Flashcards – Mathematics

Common Angles Subject Content

Quizlet common angles

In a Year 11 lesson, doing some revision for a mock examination, one of my students mentioned that she had created a set of flashcards on Quizlet for the exact values of the trigonometric functions students are required to know for GCSE Maths. This resulted in a round of applause from the class – I am very pleased that so many students use flashcards.

How we learn is something I regularly discuss with my students. Retrieval Practice is so important for learning, we need to work out how to get information out of our students – not just how to put it in! From The Learning Scientists see these valuable resources to support learning techniques including Retrieval Practice. Note the excellent downloadable materials on study strategies. Each strategy is backed up by research.

‘Ditch your highlighter and get busy with your flashcards’ as this article in Time, summarising the comprehensive report released on Jan 9th 2013 by the Association for Psychological Science concludes. The authors, led by Kent State University professor John Dunlosky, looked at various learning tactics and rated each from high to low utility.

The authors conclude that the most effective learning techniques are distributed study sessions (last minute cramming is not effective) and more practice testing, the use of flash cards can be very helpful with this.

Flashcards AlgebraI thought I would check Quizlet to see what is currently available for GCSE Mathematics. I noticed this for GCSE Foundation for example and another set for GCSE Revision; note that you can scroll down and see all the cards in the set. The quality clearly varies, I think I’ll get writing some sets myself to use in class – watch this space for more!

A first attempt! A set including images to test the common angles.
And a second – on Circle Theorems.
Quizlet common angles

Note that Quizlet includes the option to play games using the card sets.

Quizlet match game

Quizlet Match Game

Quizlet game

Quizlet Asteroid Game

Arithmagons and more…

Jonathan Payne - Arithmagons

Arithmagon Generator – Jonathan Payne

From Jonathan Payne, try this Arithmagon Generator. This is very simple to use and would be an ideal lesson starter. I like the option to use fractions, also to mix the question types as you see in the image. It is possible to choose missing sides, mixed or missing vertices.


This has been added to my Arithmagons collection which includes all the arithmagons you could ever want from the simplest to complex numbers and Calculus for older students!

Jonathan Payne - Missing AnglesAlso from Jonathan Payne, many more lovely question generators, try his Missing Angles question generator which has numerous options including Algebraic questions.
Jonathan’s collection of generators is here.

Jonathan Hall MathsbotOn the subject of question generators, we can turn to another Jonathan! Jonathan Hall’s Mathbot.com has a wonderful collection of resources including question generators. His Differentiated Questions include numerous topics including several recent additions on Indices. These generators as you can see from the menu options can be customised to suit your class. They are also useful for student self-study.

Finally, from not a Jonathan, but John Tranter on Transum, this Custom Starter allows teachers to select the number of questions and the topics to include; scroll down the page and choose the topics you want from the Concept Selection.
Transum Revision

It is possible to save a particular selection of topics as the URL for your selection will be generated. It is also possible to drag the panels so your questions are displayed in the desired order.

The beginning of a lesson can be a good time to review previous learning, starters like these can be ideal. On the very important subject of reviewing previous learning, see Retrieval Practice.

Top Tools for Learning 2018

Jane Hart Infographic

Jane Hart, of the Centre for Learning and Performance Technologies, has published her annual list of Top Tools for Learning. The list, released on 24 September 2018, has been compiled from the results of the 12th Annual Digital Learning Tools Survey.  Jane Hart’s analysis includes details of the contributors as well as her commentary on trends.

Like last year, she has three sub-lists including Top 100 Tools for Education. As Jane indicates only 23% of the votes came from the Academic Sector, so it is interesting to look at the sub-lists as well as the overall list. The sub-lists are:

  1. Top 100 Tools for Personal & Professional Learning 2018 (PPL 100)
  2. Top 100 Tools for Workplace Learning 2018 (WPL 100)
  3. Top 100 Tools for Education 2018 (EDU 100)

The infographic made available by Jane Hart is a four-page pdf which lists the overall 200 top tools and also the top 100 tools on each of the sub-lists.

