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# Expressions, equations and inequalities

Created on 29 April 2015 by ncetm_administrator
Updated on 11 May 2015 by ncetm_administrator

# Algebra, expressions, equations and inequalities

A selection of resources.

Click on the title of the resource to expand the section for a description. Clicking on the green button within the description will take you to the resource. A summary of the topics covered is included in the blue box within the description.

## Equations (The National STEM Centre)

This resource is from the Centre for Innovation in Mathematics Teaching. It is designed to improve confidence in mathematics. Each section offers an overview of a particular topic and the key issues that will be covered, as well as highlighting some common misconceptions. Worked examples are provided to support learning and these are followed by focused exercises to practice skills. Activities to reinforce learning and offer extension opportunities are also supplied, as are topic related tests.

Topics include in part A:

• Changing the Subject
• Simplifying Expressions
• Simple Equations
• Solving Equations
• Trial and Improvement Method
• Simultaneous Linear Equations

and in part B:

• Monumental Towers
• Rectangular Grids
• Solving Equations
• Magic Squares
• Hill Walking
• Diophantine Equations

Topics: Changing the Subject, Simplifying Expressions, Simple Equations, Solving Equations, Trial and Improvement Method, Simultaneous Linear Equations, Diophantine Equations.

## Departmental Workshops - Algebra (NCETM)

This is a link to a set of departmental workshops from NCETM on number and algebra. The full range of workshops can be viewed by clicking on departmental workshops in the list on the right of the screen.

Topics: Deriving and rearranging formulae, inequalities, sequences, simultaneous equations, transformation of graphs, constructing equations

## Factorising the difference of two squares (BBC Bitesize)

This BBC Bitesize page covers factorising including the difference of two squares.

Topics: Difference of two squares

## Algebra (The National STEM Centre)

This resource is from the Centre for Innovation in Mathematics Teaching. It is designed to improve confidence in mathematics . Each section offers an overview of a particular topic and the key issues that will be covered, as well as highlighting some common misconceptions. Worked examples are provided to support learning and these are followed by focused exercises to practice skills. Activities to reinforce learning and offer extension opportunities are also supplied, as are topic related tests.

Topics include in part A

• Squares, cubes, Square Roots and Cube Roots
• Index Notation
• Factors
• Prime Factors
• Using Formulae
• Construct and Use Simple Formulae
• Substitution into Formulae
• Positive Coordinates
• Coordinates
• Applications of Graphs

and in part B

• Factors
• Sieve of Eratosthenes
• Last Digit
• Bode's Law
• Pendulums
• Coordinates
• Speed-Time Graph
• Area Under Speed-Time Graph: Distance

Topics: Index Notation, Using Formulae, Construct and Use Simple Formulae, Substitution into Formulae, Positive Coordinates, Coordinates, Applications of Graphs - Factors, Sieve of Eratosthenes, Last Digit, Bode's Law, Pendulums, Coordinates, Speed-Time Graph, Area Under Speed-Time Graph: Distance

## Solving equations (BBC Bitesize)

This section from BBC Bitesize provides a good overview of solving linear equations. Starting with equations requiring one operation to solve them, then moving on to two operations, equations with unknowns on both sides of the equal sign, equations with brackets, fraction coefficients and finally trial and improvement. There are tabs which link to; a video, an activity and a test, plus lots of interactive questions in the revise section.

Topics: Linear equations

## Solving Inequalities (Math is Fun)

This webpage from Maths is Fun looks at solving linear inequalities algebraically. There is a lot of information here so it may be best to tackle it in stages.

Topics: Linear inequalities

## Sorting Equations and Identities (Mathematics Assessment Resource Service)

This is one of many resources produced by the Shell Centre at the University of Nottingham for the MARS project in the USA. There are comprehensive teacher notes and excellent student resources. This lesson examines equations and identities using a sometimes true, always true, never true, activity. The teachers’ notes are particularly useful to anyone wishing to get to grips with the big idea(s) behind the topic.

Topics: Proof equivalent expressions

## Solving Quadratic Inequalities (Math is Fun)

This webpage from Maths is Fun looks at solving quadratic inequalities using graphical maths. This is a higher level topic which also features in A level mathematics. It builds on previous knowledge of quadratics including factorising and sketching the graphs of quadratics. There are links to other areas of the site to explain some of the terms and there are questions at the bottom of the page.

## Level 2 Algebra and graphs - Plumbers' prices (Nuffield Foundation)

This resource is from a collection of activities aimed at level 2 functional skills. You may need to scroll down the page a little to find the work called "plumbers prices". The resource includes teachers’ notes, students’ sheets, a spreadsheet and a powerpoint. This is a nice introduction to simultaneous equations.

Topics: Simultaneous equations

## Classifying Solutions to Systems of Equations (Mathematics Assessment Resource Service)

This is one of many resources produced by the Shell Centre at the University of Nottingham for the MARS project in the USA. There are comprehensive teacher notes and excellent student resources examining the concept of graphical solutions to simultaneous equations, including classifying the equations into three categories; infinite solutions, one solution, no solutions. The teachers’ notes are particularly useful to anyone wishing to get to grips with the big idea(s) behind the topic.

Topics: Simultaneous equations