Addition and Subtraction

Welcome to Addition and Subtraction!

Hello, young Mathematician! In this chapter, we are going to become experts at adding things together and subtracting (taking things away). We use these skills every day—like when we count how many toys we have or when we share stickers with friends. Don't worry if some parts seem a bit tricky at first; with a little practice, you will be a number wizard!

1. Adding and Subtracting Ones

When we add or subtract ones, we are just moving a little bit along the number line. Imagine you are a little frog jumping on lily pads!

To add ones to a number, we count forwards.
Example: \( 24 + 3 = 27 \)
Start at 24, and take 3 small jumps forward: 25, 26, 27!

To subtract ones, we count backwards.
Example: \( 28 - 4 = 24 \)
Start at 28, and take 4 small jumps back: 27, 26, 25, 24.

Quick Review:

When adding or subtracting ones, only the ones digit usually changes. The tens digit stays the same unless you cross over a ten!

2. Adding and Subtracting Tens

Adding tens is like jumping in big leaps of 10. Imagine you are in a lift going up or down floors!

Did you know? When you add or subtract a 10, the ones digit stays exactly the same. Only the tens digit changes.

Example: \( 45 + 20 \)
4 tens and 5 ones + 2 tens = 6 tens and 5 ones.
So, \( 45 + 20 = 65 \).

Example: \( 82 - 30 \)
8 tens and 2 ones - 3 tens = 5 tens and 2 ones.
So, \( 82 - 30 = 52 \).

Key Takeaway:

Think of it as \( 4 + 2 = 6 \), so \( 40 + 20 = 60 \). It's the same pattern, just ten times bigger!

3. Using Number Bonds to 100

In Year 1, you learned number bonds to 10 and 20 (like \( 7 + 3 = 10 \)). In Year 2, we use these to find bonds to 100.

If you know that \( 6 + 4 = 10 \), then you automatically know that \( 60 + 40 = 100 \)!

Common Mistake: Make sure your tens add up to 100, not 10.
Remember: 6 tens + 4 tens = 10 tens, which is 100.

4. Adding Two 2-Digit Numbers

When we have two big numbers to add, like \( 23 + 12 \), we can use a trick called partitioning. This means breaking the numbers into tens and ones.

Step-by-step:
1. Break both numbers apart: \( 23 \) is \( 20 + 3 \) and \( 12 \) is \( 10 + 2 \).
2. Add the tens together: \( 20 + 10 = 30 \).
3. Add the ones together: \( 3 + 2 = 5 \).
4. Put them back together: \( 30 + 5 = 35 \).

So, \( 23 + 12 = 35 \)!

5. Adding Three Numbers

Sometimes you might see a sum like \( 7 + 4 + 3 \). Don't panic! You can add them in any order you like.

Memory Trick: Always look for a number bond to 10 first.
In \( 7 + 4 + 3 \), we know that \( 7 + 3 = 10 \).
Now the sum is much easier: \( 10 + 4 = 14 \)!

6. The Order of Numbers (The "Swap" Rule)

Addition and subtraction have different rules about switching numbers around:

Addition: You can add numbers in any order.
\( 5 + 2 = 7 \) is the same as \( 2 + 5 = 7 \). It's like putting two piles of blocks together; it doesn't matter which pile you pick up first!

Subtraction: You cannot swap the numbers!
\( 10 - 3 = 7 \), but you cannot do \( 3 - 10 \). If you have 3 apples, you can't give away 10!

Key Takeaway:

Addition is commutative (swappable), but subtraction is not.

7. Fact Families (The Inverse Relationship)

Addition and subtraction are like opposites. One does something, and the other "undoes" it. We call this the inverse.

If you know one fact, you actually know four! Look at this Fact Family for the numbers 3, 5, and 8:
1. \( 3 + 5 = 8 \)
2. \( 5 + 3 = 8 \)
3. \( 8 - 5 = 3 \)
4. \( 8 - 3 = 5 \)

If you get stuck on a subtraction like \( 10 - 8 \), just ask yourself: "What do I add to 8 to make 10?" Since the answer is 2, then \( 10 - 8 = 2 \).

8. Solving Problems

When you read a word problem, look for clue words to help you decide what to do:

Clue words for Addition (+):
- Total
- Altogether
- Sum
- Plus
- More than

Clue words for Subtraction (-):
- Difference
- Less than
- Left over
- Take away
- How many more?

Quick Review:

Always read the question twice! Sometimes the question asks how many are left, which means you need to subtract.

You've Finished the Chapter!

Well done! You have learned how to add and subtract ones and tens, how to use partitioning, and how to find fact families. The most important thing is to keep practicing. If you make a mistake, don't worry—that's just your brain getting stronger!