Written Multiplication
Multiply two-digit and three-digit numbers by a one-digit number using formal written layout
Lesson: Written Multiplication (Short Multiplication with Carrying)
Subject · Mathematics Domain · Multiplication & Division Curriculum age band · 8–9 years (UK KS2 Year 4) Actual developmental age · 5–6 years (gifted, IQ 125–130+) Type · Procedural Centrality · Core (0.16) Taxonomy ID · mt_18fK9sQdIz Standard · uk-nc-2013:Ma/KS2/Y4/MD/4 Tailored for · Asynchronous learner with strong additive reasoning and partial multiplication fluency; emotionally 5
Why this matters
Your son already understands multiplication as repeated addition and equal groups — that's the conceptual anchor. What this lesson adds is the written convention: a compact, place-value-aware layout that scales to numbers too big to hold in his head.
The hidden curriculum here is place value under stress. When he computes 7 × 6 and gets 42, that "4" isn't a four — it's forty, and the written method is a way of recording that forty without losing it. Gifted kids often see the answer before they finish writing, which makes them impatient with layout; but the layout itself is teaching something his head can't: how our number system packs groups of ten into the next column. That insight is the foundation for long multiplication, long division, and polynomial operations years from now.
Some parents find this lesson lands in 8 minutes flat because the child has already reverse-engineered it. If so — perfect. Go straight to Stretch. The point isn't the procedure; it's the structural understanding of regrouping underneath.
Learning objective
Goal: Set out and solve a 2- or 3-digit × 1-digit multiplication using short written layout, with carrying, and explain what each carried digit actually represents.
Sentence you want him to be able to say: "I multiply the ones first. If I get ten or more, the tens part goes up top — that's the carry — and it really means tens, not ones."
Before you sit down together
Materials
- Squared paper (ideally 5mm or 1cm grid) — the grid enforces column alignment without you nagging
- Pencil with a decent eraser
- A small handful of counters or dried beans (around 60) plus 6 small cups or muffin-tin wells — for the concrete model only; you'll drop these within two minutes
- Optional: two coloured pencils — one for the multiplier, one for the carried digit
You might pre-draw a faint vertical line between the tens and ones column on the squared paper. Some 5-year-olds find the visual gutter helps them treat columns as separate "boxes."
Best time of day for this lesson
Mid-morning after a snack works well for most 5-year-olds — glucose up, post-breakfast focus not yet faded. Avoid: - Right before a nap or quiet time - Immediately after screen time (transition friction) - When he's "in flow" with something else — gifted kids handle interruption poorly
You'll likely sense within 90 seconds whether today is a procedural day or a stretch day. Follow that signal.
Activity: "The Packing Robot"
A robot packs things into boxes of ten — when it fills a box, it carries the box to the next shelf. Your job is to be the robot's note-taker.
Phase 1 — Model (5–7 minutes)
Start concrete → pictorial → abstract, but move quickly through concrete since he'll likely find it obvious.
Lay out 6 cups. Say: "The robot has 6 baskets. Each basket holds 47 bolts. Show me what that looks like." Let him build or draw 6 groups of 47 with beans/counter piles.
Then: "The robot is lazy. It doesn't want to count all of them. It only counts the ones bolts first. How many ones-bolts across all 6 baskets?"
He'll likely say 7 × 6 = 42.
"Right. 42 ones. But ones only fit on the ones shelf. So the robot packs 40 of them into 4 boxes of ten, and carries those 4 boxes upstairs to the tens shelf. Two ones stay behind."
Now write the layout on squared paper, narrating:
4 ← carried tens (write small, on top of tens column)
4 7
× 6
───
2 8 2
The little 4 up there isn't a four. It's four boxes of ten. Forty bolts, hiding in plain sight.
Highlight: "After I multiply the tens — 4 × 6 = 24 — I have to add the carried forty, not ignore it. 24 tens plus 4 tens is 28 tens. That's why we say 'multiply then add the carry.'"
Phase 2 — Guided practice (4–5 minutes)
Try 34 × 4 together. Hand him the pencil.
