About this unit
How does rewriting something in an equivalent form let us solve problems we could not solve before?
Sections in this unit
Factual
- How do the coefficients in a quadratic link to its factors?
- What has to be true before you can cancel in an algebraic fraction?
- How many solutions does a pair of linear equations have?
Conceptual
- Why do two unknowns need two equations?
- Why does rewriting an expression in an equivalent form make a problem easier?
- When is one method genuinely more efficient than another, rather than just more familiar?
Debatable
- Is there a best method for solving a system, or only a best method for this system?
- Does being able to check an answer matter as much as being able to find it?
Skills
Students should be able to:
- Select and apply an appropriate technique in an unfamiliar situation.
- Choose the most efficient method available and defend the choice against an alternative.
- Verify a result by substituting it back into the original conditions.
- Use correct notation and set out a solution as a sequence of justified steps.
- Identify and correct one’s own errors from feedback, and choose the next piece of practice accordingly.
How you are assessed
- Factorising quadratics task, Criterion B
- Systems of equations investigation, Criterion B
- Capture and recapture, Criterion D
- Cumulative summative test, Criteria A and C, with a retest
Before you start
Students arrive with:
- Solving linear equations in one unknown, including with the unknown on both sides.
- Expanding single and double brackets, recalled in Unit 1 and used throughout.
- Factorising monic quadratics by splitting the middle term, met in Year 9 and reviewed here.
- Arithmetic with numerical fractions, and highest common factor.
- From Unit 2, index laws and surds, which now appear inside equations and fractions.
- From Unit 1, sequences, which continue to appear in the do-now routines.
Check what you remember
Expanding a single bracket
Expanding double brackets
Expanding three (or more) brackets