Expressions, Equations and Formulae

Students continue to develop their algebraic reasoning skills by expanding a pair or brackets, factorising expressions, solving equations and formulae and changing the subject of a formula.

This unit takes place in Term 4 of Year 8 and follows on from setting up and solving equations.


Expressions, Equations and Formulae Lessons


Prerequisite Knowledge
  • Use and interpret algebraic notation, including:
    • ab in place of a × b
    • 3y in place of y + y + y and 3 × y
    • a2 in place of a × a, a3 in place of a × a × a; a2b in place of a × a × b
    • a/b in place of a ÷ b
  • coefficients written as fractions rather than decimals
  • simplify and manipulate algebraic expressions to maintain equivalence by collecting like terms

Key Concepts
  • Expanding brackets means to take out of brackets.  Factorising an expression is put in brackets.
  • When expanding brackets by a negative students often forget to multiply every term inside the bracket by the negative.
  • When factorising expressions the highest common factor of each term.  A common misconception is to only partially factorise. For example 9a + 12a2 is fully factorised as 3a(3 + 4a) not a(9 + 12a).
  • When solving equations involving brackets it is not always necessary to expand the bracket first.  It is often possible to divide both sides by the number outside the bracket.
  • To solve an equation you have to get the letter on its own on one side of the equation.  Begin by collecting like terms so all the letters are together.
  • When substituting known values into a formula remember to use the correct order of operations.  Students often make mistakes when substituting in negative and fractional numbers.
  • Formulae have an unknown on its own.  This is the subject of the formula.  Use the balance method and order of operations to change the subject of the formula.


Working mathematically

Develop fluency

  • Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
  • Substitute values in expressions, rearrange and simplify expressions, and solve equations

Reason mathematically

  • Identify variables and express relations between variables algebraically and graphically

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Algebra

  • Substitute numerical values into formulae and expressions, including scientific formulae;
  • Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors;
  • Simplify and manipulate algebraic expressions to maintain equivalence by:
    • Collecting like terms
    • Multiplying a single term over a bracket
    • Taking out common factors
    • Expanding products of two or more binomials
  • Understand and use standard mathematical formulae; rearrange formulae to change the subject
  • Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

 

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

Sharing an Amount to a Given Ratio

There are three common methods for sharing an amount to a given ratio.  Depending on the age group and ability range I am teaching I would choose one approach over the other two. The three methods are: Using fractions Unitary method Using a table In this blog I will demonstrate each of the three methods […]

Plotting Scatter Graphs and Understanding Correlation

To introduce plotting scatter graphs and understanding correlation I ask students to think about the relationships between different variables and to describe how they might be related. Here’s my starter activity which students discuss in pairs then present to me on mini-whiteboards. When the students have had time to discuss the matching pairs we talk […]

Plotting Quadratic Graphs on Cartesian Axes

In recent examiner reports it is noted how important it is for students to understand the properties of a parabola  when plotting quadratic graphs on Cartesian axes.  Students who have a secure understanding of parabolas can use them to correct miscalculated values in their table of results and are more likely to attain full marks […]