Christmas 2017

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.

Excel Christmas treeCraig Barton has published the TES Maths Christmas 2017 Collection which has a large collection of very varied activities which come highly recommended by teachers. 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. Try this Advent Calendar complete with worksheets for students and teachers’ notes; clear instructions are given for adapting the calendar for your own classes.


Christmas Relay – Problem Solving Puzzles

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

Oxford University Press

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 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 is always worth reading and you will find an excellent mix of news and also teaching resources, note also MEI’s Newsletters.

From ATM, this open resource, Plotting Coordinates, Santa is aimed at younger students and offers the chance to practice plotting coordinates accurately. I like the extension questions at the end on changing the coordinates.

TheMyMaths team released free Christmas activities and worksheets every weekday between 1st and 15th December. The team have helpfully collected all these activities here on MyMaths or on Twitter. On day#6, for example, see some Yuletide Algebra.

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.

On Suffolk Maths you will find this large collection including games, puzzles, relays, quizzes, constructions…..

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!

Click on the graphic below to see just how hard Santa works! (Published: December 2010 by Advertising Agency: Benedict & Helfer, Hungary.)

Christmas Infographic

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 2017 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!

Correlation & Regression

Studying Statistics with my Further Mathematicians I thought I would put some resources together. The use of Technology can really help with understanding here.

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 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

PhET – Least Squares Regression

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.

We can check Regression Calculations using this Linear Regression calculator from Social Science Statistics.

Linear Regression

Social Science Statistics – Linear Regression


On the subject of correlation coefficients, we can play a game to see how well we can guess the correlation coefficient! Guess the Correlation Coefficient.


Guess the Correlation – Omar Wagih

From Cambridge PhD student, Omar Wagih ‘Guess the Correlation‘, a rather addictive game with a purpose – Omar Wagih is collecting the data on the guesses collected and using it to analyse how we perceive correlations in scatter plots. Select About to read the rules and further details.

We also need to look at ranked data and students must be able to calculate Spearman’s rank correlation coefficient from raw data or summary statistics. Again, Social Science Statistics, offers us a calculator which will be useful for checking work.

Spearman's RanK Calculator

Social Science Statistics

Calculation details provide a useful check on work.

Note Social Science Statistics also has a calculator for calculating the Pearson correlation coefficient.


Mathematical Advent Calendars

Almost December…it’s that time of year again…!
Nrich Advent Calendars

December means Advent Calendars and Nrich have published their annual Advent Calendars, one 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.

Nrich Short Problems

Nrich Short Problems (from UKMT Challenges)

You can, in fact, find a whole collection of advent calendars on Nrich and clearly, 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? 

From Plus Magazine, their 2017 Advent Calendar brings you some of their favourite Plus videos.

Plus Magazine

Plus Magazine – Advent Calendar 2017


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

Andy Lutwyche – Christmas Advent Calendar

Also on TES you can find an excellent calendar from Mark Dawes, as mentioned earlier the year doesn’t matter – December still has the same number of days!
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 an Excel file showing the difficulty of the tasks.

Access Maths Christmas RevisionAlternatively 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.

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. For an Activeinspire resource, try this version.


Averages and Spread

The Core Maths resources, now available on STEM Learning include many excellent Statistics resources. The resources are designed to enable students to use and apply statistics in unfamiliar contexts. There are several resources with large data sets available, very useful for students to get used to working with such data sets

Many of these resources could also be adapted for younger students, with my Year 10 students (UK age 14-15) I will use the data and parts of the questions from Averages and Spread: two which explores how to calculate and interpret different measures of location and dispersion.

If we look at the first question, for example, we have the data shown here. Students are required to calculate the mean, median, mode, interquartile range, range, variance and standard deviation (these last two we can save until Year 12).

Averages and Spread 2 qn 1

I particularly like this interpretation question which we can use to give some context to the use of the upper quartile as here we have the upper quartile of 21.2 above the safe limit, suggesting that a quarter of scientists exceeded the safe limit.

The safe level for one year’s exposure is 20.0 mSv. Explain if the following statement is correct, using the data you have just calculated.

‘The scientists at CERN are working within the safe levels of radioactive exposure.’

Full solutions are given in the Teachers’ notes. The activity also includes questions on frequency distributions, one with grouped data.

Averages and Spread 2 CMSP

Core Maths Support Program

We will also be able to review some charts and diagrams using these examples, drawing a box plot for the first example and a cumulative frequency chart for the grouped data example.

For some further useful resources, on TES we have a simple but effective exercise for students to practise drawing box plots byjhofmannmaths, a good example of a time-saving resource for teachers with ready drawn grids for students.

Looking at other resources by jhofmannmaths, I see many well-received resources; I like his simple but useful Expanding simple brackets mistakes which could be a useful Starter / Plenary (or anytime!).  Silly Suzie has made some errors! I appreciate resources like this with several copies to a page – very useful if you want to get a lesson started very promptly and have just changed room – it can be that the paper beats the technology!

Erica - IntegrationTalking of silly Suzie reminds me of Erica and her errors by Andy Lutwyche. I used his  Erica’s Errors on Integration very successfully with Year 12 this week, many of whom made the same mistakes as Erica. We had some great discussions on how easy it is to make such errors and they seem to believe me more than ever that having a look at the graph is a really good idea!

Integration – Desmos & WolframAlpha

With my year 12 students (UK age 16-17) we have been looking at definite Integration. Desmos and WolframAlpha are both excellent for checking work and by using the technology we have a very clear visual representation adding to our understanding.

One of the homework questions for my students involves finding the total shaded area bounded by f(x) = x4−3x3−4x2+12x, the x-axis, the line x=−1 and the line x=3.

We could use WolframAlpha for a quick check. I like the visual representation showing students clearly that they are dealing with areas above and below the x-axis.
Definite Integral
Scrolling down the page we see that this query also returns the indefinite integral.
Indefinite Integral
For the total shaded area, students could change the limits of the query to evaluate each section.

Or we could turn to the excellent Desmos where we can very simply change the limits.

Definite Integration Definite Integration 2

If you are unfamiliar with Integration with Desmos, turn to Learn Desmos: Integrals.
Note you can explore the graph shown in the video.

We could also show students this introduction to Integration on GeoGebra.

A version of this post for students which also includes links to some useful notes and examples can be found on Mathematics for Students.
Integration notes University of Plymouth