Bubble Splat

For 7 × 8 = 56, one 8 too few is 48 and one too many is 64. The others are 49 and 63 (the 7 times table either side), 15 (7 + 8) and 65 (56 with its digits swapped). Popping 48 or 64 usually means counting up in 8s and losing your place; popping 15 means the × was read as +.

Still bubbles and mini whiteboards turn one pupil’s game into retrieval for the whole room. Each wrong bubble is a real mistake (a neighbouring fact, the two numbers added, digits swapped), so a wrong answer on a whiteboard tells you which mistake it was.

Most pupils are slower on division at first, because they get there through the multiplication fact (what times 8 makes 56?). One wrong bubble is nearly always the number divided minus the divisor (56 − 8 = 48), which catches pupils who take away once instead of dividing.

Missing-number questions are division in disguise, and they lead on to equations such as 8x = 56. The wrong bubbles are the same as for division: the answer one or two either side, the number already in the question, and the product minus that number.

The multiplication tables check taken in Year 4 in England has 25 questions from the 2 to 12 times tables, with 6 seconds for each. Pupils type answers in the real check, so popping is practice for recall, not for the check’s format. Facts that time out go into Your tricky ones, and ▶ Practise these plays just those, twice each.

A practice round holds the facts that went wrong, each twice and never twice in a row, topped up to at least 6 questions with others from the same set-up, so pupils meet the hard facts again within a minute. The best record ignores practice rounds, so it stays a fair record of the full set-up.

37 + 63 = 100. The wrong bubbles are 73 (the tens made 10 and the ones made 10, so 37 + 73 = 110), 3 (only as far as the next ten, 40), 62 (the ones made 9: 37 + 62 = 99) and 36 (63 with its digits swapped). The tens of a bond to 100 make 9, not 10, because the ones make the tenth ten. A phone shows the first three: 73, 3 and 62.

For 30 + ☐ = 100 one wrong bubble is 7: the right digit, but 7 ones, not 7 tens. The others are 60 and 80 (one ten out either way) and 30 (the number in the question). Pupils who pop 7 know the bond to 10 and need to say it in tens: 3 tens and 7 tens make 10 tens.

Each subtraction has the same answer and the same wrong bubbles as its missing-number bond, so slower subtractions mean the pupil is counting back rather than using the bond. For 7 + ☐ = 20 the first wrong bubble is 3, a bond to 10 instead of 20; for 13 + ☐ = 20 it is 17, which makes 30.

0.37 + 0.63 = 1. The wrong bubbles are 0.73 (the tenths and the hundredths each made 10, so 0.37 + 0.73 = 1.1), 0.03 (only to the next tenth, 0.4), 0.62 (0.99) and 0.36 (digits swapped): the same mistakes as for 37 + ☐ = 100, one hundredth of the size. For a bond in tenths, such as 0.3 + ☐ = 1, one wrong bubble is 0.07, the right digit in the hundredths.

47 + 38 = 85. The wrong bubbles are 75 (the ten from 7 + 8 = 15 not carried), 84 and 86 (one out), 9 (47 − 38: took away instead), 715 (15 written in the ones column) and 95 (a ten too many). A phone shows the first three: 75, one of 84 and 86, and 9. Popping 75 or 715 points to the same gap: 15 ones is 1 ten and 5 ones.

52 − 27 = 25. 35 comes from taking the smaller digit from the larger in each column (7 − 2 = 5, 5 − 2 = 3), and also from exchanging a ten but not taking it away. It is the first wrong bubble whenever a subtraction needs an exchange. The others are 24 or 26 (one out) and 79 (52 + 27: added instead).

With Never, 43 + 5 and 48 − 5 stay inside the ten; with Always, every addition carries (47 + 8) and every subtraction exchanges (52 − 7). Crossing is the main difficulty dial for mental calculation. With Always, the first wrong bubble for every addition is the answer with the ten not carried (47 + 8 → 45), and for every subtraction it is the smaller digit taken from the larger (52 − 7 → 55).

370 + 50 = 420. 320 is the hundred not carried (7 tens + 5 tens = 12 tens, which is 1 hundred and 2 tens), and 375 is 5 ones added instead of 5 tens. 410 and 430 are one ten out. Saying “7 tens and 5 tens make 12 tens” out loud, as with ones, is often what fixes it.

−3 − 5 = −8. The wrong bubbles are 2 (−3 + 5: added instead of subtracting), 8 (the right size with the wrong sign) and −2 (3 − 5: the signs ignored), plus −9, −7 and −10 as near misses. A phone shows only the first three: 2, 8 and −2.

3 − (−5) = 8 and 3 + (−5) = −2. Each one’s answer is the other’s first wrong bubble: −2 (3 − 5) for the first and 8 (3 + 5) for the second, so the game checks whether pupils read both signs. Subtracting a negative usually causes more wrong pops; zero pairs on the Double-Sided Counters show why taking away −5 adds 5.

For −3 + 5 = 2, the bubble 1 catches pupils who count the numbers −3, −2, −1, 0, 1 instead of five jumps. On a wide screen every + or − question that crosses zero, with a jump bigger than 1, has this bubble. Negatives only in the first number keeps to Year 6 work: counting on and back across zero, and the difference between temperatures.

The first wrong bubble for every × and ÷ question is the answer with its sign changed: −24 for (−4) × (−6) = 24, and −4 for (−24) ÷ (−6) = 4. The next two are neighbouring facts with the right sign (two of 18, 20, 28 and 30 for (−4) × (−6); 3 and 5 for (−24) ÷ (−6)), so popping the sign-changed bubble means the times-table fact was right and the sign rule wasn’t. A phone shows just these three.

The sign errors are the same as within ±10 (−45 − 38 = −83, with 7, 83 and −7 as the first three wrong bubbles), but the calculation underneath is now a 2-digit addition or subtraction. Slow answers to questions such as −45 + 38 usually come from working out 45 − 38, not from the sign.

8 is always a wrong bubble for −3 − 5 = −8. Pupils who have just answered (−3) × (−5) = 15 often carry “two negatives make a positive” over to −3 − 5. Taking turns means each question needs its own rule, which is exactly what a block of only × questions hides.

Mixed rounds are usually slower and feel harder, because each question needs you to recognise what kind it is before you answer. Studies of interleaved practice (for example Rohrer and Taylor, 2007) found it helped pupils choose the right method later, even though practice felt harder. Use a mix after each game has been practised on its own.

Both are the same bond, one hundredth of the size: 37 and 63 make 100, so 0.37 and 0.63 make 1. Their wrong bubbles match as well (73 and 0.73, 3 and 0.03). Pupils who are fast on 100 and slow on 1 have not yet linked hundredths to the bond they already know.

Each side is dealt its own questions from the same set, so neither player can copy the other. The end card shows both players’ times and wrong pops, so a fast player who popped wildly can be compared with a slower, careful one.

With Clear the board the answers to the next few questions share one board and leave when they are popped, so the last question on each board is a choice between two bubbles: it is quick and satisfying, but partly elimination rather than recall. New bubbles every question gives each question its own wrong answers, so the tenth question is as hard as the first. A sensible routine is Clear the board to warm up, then New bubbles to check.

The best for a sprint is the most right answers, then the fewest wrong pops. Pupils who tap everything get a high wrong count straight away, which makes the end card a talking point about accuracy as well as speed.