5 Maths Gems #183

Welcome to my 183^rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Factor Trees
I love the recent MathsPad updates. They've added a factor trees tool which is available to non-subscribers. There are multiple methods for finding prime factors - factor trees are a popular choice. This tool is great for demonstrating the process - you can enter pairs of factors, then decide whether each is a prime number or not. 

Another fantastic addition to MathsPad is a Describing Transformations Tool. This one is only for subscribers (most of my readers are probably subscribers, given how often I write about how good MathsPad is!). This tool can be used to demonstrate reflections, rotations, translations and enlargements (including fractional and negative). 

The team at MathsPad has also continued to expand their large collection of excellent curriculum booklets. Further Trigonometry is the first booklet published from their Year 11 Higher curriculum.

2. Is It Plausible?
I like @AMercerMaths's "Is it plausible?" discussion activity - an extract is shown below. Students often don't have a good sense of how big things are. 

3. Area Backwards

@drpas1001 shared a resource 'Area 51' where students work backwards in area questions. I've added this to my resource library.

4. Enlargement

Thank you to @giftedHKO for sharing a nice enlargement resource with lots of practice on a single page.

5. Transum

It's been a while since I've given Transum a shout out - new teachers might not know how much useful stuff is on there. I like the self-marking exercises - my daughter is in Year 8 and if she needs a bit more practice on a topic then I suggest she completes a Transum task, like this indices exercise.

I also use some of the tasks in lessons, for example when introducing identities to Year 11 recently, we completed this sorting activity on the board. 

@Transum recently tweeted about a new activity for recognising graphs. 

The huge collection of activities on this website continues to grow. If you've not visited before, it's definitely worth exploring.

 

Upcoming Conferences

Nothing much happens in the winter months but there will be conferences for maths teachers in the Spring term. Complete Maths will hold a conference on a Saturday in March (date and location yet to be announced) and there will be a joint Conference of Mathematics Subject Associations, 'Future Proofing the Curriculum' on 14th - 16th April 2025. 

Update

I'm very fortunate to get a two week October half term. I've had a lot of school work to catch up on over half term so I haven't had time to do much on my blog, except a few updates to my resource libraries (I've added Dr Austin's new A level resources). 

When we return to school next week we have Maths House Week which is an annual event at my school (every department has to run a House Week). For this I have to deliver the same assembly five times (I've written two and I need to choose one to deliver. One assembly is on primes - following the recent discovery of a new prime number - and the other is about Ramanujan). We will also run a number of activities including a treasure hunt and a puzzle competition. I blogged about these activities last year in Gems 176. 

I'm still seeking someone to join my team in January or February - this could be a temporary role (covering maternity leave) or permanent role - we're really flexible (but ideally the candidate will have experience of teaching mechanics at A level). Please get in touch if you want to chat about this. 

Finally, thank you to @aap03102 who featured the lovely game Do Not Find the Fox in a recent newsletter. 

Vectors for Enlargement

I'm going to do a series of short posts on approaches or methods that teachers might not have seen before. I'm very aware that there will be many people who already use these approaches, but I figure that not everyone will have seen them so they are worth sharing.

Today, vectors for enlargements. I first saw this on Twitter years ago but I can't remember who tweeted it (apologies!). Later I saw my former colleague Lizzie Stokes (@misstokesmaths) using this approach in her teaching.

How I used to teach enlargement
I'll illustrate my previous method with a negative enlargement question:

I'd tell my students to draw a line to any vertex from the centre of enlargement. Then I'd tell them to count how many squares they've moved to get to the first vertex. I always modelled this slowly on the board. I showed the process of counting carefully ('count the corners, not the spaces!') because I find they often miscount.

Then I circled the scale factor and said that because the scale factor is negative two, to find the image they have to double the distance from the centre of enlargement. But because it's negative, they have to go in the opposite direction from the centre. So in this case, we started by going two units right and one unit up so now we have to go four units left and two units down. I emphasised that we're going the opposite direction because it's a negative enlargement. We then do the same thing for each of the other vertices in turn. At the end, all the corresponding vertices should be joined with straight lines going through the centre of enlargement. If not, you've miscounted!

I'd show another example with a different scale factor, then get them to practise a lot of these on printed worksheets. It was normally a relatively quiet lesson as they all had to do a lot of counting! I'd go round berating them for using pen when I'd told them to use pencil ten thousand times.

In hindsight I realise that this method could be better. It works fine for super smart students (most things do!), but others struggled with it. One problem is that you have to hold lots of details in your head while you work though the question. Another problem is that the method is different to the method for positive enlargement - there's an extra thing to remember.

How I now teach enlargement
They start by labelling each vertex with a letter and then finding the vector that takes them from the centre of enlargement to each vertex. They are already fluent in using vectors from our work on translation so this should be straightforward.

They write down the vectors rather than trying to hold the information in their head like they did before. Then all they have to do is multiply each of their vectors by the scale factor, and this gives them the vector for each of the vertices of the image. So they know exactly where to draw the image - it's all calculated and recorded before they start drawing.

I've used 'Year 11' vector notation in the picture above for clarity, though it's not essential at this stage.

This method is identical regardless of whether we are enlarging with a positive or negative integer or a fraction. So suddenly negative enlargements are no harder than positive enlargements (assuming students know how to multiply negatives). A clear and consistent method all round - I don't know why I didn't always do it like this.

Any others?
I hope that was helpful if you'd not seen it before!

I've blogged a number of times before about alternative methods for various topics (see my posts tagged 'methods'). If there are any approaches or methods that you use that you think other teachers might not use, I'd love to hear them! Please comment below or email me or tweet me.