Number Bonds

For Elementary Students

What Are Number Bonds?

Number bonds are pairs of numbers that add together to make a specific total.

Think about it like this: If you have 10 fingers, how many different ways can you hold some up and some down?

• 1 finger up + 9 fingers down = 10 fingers total
• 5 fingers up + 5 fingers down = 10 fingers total
• 7 fingers up + 3 fingers down = 10 fingers total

These are all number bonds for 10!

Number Bonds to 10

These are the most important pairs to memorize:

Why Number Bonds Help

If you know these by heart, adding becomes super fast!

Example: What is 7 + 5?

If you know that 7 + 3 = 10, you can think:

• Break 5 into 3 + 2
• Add 7 + 3 = 10
• Then add 10 + 2 = 12

So 7 + 5 = 12 — and you did it in your head!

Number Bonds to 5

These are even easier:

• 0 + 5 = 5
• 1 + 4 = 5
• 2 + 3 = 5
• 3 + 2 = 5
• 4 + 1 = 5
• 5 + 0 = 5

Think of one hand: 5 fingers can be split in many ways.

For Junior High Students

Number Bonds to 20

Once you master bonds to 10, bonds to 20 become easy. Just think of them as "10 plus something" paired with "something else."

Shortcut: If you know 7 + 3 = 10, then 17 + 3 = 20 (just add 10 to both sides).

Number Bonds to 100

These follow the same pattern:

• 10 + 90 = 100
• 20 + 80 = 100
• 30 + 70 = 100
• 40 + 60 = 100
• 50 + 50 = 100
• 60 + 40 = 100
• 70 + 30 = 100
• 80 + 20 = 100
• 90 + 10 = 100

Pattern: Notice that the tens digits always add to 10! If you know bonds to 10, you know bonds to 100.

Using Number Bonds for Mental Math

Problem: What is 27 + 8?

Strategy:

1. You know 7 + 3 = 10
2. Break 8 into 3 + 5
3. Add 27 + 3 = 30
4. Add 30 + 5 = 35

Answer: 35

Problem: What is 68 + 32?

Strategy:

1. You know 68 + 32 = ?
2. Notice 60 + 30 = 90 and 8 + 2 = 10
3. So 90 + 10 = 100

Answer: 100

Why This Works

Number bonds help you "make tens" or "make hundreds" — a strategy that makes adding much easier because our number system is based on groups of 10.

Practice