Key takeaways
- A number bond is a simple diagram showing how a whole number breaks into two parts — for example, 10 splits into 6 and 4.
- It is drawn as a part-whole model: the whole sits in one circle, connected by lines to two smaller circles holding the parts.
- Number bonds make the link between addition and subtraction visible, because the same three numbers form a fact family: 6 + 4 = 10, 4 + 6 = 10, 10 − 6 = 4, 10 − 4 = 6.
- They are a core tool in mastery and Singapore-style math (used by programs like Maths — No Problem! and White Rose), taught through a concrete → pictorial → abstract progression.
- Bonds to 10 are the anchor set: 0+10, 1+9, 2+8, 3+7, 4+6, 5+5 — six pairs worth committing to memory before moving to 20 and 100.
A number bond is a picture of a simple idea: a whole number is made of parts. If you have 10 counters and split them into a group of 6 and a group of 4, you have shown a number bond — 6 and 4 bond together to make 10. The diagram that captures this is the part-whole model: the whole number in a circle at the top, joined by two short lines to two smaller circles holding the parts underneath.
That sounds almost too simple to matter, but number bonds are one of the highest-leverage models in early math. Once a child sees that 10 is 6 and 4 — and also 7 and 3, and 8 and 2 — addition stops being a mystery and subtraction becomes the same picture read a different way. Instead of memorizing hundreds of unrelated facts, students learn a small set of part-whole relationships and use them flexibly. That is the difference between fragile recall and real number sense.
What a number bond actually shows
Every number bond links three numbers: one whole and two parts. Cover any one of the three and you have a question. If both parts are showing, the student adds to find the whole (6 + 4 = ?). If the whole and one part are showing, the student subtracts — or counts on — to find the missing part (10 = 6 + ?). This is why a single number bond is really four number sentences at once, known as a fact family.
Part-whole diagram
The whole in a top circle, two parts in circles below, joined by lines. The abstract form of every number bond and the one students eventually draw from memory.
Ten frame
A 2x5 grid of ten spaces. Filling 6 and leaving 4 empty shows the bond to 10 concretely, and makes 'how many more to 10?' obvious at a glance.
Counters and cubes
Physical objects a child can physically split into two groups. This is the concrete stage — students should move real things before they draw or write anything.
Fact family
The two addition and two subtraction sentences a single bond produces, e.g. 3+7=10, 7+3=10, 10-3=7, 10-7=3. The bridge from picture to arithmetic.
Number bond examples: bonds to 5, 10, and 20
Students work up through the whole numbers in stages, mastering one set before the next. Here are the sets they meet first:
- Bonds to 5 (the starting point in kindergarten): 0 and 5, 1 and 4, 2 and 3. Just three pairs, small enough to build with fingers or cubes.
- Bonds to 10 (the anchor set everything else leans on): 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5. Six pairs. Because addition is commutative, 3 and 7 is the same bond as 7 and 3 — so there are six pairs to know, not twelve facts to memorize.
- Bonds to 20: once bonds to 10 are automatic, students extend them — 13 and 7, 15 and 5, 12 and 8. Many are just a bond to 10 with a ten added on: if 3 + 7 = 10, then 13 + 7 = 20.
- Bonds to 100 (with tens): 30 and 70, 40 and 60, 25 and 75. The same six bonds-to-10 pattern, scaled up, which is exactly why the bonds to 10 are worth over-learning.
The payoff shows up in mental math. A student who knows 8 and 2 make 10 can solve 8 + 5 by first making 10 (8 + 2) and then adding the leftover 3 to reach 13 — the 'make ten' strategy that number bonds set up directly.
The Common Core kindergarten standard that asks students to find the number that makes 10 when added to any number 1–9 — a number bond to 10 in all but name. Fluency within 20 follows in standard 2.OA.B.2 by the end of grade 2.
