Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
15 questions · official format, shuffled order
1 4 + 6 × (9 − 2) ÷ 3 = ?
Show worked solution
9 − 2 = 7. 6 × 7 = 42. 42 ÷ 3 = 14. 4 + 14 = 18. (14 forgets the 4; 46 forgets the ÷ 3.)
2 A box of 24 pencils is shared among 5 children as equally as possible, and 4 pencils are left over. Which number sentence shows this?
Show worked solution
5 children × 4 pencils each = 20, plus 4 left over makes 24: 24 = 5 × 4 + 4. The others are either untrue (24 = 5 + 4 × 4 gives 21) or do not describe the sharing.
3 The same number goes in both boxes. What is it?
Show worked solution
7 boxes equal 4 boxes plus 36, so 3 boxes equal 36 and one box is 12. Check: 7 × 12 = 84 and 4 × 12 + 36 = 84.
4 Every ● has the same value and every ▲ has the same value. What is ● + ▲?
Show worked solution
Adding gives ● ● ● + ▲ ▲ ▲ = 60, which is three of (● + ▲). So ● + ▲ = 60 ÷ 3 = 20. (● is 11 and ▲ is 9.)
5 In this magic square every row, column and diagonal adds to the same total. What number goes in the bottom-left cell?
Show worked solution
13 + 6 + 11 = 30. Bottom row: ? + 14 + 7 = 30, so 9. (Check the left column: 13 + 8 + 9 = 30 ✓.)
6 In this sequence each term is the sum of the two terms before it. What is the sum of the two missing terms?
Show worked solution
5 + ? = 13, so the second term is 8. Then 8 + 13 = 21 (and 13 + 21 = 34 ✓). 8 + 21 = 29.
7 Lena works out 50 − 6 × 4 + 9 and gets 35.
1 Lena is correct.
2 If brackets are put around 50 − 6, the answer becomes 185.
3 If brackets are put around 4 + 9, the answer becomes 100.
Which statements are correct?
1 Lena is correct.
2 If brackets are put around 50 − 6, the answer becomes 185.
3 If brackets are put around 4 + 9, the answer becomes 100.
Which statements are correct?
Show worked solution
50 − 24 + 9 = 35 (1 ✓). (50 − 6) × 4 + 9 = 176 + 9 = 185 (2 ✓). 50 − 6 × (4 + 9) = 50 − 78 = −28, not 100 (3 ✗). 1 and 2.
8 A team won 19 medals, all gold or silver. A gold is worth 3 points and a silver 1 point, and the team scored 41 points. How many golds did it win?
Show worked solution
41 − 19 = 22 extra points, and each gold adds 2, so 11 golds. Check: 11 × 3 + 8 × 1 = 41 ✓.
9 A number goes into this machine and 16 comes out. What was the number?
Show worked solution
16 × 2 = 32. 32 + 7 = 39. 39 ÷ 3 = 13.
10 Which symbol goes in the box to make the sentence true?
Show worked solution
3 × 4 = 12, so the sentence is 5 □ 12 − 2 = 15, which needs 5 □ 12 = 17: +. (− gives −9 and × gives 58.)
11 What is the value of ♠?
Show worked solution
♣ × ♣ = 49, so ♣ = 7. Then ♦ = 20 − 7 = 13. Then ♠ = 13 − 5 = 8.
12 Which expression is equal to 18 × 7?
Show worked solution
18 × 5 + 18 × 2 = 90 + 36 = 126 = 18 × 7. The others give 78, 138, 159 and 43.
13 4 × □ − 9 is less than 30, and □ is a whole number. What is the largest number □ could be?
Show worked solution
4 × □ < 39. 4 × 9 = 36 works and 4 × 10 = 40 does not, so 9. Check: 36 − 9 = 27, less than 30 ✓.
14 In this sequence each term is the sum of the three terms before it. What is the last term?
Show worked solution
2 + 5 + ? = 15, so the third term is 8. The last term is 5 + 8 + 15 = 28.
15 Ava and Ben have 50 stickers between them. If Ava gave Ben 6 stickers, they would have the same number each. How many stickers does Ava have?
Show worked solution
Equal shares of 50 are 25 each. Ava had 25 + 6 = 31 and Ben had 25 − 6 = 19. Check: 31 + 19 = 50 ✓.