5 Maths Gems #185

Welcome to my 185^th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Admissions Tests and A Level Resources 

Every year in the Spring Term ‪@ecrmaths runs a series of information sessions for her Year 12 students on the main STEM admissions tests (TMUA, MAT, STEP, PAT and ESAT). She has shared her slides for her 2025 sessions. This is incredibly generous and helpful of Emily - I need to run similar sessions myself but had nothing prepared. Her resources are excellent so this will save me a lot of time and really benefit my students. 

Speaking of A level, did you see the recent new resources on Edexcel Emporium? They have shared A Level Maths Exam-Style Topic Tests for Statistics and Mechanics.  These questions are new and have been reviewed by the examining team - they are not just collections of old questions. They have also published a set of Mock Papers for AS Further Maths - this was very much needed. 

2. Constructions Booklet

Thank you to Tom Riley for sharing his workbook for constructions and loci. 

Tom has also provided some words of wisdom on teaching this topic (see his Bluesky thread for more detail):

1. Start with lots of practice of just drawing circles with compasses.
2. Go into lots of depth on each construction before moving on so that students become familiar with the language early (e.g. shading, showing points, use of scales).
3. Interleave where possible (e.g in the booklet you see circles then perpendicular bisectors then circles with perpendicular bisectors).
4. Include tasks where students have to identify which construction to use (extract below).
5. Use a visualiser.

3. Literacy and Oracy

Oracy is a big focus for a lot of schools at the moment. At my school we have done loads of CPD on it for the last three years (!) but it continues to be something we need to develop across the school. 

‪MrLevMaths‬ helpfully shared a slide from discussions he'd had in department CPD about the link between student oracy, mathematical communication and understanding. How do you ensure students know which expression you mean when you are explaining? How do you explicitly teach them to talk about their maths?

 

Teachers all say these things differently. For C above, would you say the words "lots of" "multiply" "all over"? This is a really interesting thing to cover in department CPD. 

You might be interested in the 'Maths Pronunciation Project' video I made a few years ago. Even the way we say x⁴ differs between teachers.

4. Transum

I spotted a tweet from @Transum about their interactive circles parts vocabulary tool. It might help students appreciate the number of different shapes a sector can have, and prompt questions about major/minor and whether a segment can be a semicircle. 

Transum is full of lovely tasks and tools. For example check out Tim Honeywill's Indices Challenge. 

Transum has also added three more panels to their popular Refreshing Revision tool which can be customised by the teacher.

5. Congruency

@hartmaths shared some congruency questions that he used with his Year 11s. There's lots of interweaving here - these questions feature angles in parallel lines, properties of shapes and circle theorems.

Update

La Salle have said on Twitter that Mathsconf37 will be on 15th March in Sheffield. Tickets are not yet on sale but apparently they will be soon. I've prepared a workshop for this conference called 'Fun with Factorising' which I am very excited about. If you enjoy algebra, come along!

I have a vacancy at my lovely school - we're looking for a maths teacher to join us in September. We're a mixed comprehensive school in South London/Surrey. We have great behaviour and attitudes, happy students and excellent maths results (our first two maths P8s were 1.26 and 1.22. 50% of our students got a Grade 7+ at GCSE last year, and 94% got 4+). My team are friendly and brilliant and it's a real pleasure to work with them. We are particularly in need of someone who can teach mechanics at A level, and we can offer a timetable that is majority A level teaching if desired. But if you're considering applying and you're not an A level teacher, please do go ahead and apply as we can be flexible on this. The closing date is Monday 27th January so apply quickly, or get in touch this weekend if you have questions. We will interview over the next couple of weeks. More information here. 

Finally, don't forget to check out Dr Austin's new resources - they cover circles, ratio, averages and mechanics. I particularly like her Area and Perimeter of Sectors with Pythagoras Practice Grid.

5 Maths Gems #20

Hello. I'm pleased to present my 20th gems post today - a milestone! Twitter has been quiet this week because Christmas took our minds off work for a couple of days, but I've still got some great ideas for you. The Christmas holidays are short and busy so it won't be long before you're back to planning lessons - I hope this post gives you some inspiration for the Spring term.

1. Factorising Quadratics
You know Don Steward's blog is the best thing since sliced bread, right? His catalogue of fantastic rich tasks is updated all the time. I really liked his recent posts on product puzzles. He started with a set of questions like this:

In Question 1 above, you can see that the top left cell has to contain a 3 because it's a factor of both 3 and 6. The rest of the cells can be completed quickly once one common factor has been established. This is a simple example but Don develops the questions to become increasingly difficult, some having multiple solutions. 

