Number bonds to 9
Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)
Lesson: Number Bonds of 10 — Making Tens
Subject: Mathematics · Domain: Addition & Subtraction · Age band: 4–6 (tailored for gifted 5y9m) Type: Procedural · Centrality: Foundational (0.26) · Taxonomy ID: mt_e8CZ7E5qW7 Standards: CCSS-Math K.OA.4 · UK NC 2013 Maths/Y1/AS/2 Tailored for: Asynchronous learner — strong computation, needs conceptual anchoring and depth
Your son has likely done this. He can probably tell you 6 + 4 = 10 without blinking. The question is whether he sees the structure — whether "making ten" is a tool he reaches for automatically when staring at 8 + 5, or whether it's just a fact he memorized. This lesson is about checking that bridge and then opening the door to where he actually wants to be: using bonds of 10 as a strategy inside larger problems.
Why this matters
Number bonds of 10 are not really about 10. They are about complements — the idea that every quantity has a partner that completes a target. This is the conceptual backbone of:
- Making-ten strategy (8 + 5 → 8 + 2 + 3 → 10 + 3)
- Regrouping in multi-digit addition (carrying happens at the 10-boundary)
- Bridging through 10 in subtraction (14 − 6 → 14 − 4 − 2)
- Mental math fluency — the difference between a child who calculates 7 + 8 and one who knows it's 5 from 10 and 3 more
For your son, who is already multiplying and playing with fractions, the risk isn't that he can't do this. The risk is that he's been doing it procedurally so long that the structure is invisible to him — and when he hits 47 + 28 in column addition, the regrouping step feels arbitrary rather than inevitable.
This lesson makes the structure visible, then extends it.
Learning objective
Your son solidifies instant recall of all pairs that make 10, and can articulate why "making ten" is a powerful strategy for breaking problems apart.
Sentence you want him to be able to say: "If I know 7 and 3 make 10, I can use that to solve harder problems — because 10 is easy to work with."
Before you sit down together
Materials
- Two colors of small objects (counters, dried beans, LEGO bricks). Two colors matter because you want him to see the pair — 7 blue and 3 red makes 10. One color lets the pair hide.
- A ten-frame drawn on paper (2 rows of 5 squares). If you don't have one, draw it. The frame makes "ten" spatial rather than just numerical — and spatial memory is sticky.
- A deck of cards (A–9 only, face cards removed) — for a fast game at the end.
- Optional: number bond template (three circles connected — whole on top, two parts below). Some gifted kids find this notation clarifying; others find it babyish. Offer, don't impose.
Best time of day for this lesson
Mid-morning, after a snack and some physical movement. At 5y9m, his prefrontal resources are sharpest then but his body still needs to have moved recently — don't pull him from quiet play straight into math. Avoid late afternoon and pre-meal times; gifted kids who are hungry produce spectacular meltdowns over normally trivial tasks.
Activity: "Ten-Makers"
Type: Procedural — Model → Guided practice → Independent practice → Wrap-up Total time: 15–20 minutes (but see Stretch note — this may compress fast)
Phase 1: Model — 4 minutes
Place the ten-frame in front of him. Put 7 blue counters on it — fill the top row and two of the bottom row.
Parent dialogue example: "Look at the frame. How many squares are filled?" → He says 7. "How many are empty?" → He says 3. "So 7 and 3 make..." → He says 10. "That empty space — the 3 — is called the complement. It's the number that completes the ten. Every number inside 10 has a complement. Want to see how fast you can find them?"
If he shrugs or says "that's easy" — good. Note it and move to Phase 3 faster. Don't linger where he's comfortable.
Phase 2: Guided practice — 5 minutes
Work through the bonds together using the frame. Place 4 counters. Ask how many more to fill the frame. Repeat for 2, 6, 9.
As he answers, name the pair: "4 and 6 — bond to ten." "2 and 8 — bond to ten."
Then try it without the frame:
Parent dialogue example: "Okay, I say a number, you say its complement to ten. Ready? ... 5." → He says 5. "7." → He says 3. "1." → He says 9.
