Algebraic Manipulation
Overview
This half term focusses on building on learning from Year 8 with expanding and factorising expressions and work with algebraic conventions to develop conceptual understanding of the distributive law with double brackets and quadratic expressions. The links between area and expanding expressions are also explored and fraction arithmetic is revised and extended to include algebraic fractions.
*Lessons 12 and 15 may be used to recap the 4 rules of fractions. You could use one or more of the lessons from Year 7 Spring 2 depending on the students’ understanding which can be assessed using the Exit Ticket from Lesson 11.
Building on
Arithmetic with directed number and fractions (KS2 & Year 7)
Expanding and factorising expressions (Year 8)
Collecting like terms and simplifying algebraic expressions (Year 7)
Area of 2D shapes (Year 7 & Year 8)
Powerful Knowledge
- Expand and simplify two or more brackets
- Factorise quadratic expressions with a = 1 and a > 1
- Recognise and factorise expressions using the difference of two squares
- Simplify algebraic fractions by factorising
- Multiply and divide algebraic fractions
- Add and subtract algebraic fractions
Lesson Resources
Lesson resources detail the consistent methods and representations used within this half term.
| Lesson 1 | The distributive law |
| Lesson 2 | Expanding double brackets |
| Lesson 3 | Expanding double brackets including negatives |
| Lesson 4 | Using identities to expand brackets |
| Lesson 5 | Factorising (positive terms) |
| Lesson 6 | Factorising problems |
| Lesson 7 | Factorising using the difference of two squares |
| Lesson 8 | Factorising harder quadratics |
| Lesson 9 | Consolidating factorising quadratics |
| Lesson 10 | Cancelling algebraic fractions 1 |
| Lesson 11 | Cancelling algebraic fractions 2 |
| Lesson 12* | Recap of multiplying and dividing fractions |
| Lesson 13 | Multiplying algebraic fractions |
| Lesson 14 | Dividing algebraic fractions |
| Lesson 15* | Recap of adding and subtracting fractions |
| Lesson 16 | Finding an algebraic LCM |
| Lesson 17 | Adding and subtracting algebraic fractions 1 |
| Lesson 18 | Adding and subtracting algebraic fractions 2 |