There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Algebra. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Algebra Starters:

Add 'em: 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.

Algebraic Product: Finding the value of the expression is easier than you think!

Coordinate Distance: Find k given that(-2,k) is 13 units away from (10,9)

Exceeds by 99: Find the number whose double exceeds its half by exactly 99.

Key Eleven: Prove that a four digit number constructed in a certain way will be a multiple of eleven.

Reverse Connection: Find a general rule for the difference between a two digit number and that same number with the digits reversed.

Simplify: Simplify an algebraic fraction

Square in Rectangle: Find the area of a square drawn under the diagonal of a rectangle

Two Equals One: What is wrong with the algebraic reasoning that shows that 2 = 1 ?

X Divided by 2Y: Why do different calculators not agree on the order of operations?

#### 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.

Transum.org/go/?to=thoan

### Curriculum for Algebra:

#### Year 6

Pupils should be taught to use simple formulae more...

Pupils should be taught to express missing number problems algebraically more...

Pupils should be taught to find pairs of numbers that satisfy an equation with two unknowns more...

#### Years 7 to 9

Pupils should be taught to 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
- ab in place of a ÷ b
- coefficients written as fractions rather than as decimals
- brackets more...

Pupils should be taught to substitute numerical values into formulae and expressions, including scientific formulae more...

Pupils should be taught to understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors more...

Pupils should be taught to 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 more...

Pupils should be taught to understand and use standard mathematical formulae; rearrange formulae to change the subject more...

Pupils should be taught to model situations or procedures by translating them into algebraic expressions or formulae and by using graphs more...

Pupils should be taught to recognise and use relationships between operations including inverse operations more...

Pupils should be taught to use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement) more...

Pupils should be taught to interpret mathematical relationships both algebraically and graphically more...

Pupils should be taught to interpret mathematical relationships both algebraically and geometrically. more...

#### Years 10 and 11

Pupils should be taught to simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by: factorising quadratic expressions of the form x2 + bx + c, including the difference of 2 squares; {factorising quadratic expressions of the form ax2 + bx + c} and by simplifying expressions involving sums, products and powers, including the laws of indices more...

Pupils should be taught to know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments {and proofs} more...

Pupils should be taught to where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of 2 functions as a ‘composite function’} more...

Pupils should be taught to identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square} more...

Pupils should be taught to solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph more...

Pupils should be taught to {find approximate solutions to equations numerically using iteration} more...

Pupils should be taught to translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or 2 simultaneous equations), solve the equation(s) and interpret the solution more...

Pupils should be taught to solve linear inequalities in 1 {or 2} variable {s}, {and quadratic inequalities in 1 variable}; represent the solution set on a number line, {using set notation and on a graph} more...

#### Years 12 and 13

Pupils should be taught to understand and use the binomial expansion of (a + bx)n for positive integer n; the notations n! and nCr link to binomial probabilities. Extend to any rational n, including its use for approximation more...

Pupils should be taught to solve equations approximately using simple iterative methods; be able to draw associated cobweb and staircase diagrams more...

Pupils should be taught to work with quadratic functions and their graphs. The discriminant of a quadratic function, including the conditions for real and repeated roots. Completing the square. Solution of quadratic equations including solving quadratic equations in a function of the unknown. more...

Pupils should be taught to solve equations using the Newton-Raphson method and other recurrence relations of the form xn+1= g(xn) Understand how such methods can fail more...

Pupils should be taught to solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions. Express solutions through correct use of 'and' and 'or', or through set notation. Represent linear and quadratic inequalities such as y > x + 1 and y > ax2 + bx + c graphically more...

Pupils should be taught to use numerical methods to solve problems in context more...

Pupils should be taught to manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the factor theorem. Simplify rational expressions, including by factorising and cancelling, and algebraic division (by linear expressions only) more...

Pupils should be taught to understand and use composite functions; inverse functions and their graphs more...

Pupils should be taught to decompose rational functions into partial fractions (denominators not more complicated than squared linear terms and with no more than 3 terms, numerators constant or linear) more...

#### International Baccalaureate

See the Number and Algebra sub-topics, syllabus statements, exam-style questions and learning resources for the IB AA course here.

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

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### Notes:

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".

### Algebra Teacher Resources:

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.

### 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.

Quadratic Equations: 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.

Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world.

### Algebra 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.

Featured Investigations

Painted Cube: The classic Painted Cube investigation. How many faces of the smaller cubes are painted blue?

### Algebra Videos:

Transum's Algebra Video

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.

Quadratic Equations Video: Learn the common methods of solving quadratic equations by factorising and by using the quadratic formula.

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.

### Algebra Worksheets/Printables:

Simultaneous Equations Extension Exercise: An exercise that appeared in an algebra book published in 1895. It starts with basic questions but soon gets tricky!

Links to other websites containing resources for Algebra are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

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### Other

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#### Polynomial Division

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

Transum.org/go/?to=pdv

### Teaching Notes:

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Wednesday, November 15, 2017

Fleur, New Zealand

Thursday, February 8, 2018

"Hi I love this thanks. Other things (or things I can't find!) are algebra with power to the power e.g. (2a^3)^2 and expanding brackets e.g. 4x(x+3), Thanks.

[Transum: Thanks for your comments Fleur. The first thing you mentioned can be found in the Indices exercise and the second thing can be found in the Brackets exercise. I hope that helps.]"

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