5 Maths Gems #167

Welcome to my 167^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Polypad

I've blogged about Polypad before, and used it myself in a lesson on nets last week. My students were suitably impressed! Recently there's been a series of tweets about some really cool stuff that Polypad can do - these are definitely worth a look. Click on the tweets below to see the animations in action, and check out @MathigonOrg's feed for more like this. I particularly like what you can do with factors.

It’s awesome how how Ss can explore greatest common factor of any set of numbers in @MathigonOrg #Polypad — especially when number fact fluency isn’t quite there yet. For many Ss, automaticity can develop through playful explorations like these! https://t.co/HgqAGlaGXg #MTBoS… https://t.co/Zk8W8FU5mG pic.twitter.com/wZ5QHE8HwV

— Tim Brzezinski (@TimBrzezinski) February 12, 2023

How does scaling a hexagon's side length impact the 4 animations on Polypad? What will stay the same? What will change?

Learn about these new features in the latest "What's New" video at https://t.co/oSXzdL2Bq4@MathigonOrg @desmosclassroom @Amplify #iteachmath #mtbos pic.twitter.com/JAzZnsIJLM

— David Poras (@davidporas) February 17, 2023

Visually solving equations w/fractions as coefficients in @MathigonOrg #PolyPad. https://t.co/vgrvly7vVK @desmosclassroom @Amplify #math #MTBoS #ITeachMath #algebra pic.twitter.com/2bXs2Gk6fP

— Tim Brzezinski (@TimBrzezinski) February 17, 2023

2. Fingertip Knowledge
@mathsmrgordon has shared a set of fingertip knowledge documents for Foundation Tier GCSE. These are like self-quizzable knowledge organisers, similar to my Knoweldge Quiz books, but with calculations as well as factual recall. 

You can download these documents for algebra, number, ratio and proportion, charts and averages, probability and geometry and measure. Thanks Ben!

3. Standard Form
@nathanday314 continues to produce amazing resources. His Calculations with Standard Form Booklet is full of excellent tasks with loads of challenge. Here are a couple of examples:

Nathan also produced some Star Wars Pythagoras Challenges which I love:

4. Kinematic Graphs

I taught tangent to a curve and area under a graph to Year 11 a couple of weeks ago and spotted these two tweets about kinematic graphs. These are helpful for both maths and physics teachers.

I'm a sucker for a pretty graphic - and how pretty are these! https://t.co/epPwAsVG2j
So many fab comics on here for Mechanics and Physics #mathsTLP pic.twitter.com/R2q8KbvnpH

— Christine Norledge (@MissNorledge) January 29, 2023

Created this table fill for velocity-time graphs pic.twitter.com/fecWPsOCGW

— Miss E (@Miss_R_Em) August 25, 2022

5. Same and Different
Thank you to @KarenCampe for sharing her brilliant blog post 'Same and Different'. This post is about a thinking strategy Karen uses for discussion in her lessons in which she asks students to compare and analyse features of two mathematical situations. Here are a few examples.

The first shows two subtraction problems: 5 – 2 (top) and 2 – 5 (bottom).

And this one is for gradient and y intercept:

And here's one on simultaneous equations:

And one on notation:

There are loads more examples in Karen's blog post.

Update

My school finally had its much-awaited first visit from Ofsted. They did a deep dive in maths. I'm really proud of my wonderful team - they're all superstars. Here's seven tenths of my department celebrating the end of a challenging week:

Over half-term I was busier than usual on my blog, publishing three posts:

• Ten Videos for Maths Lessons
• Area in Depth (sharing an exciting new video from me and Craig Barton, sponsored by AQA)
• Ratio by Sam Blatherwick (a #doseofdon post)

I received two lovely parcels: David Acheson's excellent new book 'The Spirit of Mathematics' (with thanks to Oxford University Press) and a new Casio 991CW, engraved with my name (with thanks to Stephen at Science Studio).

