Year 7 - Maths
Problem solving with factors, multiples, squares and cubes
Properties of number: factors, multiples, squares and cubes
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Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils develop their understanding of factors and multiples, then extend this knowledge to learn general divisibility tests for integers and develop strategies to determine the highest common factor and lowest common multiple of two or more integers.
Lesson Summary
You will learn to use your knowledge of factors, multiples, squares and cubes to solve problems.
Key Notes
- Knowledge of factors and multiples can be used to solve problems
- Knowledge of squares and cubes can be used to solve problems
- Knowledge of squares, cubes, multiples and factors can used to solve problems
Vocabulary To Learn
- Square number: A square number is the product of two repeated integers
- Cube number: A cube number is the product of three repeated integers
- Multiple: A multiple is the product of a number and an integer
- Numerical factor: A numerical factor is a factor that is an integer
Common Mistakes To Avoid
- Real life measurements aren't always integers. Use of integers can give more a practical application
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Knowledge of factors and multiples can be used to solve problems. Knowledge of squares and cubes can be used to solve problems.
2. Use this key word in a maths sentence and explain it clearly. 'Square number'
A square number is the product of two repeated integers. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Real life measurements aren't always integers. Use of integers can give more a practical application. Correction: e.g. find the largest with 200 blocks, the cbrt(200) is not an integer so we use 5 x 5 x 5 =125.
More Lessons In This Unit
- Calculating integers from their prime factor expressions Study Guide
- Checking understanding of factors, multiples, squares and cubes Study Guide
- Checking understanding of prime numbers Study Guide
- Divisibility tests for 2 and 3 Study Guide
- Divisibility tests for 4 and 8 Study Guide
- Divisibility tests for 5 and 10 Study Guide
- Divisibility tests for 6 and 9 Study Guide
- Expressing an integer as a product of its prime factors Study Guide
- HCF or LCM Study Guide
- Highest common factor Study Guide
- Listing factors Study Guide
- Listing multiples Study Guide
- Lowest common multiple Study Guide
- Power notation Study Guide
- Powers and roots using a calculator Study Guide
- Securing understanding of factors, multiples, squares and cubes Study Guide
- Square and cube numbers Study Guide
- Square and cube roots Study Guide
Browse all guides in the Year 7 Maths guide library.