5 Maths Gems #93

Welcome to my 93^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. It's the summer holidays! Many of you will be on a Twitter break right now, so this post will fill you in on some things you might have missed in the last couple of weeks.

It was in the summer holidays - four years ago this week- that I first started writing my gems posts. You can see the full collection here.

1. Triangles
Thanks to John Rowe (@MrJohnRowe) for sharing this right-angled trigonometry activity. Students have the find the length x.

Benjamin Leis‏ (@benjamin_leis) has blogged about his approach to this problem here.

If you like this then you might also enjoy this problem from UEA which requires knowledge of the sine and cosine rules - I featured it in Gems 54. It takes a while to solve! 

You might also like the angle chase problems I shared in Gems 35. I love angle chases!

Speaking of triangles, thanks to Mark Horley (@mhorley) for sharing @DrPMaths' triangle generator. This helpful tool creates possible triangles with integer sides, area and height. If you make your own resources then this will be helpful to ensure you don't include impossible triangles.

2. Sums and Products
Thanks to Shaun Carter (@theshauncarter) for sharing a new resource which he calls 'Diamond Problems'. He blogged about it here.

The questions are similar to those on this shorter 'Sum Products' worksheet which I always use before my students start factorising quadratics. Of course, as Shaun says in his post, these puzzles are suitable for students of any age even if they're not studying quadratics - they are good practice for working with negative numbers and decimals.

Thanks also to Meredith Purser (@MeredithPurser) for suggesting that students first work out the rule themselves before completing the blank grids.

We present this as a puzzle before showing the actual rule! The Ss LOVE the challenge of figuring out what the pattern is. Lots of gasps and reminders NOT to give it away. :) pic.twitter.com/VDgGQTdzoq

— Meredith Purser (@MeredithPurser) 21 July 2018

3. #midweekmaths
The White Rose Maths Secondary Twitter account (@WRMathsSec) is sharing a weekly problem throughout the holidays using the hashtag #midweekmaths. 

It's worth following @WRMathsSec because they regularly share lovely tasks for students. 

Also check out their new secondary five year plan.

4. Interleaved Homework
I have always set homeworks that directly relate to the topic I'm teaching, but for the last couple of years I have been meaning to change that. Continually revisiting past topics through homework is a great way to help students remember things.

Thanks to David Wees (@davidwees) for sharing 125 interleaved practice assignments - although these are aligned to a specific curriculum, it's so helpful to see the format and approach. This is definitely on my list of things to start doing!

5. Geogebra Whiteboard
I know many of you already use Geogebra, but you might not have seen this beta version of Geogebra Whiteboard. Thanks to Pip (@AccomplishEdu) for sharing this. The interface is brilliant - it's so easy to construct and annotate diagrams. Have a play with it and you'll see what I mean.

Many maths 'revision' videos just tell students procedures, assume understanding & student's repeat the procedure. Playing with new @geogebra IWB I have created this little 'interactive'- intended as a reminder to the student not a procedure to follow. When you think you learn! pic.twitter.com/tiOj0JjMjK

— Pip - Mathematics (@AccomplishEdu) 3 August 2018

Update
I've updated my conference listings for 2018/19. There are lots of great events coming up. Next term I intend to go to #mathsconf17 and MathsJam. And I hope to announce my own event soon...

I've been working on my A level resource libraries - they need a total rewrite because of the new A level specifications. It's a huge, time consuming job!

If you're a member of The Mathematical Association and interested in volunteering, please get in touch. I chair the Publicity and Media Committee and am looking for a couple of new members of my committee. I'm also looking for people to help man the MA bookstand at conferences. Please let me know if you can help. A small honorarium will be paid to conference volunteers.

