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.
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 WolframAlphawhich 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.
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.
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.
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!
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!