Year 8 curriculum
Algebra

Extend and apply the distributive law to the expansion of algebraic expressions

Factorise algebraic expressions by identifying numerical factors

Simplify algebraic expressions involving the four operations
Assumed knowledge:
Basic whole number operations
Operations of directed numbers
Order of operations (BOMDAS)
Writing simple expressions
Identifying like terms
Simplifying fractions
Identifying HCF
Common misconceptions:
Not understanding/recognising a number followed by a letter means multiplication
(e.g. 2b means 2×b not 2+b)
Collecting unlike terms (e.g. 2a+3b=5ab), as the result of the above misconception.
Confusing laws associated with directed numbers. That is, applying laws associated
with multiplication and division, to addition and subtraction. (E.g -2 + 4 = -6)
Key terminology:
Variable
Unknowns
Coefficient
Constant
Term
Like terms
Expression
Formula
Substituting
Simplifying
Expanding
Distributive/associative/commutative/identity/inverse law
Factorising
Key understanding:
A variable is a letter or symbol that is used in place of a number.
Variables may represent a single number, or they may be used to show a
relationship between two or more numbers.
When writing expressions with variables, it is important to remember the following
points: (a) The multiplication sign is omitted.
(e.g. 8n means ‘8 x n’ and 12ab means ‘12
x a x b’)
𝑦
(b) The division sign is rarely used. (e.g. y ÷ 6 is shown as 6 )
Replacing a variable with a number is called substitution.
When substituting into an expression with brackets, remember to place a
multiplication (x) sign next to the brackets.
Use directed number laws where appropriate
When simplifying expressions, we can collect (add or subtract) only like terms.
Like terms are terms that contain the same variable parts.
When multiplying variables:
(a) the order is not important. For example, d x e = e x d.
(b) place the numbers at the front of the expression and leave out the x sign.
When dividing variables, rewrite the expression as a fraction and simplify it by
cancelling.
When the same variable appears on both the top and bottom lines of the fraction, it
may be cancelled.
Removing brackets from an expression is called expanding the expression.
The rule that is used to expand brackets is called the Distributive Law.
After expanding brackets, collect any like terms.
Factorising is the opposite process to expanding.
Factorising a number or expression involves breaking it down into smaller factors.
To find the highest common factor (HCF) of algebraic terms, follow these steps. (a) Find the highest common factor of the number parts.
(b) Find the highest common factor of the variable parts.
(c) Multiply these together.
To factorise an expression we place the highest common factor of the terms outside
the brackets and the remaining factors for each term inside the brackets.
Key skills:
Observe number patterns and discover the rules by which a pattern is produced.
Use variables in formulas to show the rules for number patterns.
Recognise that multiplication happens when a letter/s immediately follows a
number.
Always place variables after their coefficients.
Always write variables in alphabetical order (e.g. 2dba should be written as 2abd)
Evaluate an expression by substituting known values for variables in it.
Simplify expressions by adding or subtracting like terms.
Expand factorised algebraic expressions using the distributive law.


a(b + c) = ab + ac.
a(b – c) = ab – ac.
Use the associative law for addition and multiplication when necessary.


(a + b) + c = a + (b + c) = a + b + c.
(ab)c = a(bc) = abc.
Use the commutative law for addition and multiplication when necessary.


a + b = b + a.
ab = ba.
Use the identity law for addition and multiplication when necessary.


x+0=0+x=x
xX1=1Xx=x
Use the inverse law for addition and multiplication when necessary.


x + -x = -x + x = 0
1 1
xXx=𝑥Xx=1