Year 7 - Maths
Power notation
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 understand and use correct notation for positive integer exponents.
Key Notes
- There is special notation for squares and cubes and each part can be named.
- Repeated multiplication of the same number can be written using integer exponents.
- Numbers written with positive integer exponents can be expressed as products of the base.
- Products that include repeated multiplication of different base numbers may be simplified using exponents.
Vocabulary To Learn
- Base: The base is the number or term that has been multiplied by itself.
- Exponent: An integer exponent identifies how many times the base number has been multiplied by itself.
Common Mistakes To Avoid
- When different bases are used student multiply the bases. e.g. 2 x 5^2 = 10^2
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There is special notation for squares and cubes and each part can be named. Repeated multiplication of the same number can be written using integer exponents.
2. Use this key word in a maths sentence and explain it clearly. 'Base'
The base is the number or term that has been multiplied by itself. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When different bases are used student multiply the bases. e.g. 2 x 5^2 = 10^2. Correction: Calculate and compare the 2, 2 x 5^2 = 50 & 10^2 = 100.
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
- 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.