For a collection of school GeoGebra Mathematics applets, try this app on Android
Some students may have seen the excellent credit card size information sheet full of mathematical formulae from Loughborough University. This is also available as a free app for your mobile phone.
From MEI and Sigma, an excellent app, Sumaze has puzzles involving arithmetic, inequalities, the modulus function, indices, logarithms and primes. (App Store for iOS and Google Play Store for Android.)
A second app, Sumaze2! has puzzles on fractions, decimals, percentages, primes and digits. (App Store for iPhone and iPad and in Google Play Store for Android.)
Note the classroom poster available describing both apps.
Emma Bell has written on both here.
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.
Signing up to Brilliant! allows users to join an international community and get access to great problems at various levels, including questions suitable for younger students and at the other end of the scale many rather more advanced problems!
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 solveme.edc.org to play SolveMe Mobiles (also available for the iPad.)
Numbers is similar to Countdown. Use the given numbers to achieve the target.
There are over 200 levels. I’m not sure the levels have a lot to do with increasing difficulty – look at level 61 here for example – this is much easier than some of the earlier problems. When I first started playing I didn’t realise you could click on intermediate results as you see in the illustration here and actually managed several levels without doing so! Dave Gale has written a post on the app here.