**1. Polygraph**

There's been a lot of buzz about Desmos' new Polygraph activities. They're mathematical versions of Guess Who, designed to 'foster the pleasure and the power of words without the drudgery of the lists'. There are currently four Polygraph activities:

Let's look at Polygraph: Parabolas. Students work in pairs (a picker and a guesser) on separate tablets, phones or computers. The picker selects a graph from a set of parabolas. The guesser sees the same set of parabolas - their task is to identify which graph the picker has chosen by asking a series of yes/no questions. For example they might ask about the number of roots or the location of the vertex or y-intercept. The guesser types their questions and the picker responds with yes, no, or don't know. The guesser keeps asking questions until they are able to identify the chosen graph.

Students then have the opportunity to analyse and refine their questioning, and you have a class discussion to formalise the mathematical vocabulary.

As with Desmos' awesome Water Line activity that I described in Gems 13, it's incredibly quick and easy to get started. I'm going to be teaching quadratics to Year 10 shortly and can't wait to use the Parabolas activity. And I plan to use the Linear Graphs version with my Year 9s too.

Extract from Polygraph: Lines |

**2. Point, Point, Gradient**

Tina Cardone (@crstn85) shared this lovely activity 'Point, Point, Slope' by Michael Fenton (@mjfenton). It's a simple but effective lesson idea in which students have to use any digit from 2 to 9 to create two points - you could give them post-its or number tiles to shuffle around. You provide criteria, such as 'create two points which determine a line with the greatest possible gradient'. Read the full post for more ideas. There's loads you could do with this activity, for example you could ask your students to use six different digits (from 0 - 9) to create three points which lie on the same line. It's a good way to develop understanding of linear graphs and I think it would work well at both GCSE and AS level.

Michael's blog is full of excellent ideas. For example in Two Fractions students place digits and operators in the boxes below to make an expression with the greatest possible value.

This reminds me of the Blanks activities I featured in Gems 17, which you can read more about in Sarah Aldous' post Logarithm Questions Around the Room.

I liked Davis Wees' (@davidwees) tweet about owning multiplication facts.

There's probably an interesting psychological discussion to be had here - would relying on someone else make students less likely to remember facts, or would the association create a memory trigger as David suggests? I think it's the latter. Like Colin, I once had a sixth form student called Suzy who was always very vocal in class about 'not forgetting the plus C'. I still hear Suzy's voice whenever I do indefinite integration!

Back in Gems 13 I talked about making your students 'Number Experts'. I shared two websites that are useful for finding out properties of numbers (numbergossip.com and numdic.com). Both websites are excellent - for example, numbergossip.com tells me that 28 is a perfect, composite, happy number, and numdic.com (which wins the prize for funniest URL) gives me the binary and Roman Numeral representations of 28. I've now discovered a new website - the Number Property Calculator - which I like because of the way it gives information about the meaning of the number properties. Here's a small extract from what comes up when I search for 28:

I found this website when I was browsing through old posts on Math Munch. Math Munch is a 'Weekly Digest of the Mathematical Internet'. It's packed full of fantastic resources and ideas so it's definitely worth subscribing to receive weekly email updates, and you can follow them on Twitter too (@MathMunch).

Andy Shaw (@Squidworm74) pointed me in the direction of these lovely Euclid videos on YouTube by Shoo Rayner (@shoorayner). They are fantastic videos and I can't wait to share them with my Year 7 students. Check out the full playlist here. Here's an example about different types of triangles:

That's it for this week. I hope you've found some inspiration in this post. I'll leave you with this brilliant video by the ever awesome Vi Hart - The Gauss Christmath Special. Thanks to Chris Smith (@app03102) for sharing this.

Have a wonderful Christmas!

Michael's blog is full of excellent ideas. For example in Two Fractions students place digits and operators in the boxes below to make an expression with the greatest possible value.

This reminds me of the Blanks activities I featured in Gems 17, which you can read more about in Sarah Aldous' post Logarithm Questions Around the Room.

**3. Owning Facts**I liked Davis Wees' (@davidwees) tweet about owning multiplication facts.

**4. Number Properties**

Back in Gems 13 I talked about making your students 'Number Experts'. I shared two websites that are useful for finding out properties of numbers (numbergossip.com and numdic.com). Both websites are excellent - for example, numbergossip.com tells me that 28 is a perfect, composite, happy number, and numdic.com (which wins the prize for funniest URL) gives me the binary and Roman Numeral representations of 28. I've now discovered a new website - the Number Property Calculator - which I like because of the way it gives information about the meaning of the number properties. Here's a small extract from what comes up when I search for 28:

**5. Drawing Euclid**

That's it for this week. I hope you've found some inspiration in this post. I'll leave you with this brilliant video by the ever awesome Vi Hart - The Gauss Christmath Special. Thanks to Chris Smith (@app03102) for sharing this.

Have a wonderful Christmas!

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