12, after four teal steps of +3 landing on 3, 6, 9 and 12. The arrow points right because 3 is positive. With 🙈 Predict on, the answer waits for a fifth press, so ask for a prediction every time.

Tapping sets the size of each step. 4 × 5 = 20 is off the line, so the tool cuts the steps to 2 × 5 = 10 and says so. Tapping −2 gives 2 × (−2) = −4, with the arrow now pointing left.

56 needs 0 to 100 (0 to 24 and 0 to 48 are too short). (−3) × (−4) = 12 stays on 0 to 100: you face left of 0 but walk backwards, so every stop (4, 8, 12) is positive.

“4 lots of 3: 3 + 3 + 3 + 3”, with one 3 turning dark as each step lands, and “= 12” when the answer is revealed. The first number counts how many 3s are added.

Yes: each mode keeps its own work and undo. 🗑 (tapped twice) starts just one mode again, and undo (U) brings it back.

5, 10, 15, 20: the step stays 5 and there is one more step each time, so the answer goes up by 5. 8 × 5 = 40. The first number counts the steps.

3, 6, 9, 12: up by 3 each time, because each of the 3 steps gets 1 longer. Compare with the last question, where the answer went up by the step size.

4, 8, 12, 16, 20 and 24: the 4 times table. Every step lands on a ring, and 5 × 4 = 20 is the fifth ring from 0.

4 (6 × 4 = 24), 6 (4 × 6 = 24) and 4 (5 × 4 = 20, as 5 × 5 = 25 is off the line). The arrows stop when the answer would leave the line, which is the biggest multiple that fits.

0, 7, 14 and 21: the start, each stop and the answer are always labelled. On an empty line the labels are exactly the multiples of 7 you pass.

Both give 12, but 4 × 3 is four steps of 3 and 3 × 4 is three steps of 4. The answers always match (multiplication is commutative) even though the journeys don’t.

Both are 18: nine 2s, or two 9s (9 + 9). Choosing the order with fewer steps is a useful mental strategy.

Both land on −10. (−2) × 5 faces right and walks backwards 2 steps of 5; 5 × (−2) faces left and walks forwards 5 steps of 2.

Both are 7: one step of 7, or seven steps of 1. Multiplying by 1 leaves a number unchanged.

−12. The arrow points left because −4 is negative, and you walk forwards 3 steps of 4, so all three steps are amber, landing on −4, −8 and −12.

12, 9, 6, 3, 0, −3, −6, −9, −12: down by 3 each time. The pattern carries on past 0, which is why 3 × (−4) = −12, the mirror image of 3 × 4 in 0.

“4 lots of (−3): (−3) + (−3) + (−3) + (−3) = −12”. Adding negative numbers moves further left each time.

All four are −12, made from the factor pairs of 12 with a negative step. The more steps there are, the shorter each one is.

4 steps, landing on −20; a fifth would reach −25, which is off the line. On the positive side, 4 × 5 = 20 is also the limit.

−6. You face right (3 is positive) and walk backwards 2 steps, so you move left. The facing arrow is teal but the steps are amber: the colours show facing and moving separately.

“Take away 3 lots of 4: 0 − 4 − 4 − 4 = −12”. A negative number of steps takes groups away, starting from 0.

6, 4, 2, 0, −2, −4, −6: down by 2 each time. 0 × 2 = 0 (no steps), and the pattern continues below zero, so (−1) × 2 = −2.

−7, −5 and 8. One step backwards lands on the opposite number, the same distance from 0 on the other side.

Four: (−1) × 10, (−2) × 5, (−5) × 2 and (−10) × 1, one for each factor pair of 10.

6. Face left (−3 is negative), walk backwards 2 steps, so you move right: the arrow is amber and the steps are teal. Facing left and walking backwards is the whole reason (−) × (−) is positive.

6, −6, −6 and 6. The answer is positive when the signs match and negative when they differ; the size is always 6.

“Take away 3 lots of (−4): 0 − (−4) − (−4) − (−4) = 12”. Subtracting −4 moves 4 to the right, so taking away three of them lands on 12.

−9, −6, −3, 0, 3, 6, 9: up by 3 each time the step size drops by 1. Keeping the pattern going past 0 gives (−3) × (−1) = 3 without any walking.

1, 4 and 9. (−4) × (−4) = 16 needs −24 to 24. A number times itself is never negative: matching signs always give a positive answer.

