Mathematical Miscellany #37

Screenshot_20200222-073804_MathFrom Microsoft, Math Solver, an app available for Android and iOS.
Either write a problem on the screen, type it or use the camera to scan a printed or handwritten maths photo and you will get a step by step explanation and any appropriate graphs. Additionally you get similar problems and online video lectures. Several languages are supported.

I like the choice of methods presented; here you can see that a quadratic is solved and you are given the choice of methods for a step by step solution – an easy way for students to compare methods.

Supported problems are as follows:

● Elementary: arithmetic, real, complex numbers, LCM, GCD (HCF), factors, roman numerals
● Pre-Algebra: radicals and exponents, fractions, matrices, determinants
● Algebra: quadratic equations, system of equations, inequalities, rational expressions, linear, quadratic and exponential graphs
● Word problems on maths concepts, number theory, probability, volume, surface area
● Basic Calculus: Summations, Limits, derivatives, integrals
● Statistics: Mean, Median, Mode, Standard Deviation, permutations, combinations

Select the icon in the top left for examples. I was curious about ‘word problems’; given examples are for example ‘Is 21 a prime number?’ and ‘Probability of rolling 1 dice and getting a 2?’

A little more experimenting needed I think, I tried an integration in this app (Android) and also using Photomath. The Microsoft app simply gave me a solution here with no step by step explanation, though it did reference similar problems from a web search; PhotoMath presented a complete explanation of the integration by parts.
Microsoft & PhotoMath

A reminder that for a really clear visual representation then WolframAlpha is excellent; the graph is returned with the query. Step by step solutions come with a subscription but the free option is so useful for checking answers and the visual representations mentioned.
WolframAlpha integral


I have mentioned the wonderful problem collection on Open Middle before, if you are not familiar with Open Middle do explore these excellent problems; you can read more about the type of problems you will find on the site on the About page. Note you can search by grade using the drop-down menus.

We could try Coordinate Parallelograms:Coordinate Parallelograms

Tim Brzezinski (@Brzezinski_Math) has started a brilliant collection of Open Middle themed problems on GeoGebra. Under Coordinate Geometry you will find his GeoGebra version of the problem.

GeoGebra problems

Brzezinski GeoGebra Open Middle


Algebra KO extract Nicola WhistonI wrote earlier on Knowledge Organisers, Nicola Whiston has started a collection of Knowledge Organisers which follow the White Rose Schemes of Learning, she is sharing the collection here, via Dropbox. These are really attractive and I think will appeal to students; they certainly appeal to me! I have updated that earlier post with Nicola’s resources.


Quanta Magazine have published this wonderful Map of Mathematics, to quote Quanta Magazine:

From simple starting points — Numbers, Shapes, Change — the map branches out into interwoven tendrils of thought. Follow it, and you’ll understand how prime numbers connect to geometry, how symmetries give a handle on questions of infinity.


For very young children, the Department for Education has announced 6 new apps available to improve reading, writing and speaking.

Following a competition to find the best educational apps for parents to engage young children in learning at home, the apps chosen cover activities ranging from interactive story books, handwriting exercises using Artificial Intelligence, and educational video games. The apps are published on the Hungry Little Minds website.

The expert panel who accredited the apps, chaired by Professor Jackie Marsh of the University of Sheffield and appointed by the Department for Education, included children’s digital media consultants, early learning charities and researchers at universities.