Top Tools for Learning 2019

As 2019 draws to a close it seems appropriate to mention Jane Hart’s annual Top Tools for Learning 2019, an annual list I have always been interested to see.

With the majority of respondents coming from the workplace and just 22%  from education, perhaps a list of particular interest to readers of this blog is the Top Tools for Higher Education (EDU100). I was interested to see that Padlet, an excellent online noticeboard which has been around for a long time remains popular, and verified for me by a favourite source, Richard Byrne’s Free Technology for Teachers in his ‘My Favorite New & Updated Tools in 2019‘ post.

Excel is quite rightly, in my opinion highly placed. I regularly use Excel resources; just a few examples of some favourites:

Complex Loci - Mike Hadden

Complex Loci – Excel Files, Mike Hadden


See STEM Learning, part of the A Level (16+) Resources series.

Another app remaining popular is Kahoot (Classroom response tool) which is very easy to use and free for teachers and students.

For free photos to do anything you like with try Unsplash.

Photo by Marivi Pazos on Unsplash

Futoshiki and other puzzles

FutoshikiI first came across and enjoyed a Futoshiki puzzle in the Guardian puzzles section.

Work out the digit that goes in each cell. In this 4×4 example, the digits from 1 to 4 must appear exactly once in each row and column.

Initially, some digits might be revealed and additionally, the board might also contain some inequalities between the board cells; these inequalities must be respected and following them will help you find the missing digits.

Futoshiki2In the above puzzle, difficulty level, easy, we see that the fourth column already has a 1 and a 3, the remaining digits 2 and 4 can only be placed one way as we have to follow the inequality sign.

On from Vlad Daskalu, you can generate puzzles of sizes from 4×4 to 9×9 and choose one of 4 difficulty levels.

Other sites offering these puzzles include Brain Bashers where you can play a wide variety of puzzles, see the choice from the home page

There is, of course, an app for that, you’ll find Futoshiki available for Android and iOS.  The holidays offer a chance to explore some more puzzle apps and games. I have some details of various apps on this page.  Have you tried PhotoMath? Some of my Sixth Form students were checking some integration examples using this recently, it seems very easy to use and for the examples I tried looked very helpful.

MEI’s Sumaze series is most impressive, I think I’ll try Sumaze Adventure this Christmas.

For many more online puzzles to amuse you over the holidays try the Puzzle collections on Mathematics-Games.
Yohaku is a puzzle that will test your number sense and problem-solving skills. Each Yohaku puzzle is either an additive or a multiplicative puzzle. You must fill in the empty cells such that they give the sum or product shown in each row and column as well as satisfying a rule if given.


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.

Christmas 2019 Update

See Christmas Resources for the always updated Christmas collection.

Remember we have the wonderful collection of Advent Calendars to use in the run up to Christmas. I was amused at a comment from Plus Magazine regarding the inclusion of cute kittens wherever possible! Behind Door 1 of their 2019 advent calendar you will find the story of a rather important cat: Schrödinger’s cat!

Some further additions to the Christmas 2019 collection

ATM Midwinter MagicFrom the ATM for younger children, Midwinter Mathematics is a downloadable collection of mathematical activities, problem-solving and investigations that are suitable for the winter term for Primary Classrooms. Check ‘Look Inside’ for two free activities, Christmas Stockings where children can think about systematic listing strategies by working out the number of arrangements of Christmas Stockings and Paper Chains, a practical task where children use a piece of A4 paper to make the longest paper chain they can.

On the subject of paper chains, with a twist on the relay idea this TES resource, Chrismas Paper Chains, has students racing to make the longest Christmas paper chain.

Available from STEM Learning, Winter Mathematics from the Shropshire Centre for Mathematics education consists of twenty eight winter-themed activities for younger students (ages 5-11). The collection consists of a variety of investigations, puzzles and games covering many aspects of mathematics.

Also available on STEM Learning, see Christmas Puzzles; The National Centre for Excellence in the Teaching of Mathematics (NCETM) published four seasonal puzzles from Amusements in Mathematics by Henry Ernest Dudeney, published in 1917, in their Secondary magazine. I have mentioned Henry Ernest Dudeney’s – Amusements in Mathematics before (see Free Books), the Kindle edition is free. Several categories of puzzles are available. A search on Christmas returned 23 puzzles, solutions are all provided.

Perton Maths Christmas Challenge 1I often mention the Perton Maths Department, check #PertonChristmaths for their seasonal Challenge collection.

MEI Festive Challenges

MEI’s November / December 2017 M4 Magazine has been mentioned in the 2019 collection ( an excellent collection of 10 puzzles and challenges for your students with full teacher notes and solutions). Additionally, we have MEI’s November Primary Newsletter which includes some fun festive puzzles for Primary students.

