Wishing educators and students everywhere a very **Happy New Year**.

Visit the page **Happy New Year** for ideas for Mathematics classrooms.

Wishing educators and students everywhere a very **Happy New Year**.

Visit the page **Happy New Year** for ideas for Mathematics classrooms.

**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.

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

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!

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.

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**.

See **Christmas Resources** for the always-updated Christmas collection.