^{th}gems post!

This is a big milestone for me. I've published 327 posts since I started writing my blog four and a half years ago. One hundred of those posts have been part of my 'Maths Gems' series - each one has featured a selection of news, ideas and resources for maths teachers.

I used to write one gems post a week (I was on maternity leave!) but now I work full-time I only manage one or two gems posts a month. Twitter still provides a constant stream of material to pick from, so I continue to summarise and share some of the best ideas, in the hope that I can get these ideas into classrooms all over the world.

To celebrate the fact that this is my 100th gems post, I'll be recording a special podcast with Craig Barton next weekend. In preparation for this podcast Craig wants you to choose your favourite gem (there are 500 to choose from, all indexed here). Tweet, DM or email Craig (or comment below) to explain why you chose it, and it could end up on the show.

On with the gems...

**1. Mastery Learning Cycle**

Over the course of the last two years Mark McCourt (@EmathsUK) has published a series of posts on mastery. You must read these excellent posts if you haven't already! Oliver Caviglioli (@olicav) and Mark have worked together to create a poster which visualises Mark's model of the Mastery Learning Cycle.

This is just an extract - download the poster to understand what it's all about. This is definitely something to share with all trainee maths teachers (and probably all experienced maths teachers too).

No doubt Mark's book 'Teaching for Mastery', due to be published in Spring 2019, will be a must-read too.

**2. Manipulatives**

If you want to use manipulatives in your teaching but don't know where to start, Craig Barton and Bernie Westacott have recorded a video podcast that you will find very useful. You can access the videos through Craig's Youtube playlist. For example here Bernie explains how to use manipulatives to teach negative numbers:

I've blogged before about Jonathan Hall's (@StudyMaths) amazing library of virtual manipulatives. It has continued to grow.

One of the new additions is a bar modelling tool. It's very easy to use and I'm sure lots of teachers will find it helpful.

**3. Indices Tasks**

Miss Konstantine (@GiftedBA) shared a task for exploring indices. Students sort the cards and find the odd one out.

Peter Drysdale (@pwdrysdale) made a Desmos version of this card sort.

I can't keep up with all the ideas and resources that Miss Konstantine (@GiftedBA) has been sharing lately! For example I enjoyed her recent perimeter problems. Check out her Twitter feed and blog for lots more great stuff.

Speaking of indices, I made an indices task for a recent Teach Secondary article. This resource is designed to be used with a Year 7 class after spending some time on index notation, but it would work with other year groups too. The full resource is here - it contains four introductory indices activities.

Here's a nice idea to help students develop an understanding of what area is. Ilona Vashchyshyn (@vaslona) challenged her students to write their name so that it covers an area of exactly 100cm

Mrs Budak (@mrsbudak) tweeted an interesting idea from @teacher2teacher that could work in every subject. At the end of an assessment students are given the opportunity to write down everything

Finally, for some reason this reminded me of another gem that I've been meaning to share for ages...

It such a simple idea little change, and so easy to do! It's worth reading the thread for discussion and ideas. Credit to Howie Hua (@howie_hua) for first tweeting about this back in May. Here's another of Howie's ideas:

I've had a busy few weeks visiting a number of different schools, including one where I saw silent teacher in action for the first time.

I helped to run the first day of a new London-wide Maths Hub Work Group on developing A level pedagogy, which is led by Carlos Karingal. We were fortunate to have a fantastic group of teachers attend and I look forward to seeing how our A level teaching develops throughout the year. In my session I talked through some of the ideas in this excellent piece written by Chris McGrane about approaches to teaching calculus.

Next week I'll be supporting Chris Reilly in running another Maths Hub Work Group - Challenging Topics at GCSE. I'll blog about this soon.

My second Teach Secondary article is now available to read online. It's about order of operations, and opportunities to interleave this topic with fractions, decimals and algebra.

Did you see that Pearson have a new series of maths textbooks coming out? It's called Purposeful Practice and you can view sample pages here.

