Category Archives: Number

362. Jaffa cake fractions

Been a while since I had time to write a blog post!

Today I was doing a fractions refresh with Year 7. I needed to instill the difference between cutting in two and cutting in half. After a quick dash to the village shop at lunchtime I was ready…

Equipment

Jaffa cakes or other easily cuttable food stuff, plate, knife, visualiser (optional)

Instructions

Stage 1: Ask a student to cut a Jaffa cake into two parts with one straight cut. The student then chooses which piece to eat and which piece to give to a friend. Having the visualiser meant the whole class could see it happen. When we did it the first couple of students were nice and cut the Jaffa cake in half. Then some of them cottoned on that they could slice off the smallest crumb and have virtually a whole Jaffa cake to themselves.

Stage 2: This time one student cuts the Jaffa cake and the other chooses the piece. Suddenly there were a lot more identical size pieces being cut

Stage 3: Discussion on the difference in meaning between “Cut into two parts” and “Cut in half”. We had a great conversation on same shape, same area, equal, fair. This was the aim of the activity as we were going to be looking at non-standard fraction diagrams

Genius or insane? One student managed to separate the orange and chocolate from the sponge base in one cut

361. Routes, Reindeer & Reasoning

Well, we are nearly at the end of a very crazy year. Congratulations on surviving it!

So, it’s been a while since the last blog post. Apologies for that. At the moment I am involved in Mixed Attainment teaching with Year 8. To finish off the term, I thought we deserved a bit of fun. We have a week of lessons left so I’m going for a mini project each lesson.

Lesson 1: Santa’s Route
I found this fab task on the Maths Drill website. There is a real chance for extension in this task, which is great for the mixed attainment classroom.

Lesson 2: Reindeer Ratios (Updated 13th Dec)
We have been following the White Rose Maths scheme for Year 8, which covers a lot of proportion and reasoning through ratio, multiplicative change and fractions. This task tries to cover some of these skills. The answers will be uploaded soon.

Lesson 3: Elf Box Packing Problem (Updated 14th Dec) Elf Box Packing Problem Solutions
This task involves using multiplicative change and fractional multiplication and division, with a dash of unit conversion. There is some work on shapes, but formulae are given where necessary. The first four pages print nicely into a folded A4 (A5) booklet. There is a help sheet for the box packing problem; this would be better printed on A4.

360. Preparing for online learning

A few tips for forward planning with Google Classroom in case of school closures, plus a few other hints and tips.

1. Check that all the correct students are on your Google Classroom class list – especially with leavers, joiners and set moves. Invite them by email if necessary. Same goes for other digital assessment platforms.

2. Check that the teachers of shared classes actually all have access to the classroom

3. Do not put everything on the Stream – it will get chaotic very quickly. Post all materials on the Classwork tab. It will automatically be put on the stream, but you will be able to categorise it.

This is an example of good practice. The classwork feed is set up with all the topics being taught, the shared teachers are identified and the tasks/resources are dated.

4. Check the functionality of your materials before you release a post to your class. If things don’t look right, convert it to a pdf. You can’t assume students have specific non-web based software. Also, you are looking to make it mobile phone friendly. The majority of kids have access to a smartphone, but you can’t assume computer access.

5. Make the most of embedding YouTube videos – copy the URL and paste it into the YouTube link when you create materials.

6. When creating assignments, think how students are going to assess – are you providing a markscheme? A link to a website with solutions or walk through? Is it a google form you can mark or auto-mark? A google doc or slide where you can actually mark each student’s work? An interactive website? Are they simply working in their regular book? In which case make sure they actually take it home.

7. Remember you can plan ahead by scheduling future tasks

8. If you want to use a digital textbook, but students don’t have access to it, you can ‘Snip’ the questions from the digital textbook and paste them into a Google Slides presentation or a document. This is probably slightly dodgy copyright wise, but if you can’t send every child home with a textbook during a school closure, it seems a reasonable stretch of copyright. You’d be using the physical books in your classroom if your school wasn’t closed.

9. It’s okay to model an answer on paper, take a photo/scan and upload it. There are many ways of doing this. Personally I use the Scribzee app as it doesn’t involve a computer and scanner.

10. Use it as an opportunity to share interesting maths with your class – the Parallel site, by Simon Singh is amazing. Also an ideal time to catch up with Numberphile videos and inspire future mathematicians.

11. I think Corbett Maths could be the main site for saving teacher sanity!

12. Exam classes are going to be tricky.
For GCSE classes sites like Mathsgenie are amazing. And don’t forget people like Access Maths, Piximaths and MsBsResources. Apologies to all the other awesome resource sites, not enough space to list them all.
For A-level Maths and Further Maths try Alevelmathsrevision and the AMSP (Further)

353. Large Data Display

If you teach A-level Maths in the UK, you will know about the prerequisite to know about the large data set for the statistics component. We use Edexcel and so need to know about eight weather locations.

Here is my Key Stage 5 corridor wall display.

I’ve got two maps – one of the World ( a freebie from the Humanities Dept) and one of the UK (£2.95 from Amazon).

