Unit 6: Equations, formulae, functions and identities
Level 1 & Level 2
Know subtraction is the inverse of
addition and use this to solve addition
and subtraction problems.
Level 3 (≈ Grade G/F)
Level 4 (Grade E)
Level 5 (≈ Grade D)
Check solutions by applying inverse
operations. Apply this to help solve one
and two step equations.
Understand halving is the inverse of
doubling.
Use basic function machines and apply
inverse operations to find missing
values.
Begin to use the BODMAS order of
operations.
Know and use the BODMAS order of
operations and understand that
algebraic operations follow the same
conventions.
Solve one step equations.
Use letter symbols to represent
unknown numbers or variables.
Begin to use simple formulae expressed
in words.
Construct, express in symbolic form, and
use simple formulae involving one or
two operations.
Use simple functions expressed in
words.
Use simple functions expressed in
symbols and develop to explore inverse
operations.
Use the knowledge that addition can be
done in any order.
Unit 6: Equations, formulae, functions and identities
Level 5 (≈ Grade D)
Level 6 (≈ Grade C)
Level 7 (≈ Grade B)
Level 8 and E.P. (≈ Grade A/A*)
Solve simple inequalities
Solve inequalities in two variables.
Check solutions by applying inverse operations.
Apply this to help solve one and two step
equations.
Know and use the BODMAS order of operations
and understand that algebraic operations follow
the same conventions.
Use letter symbols to represent unknown numbers
or variables.
Begin to distinguish the different roles of letter
symbols and algebraic conventions.
Distinguish between expressions, equations,
formulae, functions and identities.
Construct, express in symbolic form, and use
simple formulae involving one or two operations.
Substitute integers into simple formulae.
Change the subject of a formula.
Change the subject of a formulae and use to
calculate one variable, given the others, in
formulae such as V = r2h.
Simplify linear expressions.
Evaluate algebraic formulae by substituting
fractions, decimals and negative numbers.
Manipulate and factorise algebraic formulae,
equations and expressions.
Use the basic laws of indices.
Use simple functions expressed in symbols and
develop to explore inverse operations.
Use rules of indices for positive and negative,
integer and fractional values in simplifying
algebraic expressions.
Multiply a single term over a bracket and simplify
the result.
Multiply two expressions of the form (x + n) and
simplify the resulting quadratic expressions.
Multiply two linear expressions.
Factorise expressions by taking out a common
factor.
Start to use algebraic expressions for simple
proofs.
Know and use the identity for the difference of
two squares: a2 – b2= (a + b)(a – b)
Use functions expressed symbolically and find
their inverses using inverse operations.
Use algebraic methods to solve simultaneous
linear equations in two variables.
Use algebraic methods to solve simultaneous
equations in two variables where one equation is
linear and the other is quadratic.
Formulate and solve linear equations with integer
coefficients and involving brackets and unknowns
on both sides.
Solve simple non-linear equations by algebraic and
trial-and-improvement methods.
Solve quadratic equations.