You might say: "Be the robot. Tell me what to write and I'll write it — or you write and I'll check."
Let him lead. If he multiplies tens first (4 × 4 = 16, then 4 × 3 = 12), don't correct yet — note it for misconceptions below.
Try a second: 56 × 3. This time the carry from ones is bigger (6 × 3 = 18, carry 1).
Phase 3 — Independent practice (3–5 minutes)
Give him 234 × 5 on squared paper.
This is the moment — three digits means carrying can ripple. Watch what he does with the tens column: after multiplying 3 × 5 = 15, plus the carried 2 from ones, he gets 17 — that "1" is a hundred now. He has to carry into the hundreds column.
Resist the urge to hover. Walk away and make tea if you can.
Phase 4 — Wrap-up (2–3 minutes)
"Before we check, what's a sensible guess? If 200 × 5 is 1000, should our answer be bigger or smaller than 1000?"
Estimation check: 234 × 5 ≈ 200 × 5 = 1000, slightly more — actual answer 1170.
If his answer is 1015, you've got a carrying misconception — see table below. If it's 1170, you can move on. If it's wildly off (e.g., 1190), check his times-tables fluency rather than his method.
Kid-response scripts
| He says... | What's happening | You might try... |
|---|---|---|
| "I can just do it in my head, I don't need to write it" | Strong mental maths — but this is where conceptual gaps hide in gifted kids | Affirm genuinely, then ask him to teach the method to a stuffed animal. If he can't explain why the carried 4 is forty, the procedure is shaky |
| "Why is the little 4 so small?" | Excellent — he's noticing notation conventions | Celebrate the question. "That's a code so we don't confuse it with the real digits. Mathematicians use size and position to mean different things. Spotting that is actually clever." |
| "This is boring / too easy" | Probably true — he's past 2-digit × 1-digit | Skip to Stretch immediately. Boredom is the enemy of gifted learners |
| "I multiplied everything and there was no carrying" | He may be selecting problems that avoid carrying, or multiplying without recognising the regroup | Give him 68 × 7 — carrying is unavoidable. If he writes 426 (no carry), he's doing column-by-column without regrouping |
| "I'm done" (very fast) | Possibly correct, possibly misaligned | Ask him to circle the most important digit in his answer and tell you why — quick diagnostic |
| "I hate writing it all down" | Very common with gifted kids; mental work feels faster | Validate it. "Your brain is faster than paper right now. But pretend we're sending this to a friend across the world — they can't see your head. Paper is how brains talk to other brains." |
| "What if there's a zero in the number?" | He's already generalising — this is a stretch doorway | Follow his lead. Try 305 × 4. The zero isn't nothing — it's a place-holder doing important work |
Common misconceptions to watch for
| What you see | What's actually going on | How to gently address |
|---|---|---|
| He multiplies left to right (tens first, then ones) | Pattern-matches from addition/subtraction; logically reasonable but breaks once carrying appears | Don't correct directly. Ask: "If 7 × 6 is 42, where do the four tens need to go?" Let him feel the conflict — ones-column-first exists because of carrying |
| Forgets to add the carried digit (multiplies only) | Treating the carry as decoration, not as part of the calculation | Two colours: carry in red, product in pencil. Then physically point: "Multiply... now add the red one. Two steps, every column." |
| Treats the carried digit as ones, not tens/hundreds | Place value is procedural on paper but not internalised | Write the carry as "40" instead of "4" the first few times. Let him see the actual quantity. Fade the zero once he's fluent |
| Columns drift / misalign | Fine-motor skill — he's 5, this is age-appropriate | Use squared paper and a drawn vertical gutter. Don't make handwriting the bottleneck of a maths lesson |
Stretch (where the real lesson lives for your son)
Pick one or two — these are 5-minute doorways, not worksheets.
-
Zero as a digit: 305 × 4 and 480 × 7 When a zero sits in the tens place, multiplying gives zero — but the column still matters. Have him predict what happens before computing. Some gifted kids initially treat the zero as "skip" and lose a place-value slot.