In other news:

• Corbettmaths (@Corbettmaths) has made his new Corbettmaths Primary website live. It features loads of videos, question papers and 5-a-days.
• The MA's latest Equals Magazine has been published. This free magazine focuses on maths and SEND.
• Read this great article "How to Talk About the Fields Medal at Your Next Cocktail Party" by Evelyn Lamb.
• You'll also enjoy this brilliant post from Alan Parr "... Tables Not Well Known" about teaching times tables in the 1800s. 
• Congratulations to Nira Chamberlain, winner of the #bigmathoff. You can read a final write-up of the competition here.

I'll leave you with this arithmetic maze from @MathforLove, shared by @MathsEdIdeas. Without passing through the same cell twice, what’s the largest total you can make? This might be a nice activity for Year 7 to have a go at in September.

Some Things I've Tried

The last eight weeks have been the busiest I've ever experienced. There's been lots of factors at play to make this period particularly exhausting, both at school and at home - it doesn't help that my 17 month old daughter still doesn't sleep at night! A break is much needed. Half term also provides a good opportunity to reflect on some new things I've tried this term.

Source: The Guardian/ Ros Asquith

1. Famous Five
This is an idea from @mccreaemma which I featured in Gems 35. It works like this:

1. Before each Year 10 lesson, I write the words 'Famous Five' on the board.
2. As my students arrive I have a starter activity ready for them. 
3. Under the title Famous Five, I write the names of the first five students to settle down and start working. They LOVE being on this list! It's getting harder to choose the Famous Five because they've all responded so well to this.
4. At the end of the lesson I say, "If you're on today's Famous Five list you can leave now, the rest of you pack up and stand behind your chairs quietly". The Famous Five dash out of the room.

The funny thing is that some of these students have registration in the same room immediately after my lesson, so they have nowhere to rush off to! They just like the glory of being Famous Five. 

This has been a really successful initiative to minimise faff at the beginning of my lessons. Also, because it's a bit different to what they're used to, it has helped me build a good relationship with this class. Huge thanks to Emma Mccrea for sharing the idea - do read her original post to see how it works for her.

2. Assessment 

I've been doing fortnightly quizzes with my Year 10 class since the start of this term. These are open book tests covering the key skills learnt in the preceding fortnight. To make these quizzes I draw on a variety of sources and keep the format consistent - each quiz is 15 minutes long and consists of 12 multiple choice questions.

These quizzes have quickly become an established routine. Most students take full advantage of the 'open book' rule - during the test I see them looking back through their exercise books at notes and examples. This encourages good note taking during lessons.

I grade the quizzes A, B or Not Yet (inspired by this post from Sarah Hagan). If a student receives a 'Not Yet' then they haven't demonstrating sufficient understanding of the topic so they have to take another quiz after school the following week. Of course there has to be remedial action between receiving a 'Not Yet' and resitting the quiz - these students either see me for help after lessons, or I send them links to Corbett Maths or Hegarty Maths videos.

My first quiz resulted in 13 Not Yets and only 8 As. A worrying number of students couldn't multiply decimals so I taught the topic to the whole class again using a different approach. The results were much improved in the retake.

These quizzes only take about 30 minutes to mark - in those 30 minutes I gain a valuable insight into my students' understanding. I hope that these regular low stakes quizzes will encourage my students to remain focused, take good notes and seek support. Do read Kris Boulton's post 'How tests teach and motivate' which inspired me to start doing these quizzes. So far it's been a great success.

3. Modelling Good Work 

Every classroom in my department has a visualiser. Unfortunately none of them seem to work (probably due to recent software updates) so this foiled my plan to utilise visualisers this year to show examples of student work. Instead, I take photos of good work while I'm marking. There's no point in telling students that they should set their work out better without giving examples.

I've been trying this out with my Year 12 class. They're studying S1 and we've been working on summarising data (eg mean and standard deviation of continuous data). It's easy to make accuracy slips in these calculations and students who fail to show clear workings in exams could end up scoring no method marks.

The picture below is an example of a student's answer to a standard deviation question - I showed this photo to the class when I returned their most recent homework. Few students in this class had received full marks for this question.

