Searching for questions – part 2

Searching for questions – part 1

This post is the second in a series of posts looking at sites where you can easily find resources by topic. For just the links in this series of posts, see this page which provides a useful list of such sites.


Nrich has extensive resources including problems, interactives and games. Full teachers’ notes are provided. The Resources for Teachers page has several useful links; note the curriculum mapping documents which suggest resources relating to the National Curriculum. There is a search by topic facility to find all the resources for a particular topic.

Nrich resources

Nrich Secondary


CIMT– The Centre for Innovation in Mathematics Teaching, from the University of Plymouth, an astonishing resource has free curriculum materials for all school-age students. For example, if we look at the Year 7 Course Material page as well as all the book chapters with their numerous worked examples and exercises there are also teachers’ resources including notes, slides, revision tests, activities and mental tests on each topic. The activities are varied and include investigative work.

CIMT Mental Test

CIMT Mental Test – Logic


M4THScomFrom Steve Blades, see for age 14-18. This site has an extensive library of resources. A great feature of these resources is very efficient use of space so cutting copying costs. Keep scrolling down the page – there are a lot of resources!


Exercises & solutions on David Smith's 'The Maths Teacher'

Exercises & solutions on David Smith’s ‘The Maths Teacher’

David Smith’s The Maths Teacher site has a great collection of videos for both GCSE (age 14-16) and A Level (16-18). Transcripts are available for each lesson, also exercises with worked solutions. Many of the GCSE videos would also be useful for younger students. There are also videos and written solutions to some Legacy A Level papers.

Teachit Maths KS3 Percentages code breaker
Teachit Maths KS3 Percentages code breaker

Teachit Maths though a subscription site offers its entire collection of activities as pdfs free. I have found many high quality resources here for all ages. Look at this activity on quadratic functions for example – this should really help understanding.

From Transum, well known for its Maths Starter of the Day, note the complete index of starters including the topic of the starter. The Transum site is easy to navigate, there is a clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning. The example shown here is one of the Algebra Activities found on this page. See this post for further examlples of some excellent resources including Venn Diagrams and Systematic Listing Strategies.


Transum – Algebra

 Transum Maths Map

The list of sites easily searchable for resources by topic can be found on this page.

Searching for questions – part 1

I thought it would be useful to put together a simple list of sites where you can easily find resources by topic.

For just the links in this series of posts, see this page which provides a useful list of great sites to search for resources by topic.

I want some questions on Sequences for Year 10 so I’ll use Sequences as an example.

Sequences Index Diagnostic QuestionsOn Diagnostic Questions, we can search all the Maths Questions. Under Algebra we will find Sequences. The questions are helpfully categorised as shown. For the links here to work, sign in to Diagnostic Questions

We can also use the excellent Quiz collections, do explore the variety available for all ages. The collections from the exam boards are so useful, for AQA, OCR and Pearson Edexcel, Higher and Foundation quizzes for Years 9, 10 and 11 are available. The UKMT collection includes themed topics at Junior, Intermediate and Senior level.

It is also possible to search all the Maths quizzes which have been created. As before, under Algebra we can find the Sequences quizzes.

Sequence Quizzes Diagnostic Questions

Sequence Quizzes – Diagnostic Questions

On Craig Barton’s site, you can use his Maths Topics Index page.
Sequences mrbarton topicsSelecting Sequences for example gives a further choice, if we choose Linear Sequences, we find a treasure trove of sequences resources all conveniently in one place!
mrbarton Topic Index

DrFrostOn we can browse all resources which include complete lessons as well as homework questions and assessments. Looking at Sequences we see resources for Year 7 through to GCSE/IGCSE Further Maths. Note also Dr Frost’s homework site.

gcse-inequality-example J HallFrom Jonathan Hall: mathsbot is superb. The home page provides a clear menu and the site is easy to navigate. Many of these resources allow you to generate questions by topic. See for example Differentiated questions and GCSE exam style questions.

The list of sites easily searchable for resources by topic can be found on this page and this will be added to in the next few days.

