Challenge Your Mathematics Students …

To achieve the highest grades at GCSE (taken in the UK by students age 15-16) students will need to be good problem solvers which include being able to make and use connections between different parts of Mathematics. There are many suggested resources in the Problem Solving Presentation.

For older students (16+) I have included Underground Mathematics. I have also used Undeground Mathematics resources with my very able GCSE students; see for example Introducing Calculus. There are many Underground Mathematics Resource Types. One of the types I have written on before is the Review Questions which in the words of the Underground Maths Team:

These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

Checking the Review Question type in this category we see that O/AO-level questions are included.

I see several questions here that will provide appropriate challenge for my GCSE students.
For example:


Can we fully factorise x4+4y4?
Starts with a Show that….
And then we factorise and will need to recall the difference of two squares.
We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.

Can we simplify these algebraic fractions?
Review algebraic fractions, simplifcation including the difference of two squares and quadratic equations. We could of course also talk about functions (including domain and range as these students are also studyling AQA’s Level 2 Further Mathematics)

Can we simplify these simultaneous equations of degree 1 and 2?
Solve simultaneous equations, we’ll need simplification of algebraic fractions again and we can talk about the graphical solution of equations. We will also need to factorise a quadratic, 3y2−y−80 with a coefficient which is not 1 for the square term. We have all decided we are fans of the Box Method!

You can also search on the Line and the Station to narrow your search; you can also save and categorise your favourites by creating a (free) account.


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

Scratch Mathematics Projects

My personal favourite use of Scratch is to demonstrate relationships between angles and polygons which I have written on before.

Investigating more projects on Scratch I found What’s My Number? which could make an interesting starter problem. Why can one always guess in 7 tries or less?

What's My Number project by GyroscopeBill

What’s My Number project by GyroscopeBill

(See Guess My Number (Birmingham Grid for Learning) – an alternative version of the game.)

Perhaps try Divisibility Dash from  jgordon510 and practise your knowledge of divisibility.

Quadratic Equation solverFor those who wish to learn more about Scratch syntax then looking at the code for a project such as this quadratic equation solver by proanimator is helpful. Select See Inside to see the code. If you create an account (free) you can save a copy to your own account. This code could easily be adapted as it offers the means to input some variables, perform calculations and display the results. Looking at code already written can be a great way to learn syntax – it’s certainly something I have done when learning to write Excel macros.

This slideshow requires JavaScript.

Mathematics Subject Special Update

UKEdChat Maths

The UKEdchat Mathematics Subject Special took place on Thursday 23rd October and the Session page has been updated with the complete chat.  Note that you do not need a Twitter account to view any of the links mentioned in the slideshow or in this post.
View the complete chat as a Storify Slideshow.
Storify Maths Subject Chat

I thought I would review the chat and note some interesting resources which were shared and add a few more which may be of interest. Each image of a tweet links to the appropriate site. As always I’ll qualify this with the fact that my choices here are entirely personal – they interest me and I hope will interest readers. I am making no claims that these are the best! (see Emily Nussbaum writing for The New Yorker on why she hates Top Ten Lists!)

Bell Work 1

Bell Activities
Some good ideas there that could work for any subject, I particularly like the Clever Bell Ringer Procedures – I’m sure you could be clever with post it notes for the sign in activity.

Starter Corbett
Corbettmaths – such a good site, including the starters mentioned here:

Form Time Numeracy

Form Time Ideas looks great and would make a great lesson starter

Form Time Numeracy 2

starter puzzles


I’ll second all of those. Ed’s tweet links to a KenKen solver. Also see this page for various puzzles, links are included to all the sites Ed mentions and you may find some more you like as well. For more on Find the Factors see this post.


Numeracy Shed


prime numbers
How quickly can you identify those prime numbers? This reminds me of the Sporkle site where you can test your ability to remember prime numbers or square numbers amongst many other possibilities. It is also easy to write your own quizzes.

Diagnostic Questions

Diagnostic questions – a brilliant site and new questions constantly added – for more information and how tos click the following tweet image.

Diagnostic questions



mats sticks nrich

Me too Miss H – image links to MathsSticks and more on Nrich here.

Homework ideas from JustMaths and from me:
JustMaths homework

Homework Ideas CY

 Coding is just great, image links to Scratch Junior.
See also Scratch, CodeMonkey and the Python site.

…and teach them some Excel skills!

Thank you so much to every single person who took part in the chat – it says something about you all that you take part and share ideas. 

I have mentioned many resources you may find useful in connection with many of the questions raised in the chat in my ‘Resolutions for Mathematics Teachers” reproduced here:


Thoughts This Week…

A compilation this week…

Learning and Revision
It’s still revision time with public examinations coming up and for our school we can add the younger students too as they will have school exams. Certainly resources that I will use with Year 7 (UK ages 11-12) include the spot the mistake type activity. I recently used the Transformations AfL activity for rotations successfully with Year 7 and also with Year 10 as part of their revision.

Reading Make it Stick (The Science of Successful Learning) which discusses the use of testing as a learning tool convinces me even more that mini-tests are a good idea! This week each of my three Year 10 lessons started with one which seemed to work very well and I was very pleased when two students who had to be somewhere else in the first part of one of  the lessons asked it I would send them the mini test for that day! Students need to recall information and the evidence suggests that testing is a better way of doing this than simply rereading material, a method often favoured by students. I am planning more plenary mini-tests, with the students I’ll definitely use the name I know they like, ‘Self-checks’ which I hope helps them realise they are as the authors suggest a learning tool, not something to be stressed by.

Aristotle apparently wrote “exercise in repeatedly recalling a thing strengthen the memory.”



Select image for problem on Brilliant

I do like the problems on Brilliant and looking at a problem recently, it struck me that these are an ideal sources of starters. Further details on Mathematics Starters and Plenaries.

In the news
The current UK system national curriculum levels have been removed so schools have the freedom to design their own assessments against the new national curriculum. Further details are available on the Assessment Without Levels – KS3 page.

A TES article ‘The revolution is coming, so what should you expect? suggests that the new ‘pass grade’ is to be 5 (even though a 4 is comparable to the current C grade). Equivalent grades are given by TES as follows (TES source JQC)
GCSE gradesGCSE grades chart