It's not perfect, but this student has definitely got the right idea. He's drawn out the whole table clearly and written down the formula for standard deviation. He's shown intermediate steps and his workings are very easy to follow. If only all my students set their work out like this - the worst examples were those who tried to squeeze their workings into the margin of the question paper ('Fermat-style' workings). I hope that by showing good examples to the class, the quality of work will improve. I'll report back on this later in the year!

4. Communication
At my previous school the only direct communication I had with parents was on Parents Evening. I never called, emailed or met with parents. At my new school every teacher recognises the importance of engaging parents and this is done very effectively across the school. I decided to engage the parents of my Year 10 students by way of an introductory email at the start of term, followed by half-termly newsletters. Here's my first newsletter:

I've included an update on what we've been studying, praise for students who've done particularly well, information about membership of the Society of Young Mathematicians and more.

I'd been planning to do a newsletter like this for years so I'm glad I finally did it. I found this MathedUp post encouraging - it includes a lovely example of a newsletter produced by Mo Ladak which is worth a look.

As Jim Riley (@tutor2u) said when I shared my newsletter on Twitter, "Most parents might not care - but if just one or two do, it is all worthwhile".

So that's it - four ideas that seem to be working well. I'll blog again later this year to update you on whether these initiatives continue to be effective. Thanks for reading!

Pret Homework

At #TMEpsom today - which was hosted by my lovely new school, Glyn - I did a short presentation about Pret Homeworks. This post tells the story of Pret Homeworks - where they came from, how they work, why they're great and what's coming next.

Background
Last summer Kathryn Forster, Head of Maths at the TES 'Creative School of the Year' 2015 Seaham School of Technology, tweeted some pictures of a new homework template she'd devised. It was lucky I spotted this tweet in my busy Twitter feed because it turned out to be the start of something big.

The homework pictured below is one of Kathryn's original designs. The Skill Practice element is what most standard maths homeworks involve, and remains essential, but we also have an additional four elements:

• The Literacy element requires students to learn the spellings and definitions of key words. 
• The Memory element requires students to memorise facts or formulae. 
• The Research element is a short independent research task. 
• The Stretch element provides some more challenging questions.

So the design covers knowledge, skills and enrichment all in one place.

Kathryn's homeworks are used in conjunction with peer-assessed Homework Checks in class, like the Literacy and Memory Check pictured below.

When I first saw Kathryn's idea I absolutely loved it so I featured her homeworks in my blog post 5 Maths Gems #3 back in August 2014. Kathryn and I then made a few more homeworks, and I created a page on my blog containing links to our small collection. 

I decided we needed a name for this homework format. Takeaway Homeworks were popular at the time so I put a spin on the name and went for Pret Homeworks - creating an acronym for the words 'practise, recall, extend, think'.

I asked for Pret Homework contributions through Twitter and the collection quickly started to grow. Initially I stored all the homeworks on Google Drive and linked them through resourceaholic.com, but then something went wrong - they were being downloaded so often that Google Drive stopped letting people access them. The popularity of these homeworks was quickly growing - they needed their own website. 

The Website
So prethomework.weebly.com was born. I transferred all the homeworks from my blog to a new purpose-built website. It's been incredibly popular.

I've created a number of Pret Homeworks myself, but my primary role is collator. Anyone who creates a Pret Homework for maths is asked to email it to me at resourceaholic@gmail.com and I upload it to the website. I don't edit any of the homeworks submitted, but I do encourage submissions in an editable format so teachers can tweak them if required.

We currently have around 140 homeworks from 50 maths teachers - the full list of contributors is here. If Pret Homework were a business then Kathryn would be Head of R&D, I'd be Head of Marketing, and the contributors would be our brilliantly creative workforce. My sincere thanks goes to every one of them.

Variations 

Although all the homeworks on prethomework.weebly.com are for maths, this homework format works well in other subjects. I've seen adaptations for both Science and English. I also think the homework format would work well in primary school. Our collection currently ranges from Key Stage 2 to A level including Further Maths.

