Year 10 - Maths
Checking and securing understanding of substitution
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 substitute particular values into a generalised algebraic statement to find a sense of how the value of the expression changes.
Key Notes
- Expressions and formulae in context can be evaluated for particular values.
- Changing the value of the variable changes the overall value of the expression.
- Exploring what value gives a particular solution can help you to understand the expression.
- Expressions may have multiple variables and you can substitute some or all of them for numbers.
Vocabulary To Learn
- Substitution: Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values.
Common Mistakes To Avoid
- Incorrect evaluation of expressions is common when negative values are substituted. Especially where negative values are squared or pupils rely on calculators without being confident of their use.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Expressions and formulae in context can be evaluated for particular values. Changing the value of the variable changes the overall value of the expression.
2. Use this key word in a maths sentence and explain it clearly. 'Substitution'
Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Incorrect evaluation of expressions is common when negative values are substituted. Especially where negative values are squared or pupils rely on calculators without being confident of their use. Correction: When substituting, always put brackets around the value which is substituted. This helps avoid mistakes when using a calculator as well.
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 expanding a single bracket 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 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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