Number bonds explained for parents

Homework says "find the number bond" or "make ten" - and you wonder whether that means times tables, friends of ten, or something else entirely. In Australian primary maths, number bonds are the pairs of numbers that join to make a target total. Knowing them by heart (with meaning, not only chant) is one of the quiet foundations under addition, subtraction and later place value.

This guide unpacks bonds that make 10 and 20, how they bridge into addition strategies, and simple home games. It sits beside our Prep maths, Year 1 maths and Year 2 maths year maps, and pairs with place value explained and what is a ten-frame?.

The big idea: part–part–whole

A number bond is a part–part–whole relationship. For 10, the whole is 10; the parts might be 7 and 3, or 4 and 6, or 10 and 0. Children who can see that 8 and 2 make 10 (and that 10 take away 2 leaves 8) move faster into flexible addition than children who only count every dot every time.

Teachers also say friends of ten, pairs that make ten, or partitioning. Same family of ideas. The Australian Curriculum Mathematics (version 9) builds part–part–whole and partitioning strongly across Foundation to Year 2 (Foundation, Year 1, Year 2).

Bonds to 10: the first must-know set

Most families meet bonds to 10 early - often with a ten-frame. The classic pairs are:

• 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 (and the reverses: 9 + 1, 8 + 2, and so on)

The goal is not a race. It is instant recognition with understanding: cover seven counters on a ten-frame and your child knows three spaces are empty without counting one-by-one.

At home:

• Fill a ten-frame with pasta, Lego or coins; hide some under a cloth; ask how many are hidden.
• Say "I have 6 - what do I need to make 10?" and show both parts.
• Play "make 10" with two dice or two hands of fingers.

More Prep and Year 1 context: what Prep maths covers and Year 1 maths.

Bonds to 20: the next layer

Once 10 feels solid, school stretches the same idea to 20. Useful pairs include 11 + 9, 12 + 8, 13 + 7, 15 + 5, 16 + 4 - again with reverses. Children also learn to use a bond to 10 inside a larger total: 8 + 7 can become "8 + 2 = 10, then 5 more makes 15".

Two ten-frames side by side make this visible. So does a number line labelled to 20, or a simple "rail" of twenty beads.

At home:

• Ask for pairs that make 20 while packing lunch ("we need 20 grapes - we have 12, how many more?").
• Show 14 as 10 and 4, then as 7 and 7 - both are valid partitions.

Year 2 leans harder on these flexible partitions: what a Year 2 child should know in maths.

How number bonds bridge to addition (make ten)

Number bonds are not a dead-end worksheet topic. They power the make-ten (or bridge-ten) strategy teachers use for addition across a ten:

1. Start with 8 + 5.
2. Take 2 from the 5 to complete the bond 8 + 2 = 10.
3. Add the leftover 3: 10 + 3 = 13.

The same move works for 9 + 6, 7 + 4, and later for teens and tens. Without a fluent bond to 10, children fall back to counting every finger - which works until numbers grow and speed or working memory runs out.

Subtraction uses the same map in reverse: if 7 + 3 = 10, then 10 − 3 = 7. Part–part–whole is one picture for both operations.

Place value grows on top of this: seeing 35 as 3 tens and 5 ones (and sometimes as 2 tens and 15 ones) is partitioning with larger parts. Bonds train that "numbers can be split and rejoined" muscle early.

A simple weekly home routine

1. Two minutes of naming - flash a ten-frame or hold up fingers; name the bond ("7 and 3 make 10").
2. Five minutes of making - one make-ten story (8 + 5 on a ten-frame or with counters).
3. Five minutes of playing - a short game from the list below.

Stop while it is still friendly. Confidence is part of the foundation. If evenings tip into tears, shrink the session and tell the teacher which bond or make-ten step wobbled - that is more useful than "maths is hard". For rising worry, see maths anxiety in primary kids.

Number-bond games that do not feel like homework

Hidden counters. Put 10 counters on the table; child closes eyes; you hide some. "How many did I hide?"

Memory match. Write pairs that make 10 (or 20) on cards; play concentration. Start with bonds to 10 only.

Finger flash. You show a number of fingers; child shows the complement to 10 on their hands - then say the full bond out loud.

Shop to 20. "We need 20 cents for the sticker. We have 12c. How many more?" Use play coins if you like; keep the talk on the bond, not on formal money notation yet (money deepens later in money maths at home).

