PhotoMath is a free camera calculator phone app now available on Android as well as iOS and Windows. To use point the camera towards a printed mathematical expression and the app gives the solution, step ­by ­step solutions are also available. The problem types are limited to those shown below (also see the examples here) and it can be a bit tricky to focus the camera sometimes, particularly where problems are very close together on a page but this is rather clever! I look forward to future developments.

PhotoMath problem types

Experimenting, I have found that the app works if you point the camera at a screen, so one could zoom to an appropriate size first. Try these equations in the Year 7 text on CIMT for example:

CIMT Linear Equations

CIMT Linear Equations


Select for video demonstration

Select for video demonstration on Vimeo


Good Mathematicians Can Go Backwards

Explaining to my Advanced level students recently that they need to know material like the laws of logs backwards and forwards because they don’t always immediately recognise the right hand side of a rule they know when seen in isolation, it struck me how often I talk about going backwards!

So, this week some ideas and resources for thinking backwards! (The presentation has been added to the series of Presentations pages in case I, or anyone else wishes to easily find it again!)


Box Plots with Plotly (& more Statistics Resources)

Nobel Prize winners by field
I have written on Plotly before. I will be revising Statistics with my Year 11 (UK age 15-16) class this week in preparation for their GCSE exam, so the latest Plotly blog post on Three Things That You Can Do To Explain Your Data is very timely.

I plan to use the Nobel Prize Data plots to revise Box Plots and importantly the interpretation of the plots. Whilst outliers are not on the specification for GCSE, they are for the A Level students and I believe that wonderfully clear outlier for for the Noble Peace Prize is worth a mention for all of them!

Fork and editNote that you can play with the data! If you then choose to Fork and edit, you can save the file so you can modify it for your own use; you will need to create an account (free) or sign in with social media. Choose Traces and you will see several options, you can choose to show points or not for example. Note the Style tab too where you have several options to customise your chart.

Plotly box plot traces options

Box Plots & Skew

Select the link to play with the data

You could use this to create your own charts – simply choose your theme, edit the data and choose your options to create very attractive and clear charts. I like the way the data can be displayed as well and created some simple box plots to demonstrate skew:

For more resources on Statistics see this page, also the worked examples plot

For more resources on Statistics see this page, also the worked examples here.

(Post for students on Box Plots)


World Book Day

Image – Klara Kim on flickr

Image – Klara Kim on flickr

Well we may not have World Maths Day this March (it’s in October, and I see from my blog statistics that people are looking for it!) but we do have World Book Day (5th March).

We could bring books and Mathematics together with some Statistics; have a look at this resource from TES, World Book Day Maths Data Investigation where students analyse word length and sentence length in some book extracts. UK readers who remember Statistics coursework, this brings back memories of AQA’s coursework task ‘Read All About It’ where students considered various newspapers and magazines for readability.

The extension task for the TES resource above considers the reading age of a text, you may wish to consider further readability formulae; if you paste some text to this site, Readability Formulas you can easily check statistics for your chosen text and generate a reading age according to the various tests.

I tried the text of this post for readability – college level? You should be fine!

Revision – day in and day out

That quote from Robert Collier seems so appropriate when it comes to revision. This academic year I have used the day in, day out approach even more with my students, frequently reviewing earlier work even for short sessions. I am convinced this is important in our teaching and help makes things stick for our students.

Once again we are in the final run up to examinations, so I thought time to check the various revision resources I have highlighted on this blog. The list seemed to be growing ever longer so I have created a new series of revision pages which I hope makes resources easier to find.

I’ll be combining some of the ideas with my classes, for example a treasure hunt (we will be using this TES resource – GCSE Revision – Trail Cards) will make a change but before we start wandering round the room we will discuss some hints for some of the questions first. As a starter the students will complete a worksheet with some blanks to fill in so I think they are prepared to tackle the questions. (I will upload this later).

Wishing teachers and students everywhere a successful final revision period.

Polar Coordinates – Resources

StationeryWith Year 13 I will be looking at Polar Coordinates this week. The first thing we’ll need to do is understand the meaning of polar coordinates and be able to convert from polar to Cartesian coordinates and vice-versa. So we will need some polar graph paper and Desmos! Checking my stationary list I found exactly what I needed on MathBits, scroll down the page for polar papers; one of the options usefully provides 4 smaller grids to one page.

So now to plot some points, Desmos provides a good solution

Desmos - polar coordinates

Select image for Desmos page

With two points to play with, we can understand how negative values of r and θ are displayed and appreciate that a point may be described in more than one way with polar coordinates.

The Desmos page also shows the relationship between polar and Cartesian coordinates (the Cartesian form is needed to plot the points.) On that subject, Desmos created the page below – match up the two points.
Desmos - polar & cartesian coordinates
We also need to be able to plot polar curves, Desmos is ideal for exploring polar curves; it is possible to use sliders to see how the curve is generated as values of θ increase.


On the AQA website the Teaching and learning resources page for A Level Further Maths includes three online textbooks under the Resources for students heading. The second book (Unit 03) includes a chapter on Polar Coordinates.

WolframAlpha can also be used for polar plots.

For further examples and resources, see this post on Mathematics for students.

Desmos & Valentines (& fractions and rotations!)

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

Click on the image and move that slider!

