Graphing Quadratics

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 Quadratics Explorer

PhET Graphing Quadratics

PhET Quadratics Explorer focus directrix

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.

Quadratics - pick a card

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.

Improving Learning In Mathematics is part of The Standards Unit. (The link takes you to a page where you can access all the Standards Unit resources.)
Multiple Representations

Nrich has many articles and tasks which encourage students to explore multiple representations.
Multiple Representations


Christmas 2018

Mathsbot Simultneous Grids

Jonathan Hall has given his Simultaneous Grids a festive flavour!

From the brilliant Transum Mathematics try the Christmas activities. Try ChrisMaths for example or the Christmas Numbers activity.

MD Advent Calendar
These Advent Calendars have 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 treeCraig Barton has published the TES Maths Christmas Collection which 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 here using 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!

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.

GCSE Maths Christmas Puzzles – TES

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.

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.
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 2018 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!

Mathematical Miscellany #24


Can your students solve a vexing vexillology problem? The AMSP Problem Solving Competition closes 1st February and is for any students in Years 7 to 11. Full details are available on the AMSP competition page.

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

Nrich Webinar
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.

A reminder of some of the excellent resources available from The White Rose Maths Hub Team…
The team’s GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Hub Team, @WRMathsSec is available on TES Resources.

White Rose Maths Hub problems

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 Assessment

White Rose Maths – End of Term Year 7 Higher Paper

See also, Secondary Schemes of Learning and Assessments for End of Block or End of Term. Many high-quality resources can be found on TES Resources. this search, White Rose Maths Year 7 Resources returns resources for age 11-14.

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

Mathsbot Simultneous Grids

Mathsbot – Simultaneous Grids

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


@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!


Advent – Open the Christmath Doors!

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 Dec 1st

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.

Shadt Symmetry - Nrich
Choose Dec 1st on the Nrich Secondary Calendar and we have another chance to be systematic. Nrich encourages Secondary students and teachers to print off dotty grids and circle templates to help with this year’s advent challenges. For December 1st on the Primary Calendar, we have a challenging dice problem which could also work for older students.

Note the wonderful collections on Nrich on Working Systematically.

MD Advent Calendar
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:

JCalderwood revision

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.

Access Maths Christmas Revision

Alternatively how about a Christmas Revision Calendar from Access Maths? Scroll right down this collection of very helpful GCSE Revision Resources for two Christmas Calendars, one for Foundation and one for Higher.



Mathematical Advent Calendars

December…it’s that time of year again…!

TeachIt Maths Advent Calendar

TeachIt Maths Interactive Advent Calendar

And so to the annual update on Mathematical Advent Calendars. We can start this year with a new Advent Calendar resource; checking the new resources from Teachit Maths, note the Interactive advent calendar. Teachit Maths have made this a free sample resource available to everybody. (Remember that the free subscription on this excellent site includes hundreds of high-quality pdf resources.) Teachit Maths describe the resource as an advent calendar in the form of a presentation focusing mainly on mathematics. Suitable for KS3/4. (KS3/4 is UK age 11-16). For each day you will reveal a festive fact, joke, teaching idea, activity or game.

From Andy Lutwyche we have his Christmas Advent Calendar which covers lots of different topics in number, algebra, shape & space and data and gets progressively more difficult as you go on.

Andy Lutwyche Advent Calendar

Also from Andy, try his Advent Calendar – Solving Linear Equations. Students answer the questions (the solutions are 1 to 24) and each answer links to a word; when the words are put in numerical order an entire joke is revealed! And another…for older students, Differentiation Advent Calendar where students are asked to find the gradient of a curve at a given point. Cheesy joke included!

Also on TES you can find an excellent calendar from Mark Dawes.

MD Advent Calendar

This is a lovely resource with over 30 problem-solving tasks for use in maths lessons in December. Suitable for starter activities, they span a range of abilities in KS3 and KS4. As well as the calendar the resource includes worksheets for some of the problems and an Excel file showing the difficulty of the tasks.

I do like Mark’s suggestions for use in class, he has given instructions for manipulating the resource so teachers can choose the problem they want for any day!

KS3 Calendar

For a collection of starters aimed at KS3 students try this Christmas Maths Advent Starter Calendar. This provides a nice mix of activities.

JCalderwood revision

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.

Transum AdventFrom a favourite site, where you can find so many excellent resources, Transum has an Advent Calendar. Behind each door, you will find a Christmaths activity, laugh at a cracker joke and solve a mathematical word puzzle.
(See this post for more on Transum.)

Mathsvent Calendar
Mathsvent Calendar 1 DecTry this Mathsvent Calendar from Phil Bruce. For December 1st (Saturday – so I think Friday would be a good day to start on the Advent Calendars!) put the baubles in size order along the tinsel starting with the smallest at the bottom.

Very usefully, you can find all 24 puzzles listed by topic. These puzzles are great, extensions are given for many of the problems too.


Nrich CalendarsNrich has published their annual Advent Calendars – one for Primary and one for Secondary. Secondary students and teachers are encouraged to print off dotty grids and circle templates to help with this year’s advent challenges. The Primary advent calendar focusses on activities and games using Dice.

Both Nrich and Plus Magazine have published wonderful collections of Advent resources, clearly, for an Advent Calendar, the year does not matter so we have lots of choices!

From Nrich in 2017 we have a calendar for Primary and one for Secondary each containing twenty-four problem-solving activities, one for each day in the run-up to Christmas. The secondary tasks come from the excellent Short Problems collection. (I will update this post with any new Advent resources from Nrich).

Nrich Short Problems

You can, in fact, find a whole collection of advent calendars on Nrich and as already mentioned, the year doesn’t matter! Note the different themes available – a Sudoku for each day perhaps? Or a tangram? Maybe you want to play a game?

Plus Advent
From Plus Magazine, the Plus 2018 Advent Calendar features favourite Plus podcasts; to quote Plus:

“From the secrets of the Universe to the maths of football stadiums, there should be something there for everyone.”

Like Nrich, you can find a whole collection of Advent Calendar resources from Plus Magazine. The 2017 Advent Calendarfor example, brings you some of their favourite Plus videos.

Plus Magazine

Access Maths Christmas Revision

Alternatively how about a Christmas Revision Calendar from Access Maths? Scroll right down this collection of very helpful GCSE Revision Resources for two Christmas Calendars, one for Foundation and one for Higher.

We should celebrate the women in STEM subjects, try these Advent Calendar posts.
MGA text
Did you know that Maria Gaetana Agnesi was the first woman to write a Maths textbook?
(Thank you @MEIMaths  for sharing this.)

Advent calendar Alex Pett

Alex Pett created his advent calendar complete with history and problems for each day. Alex has provided a pdf version or use as a Google document.