Algebraic Expessions

Students learn how to write and simplify algebraic expressions using the correct notation.  Learning progresses from simplifying expressions by collecting like terms to factorising quadratics.

This unit takes place in Term 2 of Year 9 and is followed by solving equations.


Algebraic Expessions Lessons

Revision Lessons


Prerequisite Knowledge
  • use simple formulae
  • generate and describe linear number sequences
  • express missing number problems algebraically
  • find pairs of numbers that satisfy an equation with two unknowns

Success Criteria

use and interpret algebraic notation, including:

  • ab in place of a × b
  • 3y in place of 3 × y
  • a2 in place of a × a, a3 in place of a × a × a and a2b in place of a × a × b
  • a/b in place of a ÷ b
  • coefficients written as fractions rather than decimals
  • brackets

simplify and manipulate algebraic expressions by:

  • collecting like terms
  • multiplying a single term over a bracket
  • taking out common factors
  • expanding products of two or more binomials
  • factorising quadratic expressions of the form x2 + bx + c, including the difference of two squares
  • simplifying expressions involving sums, products and powers including the laws of indices


Key Concepts
  • Students need to appreciate that writing with algebra applies the rules of arithmetic to unknown numbers which are represented as letters.
  • It is important to define the difference between an expression, equation and formula.
  • The multiplication symbol is omitted when using algebraic notation to avoid confusion between and ×. Quotients are written as using simplified fractions.
  • Linear (x), quadratic (x2) and cube terms (x3)cannot be collected together.
  • Understanding quadratics in the general form (x2 + bx + c) helps to factorise and expand expressions.

Common Misconceptions
  • Students often forget ab = ba = a × b and b + a = + b when collecting like terms.
  • When multiplying out brackets students incorrectly forget to multiply the second term especially with negative products. E.g., 2(x + 5) = 2x + 10 and -2(x + 5) = -2x – 10
  • When factorising expressions a common misconception is to not fully factorise. E.g., 18x + 24y can be written as 9x + 12y
  • When expanding the product of two or more brackets students often incorrectly collect the like terms associated to the linear unknown.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

How to Solve Quadratics by Factorising

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

How Write 3 Part Ratios

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out.  This is presented to the class as they come into the lesson.    Writing Equivalent Ratios  A few students immediately go […]