Here are some things you might have missed:

• I discovered a website drolivermathematics.com which features numerous resources including condensed papers for GCSE, A level and AQA Certificate in Further Maths. This is great for reducing printing costs, and I like the way the solutions are set out.
• I made a Year 11 final stretch calendar for my team to help them plan their remaining time with Year 11. Feel free to download and edit this for your school if it helps.
• @draustinmaths has been creating loads of new resources including some for indices, similarity, trig graphs and recurring decimals. Check out her website draustinmaths.com to download her resources.
• @Arithmaticks shared a great blog post 'Year 11 Staple Challenge' about a clever way to use past papers with GCSE students.
• @MattTheApp shared an exciting new feature on his website: a blank whiteboard interface with a large range of tools. It has everything from a protractor to a number line to an onscreen timer.

As we head into Spring, there's loads to look forward to. #mathsconf31 in Bracknell will be great - I'm very much looking forward to presenting on Pythagoras which is one of my favourite topics. La Salle is still looking for presenters for this conference and I strongly encourage teachers to submit workshop proposals. I'll also be taking forty Year 10 students to Maths in Action on 7 March which will be brilliant. And I'll be going to the Christopher Zeeman Medal Lectures and Ceremony at the Royal Society on 22 March. The Spring term ends with the Joint Conference of the Mathematics Subject Associations at Warwick University. I love a residential campus conference! So there's lots of fun stuff coming up. On the flip side, over the next two weeks I'll have 127 Year 11 mock papers to mark, which is a bit less fun... I'm sure lots of you are in the same boat.

I'll leave you with a set of GCSE revision memes (first shared by Paul Collins years ago - and I've added some more). We've put a few up in the maths corridor in the run up to mocks to lighten the mood and get people smiling. Don't forget, if you're looking for revision resources for Year 11, there's an extensive collection here.

Two Maths Apps for Children

A little while ago I had a comment on my blog from a parent who asked if I could recommend some apps for their children. I couldn't at the time, but now I can. I recently did some work researching some of the best apps related to maths, logic and problem solving for all Key Stages (from age four through to eighteen). There are many! In the process of doing this research I downloaded some brilliant apps for my own children to try out. My daughters Maddie (7) and Hettie (5) got to be my guinea pigs, and thankfully they really loved the apps I chose for them. I've decided to write about two of my favourite apps here. This is the first time I've written a post aimed at parents rather than teachers. Note that I bought these apps myself - no one has paid me to promote their app (I don't do that!).

Thinkrolls
As I write this post my five year old is sitting next to me playing Thinkrolls. She loves it! Every now and then she asks me to give her a hint when she gets stuck. I try not to give her a hint - I know she can work every level out herself, once she's had a think about it. Thinkrolls is a beautiful little game and absolutely perfect for her age. Easy mode is aimed at three to five year olds and hard mode is for ages five to eight. The idea is to move cute little characters around mazes. It takes logic and creative thinking. It's super fun, and well worth the £3.99.

I've always been really hesitant about paying for apps but now I realise that's a bit silly - I buy books and board games, I rent films and subscribe to Netflix, I pay for swimming lessons and Kung Fu and so on - so I'm not sure why I thought that I shouldn't spend £3.99 on a clever little educational app.

I'm very pleased to see that the developer of Thinkrolls has a number of similar apps so that when we finish the first Thinkrolls we can try another one in the series. 

Slice Fractions
My seven year old has been playing Slice Fractions. This is directly related to the maths curriculum but I don't think she thinks of it as a maths game. To her it's just a game involving woolly mammoths in funny hats.

She's done a little bit of work on fractions at school but she's very much a novice. As soon as the app introduced fraction notation she started to find it a bit tricky because she doesn't know the basic concepts (eg what a quarter is), but she's not been put off. She loves it and she seems to be picking up the concepts pretty quickly. The makers of this app say that research shows that "Slice Fractions significantly improved students’ performance in a very short amount of time". So perhaps this game will help to develop my daughter's understanding of fractions, as well as giving her opportunities to solve problems and think logically. And even if it doesn't help her understand fractions better, then there's no downside because to her it's just a fun game.