Source: Common Core State Standards for Mathematics
How to teach number bonds step by step
- 1
Start concrete, with real objects
Give students a small handful of counters, cubes, or even pasta pieces and have them split the group into two parts. Say it out loud: 'Five is four and one.' Do this before any diagram appears — the physical splitting is what the picture will later stand for.
- 2
Move to the pictorial part-whole model
Draw the three-circle diagram and place the objects into it: whole on top, two parts below. This is the middle stage of the concrete → pictorial → abstract progression that mastery math is built on. Students should draw their own before working without one.
- 3
Introduce the missing part
Fill the whole and one part, leave the other blank: '10 is 6 and ___.' This turns the same diagram into a subtraction problem and is where 'counting on' becomes a natural strategy. Missing-part bonds are the single most useful practice format.
- 4
Write the fact family
For each bond, have students record all four sentences: two additions and two subtractions. Seeing 3+7, 7+3, 10-3, and 10-7 come from one picture is the moment addition and subtraction click together as inverse operations.
- 5
Over-learn the bonds to 10
Drill the six bonds to 10 until they are instant — through quick 'show me the partner to 10' games, ten-frame flashes, and daily warm-ups. Automatic bonds to 10 are the foundation for regrouping, bridging through ten, and later column addition.
- 6
Extend to 20, 100, and decimals
Once bonds to 10 are secure, stretch the pattern: bonds to 20, bonds to 100 in tens, and eventually bonds to 1 with decimals (0.3 and 0.7). The model never changes — only the whole does — which is why it repays the early investment.
Number bonds vs. flashcard drilling
| What you compare | Number bonds | Flashcard drilling |
|---|---|---|
| What students learn | Part-whole relationships they can reason from | Isolated facts to recall one at a time |
| Addition and subtraction | Linked — one bond gives a whole fact family | Taught and practiced separately |
| When a fact is forgotten | Student rebuilds it from a known bond | Nothing to fall back on |
| Supports mental math | Yes — sets up make-ten and bridging | Rarely transfers to strategy |
| Best used for | Building number sense from K–grade 2 | Quick fluency checks once bonds are understood |
Number bonds and flashcards are not enemies — the point is order. Build the understanding with part-whole models first, then use quick drills to make the bonds automatic. A student who has only memorized facts is stuck the moment one slips; a student who understands that 10 is made of 6 and 4 can always rebuild it. That resilience is the whole reason mastery curricula lead with the part-whole model.
A few classroom adaptations keep the model working across a range of learners. For students who need more support, stay at the concrete stage longer and use a ten frame so the 'gap to 10' is visible. For students ready to push on, ask for all the bonds of a number and have them prove the set is complete. For a fast formative check, hand out a page of missing-part bonds and watch who counts on their fingers versus who just knows.
Hand out ready-made number bond practice in seconds
Generate printable number bond and fact-family worksheets for bonds to 5, 10, 20, or 100 — differentiated for any grade, with answer keys.
Try the AI worksheet generatorFrequently asked questions
A number bond is a simple diagram that shows how a whole number is made of two parts. It is drawn as a part-whole model, with the whole in a top circle joined to two smaller circles holding the parts. For example, 10 breaks into a bond of 6 and 4.
The bonds to 10 are the pairs that add to make ten: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. Because addition is commutative, there are six pairs to learn, and mastering them is the foundation for mental math and regrouping.
Number bonds build number sense by teaching part-whole relationships instead of isolated facts. They make addition and subtraction visible as inverse operations through fact families, and they set up mental-math strategies like 'make ten,' which support all later arithmetic.
Number bonds usually start in kindergarten with bonds to 5 and 10, extend to bonds to 20 in first grade, and reach bonds to 100 by around second grade. In the UK they are introduced from Reception through Year 2. The same model is later reused for decimals and larger numbers.
A number bond is the picture — the part-whole diagram linking a whole to its two parts. A fact family is the set of four number sentences that same bond produces: two additions and two subtractions. One bond of 3, 7, and 10 gives the fact family 3+7=10, 7+3=10, 10-3=7, and 10-7=3.