Make-ten race (gentle). Roll a die, add it to 8 (or 9 or 7) using make-ten; celebrate the strategy aloud, not only the answer.

Keep each game under ten minutes. The win is flexible thinking, not stopwatch speed.

Common mix-ups (and kinder fixes)

Thinking bonds are only "times tables." Bonds are addition/subtraction pairs. Multiplication facts come later; do not mash the two labels together. (When tables arrive, see times tables explained for parents for the concept side, and times tables without tears for the practice-order sibling.)

Counting every time instead of knowing the pair. Counting on is a valid early strategy. Gently move toward "I see 7, so 3 to make 10" with ten-frames so the bond becomes a sight fact, not only a chant.

Knowing 7 + 3 but freezing on 3 + 7 or 10 − 7. Practise all three directions of the same bond: part + part, reverse order, and take-away from the whole.

Racing bonds to 20 before 10 is solid. If make-ten for 8 + 5 still needs finger-counting of the 2, stay with bonds to 10 a little longer. Depth beats early width.

Mixing "make ten" with "add the digits." For 28 + 5, children sometimes add 2 + 8 + 5 without respecting place. Keep early make-ten stories inside one ten (or teen totals) until place value is steady.

If bond wobbles sit inside a broader "are they behind?" worry, see Is my child behind in maths?.

How this links to other guides

• Prep maths - early number, subitising and first partitions
• Year 1 maths - part–part–whole to 10 and early make-ten
• Year 2 maths - bonds to 20 and flexible partitioning
• Place value explained - tens and ones built from the same split-and-join idea
• What is a ten-frame? - the classic model for bonds to 10
• Times tables explained - equal groups and arrays after bonds are solid

A useful parent-teacher question: "Which totals are you bonding to this term - 10, 20, or both - and which models (ten-frame, number line, counters)?" Matching home language reduces crossed wires.

FAQ

When do children learn number bonds at school?

Part–part–whole and pairs that make 10 appear strongly in Foundation and Year 1; bonds to 20 and make-ten strategies deepen through Year 1–2. Schools vary in language ("friends of ten", "number bonds", "partition"), so ask what phrase your child's class uses.

My child can count on but is slow. Is that a problem?

Counting on is a stage, not a failure. Use ten-frames and hidden-counter games so some bonds become automatic with meaning. Speed without understanding is not the aim.

Should we use worksheets or games?

Short, concrete games usually teach bonds better than long written lists - especially in Prep to Year 2. A few written number sentences are fine once the picture is clear.

Are number bonds the same as fact families?

Closely related. A fact family for 7, 3 and 10 is 7 + 3 = 10, 3 + 7 = 10, 10 − 3 = 7, 10 − 7 = 3. Bonds name the pairs; fact families show the addition and subtraction sentences together.

Do we need special equipment?

No. A drawn ten-frame, counters, fingers and playing cards are enough. Fancy kits are optional.

A calm next step

When bonds to 10 feel settled and you want a wider number-skill snapshot at home, Ziado's free check is a one-off, roughly 10-minute adaptive diagnostic with partial results only - no account and no card. The full placement unlocks after signup. It is not NAPLAN practice and it is not the full product; Ziado's ongoing path is adaptive maths (Foundation–Year 6) plus phonics reading (Foundation–Year 4). Explore Ziado maths if you want practice that can meet early number and place-value skills at the right step. Individual and Family plans, if you continue later, start with a 14-day free trial of the full app — see pricing for current plans.

Ready for take-away and difference stories that use those bonds? See subtraction explained for parents.

After bonds settle, equal-jump count-bys bridge into early × facts — see skip counting explained for parents.

Doubles are the “same + same” special case of bonds — see doubling and halving for parents.

Bonds power make-ten; for the full addition progression see addition explained for parents.

Bonds help friendly adjustments; for rounding then checking reasonableness see estimate before you add.

For the bridge-to-ten move itself (finish the ten, add the leftover), see make ten bridging for parents.

Conservation of quantity (spread vs bunched) underpins early number sense — see spreading out counting explained.

Number bonds build on solid counting principles — see three counting skills explained.

Familiar dice and ten-frame patterns build on subitising — see subitising explained for parents.

Number bonds and pairing lead into odd/even — see odd and even explained for parents.

Number bonds fuel early equal-group stories — see equal groups explained for parents.

Number bonds and match-and-compare sit together early — see comparing numbers explained for parents.