Last updated 2026-09-13. Written by the TernQuest team. This guide is for parents of kindergartners and 1st graders whose child is adding on fingers and needs a way to add within 20 that does not depend on counting every time.
What is a number bond?
Direct answer: A number bond is the relationship between a whole and its two parts: 7 is made of 5 and 2, so 5 + 2 = 7, 2 + 5 = 7, 7 - 2 = 5 and 7 - 5 = 2 all come from the same bond. Teachers draw it as three circles, the whole on top and the parts below. Children learn the bonds for every number up to 10, and those bonds become the raw material for adding and subtracting within 20.
The idea underneath is part-part-whole: any number can be broken into two parts, and those two parts always put back together to make the whole. Once a child sees numbers this way, addition and subtraction stop being separate operations and become two views of the same picture.
Quotable version: "A number bond is one picture, four facts: 7 is 5 and 2, so 5 + 2, 2 + 5, 7 - 5 and 7 - 2 come for free."
Which number bonds should a child learn first?
Direct answer: The bonds to 5, then the bonds to 10, then the bonds inside each number from 6 to 9. Bonds to 10 are the most important set because the make-ten strategy depends on them being instant. Adding and subtracting within 10 is a kindergarten year-end expectation and fluency within 10 is expected by the end of 1st grade under California Common Core; your school's pacing may differ.
| Whole | Bonds (parts) |
|---|---|
| 5 | 0+5, 1+4, 2+3 |
| 6 | 0+6, 1+5, 2+4, 3+3 |
| 7 | 0+7, 1+6, 2+5, 3+4 |
| 8 | 0+8, 1+7, 2+6, 3+5, 4+4 |
| 9 | 0+9, 1+8, 2+7, 3+6, 4+5 |
| 10 | 0+10, 1+9, 2+8, 3+7, 4+6, 5+5 |
Each pair also reads the other way round (4+6 and 6+4), which the child should notice rather than be told.
How do you teach number bonds at home?
Direct answer: With objects first, then pictures, then numbers. Take a whole (say 6 blocks), split it into two piles every way you can, and say the bond aloud each time. Then draw the three-circle picture. Only after the child can split objects and draw the bonds should you move to bare numbers and flashcards.
The three-stage routine
- Concrete. Six counters and a piece of string to divide them. "Split 6 into two groups. What did you get? 4 and 2. Now a different way." Keep going until every bond is found. Do a different whole each day.
- Pictorial. Draw the number-bond circles: 6 on top, two empty circles below. The child fills in a pair. Ten frames (below) belong here too.
- Abstract. Say "6 is 4 and..." and wait. Flashcards with a missing part. Then the four facts: 4 + 2, 2 + 4, 6 - 2, 6 - 4.
Five minutes a day on one whole is plenty. Rotate through 5 to 10 and come back around; by the second pass most bonds are quick.
Games that carry the practice
- Hide the part. Show 8 counters, cover some with your hand. "How many are hiding?"
- Bond snap. Cards 0 to 10; turn two over; if they make 10, keep the pair.
- Finger flash. Hold up some fingers and fold the rest. "I'm showing 7. How many are folded?" (3, because 7 and 3 make 10.)
- Tea for ten. Ten teddy bears, two tables. How many ways to seat them?
What is a ten frame and why does it matter?
Direct answer: A ten frame is a rectangle divided into two rows of five boxes. Placing counters in it shows any number up to 10 as a picture of "how far from ten": 8 fills the top row and three of the bottom row, leaving two empty boxes, so a child sees 8 and 2 make 10 without counting. It is the single most useful drawing for the make-ten strategy.
Draw one on paper or an index card. Use coins, cereal or buttons as counters, always filling the top row left to right first, then the bottom row. Ask "How many? How many empty?" for numbers 5 to 10 until the answers are instant.
What is the make-ten strategy?
Direct answer: Make-ten is a way to add two numbers whose sum is between 11 and 20 without counting on fingers. To add 8 + 5, take enough from the 5 to fill the 8 up to 10 (that is 2), then add what is left (3): 8 + 5 becomes 10 + 3, which is 13. It works because the child already knows the bond 8 + 2 = 10 and the bond 5 = 2 + 3, and because adding anything to 10 is easy.
Worked examples
| Problem | Make ten | Leftover | Answer |
|---|---|---|---|
| 8 + 5 | 8 + 2 = 10 | 5 - 2 = 3 | 10 + 3 = 13 |
| 9 + 6 | 9 + 1 = 10 | 6 - 1 = 5 | 10 + 5 = 15 |
| 7 + 4 | 7 + 3 = 10 | 4 - 3 = 1 | 10 + 1 = 11 |
| 6 + 7 | 7 + 3 = 10 | 6 - 3 = 3 | 10 + 3 = 13 |
Note the last row: it is easier to make ten from the bigger number, so a child should learn to start from whichever addend is closer to 10.
Teaching it with two ten frames
- Show 8 counters in one ten frame and 5 in another.
- Ask: "How many empty boxes in the first frame?" (2.)
- Move 2 counters from the second frame into the first. Now the first frame is full: 10.
- "How many are left in the second frame?" (3.) "So 10 and 3 is..." (13.)
- Say the whole thing back: "8 + 5. I took 2 to make 10. 3 left. 13."
Repeat with 9 + 4, 7 + 6, 8 + 7. After a week or so of moving counters, ask the child to imagine the frames and say the steps aloud without touching anything. That transition from moving to imagining is the goal.
Why does memorizing facts without number bonds stall?
Direct answer: Because a memorized fact is a single dead end, while a bond is a tool. A child who has memorized "8 + 5 = 13" and forgets it under pressure has nothing; a child who knows make-ten can rebuild it in a few seconds. The same bond also drives subtraction (13 - 5: take 3 to get to 10, then 2 more, so 8) and later scales up (80 + 50, 0.8 + 0.5). Memorization comes naturally after understanding; it rarely works before.
This matters most for children who are already anxious about speed. Counting on fingers for every sum is slow, which makes timed work stressful, which makes children hide the fingers and guess. Bonds replace the counting with a picture, and the speed follows without drills. See math anxiety in kids for why this order matters, and addition within 20 strategies for how make-ten sits alongside doubles and counting on.
When should a child use make-ten, and when is it overkill?
Direct answer: Use make-ten for sums that cross 10 (7 + 5, 9 + 8). For sums within 10, the bonds themselves are the fact. For doubles (6 + 6) and near doubles (6 + 7), a doubles fact is faster. Good 1st and 2nd grade math is about picking the strategy that fits, not forcing one strategy onto everything.
Where a game fits: once the child can do make-ten with counters and is ready to practise it in their head, short bursts of untimed practice help make it automatic. TernQuest's 1st grade addition games are built around these strategies and one child can use it free, but if your child has not yet split a pile of 6 blocks into 4 and 2 with their own hands, an app is the wrong starting point; do the counters and ten frames first. The full list of what 1st grade expects, including fluency within 10, is in the 1st grade math skills checklist.
Related reading
- Addition within 20: 5 strategies kids actually use — make-ten alongside counting on, doubles and near doubles.
- 1st grade math skills checklist (2026) — where bonds and make-ten sit in the year.
- Place value explained for parents — why "ten" is the number everything is built around.
Next step
When the counters have done their job and your child needs repetitions, TernQuest has untimed 1st grade addition games aligned to California Common Core and is free to start for one child. Keep a ten frame on the fridge either way.