It is fascinating to note the tools which have made it onto all 12 lists, as well as looking at the enduring tools over the last 5 years or so. Using the 2007-18 A-Z I thought I would have a look at these and created a spreadsheet to see which tools are in all 12 lists, also an average position over the last 3, 5 and 7 years.

Looking at the new entries on the 2018 list, I am delighted to see a personal favourite, WolframAlpha which has finally made it onto the top 100 list for Education!

Looking further at the Top 100 Tools for Education (filter EDU100, note you can choose to show all 100 on the list) I see some personal favourites!
(Top Tools 2018 – Education for an Excel Spreadsheet).

Excel is quite rightly highly placed. I regularly use Excel resources; just a few examples of some favourites:

Normal Trainer


See STEM Learning, part of the A Level (16+) Resources series.

A few more for investigation …
KahootKahoot (Classroom response tool) is very easy to use and free for teachers and students. In a few minutes, I created a quiz on Directed Numbers … (not very exciting – just a test, very easy to create.) Kahoot qn

Another popular quizzing tool I know some of my colleague’s use is Quizlet.

Seeing Padlet (online discussion board) ascending the list reminded me of this very easy to use tool. I shall try this with Year 7!
Padlet equations

Unsplash – beautiful free photos to do anything you like with!

Photo by Marivi Pazos on Unsplash

Apart from illustrating Unsplash, I can have pictures of flowers to illustrate a mathematical connection! From Science News reading Fibonacci’s Missing Flowers we discover that the most common number of petals is five and whilst there are many flowers with the number of petals a Fibonacci number there are also flowers with four, six, seven or nine petals!


Factorisation of Quadratic Expressions

Looking forward to the first London Maths event of the year, I was reminded of Colin Foster’s wonderful Mathematical Etudes site. To quote Colin Foster:

Mathematical Etudes are creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises.

(The session charge of £10 covers you not only for this session but also for the 5 remaining sessions of the 18/19 academic year. The sessions are free for trainee teachers in their ITT year.)

Note the Etudes by topic at the foot of the page; Number, Algebra, Geometry, Probability & Statistics are available. Looking at Algebra for example, under Solving Equations we see Connected Quadratics. Intrigued by Lyszkowski’s method of factorising quadratics mentioned led me to another excellent lesson plan of  Colin Foster’s on Quadratic Equations. I really like the starting activity in this lesson which should promote a deeper understanding of factorising quadratic expressions.

I have written before on the ‘Box Method‘ for factorising quadratic expressions where the coefficient of x2 is not 1 and note Quadratic Grids from Underground Mathematics will help students develop and understand the method.

Lyszkowski’s method seems even simpler, avoiding the manipulation required by conventional methods.

Lyszkowski's method

Lyszkowski’s method 

I think I’ll see what year 11 think of this!

16+ Mathematics Resources

crashMaths Skills Check

crashMaths Skills Checks

crashMaths has been added to the 16+ series of pages. The growing library of resources now includes a set of very useful Skills Checks, with solutions, on Pure content from Year 1 of the A level specification. The site includes many practice papers and mark schemes.

With all A Level courses now linear, Retrieval Practice is essential. From crashMaths these AS Maths Key Skills Check worksheets will be very valuable for Year 13 in the second year of their A Level course. The Skills Checks are all on Pure Mathematics.


Further recent updates to Advanced Level resources include:

From Edexcel, A Guide to using GeoGebra when teaching AS and A Level Mathematics. This guide links to numerous GeoGebra files clearly mapped to the specification content.

Edexcel GeoGebra AS & A Level Mathematics

This guide has been added to The Use of Technology Page, also to the latest update of this file on technology resources mapped to content which can be found on The Use of Technology Page. The file includes links to instructions for the Casio ClassWhiz calculator.

Updates to the Further Mathematics content include this link to a post on Maclaurin Series for students which includes Desmos pages. The post also links to some useful notes and examples for students.
Maclaurin Series cos x

For Further Maths, this post on the new topic of Differential Equations may be useful. Again, notes and examples are linked to, also instructions on using WolframAlpha to check work on Differential Equations. WolframAlpha is also useful for checking work on Matrices.

The teaching of Polar Coordinates offers an ideal opportunity to use Technology.
Desmos polar slider