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SSDD stands for Same Surface, Different Deep.

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SSDD stands for Same Surface, Different Deep.

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What are SSDD Problems? SSDD stands for Same Surface, Different Deep. I introduced SSDD problems in my first book, "How I wish I'd taught maths: Lessons learned from research,...

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Set of 365 tasks - one per day - Mix of different topic question for a quick recap of past concepts at 4 different levels

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The Corbettmaths 5-a-day for GCSE, Primary, Further Maths and more

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Omitting an additional step in each worked example allows pupils to build up to independent problem solving, having seen (and worked through) each solution step multiple times.

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(Skip to the resources by clicking here)

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Maths Venns is my collection of Venn Diagram activities covering many mathematical ideas. Students must think hard to find examples that meet different combinations of criteria in order to complete the diagram.

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Maths Venns is my collection of Venn Diagram activities covering many mathematical ideas. Students must think hard to find examples that meet different combinations of criteria in order to complete the diagram. Are some regions impossible to fill, or have students simply not found an example yet?

You can search for different topics using the Topics menus above, and you can find out more about Maths Venns on this page.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using these sequences effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the activities on the Maths Venns website are:

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Rich Venn Diagram maths activities from Craig Barton @mrbartonmaths

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Inquiry Maths https://www.inquirymaths.com/home/algebra-prompts/algebraic-fractions is a model of learning that encourages students to regulate their own activity while exploring a mathematical prompt (an equation, a statement or a diagram).

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Inquiry Maths is a model of learning that encourages students to regulate their own activity while exploring a prompt (an equation, statement or diagram). Inquiries involve questioning, conjecturing, generalising and proving and, when required, listening to or giving an explanation. In Inquiry

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Nrich Secondary links - Develop Mathematical Thinking and Problem solving skills 

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https://nrich.maths.org/teachers/secondary

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http://www.mmlsoft.com/index.php/products/tarsia - Download the software from this link

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arrow_back Back to Rich Tasks

Tarsia Jigsaws

On this page you will find links to all my Tarsia files, as well as hints and tips for making the most out of this amazing piece of free software.

Contents

Please, please, please do not email me if you have any problems with the Tarsia Jigsaw software. I did not create the software, I do not know how it works, I am not affiliated with it in any way, I am merely a teacher who has written lots of free jigsaws using it and wants to share them. Any technical problems, please contact the creators, Hermitech Laboratory, via their website here.

Here are the solutions to some of the most common problems:

I get a load of random code when I try to open a jigsaw

Have you actually downloaded the free Tarsia Jigsaw software? You can get it on the creator's website here.

I have the software, but the jigsaws won't open when I click on them via your website

You can get it on the creator's website here.Try clicking on them, choosing Save instead of Open, and then opening them directly in the Tarsia Jigsaw software itself by going to File > Open.

That still did not work

Maybe try speaking to your tech people at work

I cannot display spaces between words on the jigsaw

On the Input screen, go to Style, and choose Text

I have a load of Tarsia Jigsaw files on my computer, but they won't open

Try opening the Tarsia Jigsaw software first, then opening to the jigsaws from within the programme itself by going to File > Open.

Is there a version of Tarsia available for the Mac?

I do not think so, but again, please contact the creators.

I cannot add images to my Tarsia Jigsaws

It is possible to do this, but it is a bit tricky. This blog post should help

What are Tarsia Jigsaw files?

Tarsia is a piece of freely available software which allows teachers to create a wide range of jigsaws, domino and follow-me activities very easily.

Why are Tarisas so great?

I have been using Tarisa jigsaws for the past 11 years of my teaching because:
- You can easily create wide range of activities, including jigsaws of various shapes and sizes, dominoes, matching rectangular cards and follow-me cards.
- The teacher does not need to spend time cutting up the jigsaw as the software automatically jumbles up the pieces of the jigsaw in the Output section, thus allowing the teacher to simply print out a copy and hand it to the students to cut out and assemble
- Key Point: There are plenty of ways of adding richness and challenge to Tarsia jigsaw activities, as I explain in the "Twists" section below.

How can I get the software?

