Year 10 - Maths
Checking and securing understanding of expanding a single bracket
Algebraic manipulation
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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 algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.
Lesson Summary
You will learn to use the distributive law to multiply an expression by a term.
Key Notes
- The term could have any form such as fractional or algebraic and may contain exponents.
- The expression may be comprised of multiple terms.
- If either the term or expression are identical to another term or expression, these can be combined.
Vocabulary To Learn
- Distributive law: The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.
Common Mistakes To Avoid
- Pupils find simplifying expressions which are the difference of two bracketed expressions difficult.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The term could have any form such as fractional or algebraic and may contain exponents. The expression may be comprised of multiple terms.
2. Use this key word in a maths sentence and explain it clearly. 'Distributive law'
The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils find simplifying expressions which are the difference of two bracketed expressions difficult. Correction: There are two equivalent methods detailed in learning cycle two. Spend time on both, getting pupils to explore their equivalence. If pupils are struggling, considering subtraction as adding the negative value is the easiest to model.
More Lessons In This Unit
- Advanced problem solving with algebraic manipulation Study Guide
- Checking and securing understanding of changing the subject Study Guide
- Checking and securing understanding of factorising Study Guide
- Checking and securing understanding of forming linear equations Study Guide
- Checking and securing understanding of simplifying Study Guide
- Checking and securing understanding of solving and interpreting linear equations Study Guide
- Checking and securing understanding of substitution Study Guide
- Checking and securing understanding of the product of two binomials Study Guide
- Factorising a quadratic expression Study Guide
- Factorising quadratics of the form ax^2 + bx + c Study Guide
- Factorising using the difference of two squares Study Guide
- Further algebraic terminology Study Guide
- Problem solving with algebraic manipulation Study Guide
- Solving complex quadratic equations by completing the square Study Guide
- Solving quadratic equations by completing the square Study Guide
- Solving quadratic equations by factorising Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
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