Square, Cube and Common Multiple Problems

Year 6 maths worksheets on square numbers, cube numbers and common multiples: 36 questions in three levels (All, Most, Some) with answers. Free PDF.

7-page A4 PDF from the Tiger Shark Education question bank. All: Work out square and cube numbers. Most: Solve problems with arrays, squares and cubes. Some: Use common multiples to solve problems. Each level is two pages of six questions, each with a squared working area, and the last page has every answer, with short working for multi-step questions. Each level is also available as its own 3-page PDF. Example questions from the Some level: Two lighthouses flash: one every 3 seconds, the other every 4 seconds. They have just flashed together. After how many seconds will they next flash together? / Two swimmers finish a lap every 2 seconds and every 5 seconds. They start together. After how many seconds are they next at the start together?

What are square numbers, cube numbers and common multiples? A square number is a number multiplied by itself (5² = 25) and a cube number is a number multiplied by itself three times (2³ = 8). Common multiples are numbers that appear in two times tables (12 is a common multiple of 3 and 4). These ideas feed into area, volume and solving problems with patterns.

Common mistakes and tips: The most frequent error is reading 5² as 5 × 2 = 10 instead of 5 × 5 = 25, and 2³ as 6 instead of 8. Drawing squares and cubes with counters or multilink makes the meaning concrete. For common multiples, listing multiples of each number side by side helps children spot the lowest common one.

In the KS2 SATs, this topic can appear on the arithmetic paper, on the two reasoning papers, or both. Reasoning questions often wrap the skill in a context or ask children to explain an answer, so the three levels on this sheet build from fluency to the kind of problem pupils meet in the test.

Ways to use it: whole-class differentiation (three levels for the same lesson), focused intervention for children working towards the expected standard, homework, or targeted revision before the SATs. Set one level as a quick assessment and use the answers to decide who needs another lesson on the topic.

Building fluency over time: revisiting this topic little and often throughout the year, rather than only in one unit, helps children retain it for the SATs. A few questions from the All or Most level make a good retrieval starter several weeks after the topic was first taught.

Use All for children working towards the expected standard, Most for secure Year 5 skills and Some for SATs-standard practice: three entry points to the same lesson. Suits whole-class differentiation, intervention groups, homework and SATs revision, and upper KS2 generally.

Part of a set of 42 Year 6 maths topics.