Slice Fractions is £3.99, and there's a sequel (Slice Fractions 2).

If you have children a similar age to mine, I recommend both Thinkrolls and Slice Fractions. In my opinion they're worth buying.

The other maths apps that are really well respected are those from Dragonbox. They have apps for kids from age four up to teenagers (including algebra for both five and twelve year olds). I haven't tried them yet but I've heard they are awesome.

By the way - I haven't featured the brilliant apps Box Island and Sumaze Primary here because I've blogged about them before. I should mention Numberblocks though - they have two lovely apps, one of which is free.

Enjoy!

My guinea pigs!

5 Maths Gems #108

Welcome to my 108^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. SMP
Christian Bokhove (@cbokhove) and his team have been working on this project for a while so it's exciting to see the launch of smp2.co.uk. They have created PDFs of dozens of old SMP maths textbooks and booklets. Read about the aims of the project here.

Click ‘Access to SMP’ to register and download the materials. It's free and there's absolutely loads of material to look through. It's hard to know where to start! I'm very grateful to those involved for all their hard work on this.

Here's a randomly picked example of a task on calculator use. It's from Book G1.

And here's part of a task from a Level 3 booklet 'Coordinates 2 - Extension'.

2. Storyboarding
Thank you to Dale Chapman (@MrChapmanMaths) for sharing his storyboarding idea. This is where students create a simple set of instructions with pictures to explain a procedure. I blogged about a really similar idea for teaching constructions in Gems 30 back in 2015, but subsequently forgot all about it so this is a great reminder! Plus it's good to see it in use for bearings, and I wonder what other topics would lend themselves well to storyboarding.

3. GCSE Revision
As always at this time of year there's been a flurry of new revision resources.

• Grant from Access Maths (@AccessMaths) shared another Progressive Overload grid - this one is for ratio and proportion.

• The maths team at Delta Trust (@deltatrustmaths) shared a load of free revision resources on TES including crossover maths starters, revision booklets and revision grids. 

• Simply Effective Education sells Key Cards, which is (in my opinion) the best GCSE revision app available for maths and science. They have also shared some free revision races on TES. 

• I was asked to make a PowerPoint to accompany Mr Knowles' (@SK18Maths) Foundation algebra revision booklet . It was designed to be used in short daily form time interventions but can be used in longer revision lessons too.

 

• Andrew Taylor at AQA sent me another paper to go with the old AQA Additional Maths Pilot papers I blogged about in Gems 106. 
• I continue to regularly update my GCSE revision resources page. Throughout the exam period I will keep a permanent link to this page at the top right of resourceaholic.com.

4. Fill in the Gaps
At Educating Northants last week Craig Barton (@mrbartonmaths) shared a new type of resource: Fill in the Gaps. We had a go at it during the workshop and it was brilliant. Try it and you'll see what I mean.

Go to variationtheory.com to download this ratio task, plus one for percentages and one for quadratics.

5. A Level Resources
Tom Bennison (@DrBennison) shared a 'Question a Day' revision resource for Year 13. 

@MrsGRVHS shared a padlet for A level maths with links to resources and useful websites.

@naikermaths added another AS Pure Practice Paper to the collection. These papers contain old specification exam questions but they are organised for the new specification so they are helpful for revision. The mark schemes for these AS Practice Papers can now be accessed without a password to help students in their revision for their A level exams.

Finally, while looking at MEI A level things on OCR's website, I discovered this command words summary. I have added this to my displays page.

Update
I've been to three lovely conferences in the last two weeks - Habs Girls, Educating Northants and the London Thames Hub Primary Maths Conference.

At Educating Northants I recorded a Conference Takeaways podcast with Craig Barton that you can listen to here.

I also went out with my friends Gill Leahy and Dil Dias from the London Thames Maths Hub to see Hannah Fry do a talk about her book Hello World. It was brilliant.

During Educating Northants I went to a workshop on primary mastery by Nicky Moksa and she shared this grid of number facts. You can read more about it on the NCETM website here and here.