I’ve included summary information from the CrashMaths booklet.

Of course, you can’t talk about UK weather data from the storm of 1987 – Michael Fish makes a special appearance.

351. No more glue sticks

Apologies for the infrequent blog posts. Life happens.

I thought I’d share an inspired idea that I saw on Twitter. AJSmith (@MrSmithRE) shared this brilliant video on how to efficiently use hole punched exercise books.

Hole punching exercise books

I converted to using A4 exercise books with Year 11 in September and the improvement was amazing. From low ability students who wanted to bin their Year 10 notes (Do I have to keep them?), to so much pride in their work that they are still using their A4 exercise books for personal study and revision whilst on study leave.

Now I’ve seen this video on tagging notes together, this could be a game changer. Fewer sheets stuck in means fewer pages filled with stuck in sheets, which means the books will last longer. So the Department saves on the cost of both glue sticks and exercise books. Those infuriating students who seem incapable of sorting out their books have got one less excuse now.

I plan on using this with my new Year 10 class in September – they are the exact opposite of my previous GCSE group, so this should make for an interesting comparison. I’ll feedback how it goes.

Now go and watch that video and start saving for an industrial strength hole punch.

345. Practical percentage skills

It’s perfectly obvious that fluency in the use of multiplication tables directly impacts students ability to divide. This grows into confidence with algebra and reverse operations. Students are able to see the links between the concepts. Our understanding of the importance of such skills is part of the success of programmes such as TTRockstars and Numeracy Ninjas.

Why is it then that so many textbooks, websites and resource banks keep the manipulation of percentages as separate skills sets? Percentage increase / Percentage change / Reverse percentages. We know that when concepts overlap, fluency increases when these links are pursued. So that’s what I set out to do.

I have a bright Year 8 class and started working on percentages with them. It didn’t take much to have them confident using equivalent decimal multipliers to find percentages of amounts. Using a multiplier for increase/decrease was a walk in the park. Then finding percentage change came up. Over the years I’ve seen a lot of students get very confused with half remembered methods:

“Which do I take away?”

“What number do I divide by?”

“Is this calculation the right way around?”

I tend to teach new value divided by old value and interpret the answer. It got me thinking – why am I teaching them this? They can increase by a percentage using a multiplier, why can’t they rearrange their working to find the actual percentage? Same goes for reversing a percentage.

After a good discussion, I used this worksheet to recap and develop their skills:

Percentages Linking concepts questions

Percentages Linking concepts answers

Warning: “Original Amount” section, question (d) is a tricky one.

As with all new approaches, it’s always good to see if it worked. I set the following task from Don Steward’s website:

MEDIAN percent problems

I have GCSE students who wouldn’t know where to start on those questions, yet my Year 8 with their ‘have a go’ attitude were absolutely awesome. I’m definitely using this method again!

342. Revision jotters

With the exams looming large, I thought I’d share how my class have been revising. To give you some context roughly a third of the class are doing Foundation GCSE, aiming for at least a Grade 4. The rest are doing Higher and aiming for a Grade 5 or better. We have three, one hour, lessons a week. I’m rotating between doing an exam paper, a whole class revision activity (eg a revision clock) and tiered revision.

I know if I tell the students to revise independently the results are going to be mixed. Some will be brilliant, some will be more laid back. To resolve this I pick a topic (or two) from each tier that I know they need to improve on from or that they have requested. It’s helpful if there is a theme to the work. I’ve recently done things like y=mx+c (F) with plotting inequalities (H).

Now the genius part: PixiMaths revision jotters

How to run the session

Photocopy a big stack of revision jotters. If you are doing black and white copying, use the b&w version. We requested the b&w version and, because PixiMaths is awesome, it is now on the website.

Clearly put on the board which topic each tier is revising

Eg Foundation: exact trig values, Higher: trig graphs

Give students 5-10 minutes to fill their revision jotters with everything they know. Have textbooks or maths dictionaries available to fill in the gaps. You may find that Higher students want to do the Foundation topic too – no problem, just make sure they have two jotters. Due to the complexity of the Higher topic, they will need more time to make initial notes.

My students are allowed headphones in revision sessions. At this point it’s headphones in for Higher and out for Foundation.

Do a skills recap on the board (exact trig values), with maybe an exam question too. Students can ask questions on the topic and add to their jotter. Then have a worksheet for students to do eg Corbett Maths or KeshMaths GCSE exam questions booklets. They can refer to their revision jotter or scan the Corbett Maths QR code for extra help.

Swap over. Headphones in for Foundation and out for Higher.

Repeat the process for Higher, with drawing trigonometric graphs. Issue an appropriate worksheet.

Once you’re done, make a judgement call. Are there students who could push it further? Maybe transform a trig graph or problem solve? Go for it. Foundation are busy, Higher are busy, spend some time stretching your most able. Every mark counts.

A huge thank you to PixiMaths for the revision jotters (and everything else).

Examples of students’ work

Shared with permission of students. You can see that they have personalised them to meet their needs and some are a work in progress. Also, the b&w jotter photocopies so nicely.