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 Rewrite 8 + k using the commutative law so that the letter comes first. (as a simplified expression)
Show worked solution
8 + k is the same as k + 8.
2 Rewrite y × 6 with the number in front. (as a simplified expression)
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y × 6 is the same as 6 × y, written 6y.
3 Is 10 − 3 equal to 3 − 10?
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10 − 3 = 7 but 3 − 10 = −7, so the answer is no. Subtraction cannot be swapped.
Level 2 · Core
4 Simplify 2 × m × 6. (as a simplified expression)
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2 × 6 = 12, so the expression becomes 12m.
5 Use the distributive law to write 5(x + 3) without brackets. (as a simplified expression)
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5 × x = 5x and 5 × 3 = 15, so the answer is 5x + 15.
6 Work out (3 + 5) + 7 and 3 + (5 + 7). What single value do both give? (as a number)
Show worked solution
(3 + 5) + 7 = 8 + 7 = 15, and 3 + (5 + 7) = 3 + 12 = 15. Both give 15.
Level 3 · Challenge
7 Use the distributive law to write 6(y + 5) without brackets. (as a simplified expression)
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6 × y = 6y and 6 × 5 = 30, so the answer is 6y + 30.
8 Work out 8 × 34 by splitting 34 into 30 + 4 and using the distributive law. (as a number)
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8 × 30 = 240 and 8 × 4 = 32, so 8 × 34 = 240 + 32 = 272.
9 A rectangle is 4 cm tall. Its base is split into two parts of length n cm and 6 cm. Write an expression for its total area, without brackets. (as a simplified expression)
Show worked solution
The two pieces have areas 4 × n = 4n and 4 × 6 = 24, so the total area is 4n + 24 square cm.