Year 6 - Maths
Explain how to use the associative law to multiply efficiently
Multiplying and dividing by 2-digit numbers
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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 will extend their understanding of formal calculation strategies to multiply and divide by 2-digit numbers, explaining when other strategies are more efficient.
Lesson Summary
You will learn to explain how to use factorisation and the associative law to multiply efficiently.
Key Notes
- Multiplication can be simplified by factorising one of the factors.
- Look at the factors to identify which are composite numbers.
- Composite numbers can be factorised.
- Multiplication is commutative.
- Factors can be grouped in different ways and the product remains the same.
Vocabulary To Learn
- Associative law: The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.
- Composite number: A composite number is an integer with more than two factors. All integers greater than 1 are either composite or prime.
Common Mistakes To Avoid
- Pupils can identify factors of a 2-digit number but do not consider efficiency when multiplying.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Multiplication can be simplified by factorising one of the factors. Look at the factors to identify which are composite numbers.
2. Use this key word in a maths sentence and explain it clearly. 'Associative law'
The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils can identify factors of a 2-digit number but do not consider efficiency when multiplying. Correction: Draw attention to factor pairs and those which result in easier calculations e.g. pupils often find multiplying by 4 or 5 easier than 7, or can apply doubling when multiplying by 2.
More Lessons In This Unit
- Dividing by a 2-digit divisor including using long division Study Guide
- Dividing by a 2-digit divisor with a remainder Study Guide
- Dividing numbers with up to 4 digits by multiples of 10 Study Guide
- Explain how to multiply a 3-digit number by a 2-digit number Study Guide
- Explain how to use long multiplication to multiply a 3-digit by a 2-digit number Study Guide
- Explain how to use long multiplication to multiply a 4-digit by a 2-digit number Study Guide
- Explain how to use long multiplication to multiply two 2-digit numbers regrouping ones to tens Study Guide
- Explain how to use long multiplication to multiply two 2-digit numbers with regrouping Study Guide
- Explain when it is efficient to use factorising or long multiplication to multiply by 2-digits Study Guide
- Solve problems involving remainders in context Study Guide
- Solve problems with 4-digit dividends using factors and long division Study Guide
- Use long division with decimal remainders Study Guide
- Use long division with fraction remainders Study Guide
- Using short and long division to divide by a 2-digit divisor Study Guide
Browse all guides in the Year 6 Maths guide library.