The design works well for classwork too. Danielle Bartram has made a number of worksheets which were inspired by the Pret Homework format.

Perimeter worksheet from missbsresources.com

Feedback 

I recently asked on Twitter for feedback from teachers who use Pret Homeworks. I received loads of enthusiastic replies. Some schools are now using these as standard homeworks across the maths department, in other schools one or two teachers are using them every now and then. Either way, the feedback is excellent. Teachers report that the quality of work submitted is often high and that students enjoy completing Pret Homeworks.

Thanks to all the teachers who shared examples of students' work. It's amazing to see Pret Homeworks in action! 

Pret Homeworks also featured as Craig Barton's Resource of the Week in November 2014.

What's next for Prets?
The collection of Pret Homeworks continues to grow. Eventually I may need to upgrade the website to make it easier to search by topic and Key Stage.

During the next school year I hope to see more Pret Homeworks for Key Stage 1 and 2, and for other secondary subjects.

I'm excited by the work being done at Burford School where they are making Pret Homeworks to fit into their new GCSE Schemes of Work. Their homeworks are very cleverly differentiated - these will be uploaded to prethomework.weebly.com soon.

There's still lots of buzz around Pret Homeworks. Have you tried them yet? Do let me know what you think.

Huge thanks to Kathryn Forster for the idea - she's been an inspiration to many.

My short presentation from #TMEpsom is available here.

5 Maths Gems #31

Hello and welcome to my 31^st gems post. This is where I share some of the best teaching ideas I've seen on Twitter.

1. Ratio tables
The new GCSE is going to have an increased focus on proportional reasoning. I enjoyed @MissNorledge's post about using ratio tables for non-calculator conversions. It's a logical way to structure thinking.

Miss Norledge helpfully provides a 'Master the Basics' worksheet on ratio tables. She has also written excellent posts about using ratio tables for percentage calculations and proportional reasoning.

This approach can be used for any kind of conversion. I despair when I overhear my Year 12s desperately trying to remember the 'formula' for converting between radians and degrees. "Do I multiply by 180 then divide by pi...? Or is it the other way round?". It's far easier to memorise π radians = 180^o then make proportional adjustments. Simple.

2. Trigonometric Graph Transformations
Jon Orr (@MrOrr_geek) has written a series of Trigonometric Function Transformation Challenges in Desmos. These look great for teaching trig graph transformation - in each challenge, students have to work out the equation of the transformed function - an example is shown below.

3. Diagnostic Assessment

I really like the look of Alexander Cameron's (@AlexandeCameron) diagnostic assessments. Here's an example:

For more information about Alexander's assessments see his TeachMeet presentation.

4. Number Properties
I also like this excellent activity shared by @DJUdall.

5. Lowest Common Multiple Hot Dogs
I've never thought to use this video from Father of the Bride in a lesson on Lowest Common Multiple.



Thank you to @MrPontinMaths for sharing this and an associated worksheet - 'The Hot Dog Buns Dilemma'.

Update
If you haven't seen my Pret homework website then do have a look. Lots of teachers tell me that they use Pret homeworks very successfully. I love seeing examples of students' work - these impressive examples of Pret homeworks were shared by @missradders. 

Did you see the Venn Diagram Subject Knowledge Check I produced ? This is designed for teachers who haven't taught Venn Diagrams before so they can prepare for the new GCSE. I plan to make these for every new GCSE topic.

Speaking of GCSE, presumably you saw the Ofqual announcement this week about the difficulty of the new maths GCSE. Expect more Sample Assessment Materials by the end of June. If you missed the announcement, there's a short video summary below (what's with the weird change in camera angle?!). This extract from the Ofqual study is really interesting - it ranks the GCSE questions in order of difficulty.



If you missed this post from mathwithbaddrawings.com about UK vs US mathematical terminology then do have a read, it's very entertaining. I'm pleased to say I've never called an index an indice!

Finally, if you haven't seen the updated speaker list for the upcoming National Mathematics Teacher Conference then do have a look. Less than one month to go now - hope to see you there.

