Year 7 - Maths
Checking understanding of factors, multiples, squares and cubes
Properties of number: factors, multiples, squares and cubes
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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 state the factors and multiples for different numbers and identify square and cube numbers.
Key Notes
- Multiples of a given number are the product of that number and an integer.
- Factors of an integer can be identified by checking for a remainder when dividing.
- In the statement factor x factor = product, the product is a multiple of each of the factors.
- If a is a factor of b then b is a multiple of a
Vocabulary To Learn
- Multiple: A multiple is the product of a number and an integer.
- Numerical factor: A numerical factor is a factor that is an integer.
- Square: A square number is the product of two repeated integers.
- Cube: A cube number is the product of three repeated integers.
- Product: A product is the result of two or more numbers multiplied together.
Common Mistakes To Avoid
- There is often confusion between factors and multiples.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Multiples of a given number are the product of that number and an integer. Factors of an integer can be identified by checking for a remainder when dividing.
2. Use this key word in a maths sentence and explain it clearly. 'Multiple'
A multiple is the product of a number and an integer. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: There is often confusion between factors and multiples. Correction: Highlight that the number of dots in an array is the multiple and the number of dots in each column & row are the factors.
More Lessons In This Unit
- Calculating integers from their prime factor expressions 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
- Problem solving with factors, multiples, squares and cubes 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.