# data[].attributes.attachment_link.readable_text
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.

Small images of these Starters :: Index of Starters

Algebra Advanced Starters:

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?
Index of Advanced Starters

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
- a ² in place of a × a, a ³ in place of a × a × a; a ²b in place of a × a × b
- a⁄ b 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 x ² + bx + c, including the difference of 2 squares; {factorising quadratic expressions of the form ax ² + 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 nC r 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 x n+1= g(x n) 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 > ax ² + 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...

Feedback:

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait:

"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset:

"A set of real life savers!!
Keep it up and thank you!"

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the i asp?ID_Top 'Starter of the Day' page by Ros, Belize:

"A really awesome website! Teachers and students are learning in such a fun way! Keep it up..."

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich:

"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

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 ex pressions;
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:

Sort alphabetically

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.

Algebraic Perimeters: Questions about the perimeters and areas of polygons given as algebraic 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 ex pressions.

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.

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.

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 use in 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.

Iteration: Find approximate solutions to equations numerically using iteration.

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.

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.

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

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.

Quadratic Formula Song: 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.

Search

The activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.

Other

Is there anything you would have a regular use for that we don't feature here? Please let us know.

# data[].attributes.attachment_link.keywords[]
maths numeracy starter mathematics math topics teacher

# data[].attributes.attachment_link.title
Algebra Lesson Starters and Online Activities

# data[].attributes.attachment_link.description
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.

# data[].attributes.attachment_link.readable_text
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 Factors. 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.

Factors Starters:

Abundant Buses: A game based around the concept of factors and abundant numbers.

Factuples: Spot the factors and the multiples amongst the numbers in the grid.

Flabbergasted: If each number in a sequence must be a factor or multiple of the previous number what is the longest sequence that can be made from the given numbers?

Four Factors: Find four single digit numbers that multiply together to give 120. How many different ways are there of answering this question?

Hotel Digital: A puzzle about the lifts in a hotel which serve floors based on the day of the week.

Verruca Value: The Verruca Value of a word is the number of vowels multiplied by the number of consonants. How many words can you find with Verruca Value of 24?

Small images of these Starters :: Index of Starters

Factors Advanced Starters:

Back To The Factory: Find all the numbers below 1000 which have exactly 20 factors

Calendar Riddle: Work out the date of my birthday from the clues in rhyme.

Divisible by 11: Can you prove that a three digit number whose first and third digits add up to the value of the second digit must be divisible by eleven?

HCF and LCM given: If given the HCF, LCM and the smaller of two numbers can you find the other?

Nine Digit Numbers: How many different nine digit numbers are their that contain each of the digits from one to nine?

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

Weather Reports: Which five different integers multiply together to give 12?

Zero Even: Prove that zero is an even number.
Index of Advanced Starters

Suggested

Times Square

Practise your times tables with this self-checking multiplication grid.

The short web address is:

Transum.org/go/?to=timessquare

Curriculum for Factors:

Year 5

Pupils should be taught to identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers more...

Pupils should be taught to know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers more...

Pupils should be taught to establish whether a number up to 100 is prime and recall prime numbers up to 19 more...

Pupils should be taught to solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes more...

Year 6

Pupils should be taught to use common factors to simplify fractions; use common multiples to express fractions in the same denomination more...

Pupils should be taught to identify common factors, common multiples and prime numbers more...

Years 7 to 9

Pupils should be taught to use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property more...

Feedback:

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset:

"A set of real life savers!!
Keep it up and thank you!"

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich:

"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the s /Indice 'Starter of the Day' page by Busolla, Australia:

"Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students - all trying to reach their highest level and competing with their peers while also learning. Thank you very much!"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales:

"Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!"

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the i asp?ID_Top 'Starter of the Day' page by Ros, Belize:

"A really awesome website! Teachers and students are learning in such a fun way! Keep it up..."

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Notes:

A factor is a whole number that divides exactly into another whole number. We say the first number is a factor of the second number. Prime numbers only have two factors, one and themselves.

After becoming familiar with times tables pupils then practise using this knowledge by recognising factors of numbers. There are well known and some less well known divisibility tests that are of some use in solving more complex number problems.

Pupils need to know how to find the highest common factor (HCF) of two or more numbers either mentally or using a pen and paper strategy so that they can correctly manipulate fractions and algebraic expressions.

Factors Teacher Resources:

Divisibility Tests 2-12: A visual aid designed to be projected in the classroom. Here you can find the quick ways of telling whether a number is exactly divisible by the numbers two to twelve.

HCF and LCM Calculator: A demonstration of how to find the highest common factor (HCF or GCD) and the lowest common multiple (LCM) of two numbers.

Number Grids: Investigate the properties of number with these interactive number grids.

Prison Cell Problem: A number patterns investigation involving prisoners and prison guards.

Sieve of Eratosthenes: A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.

Factors Activities:

Connect 4 Factors: This a game for one or two players. The winner is the first to line up four numbers with a common factor.

Delightfully Divisible: Arrange the digits one to nine to make a number which is divisible in the way described.

Divisibility Test: Practise using the quick ways to spot whether a number is divisible by the digits two to nine.

Doughnut Dissection: A puzzle to find four different ways of making 900 by multiplying together three different numbers.

Factor Pairs: Find the factor pairs of the given numbers and arrange them in order.

Factor Trees: Create factor trees to find the prime factors of the given numbers.

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

Flabbergasted Game: This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.

HCF and LCM: Practise finding the highest common factor (H.C.F), sometimes called the greatest common divisor, and the lowest common multiple (L.C.M) of two numbers.

How Many Factors?: Work out the number of factors a number has then write them all as a list.

Number Grids: Investigate the properties of number with these interactive number grids.

Pick The Primes: Pick the prime fruit from the tree as quickly as possible. Practise to improve your personal best time.

Prime Labyrinth: Find the path to the centre of the labyrinth by moving along the prime numbers.

Prison Cell Problem: A number patterns investigation involving prisoners and prison guards.

Product Square: Arrange the given numbers in a three by three grid to obtain the diagonal, row and column products.

Satisfy: Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers.

Scallywags and Scoundrels: Arrange the scallywags and scoundrels on the chairs so that the numbers of any two sitting next to each other add up to a prime number.

Sieve of Eratosthenes: A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.

Square and Cube Roots: Find square roots and cube roots by first calculating the prime factorisation of a number.

Three Ways: Find three different ways of multiplying four different digits together to get the given target number. There are nine levels for this online challenge.

Threes and Fives: A game for two players who take turns to add a domino to the line in order to score threes and fives.

Times Square: Practise your times tables with this self-checking multiplication grid.

Factors Investigations:

Aunt Sophie's Post Office: Investigate the ways of making up various postage amounts using 3p and 8p stamps. An online stamp calculator is provided for you to check your working.

Factors Worksheets/Printables:

Divisibility Tests Worksheet: This worksheet contains a list of the divisibility tests along with a fill-in-the-table exercise.

Search

The activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.

Other

Is there anything you would have a regular use for that we don't feature here? Please let us know.

Suggested

Connect 4 Factors

This a game for one or two players. The winner is the first to line up four numbers with a common factor.

The short web address is:

Transum.org/go/?to=connect4

# data[].attributes.attachment_link.keywords[]
maths numeracy starter mathematics math topics teacher

# data[].attributes.attachment_link.title
Factors Lesson Starters and Online Activities

# data[].attributes.attachment_link.description
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 Factors. In the right column below are links to related online activities, videos and teacher resources.