Number bonds
Pairs of numbers that make 10, 20 or 100: the facts behind making ten and fact families. See them on a ten frame, then play to make them stick.
Owl Post
Thena’s owl has letters to deliver. Each door has a sum on it: pick the letter with the answer and light up the village.
What is a number bond?
Two numbers that make a whole: 7 and 3 make 10. Schools draw it as a part-whole model, the whole in one circle and its parts in two below, and build it with two-colored counters on a ten frame. Turn the counters over and watch the bond change.
Tap a counter to turn it over.
7 and 3 make 10.
- 7 + 3 = 10
- 3 + 7 = 10
- 10 − 7 = 3
- 10 − 3 = 7
One bond, four facts: that’s the fact family.
Every number bond to 10, 20 and 100
Bonds to 10
- 0 + 10 = 10
- 1 + 9 = 10
- 2 + 8 = 10
- 3 + 7 = 10
- 4 + 6 = 10
- 5 + 5 = 10
- 6 + 4 = 10
- 7 + 3 = 10
- 8 + 2 = 10
- 9 + 1 = 10
- 10 + 0 = 10
Bonds to 20
- 0 + 20 = 20
- 1 + 19 = 20
- 2 + 18 = 20
- 3 + 17 = 20
- 4 + 16 = 20
- 5 + 15 = 20
- 6 + 14 = 20
- 7 + 13 = 20
- 8 + 12 = 20
- 9 + 11 = 20
- 10 + 10 = 20
- 11 + 9 = 20
- 12 + 8 = 20
- 13 + 7 = 20
- 14 + 6 = 20
- 15 + 5 = 20
- 16 + 4 = 20
- 17 + 3 = 20
- 18 + 2 = 20
- 19 + 1 = 20
- 20 + 0 = 20
Bonds to 100, in tens
- 0 + 100 = 100
- 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
- 100 + 0 = 100
Once bonds to 10 come quickly, the rest follow: 3 and 7 make 10, so 13 and 7 make 20, and 30 and 70 make 100.
How schools teach them
In Common Core, bonds and fact families run from kindergarten to 2nd grade. Many schools call them number bonds by name, from Singapore Math and Eureka Math.
- Kindergarten
- Breaking numbers up to 10 into pairs in more than one way, and finding the number that makes 10 with any number from 1 to 9.
- 1st grade
- Adding and subtracting within 20 with strategies like making ten (8 + 6 is 8 + 2 + 4), and seeing subtraction as a missing part: fact families.
- 2nd grade
- Knowing all the sums of two one-digit numbers from memory by the end of the year, and adding and subtracting within 100.
Number bonds at home
On their fingers
Hold up 6 fingers: how many are down? Ten fingers are a bond to 10 that’s always with them.
Make 10 snap
Take the cards from ace to 9 out of a pack. Turn two over at a time: if they make 10, the first to say so keeps them.
Say the family
For every bond, say all four facts: 4 + 6, 6 + 4, 10 − 4 and 10 − 6. Taking away comes free.
Scale it up
When 3 and 7 are quick, ask 30 and what? Then 13 and what makes 20? One fact, three bonds.
More to try
Questions about number bonds
What are number bonds to 10?
The pairs of whole numbers that add up to 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5, plus the same pairs swapped, like 7 and 3.
How many number bonds to 10 are there?
Eleven, counting each order: 0 + 10, 1 + 9 and so on up to 10 + 0. That’s six different pairs if 3 + 7 and 7 + 3 count as one.
What’s the difference between number bonds and fact families?
A number bond is a pair and its whole: 3 and 7 make 10. Its fact family is the four facts that bond gives you: 3 + 7 = 10, 7 + 3 = 10, 10 − 3 = 7 and 10 − 7 = 3.
Why do number bonds matter?
They make adding and taking away quick. 8 + 5 is 8 + 2 + 3, which is 13, because 8 and 2 make 10. Bonds to 100 help with money, time and measuring later on.
When it doesn’t click
Thena draws bonds on her ten frame as she explains them, and keeps going until your child sees it for themselves.
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