# Algebra

## Activities

Think of a Number

Ten students think of a number then perform various operations on that number. You have to find what the original numbers were.

Algebraic Notation

Simplification using the normal conventions of algebra.

Writing Expressions

Listen to the voice saying the algebraic expression then write it in its simplest form.

Function Builder

An interactive function machine for patterns, numbers and equations.

BIDMAS

A self marking exercise testing the application of BIDMAS, an acronym describing the order of operations used when evaluating expressions.

BIDMAS Game

An online interactive game celebrating the order of mathematical operations.

Online Psychic

Let the psychic read the cards and magically reveal the number you have secretly chosen. What is the mathematics that makes this trick work?

Clouds

Can you work out which numbers are hidden behind the clouds in these calculations?

Algebra Pairs

The classic Pelmanism or pairs game requiring you to match equivalent expressions.

Algebragons

Find the missing expressions in these partly completed algebraic arithmagon puzzles.

Connecting Rules

If you are given the values of x and y which of these equations is correct?

Substitution

Substitute the given values into the algebraic expressions.

Collecting Like Terms

Practise your algebraic simplification skills with this self marking exercise.

Stable Scales

Ten balance puzzles to prepare you for solving equations.

Equations

A series of exercises, in increasing order of difficulty, requiring you to solve linear equations. The exercises are self marking.

Nevertheless

Players decide where to place the cards to make an equation with the largest possible solution.

Old Equations

Solve these linear equations that appeared in a book called A Graduated Series of Exercises in Elementary Algebra by Rev George Farncomb Wright published in 1857.

Brackets

Expand algebraic expressions containing brackets and simplify the resulting expression in this self marking exercise.

Changing The Subject

Rearrange a formula in order to find a new subject in this self marking exercise.

Words and Concepts

Fill in the missing words to show an understanding of the vocabulary of equations, inequalities, terms and factors.

DiceGebra

An online board game for two players evaluating algebraic equations and inequalities.

Algebraic Perimeters

Questions about the perimeters and areas of polygons given as algebraic expressions.

Matchstick Patterns

Create a formula to describe the nth term of a sequence by examining the structure of the diagrams.

Missing Lengths

Find the unknown lengths in the given diagrams and learn some algebra at the same time.

Algebra In Action

Real life problems adapted from an old Mathematics textbook which can be solved using algebra.

Superfluous

Find a strategy to figure out the values of the letters used in these calculations.

Lemon Law

Change the numbers on the apples so that the number on the lemon is the given total.

Solve To Find Fractions

Find the value of the unknown in each of these linear equations. All of the answers are fractions

Algebraic HCF

Exercises providing practice finding the highest common factor of algebraic expressions.

Algebraic LCM

Exercises providing practice finding the lowest common multiple of algebraic expressions.

Factorising

Practise the skills of algebraic factorisation in this structured online self marking exercise.

Solve these quadratic equations algebraically in this seven-level, self-marking online exercise.

Completing the Square

Practise this technique for solving quadratic equations and analysing graphs.

Identity, Equation or Formula?

Arrange the given statements in groups to show whether they are identities, equations or formulae.

Graph Equation Pairs

Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.

Inequalities

Check that you know what inequality signs mean and how they are used to compare two quantities. Includes negative numbers, decimals, fractions and metric measures.

Linear Programming

A selection of linear programming questions with an interactive graph plotting tool.

Formulae to Remember

The traditional pairs or pelmanism game adapted to test recognition for formulae required to be memorised for GCSE exams.

Recurring Decimals

Change recurring decimals into their corresponding fractions and vica versa.

Where am I with Algebra?

Find out how developed your algebra skills are and then take them to the next level.

Simultaneous Equations

A self-marking, multi-level set of exercises on solving pairs of simultaneous equations.

Pascal's Triangle

Get to know this famous number pattern with some revealing learning activities

Substitution Sort

Order the algebraic expressions according to their value with the given substitution.

Algebraic Fractions

A mixture of algebraic fraction calculations and simplifications.

Equations with Fractions

Practise solving linear equations that contain fractions in this multi-level exercise.

Iteration

Find approximate solutions to equations numerically using iteration.

Functions

An online exercise on function notation, inverse functions and composite functions.

Partial Fractions

Exercises on mastering the art of partial fraction decomposition.

Parametric Equations

Develop the skills required to manipulate a set of equations involving a paramater.

Binomial Theorem

Exercises in the process of expanding powers of binomial expressions and finding specific coefficients.

Polynomial Division

Practise dividing one algebraic expression by another in this set of exercises.

## Investigations

Function Builder

An interactive function machine for patterns, numbers and equations.

Steps

Investigate the numbers associated with this growing sequence of steps made from Multilink cubes.

Lamp Posts

What is the greatest number of lamp posts that would be needed for a strange village with only straight roads?

Crossing the River

Two men and two boys want to cross a river and they only have one canoe which will only hold one man or two boys.

Calendar Maths Investigation

Investigate the connection between the numbers in a T shape drawn on this month's calendar.

## Videos

This is the main Transum help video on Algebra.

