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 How many kilograms must be added to the right pan to balance these scales?
Show worked solution
Left 12 + 14 = 26, right 19. Gap 26 − 19 = 7 kg.
2 4 bananas weigh the same as 6 apples. How many apples weigh the same as 2 bananas?
Show worked solution
Halving: 2 bananas = 3 apples.
3 2 zots are worth 6 squigs. How many squigs are 5 zots worth?
Show worked solution
1 zot = 3 squigs, so 5 zots = 15 squigs.
Level 2 · Core
4 The left pan holds 15 kg and 8 kg; the right pan holds 30 kg. Amber adds 12 kg to the left and 4 kg to the right. Which side is heavier now? (left/right)
Show worked solution
Left 23 + 12 = 35, right 30 + 4 = 34. The left side is heavier.
5 3 pears weigh the same as 5 plums. A bag holds 6 pears and 4 plums. The whole bag weighs the same as how many plums?
Show worked solution
6 pears = 10 plums. 10 + 4 = 14 plums.
6 The scales balance. The hexagon weighs 12 kg. What does one circle weigh, in kg?
Show worked solution
3 circles = 12 kg, so one circle = 4 kg.
Level 3 · Challenge
7 3 tocks are worth 4 pips. 2 pips are worth 7 dibs. How many dibs are 6 tocks worth?
Show worked solution
6 tocks = 8 pips (two groups of 3 tocks). 8 pips = 4 groups of 2 = 4 × 7 = 28 dibs.
8 4 bananas weigh the same as 6 apples. Bag A has 8 bananas and 6 apples. Bag B has 2 bananas and 15 apples. In apples, how much heavier is Bag A than Bag B? (Write 0 if they weigh the same.)
Show worked solution
Bag A: 8 bananas = 12 apples, + 6 = 18. Bag B: 2 bananas = 3 apples, + 15 = 18. Difference 0 — they weigh the same.
9 Both scales balance. What does one square weigh, in kg?
Show worked solution
2 circles + 1 circle = 15 kg → circle 5 kg → square = 2 circles = 10 kg.