The software is available to download for free from via this link
Scroll down to the bottom of the page for "Formulator Tarsia Installation Package"
If that link isn't working, then you can also get the installer here

The license of use is here
And here is a comprehensive user manual
Screen shots and instructions are available via this link

Having selected what type of activity they wish to create, teachers use the Input screen to input as many questions and answers as they like. The software has a built-in equation editor to ensure that all mathematical symbols and expressions are available, and supports the importing of images. Teachers can then check their answers on the Table screen, before printing out the jumbled up version for the students. They can then either print out the solution or project it onto their interactive whiteboard for the students to check their answers. Completed jigsaws also make nice classroom displays. Please see the bottom of this page for a note about images in Tarsia Jigsaws.

Tarsia Jigsaw activities are incredibly versatile, and can be used for many mathematical topics and all ability levels. They promote group work and discussion, and provide a nice alternative to doing questions out of a textbook. They are an ideal way to revise or consolidate a topic. Furthermore, they can be differentiated - by writing questions of varying difficulty, you can ensure that all students can access some of the activity whilst also providing extension material for the most able.

With a bit of tweaking, Tarsia puzzles can be made even more challenging, pushing your students to think even more about the topic in hand. Ideas include:

* Tarsia: Convince Me - in my opinion, this is the ultimate way to use Tarsia Jigsaw activities! They work like this:
- Create a Tarsia (or adapt an original one) so that it contains (at least) 5 mistakes, and ensure these mistakes highlight common misconceptions students have with a particular topic
- Print off the solution slide and give it to your students (much less photocopying and no needing for scissors!)
- The student must find (at least) 5 incorrectly matched up elements, convince you that each one is incorrect explaining the mistake that has been made, and then decide what the answer should have been
- Better still, include a ? instead of an answer and challenge students to replace the ? with the correct answer
- Include a ?? instead of a question, and challenge students to come up with lots of different questions to replace ?? that could give the answer. A selection of these questions can then be given to other students to use as a rich, challenging, pupil-created homework.
This can all be set out beautifully in their exercise book, providing a challenging, rich, worthwhile activity :-)
Click here for an example of a Tarsia Convince Me activity on factors, multiples and primes

*"No Answers" Worksheet - one criticism of Tarsia is that once the students have completed the puzzle they have no record/evidence of their work and also no revision material. Gill Hillitt has a solution... simply print out the "Table" page and blank out the answers. Hand this out to the students alongside the jigsaw and they can fill in their answers here as they go. When the jigsaw has been completed, they then have a lovely record of their work. Nice.
Top Tip: To blank out answers, delete them on the input screen, but add a space (press the space-bar), otherwise you may find the answer returns!

* Supplementary Sheets - make Tarsia jigsaws much more versatile with supplementary sheets. These may involve pictures of statistical diagrams to interpret, or even secrets codes to reveal the mystery word. There are examples of all of these in my Tarsia jigsaw collection.

* Distractors - when creating (or adapting) a Tarsia and you are on the Input screen, there are tabs labelled "d1", "d2", etc. Here you can place "distractors" - i.e. a question that does not match to any of the answers, or an answer that does not match to any question. These will always land on the outside of the final, successfully completed jigsaw, and provide an excellent extra challenge for students.

* Missing Answers - choose a couple of the cards and leave the answer (or even the question!) blank so students have to fill them in for themselves

* Deliberate Mistakes - announce at the start of the activity that you have made two mistakes (or better still, a mystery number of mistakes!) in the puzzle and students must assemble the jigsaw, identify the mistakes, and correct them

* Non-unique Solutions - have a couple of the answers the same, so students have to use logic and thinking skills to assemble the entire puzzle correctly

* Order of Difficulty - when students have finished the puzzle, get them to select the three most difficult pieces to match-up and explain what makes them tricky

* Revision Lessons - get students to create Tarsia puzzles themselves on difficult topics (it is a free piece of software so can be installed on all school computers) and challenge each other to solve them

1. Leaving spaces between text

You may have discovered that if you try to type words into the Tarsia jigsaw input screen (e.g. "I Love Maths"), when you come to print the jigsaw, they appear all together, with no spaces, like this: "ILoveMaths". To solve this, you need to go to Style in the top toolbar, and change from Math to Text. That should solve the problem.

