Basic Addition

Let’s Start with a Question! 🤔

Have you ever wondered how shopkeepers know how much money to ask for when you buy more than one thing? Or how your teacher counts how many students are in class? The answer is addition - one of the most important skills in mathematics and in life!

What is Addition?

Addition is the mathematical way of putting things together or combining groups to find out how many in total. Think of it like this:

• If you have 3 toy cars and your friend gives you 2 more, addition tells you that you now have 5 toy cars.
• The symbol we use for addition is + (called “plus”)
• The answer we get is called the sum or total

Why is Addition Important?

Addition is everywhere! You use it when you:

• Count how many sweets you have altogether
• Work out how much your shopping costs
• Figure out your total score in a game
• Count days until your birthday

Addition is the building block for all other mathematics. Once you master addition, you’ll find multiplication (which is just repeated addition!), fractions, and even algebra much easier.

Understanding Addition Through Pictures

Imagine you have 4 apples 🍎🍎🍎🍎 and someone gives you 3 more apples 🍎🍎🍎.

Now you have: 🍎🍎🍎🍎🍎🍎🍎

Count them all: 1, 2, 3, 4, 5, 6, 7 - that’s 7 apples!

So 4 + 3 = 7

Teacher’s Insight 👨‍🏫

Here’s what I’ve learned from teaching thousands of students: The secret to being brilliant at addition isn’t just memorising answers - it’s understanding what addition really means. When my students can “see” the numbers combining in their minds (like the apples above), they become confident mathematicians who can solve any addition problem.

My top tip: Don’t rush! It’s better to understand 3 + 2 really well than to quickly memorise lots of facts without understanding them.

Strategies for Addition

Strategy 1: Counting On

Instead of counting all objects from 1, start with the bigger number and count on!

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

This is much faster than counting “1, 2, 3, 4, 5, 6, 7, 8” every time.

Strategy 2: Using Your Fingers

Your fingers are brilliant calculators! For 4 + 3:

1. Hold up 4 fingers on one hand
2. Hold up 3 fingers on the other hand
3. Count all the fingers: 7!

Strategy 3: Number Line Jumps

Imagine a number line (like a ruler):

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

For 2 + 5, start at 2 and make 5 jumps forward: 3, 4, 5, 6, 7 - you land on 7!

Strategy 4: Making Tens (For Bigger Numbers)

Making groups of 10 makes addition easier!

Example: 7 + 5

• Think: “7 needs 3 more to make 10”
• Break the 5 into 3 and 2
• 7 + 3 = 10, then 10 + 2 = 12
• So 7 + 5 = 12!

Key Vocabulary

• Plus (+): The symbol that tells us to add
• Equals (=): The symbol showing what the total is
• Sum: Another word for the answer in addition
• Total: How many we have when we put groups together
• Addend: The numbers we’re adding together (in 3 + 5, both 3 and 5 are addends)

Worked Examples

Example 1: Starting Simple

Problem: 2 + 3

Solution: 5

Detailed Explanation:

• Start with 2 objects: ⚫⚫
• Add 3 more objects: ⚫⚫⚫
• Count them all: ⚫⚫⚫⚫⚫
• Total = 5

Think about it: If you had 2 pencils and someone gave you 3 more pencils, you’d have 5 pencils altogether!

Example 2: Counting On Strategy

Problem: 6 + 2

Solution: 8

Detailed Explanation:

• Start at the bigger number: 6
• Count on 2: “7, 8”
• Answer: 8

Think about it: You’re already at 6, so you only need to count 2 more steps forward!

Example 3: Using Doubles

Problem: 4 + 4

Solution: 8

Detailed Explanation:

• This is a “doubles fact” - adding the same number to itself
• 4 + 4 = 8
• Doubles are special and easy to remember!

Think about it: If you have 4 cookies and your friend has exactly the same amount (4 cookies), together you have 8 cookies.

Example 4: Adding Three Numbers

Problem: 2 + 3 + 5

Solution: 10

Detailed Explanation:

• First, add 2 + 3 = 5
• Then add 5 + 5 = 10
• Or, look for pairs that make 10: (2 + 3) + 5 = 5 + 5 = 10

Think about it: You can add numbers in any order - it’s like putting fruit in a bowl, it doesn’t matter which fruit you add first!

Example 5: Making Tens

Problem: 8 + 5

Solution: 13

Detailed Explanation:

• 8 needs 2 to make 10
• Break 5 into 2 and 3
• 8 + 2 = 10
• 10 + 3 = 13

Think about it: Making groups of 10 first makes bigger numbers much easier!

Example 6: Real-Life Addition

Problem: You have 7 stickers. Your friend gives you 4 more stickers. How many stickers do you have now?

Solution: 11 stickers

Detailed Explanation:

• Start with 7 stickers
• Add 4 more: 7 + 4
• Count on from 7: “8, 9, 10, 11”
• You have 11 stickers altogether

Think about it: Addition helps us solve real problems in our daily lives!

Example 7: Adding with Zero

Problem: 5 + 0

Solution: 5

Detailed Explanation:

• When you add zero, the number stays the same
• 5 + 0 = 5 (you started with 5, added nothing, still have 5)

Think about it: Zero means “nothing” - if you add nothing to something, it stays the same!

Common Misconceptions & How to Avoid Them

Misconception 1: “Addition always makes numbers bigger”

The Truth: When you add positive numbers, yes! But later you’ll learn that adding zero keeps numbers the same (5 + 0 = 5), and you can even add negative numbers.

