Algebra

Activities

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

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

Algebraic Fractions
Activity
A mixture of algebraic fraction calculations and simplifications.

Algebraic Notation
Activity
Simplification using the normal conventions of algebra.

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

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

BIDMAS Game
Activity
An online interactive game celebrating the order of mathematical operations.

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

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

Changing The Subject
Activity
Rearrange a formula in order to find a new subject in this self marking exercise.

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

Collecting Like Terms
Activity
Practise your algebraic simplification skills with this self marking exercise.

Completing the Square
Activity
Practise this technique for use in solving quadratic equations and analysing graphs.

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

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

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

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

Function Builder
Activity
An interactive function machine for patterns, numbers and equations.

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

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

Identity, Equation or Formula?
Activity
Arrange the given statements in groups to show whether they are identities, equations or formulae.

Inequalities
Activity
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.

Iteration
Activity
Find approximate solutions to equations numerically using iteration.

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

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

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

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

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

Old Equations
Activity
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.

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

Pascal's Triangle
Activity
Get to know this famous number pattern with some revealing learning activities

Quadratic and Cubic Sequences
Activity
Deduce expressions to calculate the nth term of quadratic and cubic sequences.

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

Recurring Decimals
Activity
Change recurring decimals into their corresponding fractions and vica versa.

Simultaneous Solutions
Activity
Arrange the given pairs of simultaneous equations in groups to show whether they have no solution, one solution or infinite solutions.

Stable Scales
Activity
Ten balance puzzles to prepare you for solving equations.

Substitution
Activity
Substitute the given values into the algebraic expressions.

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

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

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

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

Investigations

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

Crossing the River
Activity
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.

Function Builder
Activity
An interactive function machine for patterns, numbers and equations.

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

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

Videos

This is the main Transum help video on Algebra.

New Way to Solve Quadratics
Activity
A computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations.

Quadratic Formula Song
Activity
A song from Math Upgrade dot com.

Simultaneous Equations (Elimination)
Activity
This video demonstrates how to solve simultaneous equations by elimination.

Simultaneous Equations (Substitution)
Activity
This video demonstrates how to solve simultaneous equations by substitution.

Visual Aids

eQuation Generator
Activity
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?
Activity
An ancient riddle which can be answered by solving an equation containing fractions.

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

Starters

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

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

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

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

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

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

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

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

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

Starter
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.

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

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

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

Starter
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?

Starter
Lost Sheep
Which algebraic expression is the odd one out?

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

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

Starter
Negative Vibes
Practise techniques for answering questions involving negative numbers.

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

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

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

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

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

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

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

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

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

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

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

Starter
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?

Starter
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!

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

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

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

84 items are currently in this category.

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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