Number Bonds to Five

Once your child can add and subtract within five, the next layer is seeing the parts inside the whole.

What we're learning

That every number can be broken into smaller numbers in more than one way
The phrase "number bonds" — what mathematicians call this idea
All the pairs that make 5: (0,5), (1,4), (2,3) and their flips

Why this matters

Number bonds are the secret engine behind mental arithmetic. A child who knows that 5 is 2-and-3 doesn't have to count every time someone asks "how many more do you need to get to 5?" — they just know.

The same pattern repeats at every level:

Bonds to 5 → bonds to 10 → bonds to 20 → bonds to 100
Each layer reuses the layer below

So the time you spend on these now pays dividends for years.

Show, don't tell

Get five small objects. Cover three of them with one hand, leave two visible.

Ask: "There are five total. I can see two. How many am I hiding?"

That moment of working out the answer — without counting, just by knowing — is the moment number bonds click.

Then switch:

Hide 4, show 1: "How many am I hiding?"
Hide 0, show 5: "How many am I hiding?"
Hide 5, show 0: "How many am I hiding?"

Repeat with different splits until the answers come fast.

The bonds to memorize

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

That's it. Six facts (or three, if you count the flips as the same fact). A kindergartener who has these cold has a meaningful head start on first grade.

Try it together

The disappearing trick. Same as above — hide some, ask for the missing piece.
Rainbow bonds. Draw a rainbow with 6 stripes. Label each end of each arc with the bond pair: 0 and 5 on the outer arc, 1 and 4 on the next, 2 and 3 on the inner. The picture itself reinforces the symmetry.
Domino sort. Find every domino with five total dots. Notice each one shows a different bond.

Watch for

Always going in order. A child who can recite "0 and 5, 1 and 4, 2 and 3" but freezes when you ask "what plus 2 makes 5?" hasn't internalized the bonds yet — they've memorized the recital. Mix up the order.
Subtraction confusion. Some children resist that 5 − 3 = 2 because "you can't see the 5 anymore." Use the hidden-objects trick to tie subtraction to bonds: "5 take away 3 is 2 because 3 and 2 make 5."

Where this is going

The bonds to 10 are next, and they're the foundation for the "make a ten" strategy that drives all of mental arithmetic in elementary school. A solid grasp of bonds to 5 makes bonds to 10 a 2-week project instead of a 2-month one.