BIDMAS Video

A reminder of the order of operations often referred to as BIDMAS, BODMAS or PEMDAS.

Substitution Video

Lots of examples of substituting values into algebraic expressions. This video is to help you do the online, self-marking exercise.

Collecting Like Terms Video

If you have forgotten what collecting like terms means watch this video for a quick refresher.

Brackets Levels 1 and 2

Learn how to remove brackets from simple algebraic expressions. This video is to help you do the online, self-marking exercise.

Brackets Levels 3 to 5

Learn how to multiply the terms inside a pair of brackets by the term outside. This video is to help you do the online, self-marking exercise.

Brackets Levels 6 to 8

Expand a pair of brackets using the clown's face method. This video is to help you do the online, self-marking exercise.

Brackets Levels 9 and 10

The final video showing how algebraic expressions containing brackets can be simplified.

Factorising Video

A reminder of how to factorise an algebraic expression. This video is to help you do the online, self-marking exercise.

New Way to Solve Quadratics

A computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations.

Learn the common methods of solving quadratic equations by factorising and by using the quadratic formula.

A song from Math Upgrade dot com.

Equations with Fractions Video

If you have learnt how to solve linear equations the next step is to solve equations with fractions.

Binomial Theorem Video

You may have learnt about the binomial expansion in class some time ago so here's a reminder to bring you up to speed.

## Visual Aids

Online Psychic

Let the psychic read the cards and magically reveal the number you have secretly chosen. What is the mathematics that makes this trick work?

Substitution Examples

A projectable set of animated examples to help prepare pupils to do the Substitution online exercise.

eQuation Generator

An unlimited supply of linear equations just waiting to be solved. Project for the whole class to see then insert the working in your own style.

How old was Diophantus?

An ancient riddle which can be answered by solving an equation containing fractions.

## Starters

Add up a sequence of consecutive numbers. Can you find a quick way to do it?

Arithmagons
This lesson starter requires pupils to find the missing numbers in this partly completed arithmagon puzzle.

BTS
You have four minutes to write down as many equations as you can involving B, T and S.

Cars
Calculate the total cost of four cars from the information given.

Chin-Ups
Work out the number of chin ups the characters do on the last day of the week give information about averages.

Christmas Presents
Work out the total cost of five Christmas presents from the information given.

Connecting Rules
Give 20 rules connecting x and y given their values.

Giraffe
The height of this giraffe is three and a half metres plus half of its height. How tall is the giraffe?

Half Hearted
Find the number which when added to the top (numerator) and bottom (denominator) of each fraction make it equivalent to one half.

Khmer's Homework
Check a student's homework. If you find any of the answers are wrong write down a sentence or two explaining what he did wrong.

Know Weigh
Find the weight of one cuboid (by division) of each colour then add your answers together.

Lemon Law
Change the numbers on the apples so that the number on the lemon is the given total.

Less Than
This mathematics lesson starter invites pupils to interpret a three part algebraic inequality.

Light Shopping
A lamp and a bulb together cost 32 pounds. The lamp costs 30 pounds more than the bulb. How much does the bulb cost?

Lost Sheep
Which algebraic expression is the odd one out?

Missing Lengths
Introduce linear equations by solving these problems about lengths.

Mystic Maths
Work out why subtracting a two digit number from its reverse gives a multiple of nine.

Negative Vibes
Practise techniques for answering questions involving negative numbers.

Planet Numpair
The sum and product are given, can you find the two numbers?

PYA
You have four minutes to write down as many equations as you can involving the given letters.

Pyramid Puzzle
Arrange numbers at the bottom of the pyramid which will give the largest total at the top.

Rabbits and Chickens
There are some rabbits and chickens in a field. Calculate how many of each given the number of heads and feet.

Rail Weigh
Use the weights of the trains to work out the weight of a locomotive and a coach. A real situation which produces simultaneous equations.

Refreshing Revision
It is called Refreshing Revision because every time you refresh the page you get different revision questions.

Same Same
A problem involving two people's ages which can be solved using algebra.

Santa's Sleigh
Work out the number of clowns and horses given the number of heads and feet.

Sea Shells
A question which can be best answered by using algebra.

Simultaneous Occasions
A problem which can best be solved as a pair of simultaneous equations.

Stable Scales
Solve these balance puzzles by taking the same away from both sides. An introduction to linear equations.

Sum of the Signs
Each traffic sign stands for a number. Some of the sums of rows and columns are shown. What numbers might the signs stand for?

Summer Holidays
How many children and how many donkeys are on the beach? You can work it out from the number of heads and the number of feet!

Think Back
A problem which can be answered by forming an algebraic equation then solving it.

THOAN
THOAN stands for 'Think of a number' and there are four randomly generated THOAN puzzles to solve.

Ticker News
A Think Of A Number problem presented as a news ticker.

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Teachers might find the complete Algebra Topic List useful.

Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas.

If this topic were split into four sub topics they might be:

Creating and simplifying expressions;
Expanding and factorising expressions;
Substituting and using formulae;
Solving equations and real life problems;

This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".

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