The next set of activities extend the same idea to algebra, starting with this:

There's lots of these to complete - excellent practice of factorising linear expressions.

The next stage of this exercise is factorising quadratics.

Conveniently I'm currently planning a Year 10 lesson on factorising quadratics. I want my students to do a lot of practice so will definitely be using this activity. The questions build up to a suitably challenging level of difficulty, ending with this one:

I want to encourage my students to factorise 'harder' quadratics (ie a > 1) by inspection. This is my preferred method (ie 'guess and test') but my students always demand that I teach them a more structured approach (eg 'the Grouping Method') which frustrates me. Their insistence on following an algorithm suggests a lack of confidence. I think the question above turns factorising quadratics into a kind of logic problem. Tackling this question without an algorithm might help my students develop the confidence to factorise harder quadratics by inspection.

One last idea for a lesson on factorising quadratics - I like the problem below from openmiddle.com. There are a number of possible solutions so you could challenge students to find a different solution to the person next to them. 

2. Angle Sense with the Interactive Whiteboard
I've been planning a Year 7 lesson on angles in which I'd like my students to estimate angle sizes. If you were asked to to draw an angle of 210^o freehand, how would you do it? I'd think of it as a straight line plus a third of a right-angle. If you have proportional reasoning skills then it's pretty easy to make an educated guess. An angle estimation activity would work perfectly well without technology (read out a series of angle sizes and ask your students to draw their freehand estimates on paper. They then check their estimates using a protractor - another useful skill). But if you want a similar activity for the interactive whiteboard then you might like this fun Estimating Angles Game from Nrich.

Another interactive whiteboard tool is 'How Far Does it Turn?' from MathsPad. This time your students have to estimate the size of the angle drawn - they could do this on mini-whiteboards so everyone is included in the activity.

While looking at these games, I stumbled across a big range of angle tools for the interactive whiteboard here. Some of these angle games are quite funny - Banana Hunt in particular made me chuckle.

If you like these interactive whiteboard games then you'll find loads at Sheppard Software. It's amusing that there's an Absolute Value Number Balls game - this concept isn't covered until Year 13 in the UK but I bet my students would love to play this game - five minutes light relief in a C3 lesson!

FlashMaths.co.uk is another great website for interactive whiteboard activities. Flash Maths was created by Jonathan Hall (@studymaths) who brings us a plethora of fantastic tools on StudyMaths.co.uk. If you haven't seen it before, check out MathsBot.com which is his simple (but brilliant) worksheet generator.

3. Big Questions

Billy Adamson (@Billyads_47) shared a fantastic set of mathematical thinking prompts 'The Big Questions'. Here's a few examples: 

Lovely open questions from Billy to generate discussion and develop understanding. There's some more good examples of open questions here:

4. Trigonometric Problem Solving

Our Year 13s' problem solving skills are tested when they're asked to simplify expressions involving trigonometric identities in C3 (like the example below).

I find that my students get frustrated when they can't spot a 'way in' straight away. They give up quickly. There's actually a pretty standard set of starting points, as described on www.intmath.com (@intmath). 

I struggle to help my students feel confident in tackling these problems, so I really like this activity from @mjfenton. Here's an extract:

The idea is that we start with a lot of structure and gradually give fewer hints until students are able to solve the problems themselves. The steps might seem logical to us, but we're experienced problem solvers. 

It's a good idea for maths teachers to try to solve unfamiliar problems every now and then (like the example below from ‏@dannytybrown) to remind ourselves that mathematical problem solving often requires patience, creativity and multiple attempts. We all experience frustration in problem solving, just like our students do, but we know that the satisfaction of eventually finding the solution is well worth it.

5. Dividing with Decimals

I've mentioned before that I love MathsPad's resources - plenty of them are free and the rest come at a cost of only £3 per month. Whether your school subscribes or not, it's worth registering for email updates in order to keep track of all the new resources. This month, the interactive resources on Decimal Calculations caught my eye. It always surprises me how many students will happily say that 40 divided by ½ equals 20. Activities like the one shown below will help tackle this misconception and encourage students to think before they answer.

That's it for this week. I'll leave you with a video from 1977 - 'Congruent Triangles' by Bruce and Katharine Cornwell (another gem found on @MathMunch). Happy New Year!