Mathematical Miscellany #78

Since it is Advent, we should start by opening a Christmath door, here’s Door 3 on Transum, the Christmas Toggle Tree; can you light up all 12 lights on the tree using the buttons to toggle the current state of the lights?

Recently added to the Advent Calendar, is Mark Anderson’s Appvent, and I am delighted to see that the first entry is Jonathan Halls’s brilliant Form Time Ideas. and remember you can also use Form Time Numeracy.

NCETM continue to add Checkpoints to their collection, the image here is on Year 8 Estimation and rounding.

On Dr Frost Maths try the new look Skill Explorer which makes it easier to combine skills from multiple topics.

From the younger students to Year 13 – here’s a wonderful resource from Susan Whitehouse, a Year 13 revision lesson, Looking at Quintics. All Susan’s resources can be found here. The revison resource was inspired by Tom Button and Tayyub Majeed. I believe Tom Button started this with his favourite quintic, y = x5 − 5x3 + 5x.

I have mentioned problems from Robert Kaplinsky before, have a look at his Open Middle Math Depth of Knowledge Matrix. Problems are provided for each grade level, the first problem in the column is of a familiar kind, the Open Middle problems classified as DOK 2 and DOK 3 are on the same topic but provide significantly more challenge.

Many problems are available as a GeoGebra resource, from Tim Brzezinski, try this brilliant GeoGebra book of Open Middle themed problems. Many problems in the GeoGebra book are exact digital analogues of those found on Open Middle’s site, with other problems characteristic of the Open Middle theme

Robert Kaplinsky also has a collection of over 70 problem-based lessons which you can now browse in a spreadsheet.

Spicy Questions is a new competition for 2023 created by 1st Class Maths. The competition is for students aged 18 or below who are studying in secondary education in the United Kingdom. The questions, stated as harder than standard exam questions and with a problem solving focuswhich are based on GCSE content are suitable for GCSE and A level students. The first question will be posted on Jan 9th, in the meantime you can try the practice question.

Some reading to finish – from Quanta Magazine, The Math Behind Wordle Guesses, you can also browse the Mathematics articles.