I'll leave you with this mathematical limerick, shared by @MrBenWard.

5 Maths Gems #30

Hi and welcome to my 30^th gems post. This is where I share some of the best teaching ideas I've seen on Twitter.

1. Construction Comics
Back in Gems 4 I featured Paul Collins' (@mrprcollins) brilliant comic resources for teaching constructions. In his post he suggests some opportunities to use these resources in the classroom.

One of Paul Collins' construction comic strips 

I haven't taught constructions this year so I've not yet had a chance to use these resources, or the awesome Euclid the Game (featured in Gems 21).

I loved the work shared by my namesake Mrs Morgan (@em0rgan) on Twitter this week. She asked her students to create their own construction comic strips for homework. The results look excellent. I'm not normally a fan of homeworks like this because they're so time consuming (both for students to produce and teachers to mark) and often they don't add much value. But in this case I think there is value in students learning the procedures by documenting the steps, in addition to practising the constructions.

2. A Level Resources

Thanks to @OxfordEdMaths for sharing a set of excellent A level assessments for C1 - C4, D1, D2, FP1, FP2, M1, M2, S1 and S2. It can be hard to find sources of good A level questions. These free resources are going to be incredibly helpful next year for topic assessments, homeworks or revision.

Speaking of A level resources, do check out the website 0a explains: Calculus (with pics and gifs) -thanks to @mathhombre and @solvemymaths for sharing this. I love the pictures and gifs on this website - they might help teachers explain concepts in calculus.

3. Homework Expectations
I've just discovered MathFour.com from Bon Crowder - it's full of creative ideas, some of which I plan to feature in future gems posts. One idea that I spotted was a 'How to Write Your Math Homework' guide. I'm going to make a version of this for my new classes in September. I can't complain about my students' work not meeting my expectations if I haven't made those expectations clear from the outset.

4. Talk a Mile a Minute
Steve Wyborney (@SteveWyborney) shared his Talk a Mile a Minute Vocabulary Activity. The video below describes the activity in detail. It involves students describing sets of words to their partner and then discussing what those words relate to. I think this would be a great activity for an end of year lesson. Have a look at Steve's post for resources. If you're looking for words for this activity then try this Vocabulary Checklist for Key Stage 3.  

5. Activities

I've seen some lovely activities and questions on Twitter this week.

@MathedUp shared this 'Negative numbers code-breaker activity with a twist'.

@OxfordEdMaths shared this question under their #AlmostMondayMaths hashtag that I mentioned in Gems 29.

@DJUdall shared this activity which links solving equations with area and perimeter.

@DJUdall also shared a question he made which combines Pythagoras' Theorem and Standard Form. 

The latter two resources were shared during last Sunday's #mathsTLP. This is a great place for maths teachers to collaborate. Do join in on Sundays at 7pm to ask for help with lessons or to offer ideas.

Update
Because my exam classes are now on study leave I had time to plan some really nice lessons this week. With my Year 10s I did a lesson on similar triangles using resources from the Mathematics Assessment Project. They had to sort eight pairs of triangles into 'similar', 'not similar' or 'can't tell', drawing on their knowledge of angle facts. This task is a lot harder than it sounds and takes about 45 minutes to complete. I really recommend it - here's an example of the work they produced so you can see what it involves.

I talked to all my students about palindromic numbers this week (I remembered to mention it every time I wrote the date on the board, because the dates were palindromic when written in the format m/dd/yy). Although many of my students could give me an example of a word that is the same forward and backward (eg racecar), most were not familiar with the word palindrome.

Those of you who use Plickers (featured in Gems 10) for formative assessment will be pleased to hear that you can now insert pictures. For example you might want to insert questions from www.diagnosticquestions.com.

That's it from me for now, but there will be another gems post soon because there's been loads of great stuff on Twitter lately. Wish me luck with my last week at my current school! My new job starts after half-term.

