## 22 November 2014

### 5 Maths Gems #15

Welcome to my 15th weekly gems post - this is where I feature some of the best teaching ideas I've seen on Twitter each week.

1. Slice The Pie
Paul Rehmet (@prehmet) has built an interactive tool to help students build numerical fluency. It's a simple fraction game - Slice The Pie - which helps students develop an intuitive sense of the relative sizes of numbers. It's not compatible with mobiles yet but would work on your interactive whiteboard. I love this. Have a play with it, I think you'll love it too. And follow Paul on Twitter because there's more to come from him.
2. Remembering Inequalities
In my post about Ideas from Shanghai I shared this visualisation which helps students remember which inequality sign is which.
All students need to do is visualise numbers as blocks - the wider end of the inequality symbol fits over the bigger stack of blocks. So if x > 2, we know x must be a number bigger than 2.

Chris Smith (@aap03102) pointed out that this doesn't work for negative numbers.
I'm sure our friends in Shanghai have a solution for this but that information hasn't filtered through to us, so let's come up with our own alternative that works for both positive and negative numbers. We just need a way for students to remember which symbol is which.

I'm really grateful to all the lovely creative tweeters who offered ideas - my favourite was this calligram from Chris.
So if x < - 8, we see the < symbol and think of the letter L, so we know x is less than -8.

Eventually students will automatically know the meaning of the symbols on sight, without having to visualise blocks or words.

These methods are far better than thinking of crocodiles - this can confuse students, as described in Nix the Tricks (extract below).

3. Squares and Cubes
I'm enjoying La Salle Education's (@LaSalleEd) new 'Problem of the Day' series.  You can search the collection by age or topic. The example below (Square Boxes) is a nice logic problem consolidating knowledge of square numbers.
If you're teaching square numbers, you might also like this 'Square and Cube Numbers Puzzle' from MathsPad...
... and this lovely square and cube numbers display from Clarissa Grandi (@c0mplexnumber).

4. Mathsticks
I recently discovered the brilliant Mathsticks website which is created by John Duffty (@johnduffty). I registered and explored - it's mostly primary stuff but some of the ideas might be helpful at Key Stage 3. Here's a couple of examples:
This calculator activity could be useful for Year 7 students to practise converting fractions to decimals. Students work in pairs, taking it in turns to select a card and read the fractions one at a time so that their partner can enter them into a calculator as decimals. The five numbers are added (the total should match the 'Check sum' on the card) and then the two students work together to solve the last question on the card.

I also love Shape Taboo. Again, students work in pairs - the object of the game is for the reader to describe the word on the card without using any of the 'Taboo' words. This is great for developing mathematical vocabulary. If you like this taboo idea then check out these excellent Mathematics Taboo Cards from Paul Collins (@mrprcollins) too.

My readers in America might like these taboo cards from @jacehan.

5. Desmos Graph Challenge
I adore Desmos and am always looking for ways to get my students using it. I particularly like the lesson described by Chris Sieling (@CjSieling34) in his post Parallel & Perpendicular Slope. Once you've taught students about the gradients of parallel and perpendicular lines, get them in a computer room (or get the iPads out, if you have them) and give them this worksheet, which I think will be very easy for them to follow independently. They are given certain lines which they plot (in Desmos, though I suppose this could be done by hand) and then they add the correct parallel or perpendicular lines to make the required shape. It's a really nice activity which will help you check their understanding of this topic.
 Extract from Desmos Graph Challenge
Here's my answer to the second question in the extract above.

To extend this task, you could have students restrict the domains of the functions, as I've done below. If you do this, it's important that they figure out how to calculate the coordinates of the vertices.

If you're teaching parallel and perpendicular lines then also check out my post linear graphs for more ideas and resources.

A request for misconceptions
When I plan lessons, I find it helpful to try to predict the misconceptions that might come up. Sometimes I'm surprised by the mistakes that students make, which are often the result of my explanations not being clear enough. Knowledge of common misconceptions comes with experience but I think it would benefit new maths teachers if they could consult a website to see examples of the sort of things students get wrong.
 A not-so-common misconception from one of Chris Smith's students
American teacher Michael Pershan (@mpershan) has a brilliant website Math Mistakes where he compiles, analyses and discusses the mathematical errors that students make. I want to set up something similar for the UK (because our curricula and vocabulary are so different), but I won't have time to do the excellent analysis that Michael does. Instead it would just be a collection of misconceptions, tagged by topic. But I still think it might be useful.

So I have a request - could you start taking photos of misconceptions in your students' work and emailing or tweeting them to me? Once I've got a small selection I'll start a website and I hope, like my Pret homework website, it will grow quickly and prove to be a helpful resource. Thank you in advance!

That's it for today. Please don't forget to vote for me! :), I'll leave you with this cute 'Math we know drama', shared by @FascinatingVids.