8. The dot starts at 3 and the teal arc is a jump of +5 to the right. With 🙈 Predict on (it is to start with), the answer stays hidden until it is revealed, so ask for a prediction every time.

The first drag makes 6 + (−4) and the second makes 6 − 4, because the + or − stays as it was. Both land on 2: an early hint that subtracting 4 and adding −4 make the same jump.

8 + 7 = 15 is off the −10 to 10 line, so the tool switches to 0 to 20 and says so; 37 + 25 = 62 moves it to 0 to 100. Typing is the quickest way to set up a calculation with big numbers.

1, 5, 1 and 2 arcs. Tens, then ones leaves 8 + 5 as one jump because 5 has no tens; Bridge 10 makes 8 + 2 + 3, the bond to 10 first. A finished line redraws straight away when the setting changes.

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

14. Counting on from the larger number (10, 11, 12, 13, 14) takes 5 hops; starting at 5 would take 9. The hops are numbered, so pupils can see the count matches the number added.

9. The first hop goes from 13 to 12, so 13 itself is not counted: you count the hops, not the number you start on. Counting the start number is the most common counting-back error.

At 10, after +2, because 8 and 2 make 10. That leaves 3, so 8 + 5 = 13. Bridging needs two facts: the bond to 10 (8 + 2) and splitting 5 into 2 and 3.

7 + 3 + 3 = 13, 9 + 1 + 3 = 13 and 6 + 4 + 4 = 14. Saying the jumps first rehearses the bond to 10 each time, and the arcs check it.

15 − 7 goes −5 to 10, then −2 to 8. 15 − 5 lands exactly on 10, so there is nothing to bridge: the tool only splits a jump that passes a multiple of 10.

Both land on 15, but 10 + 5 starts at 10 with a jump of +5 and 5 + 10 starts at 5 with a jump of +10. Addition is commutative: the answer is the same even though the picture isn’t. Compare shows both at once.

12, because 8 + 12 = 20 is the end of the line. You can subtract up to 8, landing on 0; the arrow stops because this line has no negative numbers. On −20 to 20 you could subtract up to 28.

Three: 47, 57, then 62. Counting on in tens keeps the ones digit (7) the same until the last jump, which is worth pointing out before the final +5.

40, 60, 62: +3, +20, +2. Both ways are right; bridging uses the bond 7 + 3 = 10, and partitioning keeps the tens and ones apart. Ask which pupils would use for 38 + 45, and why.

Tens, then ones: 52, 42, 37. Bridge 10: 60, 40, 37 (−2, −20, −3). Both give 37: the 37 + 25 = 62 from the last two questions, run backwards.

Bridge 10 draws +2, +30, +4 and labels each stop (50, 80, 84), which is how an empty number line is usually drawn. Tens, then ones gives +10, +10, +10, +6 instead (58, 68, 78, 84).

+2 to 40, +30 to 70, +3 to 73: the difference is 35. Counting up from the smaller number is often easier than taking away, especially across a ten.

45 hops is more than the tool will count (40), so it says so and jumps in tens and ones instead: 10, 20, 30, 40, 45. Counting in 1s only works for small jumps, which is why pupils need tens.

370, 410, 412: +5, +40, +2. The same strategy works with any numbers; a custom line zooms in on the part of the number line you need.

−2. With Bridge 10 the first jump stops at 0, after −3, leaving −2 more. Stopping at zero splits one hard calculation into two easy ones.

4 to reach 0, leaving 3, so −4 + 7 = 3. Pupils who answer −11 or −3 have usually combined the signs rather than moved along the line.

−7 − 3 = −10 (left, amber) and −7 + 3 = −4 (right, teal). A common error is −7 + 3 = −10, from thinking adding always makes a number bigger in size: on the line, adding a positive number always moves right.

0 − n lands on −n and 0 + n lands on n, the same distance from 0 on opposite sides. Each negative number is a reflection of a positive one in 0.

7: 6 − 7 = −1. You need to subtract more than the start; subtracting exactly the start lands on 0, which is neither positive nor negative.

Three arcs: +3 to −10, +10 to 0, then +5 to 5. Negative tens are landmarks too, so the same bridging works on both sides of zero.

+4, then +6, and 4 + 6 = 10. The parts always add up to the whole jump, because the stop at 0 is on the way. It is the same idea as bridging through 10.

Right, to 7. The − and the (−3) are teal in the calculation because the jump moves right: the tool colours the operation by the direction it moves, not by the sign you see. 4 − (−3) = 4 + 3 = 7.

4 − (−3): face left, walk backwards, move right (7). 4 − 3: face right, walk backwards, move left (1). 4 + (−3): face left, walk forwards, move left (1). 4 + 3: right, forwards, right (7). Two “turn arounds” (a negative number and a minus) cancel out.

Yes: 7 and 7, 1 and 1, 7 and 7. Each pair makes the same jump, so the purple message says A and B land in the same place and a dashed purple line joins the answers.

−2 − (−8) = 6 and −6 − (−4) = −2. The answer is positive when the number subtracted is further below zero than the start: −8 is below −2, but −4 is above −6.

At 0, after +6, then +3 to 3. Subtracting −9 moves 9 to the right, so −6 + 9 draws exactly the same arcs.

