Multi-digit ×/÷ & divisibility

Work out `487 × 6` using the formal written method (or the area model). Show your steps.

Art hook Draw a rectangle 487 wide and 6 tall, then slice it into 3 stacked colour bands (2400, 480, 42) whose widths on a shared bar are proportional to each part. Watching the bands add up to the full bar shows the distributive law visually.

A rope `238` cm long is cut into `7` equal pieces. How long is each piece? Then try a `239` cm rope and give the remainder.

Art hook Draw a horizontal number line 0 to 238 and drop 7 evenly-spaced tick marks; light up each 34-length segment in a rotating hue. Add 1 cm to make 239 and a tiny leftover stub appears at the end, coloured differently to show the remainder.

List every factor of `24` by finding its factor pairs.

Art hook For a number N, place N dots and try to arrange them into every possible rectangle grid (1×24, 2×12, 3×8, 4×6). Each valid rectangle is a factor pair; morph between them so the dots flow from one grid shape into the next.

Test `2730` for divisibility by 2, 3, 5 and 10 using the rules — no long division allowed.

Art hook A colour-wheel dashboard: four arcs (2, 3, 5, 10) that light green or stay grey as you type a number. The digit-sum test animates by adding the digits one at a time along a small orbit, then checking if the total is a multiple of 3.

Use the fact that `56 × 8 = 448` to find `448 ÷ 8` and `448 ÷ 56` without dividing. Explain how you know.

Art hook Show one array of 448 dots as an 8-by-56 grid. A toggle relabels the same grid as '8 groups of 56' or '56 groups of 8', so the child sees the product and both quotients in a single unchanging picture.

Skip-count to help: what is `5 × 60`? And `50 × 6`?

Art hook Place 5 dots, then multiply each into a column of 60 (or 50 dots into 6 columns). The two arrangements fill the same 300-dot rectangle, just rotated — a first glimpse of commutativity.

Fill in the area model for `53 × 4`: work out the box for `50 × 4` and the box for `3 × 4`, then add them.

Art hook A 2-cell rectangle you can drag to resize: one cell always 4 tall and 50 wide, the other 4 tall and 3 wide. The cell areas print live and their colours blend into the total.

Work out `274 × 3` with the formal written method.

Art hook Three coloured tiles of size 600, 210, 12 slide together onto a number line, stacking end to end until they reach 822.

Share `84` stickers equally among `6` children. How many each? Any left over?

Art hook Deal 84 dots one at a time into 6 orbiting bins around a circle; the counter under each bin ticks up to 14 in sync, showing the share growing evenly.

Do the short division `137 ÷ 4` and give the answer with its remainder. Then check your answer.

Art hook Animate 137 dots falling into 4 equal columns; 136 fill the columns evenly and the single leftover dot glows alone at the top as the remainder.

Find all the factor pairs of `18`, then all the factor pairs of `16`. Which number has an odd count of factors, and can you guess why?

Art hook Arrange each number as every rectangle it can make. For 16 one rectangle is a perfect 4×4 square — highlight square numbers in gold to reveal why their factor count is odd.

Sort these into divisible-by-3 and not divisible-by-3: `27`, `40`, `114`, `205`. Use the digit-sum rule.

Art hook A grid of numbered dots where every multiple of 3 lights up when the '÷3' rule is switched on, revealing a diagonal stripe pattern across the grid.

Spot the mistake: a pupil works out `216 × 4` by multiplying each digit as if it were just units — `2 × 4 = 8`, `1 × 4 = 4`, `6 × 4 = 24` — and writes a small wrong answer. What went wrong, and what is the correct answer?

Art hook Two area rectangles side by side: the wrong one loses the zeros and shrinks tiny; the correct one keeps 800/40/24 full-size, so the eye sees how much value was thrown away.

A baker packs `150` buns into boxes of `8`. How many full boxes, and how many buns are left over?

Art hook 150 dots stream into boxes of 8 arranged in a grid; 18 boxes fill and seal, and 6 loose dots hover in a leftover tray labelled 'remainder'.

Use `18 × 5 = 90` to work out `18 × 6` in your head (no full multiplication).

Art hook A bar of length 90 (five 18-blocks) with a sixth 18-block sliding on the end; the total readout climbs from 90 to 108 as the block clicks into place — the distributive law in motion.

Reasoning: `240 ÷ 6 = 40`. Without dividing again, find `240 ÷ 12` and explain using factors.

Art hook Split 240 dots into 6 groups, then let each pair of groups merge into one — the 6 groups become 12 half-size groups, and the count-per-group readout halves from 40 to 20.

Open-ended: find a 3-digit number that is divisible by 2, by 3 and by 5 all at once. How can you be sure without long division?

Art hook A number line of the 3-digit range where numbers passing all three divisibility rules bloom into flowers; the flowers land exactly on the multiples of 30, spaced evenly like beads.