9 Autumn 1

Algebraic Manipulation


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 2Expanding double brackets
Lesson 3 Expanding double brackets including negatives
Lesson 4 Using identities to expand brackets
Lesson 5Factorising (positive terms)
Lesson 6 Factorising problems
Lesson 7Factorising using the difference of two squares
Lesson 8Factorising harder quadratics
Lesson 9Consolidating factorising quadratics
Lesson 10Cancelling algebraic fractions 1
Lesson 11Cancelling algebraic fractions 2
Lesson 12*Recap of multiplying and dividing fractions
Lesson 13Multiplying algebraic fractions
Lesson 14Dividing algebraic fractions
Lesson 15*Recap of adding and subtracting fractions
Lesson 16Finding an algebraic LCM
Lesson 17Adding and subtracting algebraic fractions 1
Lesson 18Adding and subtracting algebraic fractions 2

Half Term Check up