# 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:

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!

# 340. SUVAT dilemma

If you’ve been a regular reader of this blog you may remember a post in 2014 advocating the use Duck Tape to help with practical investigations. The post was: http://mathssandpit.co.uk/blog/?p=1585

I’ve recently reused the mechanics activity with a new class of Year 12 students. They had only just started mechanics and were familiar with models and suvat equations. We timed four different objects being dropped, under gravity, down a stairwell. The items had a variety of masses: a paper helicopter, a light plastic ball, a small sponge and a dense juggling ball. We meticulously timed each drop and double checked the height.

I asked the students to work out the velocity of each object on impact with the ground. It was akin to lighting the blue touch paper and standing back …

They are a competitive bunch and raced ahead to use the correct suvat equations to calculate the velocity. Then the fireworks started!

Part of the class insisted that the juggling ball must have the highest velocity. Part of the class insisted the velocities were the same for all of the objects. The rest were catching up and wondering what all the discussion was about. I innocently gathered their ideas on the board and asked them what was going on. Those who had used initial velocity, time & distance to find the final velocity had differing answers for each object. Those who had used initial velocity, distance and acceleration had a consistent answer.

Suddenly a hand shot up and said “Because we model objects as particles, their mass doesn’t matter so we can’t use the times”. This was followed by assorted groans from the class – especially those who’d used the individual times of the objects.

The variation of the original activity was to emphasise prior learning on setting up mathematical models for solving mechanics problems. Objective achieved!

(Obviously later in the course we’ll look at the impact of mass on mechanical models, but this was early days)

# 338. Grappling with graphs

Have you noticed that textbooks are okay with graphs, until you need some interpreting graphs questions?

Image Credit: trustedreviews

I thought that mobile phone tariffs would be a good starting point for comparing fixed charges and rates. Using the iPhone X as a starting point, I’ve put together a discussion starter and couple of additional questions. All the tariffs are actual offers available at the time of writing.

You could start by looking at the graph and asking students what they notice, you could give them the tariffs and ask them to generate graphs or you could give them the data and ask them to plot the graph and derive the tariffs. It’s up to you!

The graph is deliberately vague so that students can discuss trends without getting obsessed by the detail of the numbers. Everything is downloadable below.

iphone X tariff graph

Iphone X mini investigation

Interpreting graphs

# 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:

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.

# 332. Movement Maths

I’ve got to share a new YouTube channel with you. It was created by a former colleague who is not only an ace Maths teacher, but also a trained children’s fitness instructor. ‘Movement Maths: How to survive High School Maths’ is all about daily chunks of Maths with a fitness boost.

First – it addresses basic concepts that many students forget or stress over (initially it will be aimed at Foundation students)

Secondly – the videos are engaging and show that you can do Maths and exercise anywhere (my current favourite is the airport in video 13 – how did he find an empty sp?)

Thirdly – there are recaps and summaries built in

Finally – it was reviewed by students, who loved it!

Subscribe to the Channel, get fit and see what your students think

Update: 1st June 2019

It appears all the videos on this channel have been deleted.

# 330. Still Dancing Men

You may already know about my blog posts on the ‘Dancing Man’ cipher. If not, check them out here;

34. The Dancing Cipher

97. The Dancing Cipher (part two)

Now, I have two parallel classes and I want to set the Dancing Man project as a homework, but they’ll be doing the task at different, but overlapping times. I don’t want the second class to have an unfair advantage, so I’ve written a second task. All the instructions are the same, but it’s a different text. I’m not sure whether to give each class a different text or whether to randomly assign both texts within both classes to avoid copying/generate confusion.

This text is a little more interesting than the last one … think zombies!

You can download an advanced (Beta?) copy below and I’ll update you on how it went, after I’ve done it.

Dancing Men Project 2

Letter frequency analysis project answer B

# 326. Instant whiteboard

Welcome back to school!

I must say your display boards look lovely …

What’s that? You could do with another whiteboard

Why would you need that? They’re not cheap you know!