Finally, Christmas is fast approaching so you might find a use for my collections of seasonal resources (here and here) - some are topic based and some are for enrichment. I've written various posts about Christmas presents for maths teachers over the years (here is last year's post on TeachWire if you're looking for inspiration). If you want to treat yourself during December, the MA has a Christmas advent calendar where you can get daily discounts on MA books.

I'll leave you with this lovely problem shared by James from MathsPad (@MathsPadJames). There are a range of solutions in the comments (spoiler alert!), but it can be solved in a matter of seconds without any workings using GCSE level maths.

Speaking of indices, I made an indices task for a recent Teach Secondary article. This resource is designed to be used with a Year 7 class after spending some time on index notation, but it would work with other year groups too. The full resource is here - it contains four introductory indices activities.

**4. Area**Here's a nice idea to help students develop an understanding of what area is. Ilona Vashchyshyn (@vaslona) challenged her students to write their name so that it covers an area of exactly 100cm

^{2}. Read the thread for ideas on how to extend this activity.The challenge: Write your name so that it covers an area of exactly 100 cm squared.— Ilona Vashchyshyn (@vaslona) 16 November 2018

Love the different strategies students used here. E.g. Leia, who chose to make each letter 25 cm^2. Notice the revisions on the A.#mathchat #MTBoS Cc @PaiMath pic.twitter.com/FowEQoL4I6

**5. Assessment and Questioning**Mrs Budak (@mrsbudak) tweeted an interesting idea from @teacher2teacher that could work in every subject. At the end of an assessment students are given the opportunity to write down everything

*else*they know about the topics on the test. It stops students being frustrated when a test doesn't cover the things they revised, and it's probably a good use of time to retrieve stuff from one's memory and write it down (it definitely beats sitting there waiting for the test to end!).Finally, for some reason this reminded me of another gem that I've been meaning to share for ages...

Two years ago, I was saying “do you have any questions?”. Last year I switched to “what questions do you have?” It made a difference. Today I tried “ask me two questions”. And they did! And those ?s led to more ?s. It amazes me that the littlest things have such a big impact!— Andre Sasser (@MrsSasser) 27 August 2018

It such a simple idea little change, and so easy to do! It's worth reading the thread for discussion and ideas. Credit to Howie Hua (@howie_hua) for first tweeting about this back in May. Here's another of Howie's ideas:

For tests, I dedicate the first 5 minutes to have students hold the tests and talk to their group about strategies (w/out pencils). This lowers their test anxiety AND when you walk around, you hear some of the richest math conversations. #iteachmath— Howie Hua (@howie_hua) 28 September 2018

**Update**I've had a busy few weeks visiting a number of different schools, including one where I saw silent teacher in action for the first time.

I helped to run the first day of a new London-wide Maths Hub Work Group on developing A level pedagogy, which is led by Carlos Karingal. We were fortunate to have a fantastic group of teachers attend and I look forward to seeing how our A level teaching develops throughout the year. In my session I talked through some of the ideas in this excellent piece written by Chris McGrane about approaches to teaching calculus.

Next week I'll be supporting Chris Reilly in running another Maths Hub Work Group - Challenging Topics at GCSE. I'll blog about this soon.

My second Teach Secondary article is now available to read online. It's about order of operations, and opportunities to interleave this topic with fractions, decimals and algebra.

Did you see that Pearson have a new series of maths textbooks coming out? It's called Purposeful Practice and you can view sample pages here.

Finally, Christmas is fast approaching so you might find a use for my collections of seasonal resources (here and here) - some are topic based and some are for enrichment. I've written various posts about Christmas presents for maths teachers over the years (here is last year's post on TeachWire if you're looking for inspiration). If you want to treat yourself during December, the MA has a Christmas advent calendar where you can get daily discounts on MA books.

I'll leave you with this lovely problem shared by James from MathsPad (@MathsPadJames). There are a range of solutions in the comments (spoiler alert!), but it can be solved in a matter of seconds without any workings using GCSE level maths.