8 - 0 = 8), and later you’ll learn about negative numbers where this gets more interesting!

How to think about it correctly: Subtraction usually reduces the amount, which makes sense - you’re taking things away!

Common Errors to Watch Out For

Memory Aids & Tricks

The Subtraction Song

“Minus means take away, take away! Count back to find the answer today! Start from the big one, count back some more, Subtraction is something you’ll use and adore!”

Number Bond Trick

If you know your number bonds, subtraction is automatic:

• 10 is made from 7 and 3, so 10 - 7 = 3 and 10 - 3 = 7
• 6 is made from 4 and 2, so 6 - 4 = 2 and 6 - 2 = 4

The “Counting Up” Trick

When subtracting seems hard, count UP from the smaller number instead!

• For 11 - 8, think “8 plus what makes 11?” Count up: “9, 10, 11” - that’s 3 jumps, so the answer is 3!

The Zero Rules

• “Subtract zero, nothing changes!” (5 - 0 = 5)
• “Subtract from itself, nothing remains!” (5 - 5 = 0)

Practice Problems

Easy Level (Within 10)

1. 3 - 1 Answer: 2 (Count back 1 from 3: you get 2)

2. 5 - 2 Answer: 3 (Count back 2 from 5: “4, 3”)

3. 7 - 0 Answer: 7 (Remember: subtracting zero changes nothing!)

4. 4 - 4 Answer: 0 (Taking away everything leaves nothing!)

Medium Level (Within 20)

5. 9 - 4 Answer: 5 (Count back 4 from 9: “8, 7, 6, 5”)

6. 8 - 3 Answer: 5 (Or think: 3 + 5 = 8, so 8 - 3 = 5)

7. 10 - 7 Answer: 3 (Number bond: 7 + 3 = 10)

8. 6 - 5 Answer: 1 (Just one left!)

Challenge Level (Thinking Required!)

9. 12 - 5 Answer: 7 (Count back from 12, or think: 5 + 7 = 12)

10. 15 - 8 Answer: 7 (Try counting up from 8 to 15: “9, 10, 11, 12, 13, 14, 15” - that’s 7 jumps!)

Real-World Applications

At the Shop 🏪

Scenario: You have £10 and you spend £3 on a comic book. How much money do you have left?

Solution: £10 - £3 = £7

Why this matters: Subtraction helps you work out how much money remains after you buy something!

At Home 🏠

Scenario: You bake 12 cupcakes and your family eats 5. How many cupcakes are left?

Solution: 12 - 5 = 7 cupcakes

Why this matters: Subtraction helps you keep track of quantities!

In the Classroom 📚

Scenario: There are 20 children in your class and 6 are absent today. How many children are present?

Solution: 20 - 6 = 14 children

Why this matters: Teachers use subtraction every day for attendance and planning!

Playing Games 🎮

Scenario: You had 15 lives in your video game but lost 4. How many lives do you have now?

Solution: 15 - 4 = 11 lives

Why this matters: Games are full of subtraction - lives, points, resources!

In Nature 🌳

Scenario: There were 8 butterflies on a flower. 3 flew away. How many butterflies remain?

Solution: 8 - 3 = 5 butterflies

Why this matters: Scientists subtract to track changes in animal populations!

Study Tips for Mastering Subtraction

1. Practice With Real Objects Daily

Use toys, counters, or snacks - physically removing them helps your brain understand subtraction.

2. Master Your Number Bonds

If you know which numbers make 10 (or 5, or 20), subtraction becomes automatic!

3. Link to Addition

For every addition fact you learn, you get TWO subtraction facts free! (If 3+4=7, then 7-3=4 and 7-4=3)

4. Start Small and Build Up

Master subtracting within 10 before moving to bigger numbers.

5. Count Back on Your Fingers

This strategy works brilliantly and you always have your fingers with you!

6. Practice the Tricky Ones

Keep a note of which subtractions you find hard and practice those specific ones.

7. Make it Visual

Draw pictures, use number lines, or create your own diagrams to “see” the subtraction happening.

How to Check Your Answers

1. Use addition: If 8 - 3 = 5, then check: does 5 + 3 = 8? It should!
2. Count it out: Use your fingers or draw circles to verify
3. Use a number line: Count backward and check where you land
4. Ask yourself: Does my answer make sense? (If you subtracted 2 from 5, the answer should be less than 5!)

Extension Ideas for Fast Learners

• Practice subtracting from bigger numbers (up to 50 or 100)
• Explore what happens when you subtract IN a different order (is 5-3 the same as 3-5?)
• Learn about number families (e.g., 2, 3, 5 make a family because 2+3=5, 3+2=5, 5-2=3, 5-3=2)
• Try mental subtraction: can you subtract without fingers or paper?
• Create story problems for your friends to solve

Parent & Teacher Notes

Building Understanding: The goal with subtraction isn’t speed - it’s genuine understanding. A child who truly understands what “taking away” means will be more successful than one who just memorises facts.

Common Struggles: If a student struggles with subtraction, check if they:

• Can count backward confidently
• Understand that subtraction means “removing” or “taking away”
• Know their addition facts (these help enormously with subtraction!)

Differentiation Tips:

• Struggling learners: Use lots of concrete objects and real-world examples. Practice counting backward from various numbers.
• On-track learners: Encourage mental strategies like counting back and using number bonds
• Advanced learners: Introduce larger numbers, multi-step problems, or the relationship between subtraction and division

Physical Activities: Try “subtraction hopscotch” (jump forward for addition, backward for subtraction) or “taking away” games with toys to make learning active and fun!

Remember: Every child learns at their own pace. With patience, encouragement, and the right strategies, every student can become confident at subtraction! The key is practice, understanding, and keeping it positive and playful! 🌟