Happy New Year 2019

It’s that time of year again and we can play the 2019 Year Game in our January lessons. You can preview the 2019 game now. Can your students use the digits in the year 2019 and the operations +, -, x, ÷, sqrt (square root),^ (raise to a power), ! (factorial), and !! (double factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100?
My students have always been curious about the double factorial function.

Excel has a function for computing double factorials, illustrated here.

This year I think I will show my students a few examples and see if they can work out what is going on!

Have a look at this definition from Wolfram Math World or have a look at this article on Ask Dr Math. Note the relationship between the double and single factorial functions.

We could also look back and use the excellent MacTutor History of Mathematics Archive from the University of St Andrews, Scotland. We could check today or any day for Mathematicians who were born or died on that day.

The site is searchable in several ways, including the comprehensive index of  History Topics.

We can always turn to Number Gossip from Tanya Khovanova for information on properties of a number.

2019 is a Happy Number – one of my all-time favourite investigations has to be Happy Numbers!

Happy Numbers is accessible for a range of abilities and offers a great lesson in the value of recording results carefully so you can use previous results and save yourself work! The Happy Numbers page includes additional resources, have you seen the Dr Who clip – Happy Primes?!

2019 is square free as its prime decomposition contains no repeated factors. I have found students are usually interested in these number properties and we could certainly usefully revise prime factor decomposition and come up with some more square free numbers.

2019 is also a lucky number, note that 13 is a mathematical lucky number!

We can also look at WolframAlpha which provides further information including what 2019 looks like in historical numeral forms. We could use the various WolframAlpha queries to learn how Babylonian, for example, numerals work. I have successfully used this as an interesting starter for January lessons.

The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.

For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.

From trol, Teacher Resources on Line, we can make a calendar for 2019. I do like the fold and tuck models – no glue required!

Wishing educators and students everywhere a very Happy New Year.

Have you seen…? #4

The Kent maths puzzle from The University of Kent?

The puzzle has been set to both challenge and entertain. The School of Mathematics, Statistics and Actuarial Science at the University of Kent contribute to BBC Radio 4’s Puzzles for Today.

#Have you seen…? is one of a series of short posts, simply to quickly provide links to interesting information and/or resources; a subset of the Mathematical Miscellany series.

By Colleen Young

Reading

KS3 Instant Maths Ideas – Colin Foster

For various free Mathematics books, check the Books (free) page from the Reading Series of 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:

For news, check The Independent on Mathematics; this week we have the discovery of a new Mersenne Prime. See more on this story on the Mersenne Prime website.

How about an interactive comic on the Art and Science of Memory? How to Remember Anything Forever-ish by Nicky Case (October 2018).

Such an important topic – see also Retrieval Practice.

I was very happily distracted by Nicky’s website, there is so much to explore. Try Explorable Explanations, look at these Mathematics explorations for example; try The Birthday Paradox Experiment or The Monty Hall Problem.

Explorable Explanations, Math – Nicky Case

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 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.

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.)

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

Christmas 2018

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.

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, include 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!

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 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!

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

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

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.

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.

How 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.

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)

…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.

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!