For Valentine’s Day…Make Linked Möbius Hearts

The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  We even have 9 Maths skills you need to win the Great British Bake Off!

careers-heartsFor Valentine’s Day, have a look at this post from Maths Careers with instructions on how to make this wonderful pair of linked Möbius hearts.

If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked  as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….
use-to-create-mobius-heartsNote the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper. See Valentine’s Day for the Desmos details.

To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white spce at the end – the picture here has been made using strips 10 cells long.

Valentine’s Day …

It’s that time of year again – save your money and send your loved ones (or anybody!) a math-o-gram!

..and see also “Make Linked Möbius  Hearts“.

Click on the image and move that slider!

Click on the image and move that slider!

Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!

Valentine’s Day seems an appropriate time to express love for Desmos!
Geeky people you could even use the Desmos API …

Remining with the loving theme you can also express your feelings for WolframAlpha!

I Love YOU


Valentine Relay – Chris Smith

For some Valentine class activities, try the Valentine Relay from Chris Smith and note all the other relays in this excellent set of resources. You can find more excellent resources from Chris on TES and follow him on Twitter here.

Transum Valentine Puzzle
and here’s a Valentine logic starter from Transum.


Low Stakes Testing in the Mathematics Classroom

To download:
Low Stakes Testing in the Mathematics Classroom (PowerPoint File, takes a few moments to download)

Low Stakes Testing in the Mathematics Classroom (pdf)

Slides from the BERA Conference, Learning from the classroom – Practitioner research in mathematics education – July 2016

There are many hyperlinks provided in the presentation, for ease of access these are also provided below:

Further Reading

Solving Linear Equations

A collection of resources to use to demonstrate and practise solving equations.

Student Exercises
I find Owen Elton’s worksheet, Balancing Equations on TES Resources very useful when introducing equations, the diagrams emphasise that we must do the same to both sides.
(See Diagrams in Mathematics, for more on the use of diagrams to help understanding).

Balancing Equations

Balancing Equations – Owen Elton

Linear Equations - Don Steward

Linear Equations – Don Steward

As an alternative to the balance approach, consider this doing / undoing approach, described here by Don Steward, this is an approach I use for finding inverse functions. The exercises Don refers to are here.

A2 - Mostly Algebra

A2 – Mostly Algebra

One of the Standards Unit resources, A2 Creating and solving equations (in Mostly Algebra) uses this approach, students create an equation and  then undo it; this is a great exercise for demonstrating notation. Another resource with this approach comes from the Mathematics Assessment Project (the design and development was led by the MARS Shell Center team at the University of Nottingham) Building and Solving Linear Equations lesson

For a superb collection of ideas and student exercises for solving linear equations see all Don Steward’s posts tagged linear equations. Many of these outstanding resources use a very visual approach with very clear diagrams to help students’ understanding.

Diagnostic Questions

Diagnostic Questions

There are numerous questions on linear equations on Diagnostic Questions.

WolframAlpha solve equationA simple way to check a solution to an equation of any type is to simply enter your equation as a WolframAlpha query. Note that WolframAlpha includes a graphical illustration; it is so important for students to understand how equations may be solved graphically; I always illustrate graphical solutions when we are working with Algebra to help students make these links. Desmos of course, is ideal here.
Desmos & solving equations

Centre for Innovation in Mathematics Teaching
CIMT Interactive Resources
have tutorials on equations: Linear Equations 1, Linear Equations 2, and Linear Equations with Brackets in their Interactive Resources

The following three resources work well for demonstrating the balance method of solving linear equations.

Duncan Keith’s Linear Equation Calculator is available on STEM Learning.

Choose the type of equation you require then the sequence of operations required to solve the equation.
Select Do it after each operation, for example -32 Do it were the keys selected to start the above problem.

The slideshow below shows how to use the calculator to solve equations where the unknown is on both sides.




Mathisfun has this very clear and easy to use interactive illustrating the solution of linear equations.



Circles & Tangents

Circle & tangent

Desmos – Circles & Tangents

Use Desmos to explore tangents to circle through given point

Teaching Year 10 about the equation of a tangent to a circle at a given point I have created a Desmos page. I have also created a Diagnostic Questions Quiz using questions on circles (centre the origin) from Diagnostic Questions.
(pdf: quation of a Circle & Gradient of Tangent)

(Also added to GCSE New Content page)

Further Desmos Updates

An early introduction – plot some points and functions
Desmos – points & functions (for PowerPoint file)

 Graphs-GCSE for PowerPoint file

Desmos dot to dot

Continuing with my Desmos theme (see the excellent Activity Builder from last week), a happy discovery – you can join plotted points on Desmos. This is ideal for creating cumulative frequency graphs for example – see the example in the following slides.

For completeness, so all the information and examples on Desmos are in one place, I have added pages to the Desmos series.

Note for example a little dancing with Desmos!
Desmos series

Desmos Activity Builder

A superb new addition – Desmos have created an activity builder for teachers, this enables the creation of interactive Desmos-based classroom activities. A series of pages can be created – any combination of graphs, questions or text. Having created and saved the activity a code is then associated with that  activity which your students enter at

CY Desmos Activities

A simple experiment for my first activity – identify the lines x=k and y=k.
Activities are very easy to create, the interface is intuitive; images can very easily be added by dragging them to the page.

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Once students have tried the activity and submitted answers to any questions a teacher can see all their submitted responses. This is certainly something I will be using with my students in the coming academic year. I have various slideshows for Desmos which I can now create activities for. (For more on Desmos, see these pages).

Desmos on Android

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A happy day! Desmos comes to Android and I now have the best handheld graphing calculator I have ever had! As you would expect of Desmos, it just works! Get it on Google play here. (Desmos iOS apps have been available for some time). I will certainly be asking students with Android phones to get the app.

You will find a series of Desmos Slideshows here, (these have been written with students in mind) and more on Desmos on this series of pages.

Photos by David Young



Since I will be studying the Bivariate Data section on one of our Year 13 (UK age 17-18) Statistics modules soon I was rather pleased to see that it is now really easy to use Desmos for Regression. The video shows how simple it it to use.

I tried this with some data from an A level question then also added another expression and table to see the values predicted by the model.


It is also simple to use Excel – just add the data, insert a chart – choose Scatter, then add a trend line.

Regression using Excel

Regression using Excel

…or we could just pop the points into WolframAlpha and have it do all the work to check our calculations!