2. To blank out answers

Very useful for creating worksheets as discussed above. Simply delete answers on the input screen, but add a space (press the space-bar), otherwise you may find the answer returns!

3 . Handling images in Tarsia and sharing them:

Good news - you can insert images into Tarsia. Bad news - Tarsia does not insert an image instead it inserts a link to the absolute address of the image. This means that if the images are then moved the jigsaw will lose contact and you will end up with those annoying red rectangles.

This is fine if you are creating a jigsaw to be shared on a network, so long as you first put all the images you want to use where they can be accessed by everyone you want to share with. However, if you wish to simply copy a jigsaw which contains images, then not only do the images need to be copied to where they will be accessible but also all the links will need to be changed! Alas, I have found no way of getting around this. You can find more details on adding images to Tarsia courtesy of Alan Catley by clicking here.

However, there is an alternative! Once you have placed the images in your Tarsia, you can convert Output page(s) into a pdf. This will then retain all your images, enabling you to share the file much more easily. The downside is that you won't be able to edit the Tarisa as it will be locked in the pdf, but this might be an ideal solution to get round the image issue. A nice, free pdf converter is PrimoPdf.

Please Note: I have organised all my Tarsia Jigsaws for Key Stage 3 and GCSE so they are categorised under the relevant subject area. You can find them all under the Lessons section of the Topic you are looking up.

As ever, if you have any Tarsia jigsaws to share, please email me!

Additional Tarsia Jigsaw Bundles:
Tarsia GCSE Revision
These jigsaw files are proving immensely popular and extremely useful, so if you have any of your own jigsaw files which you would like to share, then please drop me an email at [email protected] . The more the merrier! Thank you...

Many thanks to the following people for kindly donating their jigsaws to the bundle:
Peter Brooks, Plant Hill Arts College, Manchester
Judith de Villiers, Folkestone Academy, Kent
Steve Wren, Comberton Village College, Cambridge
Nisha Ganatra, Lea Manor High School, Luton
Samantha Green, The Cheltenham Ladies College, Cheltenham
Susan Verity
John White, Secondary Maths Consultant, Swindon
Karen Walker, Poltair School, St. Austell
Jenny Andrews, Richard Hale School, Hertford
Sam Powell, Sheldon Heath Community Arts College, Birmingham
Nyima Drayang, Seaham School of Technology
William Leonard, Bullerswood, Bromley
Vikki Sutton, Holmesdale Technology College
Paul Tyreman
James Gatrell, St John Plessington Catholic College
Kevin Alderson, Newcastle College
Gill Hillitt, Joseph Chamberlain College, Birmingham
Sarah Pearson, Taipei Eurpoean School
Simon Young, Erith School
Steve Sherman and Pupils, Tytherington High School
Alan Catley

Your contributions are very much appreciated!

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arrow_back Back to Rich Tasks Tarsia Jigsaws On this page you will find links to all my Tarsia files, as well as hints and tips for making the most out of this amazing piece of free software. Contents Please, please, please do not email me if you have any problems with the Tarsia Jigsaw software.

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Short tasks to encourage application of Math knowledge in different real life contexts.

Tasks are divided into three classes - Novice, Apprentice and Expert. This is not a measurement of the difficulty of the content, but indicates the extent to which they require students to autonomously apply their mathematical knowledge: Novice tasks explicitly test particular items of content knowledge, Expert tasks are far less structured and require strategic problem-solving skills in addition to content knowledge. A “balanced diet” of Novice, Apprentice and Expert tasks is needed to properly assess the Mathematical Practices.

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Archimedes famously solved a problem for a King who thought his crown might be a fake.

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Explore a new concept while teacher tracks the progress and reads every students response for continuous and prompt feedback.

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Project Math - Inquiry and investigation into new concepts 

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Project Math - Inquiry and investigation into new concepts 

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Students independently explore the concepts and come to the conclusions about the concept

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PDST Post-Primary Maths | Junior Certificate

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Exam Solutions - Video of flip classroom and students to review concepts at home 

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Exam Solutions - Video of flip classroom and students to review concepts at home 

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Looking for reliable online Maths tutor in the UK? Our experienced tutors provide tailored, one-on-one support to help students of all levels achieve their academic goals.

