Year 9 - Maths
Checking and further securing understanding of the commutative law
Standard form
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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 learn to recognise, interpret and write in standard form. Pupils then extend this knowledge so that they can order numbers written in standard form.
Lesson Summary
You will learn to state the commutative law and use it to calculate efficiently.
Key Notes
- A number can be expressed as the product of prime factors.
- By using the commutative law, you can chose which factors to multiply together first.
- Using the commutative law can make calculations easier.
Vocabulary To Learn
- Exponential form: When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
- Commutative: An operation is commutative if the values it is operating on can be written in either order without changing the calculation.
- Prime number: A prime number is an integer greater than one with exactly 2 factors. All integers greater than 1 are either composite or prime.
- Prime factor: Prime factors are the factors of a number that are, themselves, prime.
- Prime factorisation: Prime factorisation is a method to find the prime factors of a given integer.
Common Mistakes To Avoid
- Use of addition instead of multiplication when finding factors.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A number can be expressed as the product of prime factors. By using the commutative law, you can chose which factors to multiply together first.
2. Use this key word in a maths sentence and explain it clearly. 'Exponential form'
When a number is multiplied by itself multiple times, it can be written more simply in exponential form. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Use of addition instead of multiplication when finding factors. Correction: Reiterate that the product of prime factors is unique.
More Lessons In This Unit
- Checking and securing understanding of multiples of 10 Study Guide
- Multiples of 10 involving negative exponents Study Guide
- Ordering numbers in standard form Study Guide
- Problem solving with standard form Study Guide
- Writing large numbers in standard form Study Guide
- Writing small numbers in standard form Study Guide
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