YEAR 8 MATHS FOCUS

When evaluating expressions, there should be an explicit direction to replace the pronumeral with the number to ensure that full understanding of notation occurs.

The meaning of the imperatives ‘expand’, ‘remove the grouping symbols’ and ‘factorise’ and the expressions ‘the expansion of’ and ‘the factorisation of’ should be made explicit to students.

substitute into algebraic expressions and evaluate the result

calculate and compare the values of x^2 for values of x with the same magnitude but opposite sign (Reasoning)

generate a number pattern from an algebraic expression, eg 

expand algebraic expressions by removing grouping symbols, eg

 $\begin{array}{cc}3\left(a+2\right)& =3a+6\end{array}$

$\begin{array}{c}\\ -5\left(x+2\right)& =-5x-10\end{array}$

$\begin{array}{cc}a\left(a+b\right)& =a^2+ab\end{array}$

• connect algebra with the distributive property of arithmetic to determine that $a\left(b+c\right)=ab+ac$ (Communicating)

factorise a single algebraic term, eg

 $6ab=3\times 2\times a\times b$

factorise algebraic expressions by finding a common numerical factor, eg 

$\begin{array}{cc}6a+12& =6\left(a+2\right)\end{array}$

$\begin{array}{cc}-4t-12& =-4\left(t+3\right)\end{array}$

check expansions and factorisations by performing the reverse process (Reasoning)

factorise algebraic expressions by finding a common algebraic factor, eg 

$\begin{array}{cc}{x}^2-5x& =x\left(x-5\right)\end{array}$

$\begin{array}{cc}5ab+10a& =5a\left(b+2\right)\end{array}$