I'll leave you with this GCSE resource by thornn on TES (shared by @eggarsmaths on Twitter) which you might find useful for last minute exam tips over the coming weeks.

5 Maths Gems #13

In my gems posts I share some of the best teaching ideas I've seen on Twitter each week. This is my 13th gems post. I hope you're not triskaidekaphobic.

1. Flying Numbers
At Julia Smith's (@tessmaths) creativity workshop at the last maths conference, she shared an activity in which students make 'Flying Numbers' to hang from the ceiling in the classroom or corridor. It works like this: they choose a number and make that number from wood in Design & Technology (drill a hole at the top for hanging). They paint their number then use fine markers or chalk pens to decorate it with facts about that number. This is a lovely opportunity for students to use the internet to explore number properties and find out all sorts of wonderful mathematical things that are not on the curriculum. The examples below were made at the maths conference - it was a really enjoyable exercise.

Ed Southall (@solvemymaths) suggests using numbergossip.com and numdic.com for researching number properties. Of course it's important that students understand the properties they choose - do they know the meaning of all the words they use to describe their number? Prime, square, perfect, palindromic, narcissistic, repdigit... And do they know about different number systems? For example, you could make a whole lesson out of binary (see my earlier post about teaching a binary lesson).

Ed also created some brilliant 1 - 9 number posters this week - your students could create posters like this as an alternative to the 'flying numbers' activity.

Here's a related idea - Number Experts. When you get your new Year 7 class next year, assign a number to each student and tell them that during the year they will become an 'expert' in that number. For example student number 25 would accumulate interesting facts about the number 25 throughout the year, sometimes making connections to the topics they cover in maths lessons, and at the end of the year they could produce a display piece about that number. Your class could even present their number facts in a school assembly. In this enriching exercise students are given a rare opportunity to step into the amazing world of numbers and perhaps it will give them a greater appreciation for the beauty of mathematics.

Source: The Value of Teaching Mathematics, Philipp Legner, Mathigon

2. Mathigon
Speaking of beautiful mathematics, the Mathigon website is amazing! Parts of it are still under development but new stuff is added all the time - the quality is superb. The website says, "Mathigon wants to improve the public understanding of Mathematics, why it is exciting and why it is important. And there is no better place to do that than in schools! Teachers are encouraged to use the resources on this site to enrich the mathematics curriculum and show children how fun and beautiful mathematics can be". Inspiring stuff. Check out the website for yourself (the ebook is excellent!) - here's a few features to get you started:

• Alice in FractalLand is a stunning animated slideshow. Show it to your class and explore sequences, fractals, the golden ratio and more. The text at the bottom explains each concept very clearly. I love this! This is exactly the sort of thing I was referring to in my post 'A place for gimmicks?' when I said that we should make time to enrich our students' education with interesting mathematics that is not on the GCSE syllabus.
• The Primary and Secondary Treasure Hunts are very well designed. Full instructions are included and there are questions on areas of mathematics such as cryptography, primes and probability. The questions are rather challenging for the intended age groups - if I was organising an inter-school maths contest then I might use these questions.
• The video collection is due to grow - an exciting prospect if this two minute wordless video exploring triangles is a taste of things to come. 

3. Imbalance Problems
If you're not familiar with Don Steward's resources then stop reading this post immediately and check out his Median blog. Mr Steward posts new resources all the time - his last few posts have had a 'balancing' theme. First there was this post 'mobiles', then 'mobile inequalities' and finally 'mobile moments'.

In mobiles, the activities start with number problems that get progressively harder, then move on to algebraic balancing problems. Here's a numerical example which can be solved with arithmetic and logic (fill in the missing weights so that everything balances correctly). 

There are lots of variations, such as this one where the weights must add up to the number in the triangle (this is a straightforward example):

The algebraic problems develop skills in writing algebraically and simplifying expressions. In the problem below, students have to complete the missing weights to make the combined hanging weight equal to 8n.

