4 min read
Number Bonds to 10 Explained
Short answer
Number bonds to 10 are the pairs of whole numbers that add up to 10: 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5, plus turnarounds. Children learn them in Year 1 (US Grade 1) so they can add and subtract without counting on fingers.
Number bonds to 10 are the pairs of numbers that make 10, such as 7 and 3 or 6 and 4. There are six different pairs, or eleven if you count each turnaround separately, and knowing them by heart is one of the foundations of mental arithmetic.
In England, children work on number bonds and related subtraction facts within 20 in Year 1. In the US, the equivalent is Grade 1, where children are expected to add and subtract within 20 and be fluent within 10. Below is how to teach them at home, step by step.
Key points
- There are six pairs that make 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5.
- Each bond gives four facts: two additions and two subtractions.
- Teach with real objects first, then pictures, then written sums.
- The missing-number form, 7 + ☐ = 10, checks real understanding.
- Bonds to 10 lead directly to bonds to 20 and to adding across 10.
What are number bonds to 10?
A number bond is a pair of numbers that combine to make a given total. For a total of 10, the bonds are the pairs below. Children often meet them as a diagram: a circle with 10 at the top joined to two smaller circles holding the parts, for example 6 and 4.
Each bond describes a family of four facts. If your child knows that 6 and 4 make 10, they also know 4 + 6 = 10, 10 − 6 = 4 and 10 − 4 = 6. Pointing out this link early halves the amount there is to remember.
| Bond | Addition facts | Subtraction facts |
|---|---|---|
| 0 and 10 | 0 + 10 = 10, 10 + 0 = 10 | 10 − 0 = 10, 10 − 10 = 0 |
| 1 and 9 | 1 + 9 = 10, 9 + 1 = 10 | 10 − 1 = 9, 10 − 9 = 1 |
| 2 and 8 | 2 + 8 = 10, 8 + 2 = 10 | 10 − 2 = 8, 10 − 8 = 2 |
| 3 and 7 | 3 + 7 = 10, 7 + 3 = 10 | 10 − 3 = 7, 10 − 7 = 3 |
| 4 and 6 | 4 + 6 = 10, 6 + 4 = 10 | 10 − 4 = 6, 10 − 6 = 4 |
| 5 and 5 | 5 + 5 = 10 | 10 − 5 = 5 |
Why do number bonds to 10 matter?
Ten is the base of our number system, so bonds to 10 come up constantly. A child who knows that 8 needs 2 more to make 10 can solve 8 + 5 by splitting the 5 into 2 and 3: 8 + 2 = 10, then 10 + 3 = 13. The same idea later works for 38 + 5 and for column addition.
Bonds also make subtraction easier. To work out 13 − 5, a child can take 3 to reach 10, then 2 more to reach 8. Without secure bonds, children fall back on counting in ones, which is slow and leads to more mistakes as numbers grow.
The national curriculum in England expects Year 1 pupils to represent and use number bonds and related subtraction facts within 20. The Common Core standards set fluency with addition and subtraction within 10 as a Grade 1 goal.
How do you teach number bonds with objects?
Start with ten real things your child can move: buttons, dried pasta, toy cars or coins. Spend two or three short sessions here before writing anything down. The aim is for your child to see that the total stays 10 however the objects are split.
- Two hands: hold up 10 fingers, fold some down and ask, “How many are up? How many are down?”
- Hide and guess: put 10 buttons on the table, hide some under a cup and ask how many are hidden.
- Ten frame: draw a 2 × 5 grid on paper and fill it with counters; the empty squares show the missing part.
- Egg box: cut a 12-hole egg box down to 10 holes and drop in marbles; count the empty holes.
- Say it in full: encourage “7 and 3 make 10” rather than just “3”.
How do you move from objects to written number bonds?
Once your child answers hide-and-guess questions quickly, move to pictures (dots, a drawn ten frame) and then to written sums. Introduce the missing-number form, 7 + ☐ = 10, early. It asks the child to find a part rather than a total, which shows whether they understand the bond or are simply counting up.