Yes, 24. The arrow points left of 0, but walking backwards takes you right, so the stops are 6, 12, 18 and 24, all on a line with no negative numbers.

0. Five hops on the spot: a step of 0 goes nowhere, however many you take. Pupils who say 5 often think “times 0 does nothing”.

Both are 0. 0 × 7 faces right but takes no steps; 7 × 0 takes seven steps that go nowhere.

12, 8, 4, 0, −4: down by 4 each time. 4 × 0 = 0 sits exactly where the pattern says it should.

No. If neither number is 0, you take at least one step of a size other than 0, and every step moves you the same way, so you can never come back to 0.

4, so 12 ÷ 3 = 4. This is division as grouping: how many 3s fit into 12. The steps are numbered as they land.

3, so 12 ÷ 4 = 3. This is division as sharing: 12 split into 4 equal parts. The same fact, 4 × 3 = 12, gives both divisions.

6, as 24 ÷ 4 = 6. Pupils who answer 20 are subtracting instead of dividing.

−4: walk backwards 4 steps. So (−12) ÷ 3 = −4: dividing a negative number by a positive one gives a negative answer.

−6: you must face left, so each step is −6. So 12 ÷ (−2) = −6.

□ × 3 = −12 is (−12) ÷ 3, and so on. The missing number is positive when the answer and the step size have the same sign, and negative when they differ, the same rule as multiplying.

“A and B land in the same place”: both 12, with a purple line joining them. A takes four steps of 3, B three steps of 4.

Both −12, but A faces left and walks forwards while B faces right and walks backwards. Two different journeys, one destination.

Both are two teal steps of 6 to the right, landing on 12. A faces right and walks forwards; B faces left and walks backwards.

20: the tool says “A lands 20 to the right of B” (10 and −10). Changing the sign of one number reflects the answer in 0.

Neither. Questions use 2 to 10 steps and step sizes from the chosen tables, and always fit the line, so the answers run from 4 to 24.

70 (10 × 7) and 14 (2 × 7). Choosing one table turns Practice into skip-counting practice for that table.

Expect about 10, usually between 6 and 14. Each sign type is equally likely and two of the four give a positive answer; 0 never appears because both numbers are at least 2 in size.

The sheet uses the signs and tables chosen in Practice, and the answer page draws every step. Every answer is negative: facing right and walking backwards.

1.2, landing on 0.4, 0.8 and 1.2. Pupils who write 0.12 are treating it like 0.3 × 0.4; the line shows three steps of four tenths, which is twelve tenths.

It refuses: you can’t take 0.4 steps. 0.4 × 3 is still 1.2, but it means 0.4 of 3, a scaling, which the walking model can’t show. A good moment to discuss the limits of a model.

All three are 1: five fifths, two halves and ten tenths of 1.

−1.8: face right and walk backwards 3 steps of 0.6. The sign rules are the same for decimals.

0.5, so 2 ÷ 4 = 0.5. Sharing a whole number into more parts than its size gives a step smaller than 1.

4, 0 and −8, so no. Multiplying by 1 changes nothing, by 0 gives 0, and by a negative number gives something smaller. On the tenths lines, 4 × 0.5 = 2 is smaller too.

−6: (−2) + (−2) + (−2). There is only one negative number here, and adding negatives makes the answer more negative.

15: five 3s, 3 + 3 + 3 + 3 + 3. The pupil added 5 and 3; the first number counts the steps rather than being added on.

−12. The size is 12, but walking backwards while facing right moves left. Ask pupils to find the sign first, then the size.

12 each. For 12: 1 × 12, 2 × 6, 3 × 4, 4 × 3, 6 × 2, 12 × 1 and the same six with both numbers negative. For −12, one of each pair is negative, which also gives 12.

Two: 1 × 1 = 1 and 0 × 0 = 0. (−1) × (−1) = 1 doesn’t count, as the answer is not −1.

6 × 4 = 24 doubles the answer; 6 × 8 = 48 makes it four times as big, because each doubling doubles the answer.

For example 12 × 1 (twelve small steps right) and (−1) × (−12) (one long step backwards). Different numbers of steps, sizes and directions of facing can all give the same answer.

The link stores the mode, the line, the calculation, the settings and how far it has played, but not the undo history. Good questions ask for a prediction first and say which settings to use.