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.
Level 1 · Warm-up
1 If 7 + 5 = 12, what is 12 − 5?
Show worked solution
The family is 7, 5 and 12, so 12 − 5 = 7.
2 If 9 × 4 = 36, what is 36 ÷ 4?
Show worked solution
The family is 9, 4 and 36, so 36 ÷ 4 = 9.
3 The two parts of a fact family are 8 and 6. What is the whole?
Show worked solution
8 + 6 = 14.
Level 2 · Core
4 In a fact family the whole is 45 and one part is 18. What is the other part?
Show worked solution
45 − 18 = 27. (18 + 27 = 45.)
5 A fact family uses the numbers 3, 9 and 27. What is 27 ÷ 9?
Show worked solution
9 × 3 = 27, so 27 ÷ 9 = 3.
6 In a fact family the whole is 1000 and one part is 375. What is the other part?
Show worked solution
1000 − 375 = 625. (375 + 625 = 1000.)
Level 3 · Challenge
7 Two numbers multiply to 36, and one is 4 times the other. What are they?
Show worked solution
The pairs making 36 are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. In 3 × 12, 12 is four times 3.
8 Two numbers add to 30 and multiply to 200. What are they?
Show worked solution
Try pairs adding to 30: 14 × 16 = 224, 12 × 18 = 216, 10 × 20 = 200. That is the pair.
9 In a fact family the whole is 48, and one part is 3 times the size of the other. What is the smaller part?
Show worked solution
The whole is 4 equal shares (1 + 3), so one share is 48 ÷ 4 = 12. The parts are 12 and 36, and 12 + 36 = 48.
⭐ Bonus Challenge · only if the rest felt easy
10 Two numbers multiply to 32, and one of them is double the other. What are the two numbers?
Show worked solution
The pairs that make 32 are 1 × 32, 2 × 16 and 4 × 8. In 4 × 8, 8 is double 4.