Year 10 - Maths
Further algebraic terminology
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 appreciate the difference between an equation, an identity, an expression, a term and a formula.
Key Notes
- A single number or letter, or the product of numbers and/or variables.
- An expression contains one or more terms, where each term is separated by an operator.
- An equation is a statement that two expressions are equal, indicated by =
- An identity is an equation which is always true, regardless of the values substituted in.
- A formula is a mathematical rule or relationship connecting two or more variables.
Vocabulary To Learn
- Term: A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –
- Expression: Expressions contain one or more terms, where each term is separated by an operator.
- Equation: An equation is used to show 2 expressions that are equal to each other.
- Identity: An identity is an equation that holds true for all values of the variables. The symbol ≡ is used to show two expressions are equivalent and form an identity.
- Formula: A formula is a rule linking sets of physical variables in context.
Common Mistakes To Avoid
- Pupils can think the formula for the number of days in a week is w=7d because a week has seven days.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A single number or letter, or the product of numbers and/or variables. An expression contains one or more terms, where each term is separated by an operator.
2. Use this key word in a maths sentence and explain it clearly. 'Term'
A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –. 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 think the formula for the number of days in a week is w=7d because a week has seven days. Correction: Pupils should always write down exactly what the letter is representing. E.g. 'the number of days' and 'the number of weeks'. Then think about what calculation they are doing. 'To find the number of days I multiply the number of weeks by 7'. d=7w.
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 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
- 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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