Facts that should be automatic by the end of Year 2 #EducatingNorthants pic.twitter.com/ufrCdidvJi

— Jo Morgan (@mathsjem) 30 March 2019

I have made quite a few updates to my conferences page lately - there's always a lot going on in the summer term. I'm looking forward to speaking at the Kent and Medway Secondary Maths Conference on Monday 8th July.

Nikki Martin (@nikki_nzmartin) completed her work on the Primary Topics in Depth project. This series of packs feature maths misconceptions, approaches and resources for Years 1 - 6.

My daughters discovered Sumaze Primary last week which was awesome - my 7 year old was totally in love with it and really happy when she completed every level. It's an amazing maths app for young children.

I look forward to seeing lots of you at the ATM/MA conference which is coming up soon. Before then, I'm very much looking forward to some time with my family to recover from the hectic month of March.

Finally, I'll leave you with the exciting news that Desmos now does box plots! If you haven't seen this before then do have a play.

5 Maths Gems #105

Welcome to my 105^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. MathsPad
As usual James and Nicola from MathsPad have shared lots of excellent resources with subscribers in their monthly update. Their pie chart tool is great!

This month they also shared a free set of fun cross-sequences puzzles that you can access even if you don't subscribe. I've added this to my algebra resource library.

2. Similar Triangles Problem
Thanks to John Rowe (@MrJohnRowe) for sharing this problem. Similar triangles spiral to form a regular decagon. The task is to find the length marked with a question mark.

3. Missing Steps
TickTockMaths (@TickTockMaths) shared an activity where students complete the missing steps.

You can download his algebraic fractions PowerPoint here. Check out all of Richard's free resources on his blog or on TES.

4. Maths Frame
Ted Burch (@Mathsframe) has converted all his free maths ITPs from Flash to HTML5 so they will work on any modern browser. These interactive tools are useful for for both primary secondary teachers. They are very easy to use. There's loads to explore so do check out the website.

5. Posters
This lovely set of STEM role model posters will brighten up school corridors and provide good talking points.

There's also a nice set of downloadable 'Forces of Nature' posters from Perimeter Institute which includes one of my favourite mathematicians, Ada Lovelace.

Update
It's all been a bit crazy lately. On Saturday night I hosted Matt Parker's book launch in London. Thanks to all the wonderful people who helped out on the night and all the wonderful guests, it ended up being an utterly brilliant night. I had such a good time and loved every minute. After excellent and thoroughly entertaining talks in the amphitheatre from Matt Parker, Jen Rogers, Rob Eastaway, Tim Harford and Dan Schreiber, we ended the night with a show from FoxDog Studios which was the funniest thing I have ever seen! There was loads going on in the reception room too, including James Grime with an Enigma machine, Ben Sparks with 3D Geogebra, Andy Sharpe with Nrich maths games, and Chalkdust with their awesome magazine. Plus of course there was a self-playing piano performing a previously unannounced superpermuation. And the best goody bags ever.

Here's a video of my 180 guests (mostly maths teachers) thoroughly enjoying the interactive show from FoxDog Studios.

Thank you so much to everyone who came, and to our friends at Jane Street for the ridiculously generous support. I think it's time for me to retire from my event management hobby because there's no way I can ever top this one!

In other news, my books have now been printed. These books are for students (not teachers!) - they are designed to help them learn all their facts and formulae for GCSE maths and science. Please either bulk order for your students or point them in the direction of Amazon using these leaflets. I have explained how the books work in this short home video.

I'm ridiculously tired from the book launch (turns out that planning big events at short notice is a bit exhausting!), but still very much looking forward to #mathsconf18 in Bristol this weekend. I do love a mathsconf. I will have some samples of my books if you want to have a look. I will also be doing a talk about unit conversions (a technical glitch meant that people were unable to sign up to it for a while, but there is still space so please come along!), and I'll be helping to run the MA bookstand along with David Faram. Do come and say hello at some point if you're at the conference.

I'll leave you with this calculus comic from XKCD.