Click on the image and move that slider!

In what happily seems to have become an annual tradition Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!
Desmos Valentine instructions

Geeky people you could even use the Desmos API …

Valentine’s Day seems an appropriate time to express love for Desmos!
Two happy discoveries this week (thanks to Twitter):
Fractions - multiplying Rotation
Multiplying fractions and Rotation about a point. Brilliant.

Elsewhere – express your feelings for WolframAlpha!

I Love YOU

Transum Valentine Puzzle
and here’s a logic starter from Transum for Valentine’s Day!

Wishing Mathematicians everywhere a happy day and if you are a UK teacher about to start half term – have a lovely week!

Number Operations


Questions such as this can make a great starter for a lesson and provide the chance to discuss number operations and the relationships between them. Manipulating numbers like this can also help with algebraic manipulation.

Looking for some more examples of this type, I came across a really useful resource on TES, “If I know this then I also know …” by Piers Butler. This would make an ideal lesson starter. As it is an Excel spreadsheet, I thought it would be simple to add another worksheet with the answers and created the Excel file CY If_I_know_this_then_I_also_know_ which is a copy of the original, but just adds another worksheet with the answers.

Thank you Piers! I have added this to the Number collection on Mathematics Starters where you will find other ideas for Number starters.

If I know this..
For more TES (free to register) Resources, see Secondary Maths Teaching Resources. or have a look at the Secondary Maths Resource Collections which includes collections of great resources by topic.

TES Topic Specials

Revision Time Again

Algebra Snippets 2

Algebra Snippets – select image for details

I recently created a new page ‘Revision Activities’ as I could see from my WordPress statistics that posts on revision are popular.

Time to say a little more on the first item on the revision page. I am a huge fan of Corbettmaths 5-a-day. I have been using these regularly with my Year 11 GCSE class; they like them and have come to expect these at the beginning of many lessons. I print the questions for them and hand them out as they come into the room so they can get straight to work. I find that using the Windows snipping tool I can easily fit two sets on an A4 landscape page making them economical to print or copy; this is a size that can easily be stuck into exercise books which my students choose to do.

Corbettmaths 5-a-day

Corbettmaths 5-a-day

The above image shows, appropriately the higher questions for January 31st. I tend to hunt the collection looking for sets that include particular topics. Following their earlier mock exam we decided that we needed more trigonometry practise so I made sure that a trigonometry question appeared in each day’s set for several sessions; it has been very rewarding to see the speed and confidence they now seem to have on for example the sine and cosine rules. I have also sought question on topics that we have not met for some time.

I do believe that asking students to recall topics regularly is very valuable, see my earlier post  “Highlighting is a Waste of time”. Using short GCSE questions like this fits in with the distributed practice idea. Short tests can be useful too – on Monday Year 11 will be getting 10-a-day under timed exam conditions!

Thank you so much Mr Corbett from myself and my students!

Venn Diagrams

With Venn Diagrams on the new UK GCSE Mathematics specifications (an excellent addition I believe), and also on other exam specifications, I thought I would update an earlier post on Venn Diagrams and collect resources together.

CIMT Venn Diagrams

CIMT Venn Diagrams

CIMT is one of my Top >10 websites for a very good reason – when I want additional examples for any topic at any level I can always find them on CIMT! Venn Diagrams is no exception to this, you can find Venn Diagrams in the student interactive resources here and the text chapter on Logic from the Year 7 text here; in sections 1.3 and 1.4 of the text you will find examples and exercises on set notation and Venn diagrams.

Nrich too can always be relied on to provide resources – a search on ‘venn’ returns these resources.

Nrich Venn Diagrams

Nrich Venn Diagrams

teachitmaths Venn diagrams

teachitmaths Venn diagram dominoes

From teachitMaths, try Venn diagram dominoes (pdf versions of all the resources on this site are free).

Diagnostic Questions

Diagnostic Questions

On Diagnostic Questions we have a series of question like this.

On Mathisfun see Sets and Venn Diagrams; note the questions at the bottom of the page.

In the comments below Anja has reminded us of Jonny Griffiths wonderful RISPS – see in particular RISP 10.

On a similar theme – from the Further Maths network have a look at the excellent GCSE extension tasks, see NA1 for example.

These three interactives from Shodor are a good introduction to Venn diagrams:
Venn Diagrams, Shape Sorter and Triple Venn Diagram Shape Sorter 

With the Triple Venn Diagram Shape Sorter you can either set the rules or guess the rules by selecting the appropriate botton:

Some excellent activities are available from the Illuminations site.

The Shape Sorter allows exploration of geometric properties of shapes.

Select Instructions and Exploration for clear information on how to use the resource.

From the National Library of Virtual Manipulatives, this Venn Diagrams applet allows exploration of set operations such as union and intersection.

WolframAlpha can also be used.
The slideshow here shows several examples.

Update: a Twitter conversation on a fun idea!
Twitter Venn

Now if the book seems a little pricey you can get ideas from the sample pages and I’m sure teachers can get creative! Here’s some more on MailOnline

If you want to create your own there are plenty of tools to use – there is a good summary here on Cometdocs.

New Scientist Gallery - Venn Diagrams

New Scientist Gallery – Venn Diagrams

…and to take Venn Diagrams to their extremes have a look at these wonderful images from New Scientist!