These are great problems. Check out all three posts to see how Mr Steward developed the idea. It's also worth reading Paul Salomon's (@lostinrecursion) post 'More Imbalance Problems' about students creating their own imbalance problems. Thanks to John Golden (@mathhombre) for sharing this link.

4. Desmos Water Line Activity
I've long been a fan of Desmos for graphing but I've never looked at Desmos activities before. My first introduction to a Desmos activity came from reading Jon Orr's (@MrOrr_geek) post 'Describing Relationships – Active Learning'. In a lesson on what we call 'real-life' graphs in the UK, he starts by showing this video which is low quality but still worth showing.



He then uses the Desmos Water Line activity. It only takes a few seconds to register on this site and then you're ready to go - your students login to Desmos using a four-digit code, they enter their name then complete the activities. They're shown various glasses being filled with water and they have to draw the associated graph. Their answer is then illustrated so they can check its accuracy. This website really is superb and very user-friendly - you must spend a few minutes checking it out so you see what I mean. At the end of the lesson students can create their own glasses and challenge their classmates to graph them. The teacher can see what the students are doing behind the scenes, without any complicated registration process or uploading of student data.

I'm really impressed by this technology and keen to explore Desmos' other activities. The people behind Desmos are experts at creating user-friendly interfaces.

5. Three Apps
I was going to include my thoughts on the value of iPads in mathematics education today, but I've decided that there's too much to say so it deserves its own post - watch out for one in the near future. However, thanks to @Corbettmaths, I've discovered three iPad apps that are worth a mention today. These free apps would be useful in the classroom if your students have access to iPads, but they work well on iPhones too and are utterly addictive for teachers!

First, Angles? - Let's solve figures problems! by Gakko Net Inc. In this app you have to find the marked angles in problems ranging from simple triangles to parallel lines to circle theorems. It's a very simple app that lets you write workings on the screen and enter your answer - if you're correct you move onto the next question. Hints are available. Crucially, it's not necessary to progress through all the questions in a level to move onto the next level so you can jump straight to circle theorems if you want.

The same app developer also brings us Areas? which is equally well designed. Shapes are shown on a grid and you simply have to work out the areas. Again, they start off easy and become quite challenging. For example I enjoyed this question:

You can't tell what the radius is, but you can see it's between 5.5 and 6 units. The key is to realise that the answer only contains integers.

Finally, the same developer brings us Make 10 which is an order of operations game. In each question your task is to make 10 using all four numbers.

Three excellent apps - great fun for both students and teachers.

What I've been up to
My Pret homework collection continues to grow thanks to contributions from twenty helpful maths teachers. New contributors are always welcome! I'm pleased that one of my Pret homeworks featured as Craig Barton's Resource of the Week this week - Kathryn Forster (@DIRT_expert) should be very proud of her creation. If you've not used a Pret homework before then Craig Barton's video guide is worth watching. It's great to hear that the template has been adopted by Science and English teachers too. Marsha Smith (@marshasmith244) had the great idea of giving her students blank templates to create their own Pret homeworks - having created a number of them myself, I've found that creating a Pret homework does help you think about a topic in depth.

Students' Pret homework creations from @marshasmith244

This week I've been busy reading and commenting on interesting blogs - this post about the new GCSEs from Cav (@srcav) is very helpful, especially for Heads of Department who need to start thinking about which exam board they will use from next September. Do have a look at this post from Bruno Reddy (@MrReddyMaths) too - it describes the important work he's doing to transform negative mathematical attitudes.

I'm really pleased to see that the 'hashtag marking' I suggested in last week's gems post has paid off - both Debbie Hart ‏(@Debbie_Hart_UK) and Jane Appleton (‏@JaneAppleton24) have tried it.

I've been busy writing a post about circle theorems which will be ready soon. Also, after seeing some great Halloween and Guy Fawkes maths resources, I've started to collate a 'seasonal resources' page. I've seen so many good Christmas resources, it's hard to choose the best but I'm getting there.

So there you go, my 13th gems post. It wasn't scary at all.

Image source: guernseydonkey.com