My Year 10s are very smart girls and we've been working on quadratics for a couple of weeks - it's been a bit 'death by algebra' to be honest. We've practised factorising, solving, using the formula, sketching and completing the square. Today I got them in an IT room and we had a go at Polygraph: Parabolas. It was superb.

One of the huge advantages of this lesson is that it requires absolutely zero preparation. Once you've registered with Desmos, just log in and start the activity. Your students go to student.desmos.com and enter a code and their name, then off they go. You don't really need to give any instructions because Desmos does it all for you.

The majority of the lesson is like a game of 'Guess Who' but for parabolas. Each student chooses a parabola from a selection and Desmos randomly pairs them up with another student. Their partner then has to type yes/no questions to figure out which parabola they've chosen.

Behind the scenes the teacher is able to monitor all the conversations. The interface is fantastic.

Here's some examples of the questions asked by my students today:

These examples were from quite early in the lesson. Throughout the lesson I occasionally picked out really good questions and shared them with the whole class. At one point I wrote six words on the board and encouraged students to start using those words in their questions:

- Roots
- Quadrant
- Intercept
- Vertex
- Origin
- Symmetry

I was really impressed by how quickly their mathematical language developed. They started using the new words (roots, vertex and quadrant) fluently. It was a pleasure to watch. Even when they got a bit silly, they were using sophisticated terminology:

The lesson includes other tasks which reveal misconceptions, like the question below.

Overall it was a fantastic lesson. I really saw my students' mathematical vocabulary develop. I also saw progress in their understanding of quadratic graphs. The lesson was easy to plan and utterly engaging.

At the end I let them play around with Polygraph: Hexagons for 10 minutes. Wow, they really don't have a clue how to describe polygons! We'll tackle that another day though.

Well done Desmos, Polygraph rocks.

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