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!

For your A level students, Tom Bennison has a brilliant resource – Christmas Calculated Colouring.

Sign up to the IMA e16plus Newsletter which is aimed at 16 – 19 year olds who are interested in mathematics and check the latest edition which includes two competitions to enter over the Christmas break as well as various Christmas puzzles and articles.

Christmas 2019

See Christmas Resources for the always updated Christmas collection.


Christmas Tree Trim Transum

Transum Christmas Tree Trim – Level 3

From the brilliant Transum Mathematics try the numerous Christmas activities. Try Christmas Tree Lights for example, or for a great exercise in being systematic try Christmas Tree Trim with 8 levels; students must use the given lights to create different Christmas Trees.

MD Advent Calendar
This Advent Calendar collection has problems for every age from young Primary age children to A Level (UK age 16-18).

The Advent Calendar Collection, of course, includenrich-chocolates the Nrich calendars. For more Christmas Nrich resources try Christmas Chocolates    Christmas Trees      Sums of Powers – A festive Story and Elf Suits – which looks good for thinking about systematic listing strategies!

mistletoe-linesFrom Teachitmaths, create a masterpiece! Mistletoe & lines; the description reads ‘Practise your graph drawing skills with a Christmassy theme! Plot the given points to draw a Christmas tree, then add your own lines of tinsel, giving the equation of each one.’ The pdf resource is free, you just need to register with the site. Further Christmas activities are available.

For more plotting, try this ATM open resource, Santa Plotting. Plot the points given and note the challenge questions at the end.

Excel Christmas tree From earlier years some personal TES Christmas favourites include Christmas Countdown (which although designed for daily use I have also used as an end of term activity) and Santa’s Reindeer (logic and number properties) both of which I have successfully used in class. Try this Twelve days of Christmas algebra activity or try Christmas shading graphical inequalities. This Operation Christmas Tree Excel resource makes a rather nice starter, it is possible to customise the tree.


On TES we have a complete set of relays from Chris Smith; my classes have enjoyed his Valentine and Summer relays, I think we’ll use the Christmas relay to complete this term! You can find more excellent resources from Chris on TES and follow him on Twitter here.

As with all these relays from Chris – all the answers are provided – brilliant!

GCSE Christmas

These GCSE Maths Christmas Puzzles from chuckieirish look good as do the Christmas Puzzles from ryansmailes. Also from ryansnailes, try a Christmas Maths Activities Booklet.


Festive Venn Diagrams OUP

Oxford University Press have some great free resources including some Christmas themed problems for your GCSE students.

OUP Resources

Another set of Higher (Geometry) problems is here. I like their festive Venn Diagrams, they would make a nice introduction / reminder on Venn diagrams for younger students.

Oxford University Press Christmas Problems

MEI Festive Challenges

From MEI, the November / December 2017 M4 Magazine includes an excellent collection of 10 puzzles and challenges for your students. Full teacher notes and solutions are included and the problems are ready for you to project for your classes.

MEI’s M4 Magazine archives (GCSE resources are indexed by topic) include many teaching resources, note also MEI’s Newsletters.

Here’s a Christmas tree on the Desmos Graphing Calculator site. Note this is simply a collection of lines and circles, as you can see from the syntax it is very easy to restrict x or y values.
Desmos Christmas tree

christmas-presentHow about a Desmos present to review equations of lines? This Christmas present graph makes a good starter.

I also created a version where the lines are all black which means I can easily change the colour of just one of the items to clearly display each.

For more on getting creative with Desmos, see Graph Art on Mathematics for Students.


@MEIMaths shared The Christmas Tree Bauble Calculator🎄

Dr Matthew Lettington of Cardiff University has helped Admiral create an online tool to calculate how many baubles and fairy lights are needed for the perfect Christmas tree. Answer four questions to find out how many baubles and the length of fairy lights you need!

Mostly for younger children, Top Marks have put their favourite Christmas Activities together.

If you are creating any resources yourself you might want to install some Christmas fonts! (shown here: christmas lights, christmas tree and kingthings christmas)

Christmas fonts

…and a few more Christmas resources:

We could do the annual calculation and work out how many gifts are received over the 12 days of Christmas. Murray Bourne has all the answers and more on squareCircleZ or have a look at this YouTube video.

On the subject of videos, try a video advent calendar from Numberphile!

Using the excellent MacTutor History of Mathematics archive we learn that Christmas Day 1642 was celebrated on Newton’s birthday in England.

GeoGreeting Christmas

click on the image …

Christmas 2019 WolframAlpha count and other information you probably are not too worried about for Christmas Day!

Wishing you all a very Happy Christmas and New Year. Thank you for reading and for all the various comments. Have a wonderful and well-deserved break when we get to the holidays!