To be continued…

Mathematical Miscellany #17

Some updates to various pages this week…

In the reading series of pages, Research – Mathematics Learning & Teaching and Research – Learning & Teaching both provide information on research relevant for teachers in the classroom. There are links to many good, easy to read summaries included on both pages.

Recent additions to the Mathematics page includes Working Memory in Mathematics Learning which is an excellent example of the clear and concise communication of research which these Expressos from Cambridge Mathematics provide.

Also added to this page is Improving Mathematics in Key Stages 2 (ages 7-11) and 3 (ages 11-14) From the Education Endowment Foundation. The Guidance Report offers eight practical, evidence-based recommendations—that are relevant to all pupils— but particularly to those struggling with their mathematics. Note the recommendations summary poster.KS2 & 3 Maths Recommendations

On the Research – Learning & Teaching page, note Rosenshine’s Principles of Instruction, such a valuable list of research strategies teachers should know about and I believe well worth asking ourselves if we are incorporating these strategies regularly in our lessons.
Principles of Instruction

The page on free books has been checked and updated recently.

Colin Foster - Instant Maths Ideas

Colin Foster – Instant Maths Ideas

Note Colin Foster’s KS3 Instant Maths Ideas (3 books) which are freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham.

Clumsy Clive

Andy Lutwyche – resources

Included with Spot the mistake we have excellent resources from Andy Lutwyche, look at his excellent Erica’s Errors series and if we check on TES, these free resources also include plenty of errors from Clumsy Clive! I have found these work really well in class.

Finally, on the A Level Statistics page I have included from WJEC, their KS5 resource, Exploring Large Data Sets which includes several data sets and very comprehensive Teacher notes.

WJEC Large Data Set Resources

The notes include many questions to consider and also clear instructions for Excel and GeoGebra.


Happy New Year 2018

Looking at my blog statistics I see Happy New Year 2017 is popular, so time for a quick update!

New Year Game

It’s that time of year again and we can play the 2018 Year Game in our January lessons.

We could also look back and use the excellent MacTutor History of Mathematics Archive from the University of St Andrews, Scotland. We could check any day for example for Mathematicians who were born or died on that day or check the Mathematician of the Week. Or we could look at the Theorem of the day!


Number GossipWe can always turn to Number Gossip from Tanya Khovanova for information on properties of a number. We see for example that 2018 is square free; I have found students are usually interested in these number properties and we could certainly usefully revise prime factor decomposition and come up with some more square free numbers.

wolframalpha-historical-number-formsWe can also look at WolframAlpha which provides further information including what 2018 looks like in historical numeral forms. We could use the various WolframAlpha queries to learn how Babylonian, for example, numerals work. Some possible starters for January lessons here I think!

The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.


For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.


Teacher Resources on Line

We should make a calendar for 2018.
From trol, Teacher Resources on Line.


Wishing educators and students everywhere a very Happy New Year.





Relaxing at Christmas, it must be time for a puzzle! To play Diffy, draw a square and label each of the corners with some whole number. At the midpoint of each square write the (positive) difference between the numbers at the corresponding vertices. Then draw a new square through the midpoints and repeat the process. Note we ended up with four zeros.

Change the starting numbers, do we always end up with four zeros, and how many steps does this take?

Or perhaps it is rather easier to set this out as follows and use a spreadsheet to explore many possibilities.
Diffy ExcelI was introduced to Diffy at an excellent lecture by Rob Eastaway and have used this successfully since with students from Year 7 (UK age 11-12) to my Year 13 Further Mathematicians!

Having done a little further research I found an excellent post by Don Steward on Diffy where he has numerous excellent questions for students to explore.

Diffy - Don Steward

Diffy – Don Steward

Note The PowerPoint included in Don Steward’s post. We can practise our Algebra too!

Do we need to start with integers?

Diffy - Irrational
For further reading and extension, a very thorough analysis, try Diffy Boxes (iterations of the Ducci four number game) by Peter Trapa, September 27, 2006 and Joshua Zucker on Circle of Differences in Numberplay from the New York Times.