5 Maths Gems #97

Welcome to my 97^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Loci Match Up
Miss Konstantine (@GiftedBA) has shared a new loci activity. The square has side length 18cm, E is the midpoint of the square and the radius of the circle is 5cm. Students need to work out what colours match each statement, and find the area of each of the coloured sections. Alternatively you can give them the diagram and ask them and write their own statements.

I do love a loci activity that doesn't involve pairs of compasses...

It's worth following @GiftedBA on Twitter because she often shares ideas, resources and examples of student work. Check out her most recent post 'Squares/Roots using Area', and her post 'Circumference and Area of a Circle' in which she suggests an activity where students identify errors from a list. 

Inspired by this, Sarah Evans (@maths_missevans) has been trying out 'Find and Fix with Feedback' tasks. Having a list of feedback statements to choose from helps students to identify and understand mistakes and misconceptions.

2. Calculator Posters

Casio (@CasioMaths) has shared a set of high resolution posters of the Classwiz calculator for A level classrooms.

3. Pythagoras
James and Nicola from MathsPad have shared another lovely set of resources. I love their new worksheet and interactive tool for 3D Pythagoras.

MathsPad's October update was packed full of new resources for trigonometry and Pythagoras. One example is the set of Pythagoras puzzles where students are given one side and a set of possible answers for the other two. As James says, this might nudge thinking towards the theorem's converse.

Subscribe to MathsPad to access the full collection.

4. Equipment Check

A level teacher Stuart Price‏ @sxpmaths shared some things he's trying this year when marking assessments. His tests now include an equipment check for four marks - this a fun way of getting students to bring the right equipment to lessons!

Stuart uses a 'mistake' stamp when he is sure his A level students can self-correct and a 'misconception' stamp when something is fundamentally wrong.

5. Algebraic Area

Thanks to Catriona Shearer (@Cshearer41) for sharing a great set of resources on TES that she created as part of the Mathematical Reasoning at GCSE project run by Cambridge Maths Hub. I've recently discovered that lots of excellent resources are made by Maths Hub workgroups that don't end up being widely shared and I'm determined to change that!

Catriona's Algebraic Area Reasoning Tasks are based on a WJEC GCSE question about forming and solving a quadratic equation for the area of two rectangles. The tasks vary in difficulty.

For a similar set of area tasks with a more numerical approach see Catriona's Compound Area Reasoning Tasks. Also check out her set of Probability Reasoning Tasks (based on the infamous Hannah's Sweets question).

It's great that Catriona is involved in developing resources for Maths Hubs given the quality of her puzzles, which I wrote about in Gems 94. You can now download three pages of Catriona's beautiful puzzles here.

Update

I was excited to have an article about indices published in Teach Secondary magazine. It includes ten ingredients to teach indices in depth, but those ten ingredients could apply to any topic so do have a read. The full article is online here. You can also download a free resource containing four activities which you might find useful when teaching index notation.

Also look out for my article in next month's Teach Secondary magazine about algebraic order of operations.

On Friday I met up with Megan Guinan after school and we went along to the launch of Chalkdust Magazine Issue 8 at my old university UCL. We had a great time and really enjoyed the quiz. Chalkdust magazine is brilliant - you can read Issue 8 online, and if you're coming to my LateMaths event on Saturday then you'll be able to pick up a copy.

All 100 tickets have been sold for LateMaths and I've been busy making all the final arrangements over the last few days. I can't wait!

If you're a teacher in London then do join one of my Maths Hub workgroups! I'm supporting the workgroup led by Chris Reilly on the Challenging Topics in the New GCSE. In this workgroup we'll look closely at the teaching of ratio and hopefully develop and trial some new resources for this topic. I'm also supporting Carlos Karingal on the London-wide Developing A Level Pedagogy workgroup which will meet at Chestnut Grove in Balham. I'm so excited about this workgroup - I think it will have a big impact on my A level teaching. Get in touch if you want more information. Everyone is welcome to get involved.

I'll leave you with the New York Regents archive website which was shared by Benjamin Dickman (@benjamindickman). It's beautifully organised by topic and year, containing exam questions going back to 1866. I love stuff like this!