Keep sets short. Ten to twelve bonds a day, mixed in order, is plenty for a five- or six-year-old. If your child still counts on fingers for 6 + ☐ = 10, return to the ten frame for that bond the next day.
| Week | Focus | Daily activity (about 10 minutes) |
|---|---|---|
| 1 | Bonds with objects | Hide and guess with 10 buttons; ten frame with counters |
| 2 | Pictures and saying the fact | Dot cards and drawn ten frames; say “6 and 4 make 10” |
| 3 | Written sums and missing numbers | 10 to 12 sums such as 3 + ☐ = 10 and ☐ + 5 = 10 |
| 4 | Subtraction from 10 and mixed review | Mix 10 − 4 = ☐ with missing-number additions |
Practise this with a 12-week pack
Grade 1 (Year 2): 60 dated sheets with your child’s name, levelled by a quick check, with weekly answer keys. €19 once.
What mistakes do children make with number bonds?
The most common mistakes are easy to spot on a written sheet and quick to fix with a minute of objects.
- Writing the total instead of the missing part, for example 7 + 10 = 10. Read the sum aloud together and ask what goes in the box.
- Being one out, such as 6 + 3 = 10, usually from counting the starting number again. Check with a ten frame.
- Knowing 3 + 7 but not 7 + 3. Show both with the same objects turned around.
- Treating subtraction as unrelated. Ask “If 6 and 4 make 10, what is 10 take away 6?”
How do number bonds to 10 lead to number bonds to 20?
Bonds to 20 come straight from bonds to 10. If 3 + 7 = 10, then 13 + 7 = 20, because the extra ten just sits alongside. Show this with two ten frames: fill the first completely, then work on the second exactly as before.
Children should also learn the related facts within 20, such as 8 + 5 = 13 and 14 − 6 = 8, using the bridge-through-10 method. Ask questions like “9 + ☐ = 20” and “20 − 12 = ☐” once bonds to 10 are fast, and expect this stage to take a few more weeks.
| Bond to 10 | Bond to 20 | Bridging fact within 20 |
|---|---|---|
| 7 + 3 = 10 | 17 + 3 = 20 | 7 + 5 = 7 + 3 + 2 = 12 |
| 8 + 2 = 10 | 18 + 2 = 20 | 8 + 6 = 8 + 2 + 4 = 14 |
| 6 + 4 = 10 | 16 + 4 = 20 | 14 − 6 = 14 − 4 − 2 = 8 |
| 9 + 1 = 10 | 19 + 1 = 20 | 9 + 7 = 9 + 1 + 6 = 16 |
Do worksheets help children learn number bonds?
Worksheets help once your child understands bonds with objects, because they give quick, varied practice and show which bonds are still slow. Short, mixed sheets with missing-number questions work better than long lists in order.
Pencilpace’s Grade 1 packs include number bonds to 10 and 20 in the missing-number form alongside adding and taking away within 20. You can print the free sample sheet to see the format, or browse the skills on the Grade 1 maths worksheets page. Our Grade 1 maths worksheets guide has a full term outline.
Questions
At what age do children learn number bonds to 10?
Most children meet number bonds to 10 at age five or six. In England they are part of Year 1, where pupils work on number bonds and subtraction facts within 20. In the US the equivalent is Grade 1, which sets fluency with addition and subtraction within 10 as a goal. Many children start playing with pairs that make 10 earlier.
How many number bonds to 10 are there?
There are six different pairs of whole numbers that make 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. If you count turnarounds separately, such as 3 + 7 and 7 + 3, there are eleven addition facts. Each pair also gives two subtraction facts from 10.
What is the difference between number bonds and addition facts?
A number bond is the relationship between a whole and its two parts, such as 10 made from 6 and 4. Addition facts are the individual sums that come from it, such as 6 + 4 = 10. Teaching the bond rather than isolated sums helps children see the related subtraction facts at the same time, which means less to remember.
How can I tell if my child really knows their number bonds?
Ask missing-number questions in random order, such as “4 and what make 10?”, and watch for counting. A child who knows the bonds answers within two or three seconds without using fingers. Also check subtraction: if they can say 10 − 7 = 3 straight away, the bond is secure rather than just memorised as one addition.
Should my child use fingers for number bonds?
Fingers are useful at the start, because ten fingers are a natural model of 10. The goal is to move beyond them. Once your child can show a bond on their fingers, ask them to picture it instead, then to answer from memory. If they still need fingers for a particular bond, practise that one with objects for a few days.
Sources
Try it at home
Print a free Grade 1 (Year 2) sheet with the answers on page 2, no email needed. If it suits your child, a 12-week pack gives you 60 dated sheets, one for every school day (€19, full refund within 14 days).