Category Archives: Number

334. Frustrating worksheets

Now, I’m straying from my usual positivity today because I’m frustrated by a worksheet. It was set for the eldest in Primary School as non-calculator classwork to be finished at home for homework. Topic is straightforward enough: Percentage Problem solving.

First gripe: I don’t think the teacher had time to check whether the later questions were suitable to be non-calculator. There were divisions my KS4 students would baulk at. Fair enough, we’re all human, we’ve probably all misjudged an activity like that.

Main gripe: this was a paid for resource. The Primary school will be paying a yearly subscription for these worksheets and I think they are being written by someone who actually doesn’t understand percentages. Someone is being paid for writing poorly worded questions.

But it gets better (or worse depending on your viewpoint). The last question is just … Well, let’s just say I’m not a fan. I was so annoyed I picked up pencil and paper and did it myself.

The set up asks you what percentage a tree must grow by each year, if it needs to reach a certain height by a certain year. Any decent student should know that percentage is proportional and thus it will grow in proportion to its existing height each year. That’s a compound percentage problem.

I remind you this is a 10 year old without a calculator doing this work. They calculated the required growth, divided by years and multiplied by 100. The result was a recurring decimal!

I assumed compound growth and worked out the answer as 20%.

I think the person writing the question added on 20% each year, then put their final answer in the question. That is a rubbish understanding of what a child would have to do to solve the problem.

As a teacher, I am fuming that schools’ valuable depleting budgets are being wasted on dross like this. I’d like to say this is the first worksheet from this online provider with questionable mathematical knowledge, but it isn’t. A teacher has trusted that the resource they printed out was accurate and useable and will now have to go back over this in class.

Of course critics will say that the teacher should have thoroughly checked every question, but this is the real world. If there was time to do that then there wouldn’t be companies making money from charging for resources.

333. Resource of the week

Just a quick resource for you today and apologies if you are already using this!

Plickers

Not some new ‘youth slang’, but an amazing online tool. Students have an individual card with each side labelled A, B, C or D. You ask a multiple choice or True/False question, they hold up their card with their answer at the top, you scan the class set of cards.

Image credit: Plickers.com

It really is that simple and here is what to do to get started:

  1. Create a free account at www.plickers.com
  2. Download the app to a portable device with a camera (phone, tablet etc)
  3. Print out the cards
  4. Allocate the cards to your class on the website
  5. Stick the cards in your students’ books
  6. Set a question
  7. Scan the cards

I have a tablet device that I use for school purposes as I keep my phone for personal use. The only problem I had was my android tablet doesn’t have a light source or as high quality camera as my phone, but we sorted that by having students move to a brighter part of the room for scanning. Instant feedback with no handheld devices!

Finally I have to say a huge thank you to Mr L, our trainee teacher, for introducing this to the Department.

328. Slice of genius

So, I was doing my usual Human Piechart  activity when an interesting point occurred. I had the class split into a group of 20 and a group of 18 (I had a student in charge of each group so that the circles would be factors of 360). I asked the class how we could combine the groups to make a whole class pie chart. One student suggested we add together the angles and divide by two. Several other students agreed that it was a good idea.

There goes my lesson plan.

I put this prediction on the board and asked them to prove it or disprove it using hard facts. I was very impressed by the different techniques they used. Most students started by adding the angles and dividing by two, then:

  • They went to the raw data and calculated the actual answers, disproving the prediction.
  • Some looked at the angles on the ‘combined’ pie chart and worked out the number of degrees per person for each angle. They used the irregularities in angles to disprove the prediction.
  • Looking at how many degrees there were per person and using logical deduction that you cannot add the angles.
  • Others noticed that categories with the same number of people had different sized angles.

All this before they’d answered a single pie chart question! The moral of this story is: don’t ignore the wrong suggestions, embrace them and use student knowledge to dispel the myths.

327. Digital Exercise books

Sorry – haven’t invented a digital Exercise book and I don’t use iPads/tablets in class. Today I’m sharing the inventiveness of my class.

I printed out one of those brilliant Corbett Maths textbook exercises to use with a Y7 class. It was a recap task, so I stressed that students could pick the level of difficulty. They cut out the sections they were doing and stuck them in their book. Because there were lots of different questions being completed, I allowed them to use their phones to scan the QR code to access the answers. A couple asked to scan the help video QR code.

I saw a few pupils being fussy about their cutting out – why were they cutting out little bits? That’s time wasting! No one should be time wasting!

Then I checked exactly what they were doing …

… The little geniuses:

They were cutting out the relevant QR codes and sticking them in their books. If this is the level of forward thinking in Year 7, they are going to fly through GCSE revision.

325. Mrs D’s Delightful Display

Anyone else been purging their classrooms of ragged wall displays ready for a fresh start in September? But then you end up rushing displays ready for the Autumn Y6 open evenings? And you need to get to know your new classes too!

Mrs D had a splendid plan to address all these issues. The first step was to introduce the problem: step through a piece of paper. It’s a classic problem involving maximising perimeter – I remember seeing it in a children’s Annual as ‘The journey through a postcard’.

This isn’t the easiest of tasks and takes a fair bit of determination and patience. Teamwork skills are also helpful. You can really get to know your class with this activity.

Once they’ve figured out how to do this you can reflect on how they overcame obstacles. All of this can be pulled together to make an amazing wall display on problem solving.

Thank you to the excellent Mrs D for allowing me to share her idea!

324. Glamping Gallery 

I’m a hard facts, scientific evidence kinda person. I don’t do New Age aura type stuff. However I could be converted on ‘good karma’. Last September, I spent the morning supporting the local Scout group by litter picking at a Festival. Afterwards I bought one raffle ticket for £1 and was  I was lucky enough to win first prize – a ‘Glamping’ trip. Cleaning up other people’s rubbish won me a holiday!

But this is a Maths blog – surely there is some probability investigation coming next or a comparison of good deeds and good fortune?

Nah – just some holiday pictures of a mathematically pleasing nature. Enjoy!

323. Split book headache 

As we reach the end of term and peruse our new timetables, here is a simple way to keep on top of your books. With the continued belt tightening in the curriculum more of us are sharing classes with colleagues. Do you have one book or two? Should you share a book? Should you keep the books?

How about a bit of funky duck tape? You know I love it!

I’ve put this rather garish tape on the spines of the books so both the students and myself can tell whose book they are. It also reinforces the spines. The Year 8 class thought it was ingenious. My Year 9 class were rather jealous and said they wanted tape too!

(You can get the same effect by wrapping a large sticker around the spine, but it’s not as ‘cool’)

PS That’s not my class size in the picture, before anyone gets jealous. There are 33 of them in total.