Always bigger: subtracting a negative always moves right. On −10 to 10 the start is 1 to 9 and the answer is at most 10, so the numbers stay small.

A and B land in the same place (5). Subtracting 3 and adding −3 make the same jump to the left, which is why any subtraction can be written as an addition.

5: +3 to 10, then +2. Finding a missing addend is counting up, and the dashed arc with ? shows that the jump is the unknown.

7. Undoing +5 means jumping −5 from 12, the inverse operation: □ + 5 = 12 is solved by 12 − 5. The second press redraws the jump forwards to check.

9: undoing −6 is +6, from 3 to 9. Pupils who write 3 − 6 have used the same operation instead of the inverse; the purple arc goes the opposite way to the original jump.

8: the jumps are −2 to 10, then −6 to 4. Subtraction as difference: the distance from 4 to 12 is 8, whichever end you count from.

Every question is □ − b = c, solved by c + b, and each one crosses a multiple of 10, so it practises adding across a ten. Ask pupils to say the inverse calculation before they reveal.

7: the jump goes left, through 0 (−2, then −5). Subtracting 7 from 2 crosses zero, so 2 − 7 = −5.

A = 2 and B = −2, so the message says A lands 4 to the right of B. Swapping the numbers in a subtraction changes the sign of the answer: subtraction is not commutative.

The same place (8) but different pictures: B starts further right with a shorter jump. The dashed purple line joins the two answers because they land in the same place.

20: any start from −10 to 10 except 4, minus (start − 4), such as 10 − 6 or 0 − (−4). A start below 4 needs a negative number, and 4 − 0 isn’t allowed because the number can’t be 0.

Both are 15: moving the start 1 to the right and making the jump 1 shorter keeps the answer. This is compensation (9 + 6 = 10 + 5), a quick way to add 9.

Both are 4: adding 1 to both numbers in a subtraction keeps the difference the same. For 23 − 8, 25 − 10 = 15 (type it in, and the tool moves to 0 to 100).

B is −5 − 8 = −13 (or −5 + (−8)), and A is 3, so the message says A lands 16 to the right of B. Two jumps of 8 in opposite directions from the same start end 16 apart.

Never: a positive start plus a positive number always moves right from above 0. The answer is at most 20, so the start and the number are each at most 19.

→ (+) needs the start bigger than the number subtracted, and → (−) needs it smaller. Equal numbers give 0, which neither type makes.

Yes and yes: a jump left from below 0 always lands further left, so −3 + (−4) = −7 is further from 0 than −3 or −4.

Positive when the number subtracted is further below 0 than the start (−3 − (−7) = 4), negative when it is nearer to 0 (−7 − (−3) = −4), and 0 when they are equal.

Every one passes through 0, the only multiple of 10 strictly inside this line, so every answer has the opposite sign to the start. These are the questions pupils usually find hardest.

The first stop is 1, after +0.4, then +0.3 to 1.3. It is the bond to 10 again, in tenths: 6 tenths and 4 tenths make a whole. Pupils who answer 0.13 have added the digits without thinking about tenths.

5 hops of 0.1, landing on 0.7. Bridge 1 makes it −0.2 to 1, then −0.3 to 0.7.

1.2, bridging 1 after +0.1; 0.12 would be just past 0.1. With Some the line keeps 0, 0.5, 1, 1.5 and 2, plus the start, the stop at 1 and the answer.

0.3 − 0.8 = −0.5 (−0.3 to 0, then −0.5) and −0.4 + 0.9 = 0.5. The zero bridge works the same with tenths.

Two: +1 to 1.3, then +0.4 to 1.7. Adding the ones first, then the tenths, is the same as tens, then ones with whole numbers.

On 0 to 20 the Number arrow stops at 5, because the line ends at 0. On −10 to 10, 5 − 8 = −3. The rule is only true without negative numbers, and pupils who learn it often turn 5 − 8 into 8 − 5.

−7: start at −3 and move 4 left. “Two negatives make a positive” is about multiplying (and subtracting a negative), and pupils over-apply it here. Face and walk says it: 4 is positive, so face right and walk backwards.

−2 is bigger: you get there from −8 by adding 6, moving right. Numbers increase to the right everywhere on the line, including below zero; pupils who think −8 is bigger are comparing 8 and 2.

7. The answer is where you land, not the size of the last jump: −6 to 10, then −3 to 7. Labelling every stop, as the tool does, avoids reading the wrong number.

20 with a positive number: 0 + 10 up to 9 + 1, and 11 − 1 up to 20 − 10. Allowing a negative number adds another 20 (11 + (−1) up to 20 + (−10), and 0 − (−10) up to 9 − (−1)), so 40 in all.

20, from one end to the other: −10 + 20, −10 − (−20), 10 − 20 and 10 + (−20). The Number arrows stop when the answer would leave the line.

0 − 5 = −5 and 5 + (−5) = 0 are two. One of the three must be 0, and it can’t be the number (the tool never adds or subtracts 0), so either the start or the answer is 0.

Bridge 10 never makes more than three: to the next ten, the rest of the tens in one jump, then the ones. Tens, then ones can make up to 10 (0 + 100, or 1 + 99, is ten arcs).

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.