To generalise is to formulate a statement or rule that applies correctly to all relevant cases.

Checking understanding of expressions and equations

Maths

In this unit, pupils formalise algebraic notation and terms and begin to formulate an understanding of basic algebraic manipulation. This understanding is built upon in the future unit where pupils learn how to solve linear equations

In this unit, pupils learnt how to represent the structure of a problem with two unknowns using a diagram. This understanding is built upon in this unit and formalised

In this unit, pupils learn about generalisation and formal algebraic manipulation techniques such as substitution, collecting like terms and factorising.

Expressions and equations

An equation is used to show that one number or calculation is equal to another.

An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication.

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Securing understanding of expressions and equations

An unknown is a quantity that has a set value but it is represented by a symbol or letter.

A variable is a quantity that can take on a range of values.

Representing a generalised number

A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –

Expressions contain one or more terms, where each term is separated by an operator.

Mathematical conventions are notations or processes generally agreed upon.

Algebraic notation

An identity is an equation that holds true for all values of the variables. The symbol ≡ is used to show two expressions form an identity.

A formula is a rule linking sets of physical variables in context. The plural of formula is formulae.

A numerical coefficient is a constant multiplier of the variables in a term.

A constant is a term that does not change; it contains no variables.

Algebraic terminology

An unknown is a quantity that has a set value but is represented by a symbol or letter.

A variable is quantity that can take on a range of values.

Representing an unknown or variable

Generalised algebraic statements

Substitute means to put in place of another.  In Algebra, substitution can be used to replace variables with values.

Substituting particular values

Unitising means treating groups that contain, or represent, the same numbers of things as ‘ones’ or ‘units’.

Like terms are terms that have the same set of variables and corresponding exponents.

Like terms

Simplifying is to write an expression in the most efficient and compact form without affecting the value of the original expression.

Simplifying by collecting like terms

Multiplying an expression by a constant

Multiplying an expression by a term

To simplify an expression is to write it in a more efficient and compact form without affecting the value of the original expression.

Multiplying and simplifying with multiple expressions

An expression contains one or more terms where each term is separated by an operator.

Simplifying before multiplying with multiple expressions

A factor is a term which exactly divides another term.

The highest common factor of two or more terms which can be divided by all other possible common factors.

HCF is an abbreviation for highest common factor.

Factorise means to express a term as the product of its factors.

Highest common factor with algebraic terms

To factorise is to express a term as the product of its factors.

To fully factorise is to factorise to the point that remaining term or terms cannot be factorised any further.

Expressions and equations

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These lessons will be removed by end of Summer Term 2025.