For various free Mathematics books, check the Books (free) page from the Reading Seriesof pages; do you have Colin Foster’s lovely KS3 Instant Maths Ideas, the brilliant A Level worked examples from Hodder and the Shell Centre books in your collection?

Note that the Reading series includes these Research pages:

To help students understand the links between algebraic and graphical representations technology can be so helpful. Try Graphing Quadratics from PhET Interactive Simulations. Using this you can generate definitions for vertex, roots, axis of symmetry and compare different forms of a quadratic function. For your older students, you can define a curve by its focus and directrix!

PhET Graphing Quadratics

Focus & Directrix

These interactive simulations work on phones and tablets as well as desktops.

We could also use Desmos, GeoGebra or WolframAlpha to quickly demonstrate a graphical representation.

For an excellent teaching resource for looking at multiple representations of quadratics, try Pick a Card from Underground Mathematics.

Underground Mathematics – Pick a Card

Each of the cards in this interactivity describes the same quadratic function. If you reveal one card (by clicking it), can you work out the content of all the other cards? Some questions to consider and more details about the interactivity are also given.

As with all Underground Mathematics resources, teacher notes and supporting materials are provided.

See Malcolm Swan’s wonderful Improving Learning In Mathematics for commentary on using multiple representations (See section 4.2). This publication discusses effective teaching so well to help us think about just what makes a quality resource for learning.

From 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.

Craig Barton has published the TES Maths Christmas Collectionwhich has a large collection of very varied activities which come highly recommended by teachers. Craig has helpfully categorised the resources as you may need them. From earlier years some personal 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 describe the Christmas tree hereusing inequalities. This Operation Christmas Tree Excel resource makes a rather nice starter.

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!

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.

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.

TheMyMaths team release free Christmas activities and worksheets. The team have helpfully collected these activities here on MyMaths. (MyMaths 2017 collection)

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.

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

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)

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!

Christmas 2018WolframAlpha count and other information you probably are not too worried about for Christmas Day!

Wishing you all a very Happy Christmasand 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!

This and other competitions can all be found on the Competitions page of this blog.

On Wednesday, December 12th, Nrich have a pilot webinar for students and teachers. For the event, Nrich will introduce a problem and invite students to work on it for between 5 and 10 minutes. During this time, teachers can comment online to ask questions on behalf of the class, or share any ideas that have arisen in their classroom. There will also be an opportunity for classes to upload photos of their work.

This sounds excellent, certainly something to investigate. Read more here.

The booklet contains over 50 problem-solving questions suitable for KS3 and GCSE classes, answers are also provided. Also from the team, their mastery schemes of learning include Year 7 material (UK age 11-12); an assessment is also available.

White Rose Maths – End of Term Year 7 Higher Paper

So, it’s nearly Christmas, more updates have been made to the Advent Calendar collection.
We should celebrate the women in STEM subjects, try these Advent Calendar posts.

Did you know that Maria Gaetana Agnesi was the first woman to write a Maths textbook?
(Thank you @MEIMaths for sharing
this.)

Mathsbot – Simultaneous Grids

Staying with Christmas, Jonathan Hall has given his Simultaneous Grids a festive flavour!

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!

It’s December! So many mathsy doors to open!
See my updated Advent Calendar collection, with some additions since last week’s original post. Both Nrich and Plus Magazine have created 2018 Advent Calendars.

Now it’s December – you can open Transum door 1 to reveal this gem!

Transum Maths Advent Calendar

I do like this Dec 1st Transum activity. Use the given palette to make sure that all the trees are decorated differently – brilliant for thinking about systematic listing strategies. Note the different levels available.

Staying with the being systematic theme, we could work out how many triangles inside the 5-pointed Christmas star on the Problem Solving Calendar from Mark Dawes. Mark has provided useful worksheets to accompany some problems including this one.

Looking again at some of these Advent calendar resources, I think I will be using some as end of term Christmas activities for examination classes. In this category we have for example:

J Calderwood has provided three Advent Calendars – Advanced Higher, HIgher and N5 Maths for Scottish Students. A great revision resource which could be adapted for different courses.