## ALGEBRAIC TECHNIQUES

## OVERVIEW

Building on understanding of equivalence from Year 7, students will learn how to expand over a single bracket and factorise. All students will revisit and extend their knowledge of how to solve linear equations, now to include brackets and the unknown on both sides. Students will also understand how to solve formal inequalities for the first time, learning the meaning of a solution set.

Following this learners will look at sequences with more complex algebraic rules now that students are familiar with a wider range of notation.

Lastly learners will explore the ideas behind the addition and subtraction laws of indices which will be revisited when standard form is revisited when standard form is studied next term.

Medium term plan found here:

## BUILDING ON

Equivalence in Year 7

Collecting like terms

Solving one and two step equations

Working with directed numbers and fractions

Working with sequences

## POWERFUL KNOWLEDGE

- Form algebraic expressions
- Multiply single brackets, including collecting like terms
- Factorise single brackets
- Form and solve linear equations with brackets
- Understand and solve inequalities
- Solve equations and inequalities with the unknown on both sides
- Generate sequences given a rule in words
- Generate sequences given an algebraic rule
- Find the nth term of linear sequences
- Understand and use addition and subtraction law for indices
- Simplifying algebraic expressions by multiplying and dividing indices

**Brackets, equations and inequalities**

Lesson 1 – Forming Expressions

Lesson 2 – Expanding single brackets

Lesson 3 – Working with multiple single brackets

Lesson 4 – Expanding double brackets

Lesson 5 – Factorising single brackets

Lesson 6 – Solving equations with brackets

Lesson 7 – Understanding inequalities

Lesson 8 – Solving inequalities

Lesson 9 – Unknowns on both sides

Lesson 10 – Unknowns on both sides with brackets

**Sequences**

Lesson 11 – Generating sequences from words

Lesson 12 – Generating sequences from an algebraic rule

Lesson 13 – Finding the nth term of a linear sequence

Lesson 14 – Working with the nth term of a linear sequence

**Laws of Indices**

Lesson 16 – Manipulating expressions involving indices

Lesson 17 – Addition Law

Lesson 18 – Subtraction Law

Lesson 19 – Power of powers