How to think about it correctly: Addition combines quantities - and usually that means more!

Misconception 2: “You must always count from 1”

The Truth: Counting on is much more efficient! If you’re solving 8 + 2, don’t count “1, 2, 3, 4, 5, 6, 7, 8, 9, 10” - just start at 8 and say “9, 10”!

How to think about it correctly: Start from the bigger number and count forward.

Misconception 3: “The order matters in addition”

The Truth: 3 + 5 is exactly the same as 5 + 3! This is called the “commutative property” - a fancy way of saying order doesn’t matter in addition.

How to think about it correctly: Whether you put 3 apples and then 5 apples in a basket, or 5 apples and then 3 apples, you still have 8 apples!

Common Errors to Watch Out For

Memory Aids & Tricks

The Doubles Rhyme

“Double 1 is 2, double 2 is 4, Double 3 is 6, and there’s plenty more! Double 4 is 8, double 5 makes 10, Now you’re adding like a champion!”

Making Tens Trick

When numbers are close to 10, borrow from one to make 10:

• 9 + 5 = ? Think: “9 needs 1 to make 10, so borrow 1 from 5 leaving 4. Now: 10 + 4 = 14!”

The Finger Trick for Numbers to 10

Use your fingers - they’re always with you! Each finger counts as 1.

The Zero Rule

“When you add zero, nothing changes!” (5 + 0 = 5, 100 + 0 = 100)

Practice Problems

Easy Level (0-10)

1. 1 + 1 Answer: 2 (This is the smallest doubles fact!)

2. 2 + 3 Answer: 5 (Count on from 2: “3, 4, 5”)

3. 5 + 0 Answer: 5 (Remember: adding zero changes nothing!)

4. 3 + 3 Answer: 6 (Another doubles fact!)

Medium Level (10-20)

5. 7 + 2 Answer: 9 (Count on from 7: “8, 9”)

6. 4 + 5 Answer: 9 (Or think: 4 + 4 = 8, plus 1 more = 9)

7. 8 + 8 Answer: 16 (Important doubles fact!)

8. 6 + 5 Answer: 11 (Make ten: 6 + 4 = 10, plus 1 more = 11)

Challenge Level (Thinking Required!)

9. 9 + 7 Answer: 16 (Make ten: 9 + 1 = 10, then 10 + 6 = 16)

10. 8 + 3 + 2 Answer: 13 (Add the easy ones first: 3 + 2 = 5, then 8 + 5 = 13)

Real-World Applications

At the Shop 🏪

Scenario: You buy a chocolate bar for £3 and a drink for £2. How much do you spend in total?

Solution: £3 + £2 = £5

Why this matters: Every time you buy more than one thing, you’re using addition!

At Home 🏠

Scenario: You have 5 toy cars in your room and 4 in the living room. How many toy cars do you have altogether?

Solution: 5 + 4 = 9 toy cars

Why this matters: Addition helps you keep track of your belongings!

In Games 🎮

Scenario: You score 8 points in round one and 7 points in round two. What’s your total score?

Solution: 8 + 7 = 15 points

Why this matters: Addition is essential for keeping score in almost every game!

Planning a Party 🎉

Scenario: If 6 friends are coming on Saturday and 3 more on Sunday, how many friends are visiting altogether?

Solution: 6 + 3 = 9 friends

Why this matters: Addition helps with planning and organisation!

In Nature 🌳

Scenario: You see 4 birds on one tree and 5 birds on another tree. How many birds can you see?

Solution: 4 + 5 = 9 birds

Why this matters: Scientists use addition to count animals, plants, and so much more!

Study Tips for Mastering Addition

1. Practice Every Day (Just 5 Minutes!)

Do a few addition problems every day - consistency beats cramming!

2. Use Real Objects

Practice with toys, fruit, buttons - anything you can touch and count.

3. Make It Fun

Turn addition into a game! Challenge family members or race against a timer.

4. Learn the Doubles First

Doubles (1+1, 2+2, 3+3, etc.) are the easiest patterns to remember.

5. Master Counting On

This strategy will make you much faster at addition!

6. Don’t Stress About Speed Yet

Understanding is more important than speed when you’re learning. Speed comes naturally with practice.

7. Teach Someone Else

If you can explain addition to a younger sibling or friend, you truly understand it!

How to Check Your Answers

1. Count it out: Use your fingers or draw pictures to verify
2. Swap the numbers: Does 3 + 5 give the same answer as 5 + 3? It should!
3. Use a number line: Jump forward and see where you land
4. Try subtraction: If 4 + 3 = 7, then 7 - 3 should = 4!

Extension Ideas for Fast Learners

• Try adding three or four numbers together
• Explore what happens when you add bigger numbers (up to 50 or 100)
• Learn about the commutative property: 2 + 5 = 5 + 2
• Practice mental math: can you add without fingers or paper?
• Create word problems for your friends to solve

Parent & Teacher Notes

Building Number Sense: The goal isn’t just getting correct answers - it’s developing a deep understanding of what numbers mean and how they relate to each other.

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

• Can count reliably to 20
• Understand that numbers represent quantities
• Know that addition means “putting together”

Differentiation Tips:

• Struggling learners: Use lots of concrete objects (blocks, counters, toys)
• On-track learners: Encourage mental strategies like counting on
• Advanced learners: Introduce adding three numbers, or numbers above 20

Remember: Every mathematician started exactly where your student is now. With practice, patience, and the right strategies, every child can master addition! 🌟