If he's fast and accurate through all pairs, this phase is done — move on. If he hesitates on 6↔4, 7↔3, or 8↔2 (the most common sticky pairs), slow down and use the frame for those specifically.
Phase 3: Independent practice — 5 minutes
Game: "Ten-Match" (like Memory/Concentration)
Lay out cards A–9 face down in a grid. He flips two cards. If they bond to 10, he keeps the pair. If not, flip them back.
This forces him to calculate complements repeatedly without it feeling like drill. Play 3–4 rounds.
If he wants to keep going, let him — engagement is the signal here, not the clock.
Phase 4: Wrap-up — 2 minutes
Have him list all the pairs that make 10. Most kids go in order (1+9, 2+8, 3+7...). If he does this, note it — patterning is a sign of mathematical thinking, not just recall.
Then ask the key question:
Parent dialogue example: "So you know all these pairs now. Here's a harder question: why do you think making ten is such a big deal? Why do teachers talk about it so much?"
Listen. His answer tells you where to go in Stretch.
Kid-response scripts
| He says... | What's happening | You might try... |
|---|---|---|
| "This is baby math, I already know this." | He's right, procedurally. Respect it. | "You're right — so let me ask you a harder question..." → jump to Stretch immediately |
| Pauses on 6 + ? = 10 or 7 + ? = 10 | These are the most commonly weak pairs, even in kids who "know" their bonds | Return to the ten-frame for just those pairs — make them spatial |
| Counts up on fingers to find the complement | He's using a backup strategy — recall isn't automatic yet | No correction needed, but note it. Play more Ten-Match. Fluency comes from reps, not lectures. |
| "What about 5 + 5? Is that different?" | Excellent observation — 5 is its own complement | "That's a great thing to notice. Five is the only number that's its own partner. Why do you think that is?" |
| Recites all pairs in order instantly | Strong recall + patterning instinct | "Can you say them in a random order? Like... 8's partner? 2's partner?" — disrupt the recitation pattern |
| "Can we do bigger numbers?" | He's asking for the Stretch. Follow him. | See Stretch options below — especially "bonds to 100" |
| Tries to turn it into a different game | Creative mind at work — let it breathe | "That's a cool idea — let's try it." Engagement outranks your plan |
Common misconceptions to watch for
| What you see | What's actually going on | How to gently address |
|---|---|---|
| He knows all bonds cold but can't use them in 8 + 5 | The bonds are stored as isolated facts, not as a strategy | Demonstrate explicitly: "8 + 5... I need 2 to make 10, so I'll split 5 into 2 and 3. 8 + 2 = 10, then 10 + 3 = 13." Do this 2–3 times with different problems. |
| He says "9 + 1, 8 + 2, 7 + 3..." but freezes if you ask "what goes with 6?" | He memorized the sequence, not individual pairs | Disrupt the pattern: ask pairs out of order. Use the ten-frame to anchor each pair spatially. |
| He answers complements correctly but slowly (2–3 seconds) | Recall is there but not fluent — and fluency matters for the strategy to work | Play more games. Don't drill with flashcards — gamify. Speed comes from positive reps, not pressure. |
| He says "0 and 10" or "10 and 0" | Technically correct but outside the K.OA.4 frame (1–9). If he offers this, he's thinking flexibly. | "You're right — that works too. Can you find all the pairs between 1 and 9?" Affirm, then redirect. |
Stretch (where the real lesson lives for your son)
These are for if Phase 2–3 felt easy. Pick one or two, not all five. Depth over breadth.
1. Bonds to 100 (5 minutes)
"If 7 and 3 make 10, what makes 100? ... If I have 70, what's its complement to 100?" He'll likely see the parallel fast. Then try non-round numbers: "What's the complement of 63?" → This is harder (37) because it requires understanding both tens and ones complements. If he gets stuck, break it down: "How many to get to 70? Then how many more to 100?"