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Transum - Starter activities + Self check practice - with increasing difficulty at each level 

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Transum - Starter activities + Self check practice - with increasing difficulty at each level 

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Good for differentiating class practice - Level 1 to Level 8 exercises

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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.

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.

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maths numeracy starter mathematics math topics teacher

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Algebra Lesson Starters and Online Activities

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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.

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Diagnostic questions - Short exit tickets or use as  for formative assessment of learning 

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Diagnostic questions - Short exit tickets or use as  for formative assessment of learning 

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Sign in with your Diagnostic Questions account or Google, Microsoft, Twitter or Facebook.

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Mathisfun - Summary of every concept with set of 10 questions at the end of summary

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Mathisfun - Summary of every concept with set of 10 questions at the end of summary

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Math explained in easy language, plus puzzles, games, worksheets and an illustrated dictionary. For K-12 kids, teachers and parents.

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Summary of topics along with the practice questions to assess understanding

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MathBitsNotebook - On-Line Study Resources for High School Mathematics

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On-Line Study Mathematical Resources for High School Students. NY Next Generation Standards and more, JrMath, Algebra 1, Geoemtry, Algebra 2, other levels to follow.

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NCTM - Engaging activities to explore and extend concepts deeper

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NCTM - Engaging activities to explore and extend concepts deeper

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As a new year school begins, NCTM is embracing the theme guiding our upcoming Annual Meeting- Creating Spaces for Change Through Community: It Starts with You-to support your mission of providing high-quality teaching and learning for every student. Use the tools and resources below to help inspire you to bring change in your classroom, your school, and to build deeper connections in your community.

Find a resource that was helpful? Have a technique that's working in your classroom? Share it on social media using the hashtag #NCTMBacktoSchool and help spread the word!

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Back to School - National Council of Teachers of Mathematics

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Welcome to another successful school year providing high-quality math instruction for each and every student in your classroom! Whether you embarked on the first day of class already or the new school year is still around the corner, we want you to be ready! Check out these NCTM resources to get you prepared.

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IM K-12 Math is a problem-based core curriculum designed to address content and practice standards to foster learning for all. Students learn by doing math, solving problems in mathematical and real-world contexts, and constructing arguments using precise language.

EdReports, a highly-regarded independent nonprofit that reviews K-12 instructional materials for standards alignment and quality, gave IM K-5 Math, IM 6-8 Math, and IM 9-12 Math its highest rating across all three gateways for focus, coherence, rigor, mathematical practices, and usability.

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Illustrative Mathematics | v.360 Curriculum

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Don steward - deeper thinking into the concepts 

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Don steward - deeper thinking into the concepts 

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ideas and resources for mathematics teachers of 10 to 16 year olds

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Starter activity based on the topic that you are teaching.

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The panel above is powered by the most wonderful GeoGebra software. Copyright © International GeoGebra Institute, 2013

Ideas for activities

Angles in a Triangle

Show that when you move the points of a triangle the angles always sum to 180 o

Angle in a Semicircle

Show that the angle drawn in at the circumference from either ends of the diameter is always 90 o.

Polygons

Make a poster showing the basic polygons and their names. For example

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Parallel Lines

Move intersecting parallel lines to show that alternate, vertically opposite and corresponding angles are always equal.

Tangram

Accurately construct the perfect Tangram puzzle after first calculating the required lengths and angles.

Rotational Symmetry

Triangle Centres

Research different ways of finding the centre of a triangle. Investigate the conditions under which at least two of the following coincide:

Centroid

Circumcenter

Incenter

Orthocenter

Unit Circle

Show the relationship between sine and cosine in a dynamic unit circle.

Transformations

Find the transform tools then make dynamic diagram showing what each type of transformation looks like.

Related activities

Getting started with GeoGebra Geometry

The helpful video above was made by Professor Caine

Close

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The panel above is powered by the most wonderful GeoGebra software. Copyright © International GeoGebra Institute, 2013 Angles in a Triangle Show that when you move the points of a triangle the angles always sum to 180 o Angle in a Semicircle Show that the angle drawn in at the circumference from either ends of the diameter is always 90 o.