# The Grammar of Algebra This block introduces pupils to **algebraic thinking**, hence its title ‘The Grammar of Algebra’ rather than just Algebra 1. Formal methods of solving equations etc. come in later blocks. This block seeks to establish the basics, introduce pupils to the key terms and notation and establish some ways of working. It is designed to build on the limited algebra the pupils will have encountered in primary school. A key idea to establish is that **algebra can be used to generalise**. Hence we can move from showing a numerical manipulation, to a placeholder, to an algebraic representation. Some examples: $3(2+5)≡3×2+3×5$ $5(▭ +4)≡5▭ +20$ $\frac{1}{2} (x + 12) \equiv \frac{1}{2} x + 6$ Throughout this block, decimals, fractions and negatives should be mixed in as appropriate. This does not entail getting into lots of arithmetic with these types of number – that comes later. However, pupils should be able to apply simple calculations to these numbers, for example $\frac{1}{2}\times15$ or $-8 - 10$.