-
Predict the carries before computing Give him 578 × 4. Ask: "Without solving, tell me — which columns will produce a carry?" This forces attention to the structure of the multiplication, not just the answer. Strong mathematicians do this implicitly; making it explicit is gold.
-
The distributive law, exposed Write 47 × 6 = (40 × 6) + (7 × 6) alongside the column method. Ask: "Where in the written method can you see each of these pieces?" This connects procedure to the property he'll use in algebra. You're planting seeds for years from now.
-
Estimation as a sport Give five problems; he sorts them by approximate answer (closest to 500, 1000, 2000, 5000) without computing exactly. Pure number sense, fast-paced, and feels like a game rather than a lesson.
-
Make a problem with no carrying "Design a 3-digit × 1-digit problem where you never have to carry. Now design one where you carry in every column." This inverts the task and reveals deep understanding. Most kids find this genuinely hard the first time — that's the point.
Quick mastery check (60 seconds)
- [ ] Can he set out 47 × 6 on squared paper and reach 282?
- [ ] When asked "what does that little 4 actually mean?" — does he say forty, not four?
- [ ] Without computing, can he estimate 234 × 5 as "about 1000, maybe a bit more"?
If all three are clean — the lesson below is review. Spend your time in Stretch.
Formal mastery check
From the taxonomy's evidence field, your child can:
- Set out and solve 47 × 6 using short multiplication
- Set out and solve 234 × 5 using short multiplication with carrying
- Check the answer using estimation (e.g., 234 × 5 ≈ 200 × 5 = 1000)
Assessment prompt: Can you work out 347 × 6, setting it out formally in a column — multiplying each digit separately and carrying where needed?
Vocabulary to use naturally
- Carry / regroup — when ones become tens, or tens become hundreds
- Digit vs number — a digit is a single symbol; a number can have several
- Place value — what a digit is worth depends on its column
- Product — the result of a multiplication
- Layout / column method — the written convention
- Estimate — a sensible close guess, used for checking
Drop these into conversation naturally; you don't need to define them all upfront. He'll absorb them.
What comes next
Once short multiplication is solid, two natural dependents open up:
- Long multiplication (2-digit × 2-digit and beyond) — the carrying structure scales directly; he'll find this surprisingly easy if the foundations here are clean
- Multiply-and-add word problems — e.g., "4 boxes of 24 pencils, plus 12 loose pencils" — combining operations tests whether he can read structure from language
Both depend on the place-value-under-stress understanding this lesson builds. If he's wobbly here, those will be wobbly too.
If this lesson didn't land
Some days just don't. Try one of these rather than pushing through:
- Different manipulative — try base-ten blocks (physical "flats, rods, units") if beans didn't click. Some kids need to see ten as a rod, not as ten separate things
- Different time of day — come back after lunch or first thing in the morning. Attention is biological, not behavioural
- Shorten drastically — do just 23 × 3 (no carrying) and stop. Build confidence with the layout itself before adding the regrouping layer
- Skip and return — go back to arrays and equal-groups modelling for a week. The procedure will land better once the visual model is firmer
- Check the prerequisite — does he have 6×, 7×, 8× tables fluent? If he's computing 7 × 6 by skip-counting every time, his working memory is full before the layout even starts. Shore up tables, then return
Your son doesn't need to master this today. He's five. The danger for gifted kids isn't going too slow — it's going so fast they build procedure on sand. If today is sand-day, that's information, not failure.
Source
- Taxonomy ID ·
mt_18fK9sQdIz - Dataset · Mathematics curriculum taxonomy (UK NC 2013 aligned)
- Standard ·
uk-nc-2013:Ma/KS2/Y4/MD/4 - Evidence strings · Set/solve 47 × 6; set/solve 234 × 5 with carrying; check via estimation
- Generated for · Gifted 5y9m asynchronous learner (IQ 125–130+), reading 98th percentile, maths working at Y2–Y3 level
- Generated by · LessonForge adaptive planner