2. Using bonds to solve 8 + 7 (5 minutes)
Don't teach the making-ten strategy explicitly. Instead, ask: "How could knowing your bonds of 10 help you solve 8 + 7 without counting?" See if he can construct the strategy himself: split 7 into 2 + 5, combine 8 + 2 = 10, then 10 + 5 = 15. If he does, that's a genuinely important moment — it means bonds of 10 have become a tool, not just a fact.
3. Bonds to 10 with three numbers (5 minutes)
"I have three numbers that make 10. One is 4, one is 3. What's the third?" Then: "Can you find ALL the ways three different numbers can make 10?" This hits his Adding Three Small Numbers dependent topic and rewards systematic thinking.
4. Negative-complement thinking (3 minutes)
"What's the complement of 12 to 20?" "What's the complement of 7 to 15?" This generalizes the concept — making any target, not just 10. If he handles this, you're in Year 2 territory.
5. The algebra hint (2 minutes)
"If I write □ + 3 = 10, what goes in the box? What about □ + □ = 10 — how many answers does that have?" This opens the door to variables and to the idea that equations can have multiple solutions. Don't push if he's not interested — just drop the seed.
Quick mastery check (60 seconds)
- [ ] "Quick — what goes with 6 to make 10?" (expect: 4, immediate)
- [ ] "What goes with 8?" (expect: 2, immediate)
- [ ] "If you have 9, how many more to make 10?" (expect: 1, immediate)
"Immediate" means under 2 seconds and without counting. If he passes all three cleanly, bonds of 10 are fluent — move to Stretch and don't look back.
Formal mastery check
From the assessment taxonomy:
- [ ] Given 7, responds "3" to make 10
- [ ] Uses a ten-frame to find the complement to 10
- [ ] Records pairs that make 10 as equations (e.g., 6 + 4 = 10)
Parent-facing check: If your son has 6 strawberries and needs 10 for a recipe, can he quickly tell you he needs 4 more — without counting all the way up from 1?
If yes to all three: mastered. Move on, but return to Stretch items that build on this foundation.
Vocabulary to use naturally
- Complement — "the number that completes the ten"
- Bond / bond pair — "7 and 3 are a bond pair to ten"
- Ten-frame — the spatial tool itself
- Decompose — "we can decompose 5 into 2 and 3"
- Strategy — "making ten is a strategy for solving harder problems"
- Fluent — "you know these so well they're fluent — you don't even have to think"
What comes next
Number bonds of 10 is a hard prerequisite for:
- Addition and subtraction within 20 — the making-ten strategy requires instant bond recall. This is the single biggest gateway topic between here and fluent two-digit mental math.
- Number bonds (within 20) — extends the same idea to larger targets (bonds of 11, 12, 15, 20).
- Fluent adding and subtracting within 10 — all basic facts eventually pass through the bonds of 10 as a reference point.
It's a soft prerequisite for:
- Showing your working — explaining how you found a bond is a first taste of articulating mathematical thinking.
- Adding three small numbers — finding two numbers that bond to 10 within a set of three is a powerful shortcut.
If this lesson didn't land
- Switch manipulatives. Some kids don't care about counters but respond to coins (two colors of LEGO, or dimes/pennies). Try different physical objects.
- Move it to the body. Stand 10 paces apart. He stands on "7." Jump to "10" — how many steps? Do all the bonds physically.
- Shorten everything. If he's flagging, just do Phase 1 + the game. Skip the wrap-up. Come back tomorrow.
- Skip and return. If he's resistant, drop it entirely for a week. Sometimes a concept marinates better when we stop pushing.
- Check the prerequisite. If he can't decompose small numbers into pairs (e.g., "what two numbers make 5?"), that's the gap. Back up to bonds of 5 first — same structure, smaller numbers.
Source
Taxonomy ID: mt_e8CZ7E5qW7 Dataset: Core Mathematics Curriculum (K–6) Standards: CCSS-Math K.OA.4 · UK NC 2013 Maths/Y1/AS/2 Evidence strings: Given 7, respond "3" make 10 · Use ten-frame find complement to 10 · Record pairs that make 10 as equations (e.g., 6 + 4 = 10) Generated by: Lesson plan system · Tailored for gifted asynchronous learner, age 5y9m, IQ 125–130+