Mathematical Miscellany #35

Non Examples – Reasoning tasks

AL Examples & non-examples

Non-Examples – Expressions and formulae, Andy Lutwyche

From Andy Lutwyche try Non-Examples – Expressions and Formulae – Reasoning Tasks, a resource with seven sets of five questions and solutions, some of which are correct and some of which are not. Students decide which are correct and explain how they have come to their decision. The topics covered are simplifying expressions, substitution, expanding and factorising expressions including quadratics, rearranging formulae and algebraic fractions. Resources like this can promote excellent class discussion.

Also available is Non-Examples – Shapes (and Angles) – Reasoning Tasks.
For more on Non-Examples – see this post on Frayer Models.

To log or not to log – Underground Maths

To log or not to log

To log or not to log – Underground Maths

I used a favourite Underground Maths resource this week – To log or not to log? This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. I have always found that in addition to working on indices and logarithms this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!

This problem is classified as a Problem Requiring Decisions.

Students are often used to problems being posed in such a way that they have all the information that they require in order to start, and no more. Problems (especially from the real world) are very often not like this, and so resources of this type will give students the opportunity to develop the skills needed to deal with this. Some problems might not contain enough information, so students may need to decide on classifications, make assumptions or approximations, or do some research in order to move forward. Some problems might contain too much data, so that part of the challenge is to identify the useful information.

UM Powerful QuadraticsHere’s another Underground Maths task, Powerful quadratics, which will certainly give your students food for thought, as the authors state:

When students are familiar with concepts and ideas they often benefit from exploring them further to improve their understanding. These problems aim to allow this further exploration, and for example, might bring different techniques together, highlight interesting or unusual cases, or probe the definition of mathematical terms.

From Matthew Scroggs have a look at for a wonderful collection of puzzles including Advent and Christmas themed puzzles. Try Matthew’s Christmas Card 2019 with its nine puzzles – a great card for your mathematical friends!

Year 13 will get that card this week, thank you Matthew!

TeachIt Maths Advent Calendar

Teachit Maths – Advent Calendar

On the subject of Christmas, there are still loads of doors to open on those Advent Calendars and if you are looking for activities for the last week of term, try the Christmas 2019 collection.






AQA – Maths Digest
From AQA, have a look at their Maths Digest written to support Mathematics Teaching and learning. Useful whichever examination board you use, the digest offers tips and resources. I do like “Small things make a big difference” on avoiding common exam mistakes. This PowerPoint highlights where marks are often unnecessarily lost.

“Top tips for perfecting exam techniques” by Julia Smith provides her top tips to help students perfect their exam technique and to help gain crucial marks. In the article, Julia refers to AQA’s list of command words, so useful to show your students.

See also Reference for further resources on mathematical vocabulary.


In the Recommended resources section, I have reminded readers about AQA’s brilliant GCSE Mathematics: 90 maths problem  solving questions.AQA Problem Solving Questions

AQA 90 ProblemsThere is a helpful introductory section for teachers and note also the helpful Classification Tables by Strategy and by Content Area.

Em,  has a brilliant PowerPoint with all the questions and answers – see it here.


As part of the Maths Digest, you can also find information on AQA’s GCSE papers.

Working on Bivariate Data this week with my Further Maths students we were certainly able to use technology …

This GeoGebra applet allows students to move points and watch the effect on the line of best.
GeoGebra Correlation

This can be used in class by asking students to plot the points, draw their lines of best fit and then comparing with the computer. This worked really well on my phone, I simply sent myself an email with the link and was able to move points easily. This could also be used with younger classes when talking about lines of best fit.

We can also demonstrate correlation coefficients and lines of best fit with this PhET simulation on Least Squares Regression.

Correlation & Line of best fit

Choose from a range of examples or choose Custom to add your own points and guess then check the correlation coefficient. You can also draw your own line of best fit and compare it to the theoretical line of best fit. Note the option to include residuals for both your own attempt and the line of best fit.

For more on resources for Regression see this post; you could also use Desmos, GeoGebra, Excel or WolframAlpha.



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