Functions – an update


I have updated a post on functions with the excellent PhET simulation, Function Builder

The post includes several excellent resources for teaching functions. See also this further post aimed at older students.

PhET Simulations look excellent, I will be exploring more of these. I have used the Projectiles Simulation with Mechanics A Level students and have posted on this for students on Mathematics for Students. There are numerous PhET simulations covering Physics, Biology, Chemistry, Earth Science and Mathematics. Note the growing collection of HTML5 versions which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

You can download an app for iOS also for Android.

PhET Balancing Act working nicely on my phone!


Mathematical Miscellany #5

Twitter can be useful for alerting one to resources / news, note the first two items.

Problem Solving – an open access (free) book which looks at research on Mathematical Problem Solving.
Problem Solving

Note this page for a large collection of free Mathematics books.

Tools for Maths Teachers J HallJonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. Note that you can show solutions for the GCSE questions – there is a link at the bottom of the page for each question.
JHall site

The page on Apps has recently been updated, there are fuller descriptions of the various apps and note the addition of Summaze2 from MEI and Sigma. A wonderful example of a free app – Maths to make you think, visually attractive and no irritating adverts trying to make you buy the premium edition!

Sumaze Integral

In Mathematical Miscellany 4, I mentioned the excellent Linar Equations Calculator; for an excellent way to illustrate the balance method of solving linear equations, try this manipulative on Mathisfun, this is very simple to use and does not require the user to log in.
Mathisfun Algebra Balance

tickUK Results 2016 – a new page has been created which I will update as A Level & GCSE results / news comes in. As I do each year, I will provide links to the results statistics and grade boundaries for the various examination boards.

Note my Twitter Examinations list. Check this for announcements / news. (You do not have to be a Twitter subscriber to use the list.)

Whilst this is Mathematical Miscellany #5 I have been writing these compilation posts for quite some time. They were at one time ‘Thoughts this week…”. Previous posts are all filed under the category (note the Category menu on the right) Mathematical Miscellany.


I thought I would create a page for apps I come across which I find useful; these are mostly available for  Android as well as iOS. Just a small number currently, but these are all free and work very well.

Apps - Mathematics

Apps – Mathematics

Mobile Puzzles – Algebra

Mobile Puzzles

Mobile Puzzles

The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC) includes a wonderful collection of Mobile Puzzles. Visit to play SolveMe Mobiles (also available for the iPad.)

Looking at the menu, you will see categories with different levels of difficulty available from very simple puzzles to rather more complex puzzles which promote good mathematical thinking.


Students must determine the weight of each object shown which makes a good introduction to the skills required to solve equations, linear and simultaneous.

Looking at some of the Master level puzzles, you will find rather more complex puzzles:
Master Level

Note the menu in the corner of each puzzle page:
Play Menu

Selecting ‘Information’ provides extensive help; note that various tools are available so you can annotate puzzles and / or add symbols and equations.

create equation
Note that you can then drag a heart to subtract a heart from both sides:
puzzle demo
Note that under settings you can choose to show numbers in the mobile as in the illustration. If the solution is correct, the mobile will balance.

On the other hand….
puzzle demo wrong answer





PhotoMath is a free camera calculator phone app 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 in 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! The app has handwriting recognition.


Photomath Examples

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