Calling all creative thinkers!
What mathematical questions could you set from this picture?
Here are a few to start you off:
1. Sequences – do the increasing number of chocolates in each layer form a sequence (in 2D, in 3D)? If so, what is the general term? Is it geometric or arithmetic?
2. Series – if it is an arithmetic sequence, can you find the sum of a finite number of layers? Which layer would have the 1000th chocolate?
3. Geometry – what shape must the layers be in order to form this structure? Is there a pattern to the layers? Could you stack these in a different way to form an equally stable structure?
4. Money – if a standard box holds 12 chocolates, how many boxes would a 2D or 3D version of this require? What is the cost? What if they came in a larger box? Could you save money?
5. Health – how many calories are there in the tower? How far would you have to run to burn off the calories? How many ‘average’ meals is it equivalent to? How many fastfood burgers? How sick would you feel after all that chocolate?!
Instead of setting a question, why not ask your students or even your trainee teacher what questions they can come up with?
Today we have a discussion starter question for you, inspired by a trip to the shops.
My shopping cost £40.95 today. What is the smallest number of coins required to make this amount?
If I paid with two £20s and a £10 note, what is the most efficient change?
Why would someone pay £41.05, as opposed to £41?
I purchased 17 items, do you have enough information to calculate the mean?
The most expensive item was £10, the cheapest was 45p. What does this allow you to calculate?
Two luxury items cost £9 in total. If I hadn’t bought these, what would the mean have been? Does this effect the range?
When I paid I was given this voucher:
What would the shopping have cost somewhere else?
What would the mean cost per item be after this discount?
What percentage discount is this?
You could also use this as a discussion starter about the number skills you use when you go shopping.
I’m sure you’ve done or heard of people using their classroom as a basis for problem solving. How much would it cost to paint/wallpaper/carpet the room?
What about the literal cost of flooring a room?
Image credit: Pinterest
Many people have calculated that it is cheaper to use 1 cent coins rather than buy tiles. There are many examples collected together here: Keytoflow
I think this idea could be adapted to look at different sizes of coin, areas and tessellation. Even simple circular coins can tessellate in different ways – how much does this affect the cost? This is also an open task which could lead to some great strategies and discussions.
@LearningMaths suggests students could investigate the percentage area covered by different types of coin. A great extension idea!
On 5th November, I stumbled across the Skills Workshop website when I was looking for a quick Guy Fawkes Night resource. I found a nice Functional Skills task on planning a Bonfire Night party.
My Year 10 Foundation GCSE pupils really focussed on the task and actually asked for more lessons like this.
I used an activity based on units of alcohol, from this site, as an extension task.
We had some interesting conversations about how easy it is to exceed the daily allowances for alcohol consumption. PSCHE in a Maths lesson!
Have a browse of the website and see what you can find!
A nice easy question to start the term with:
You go to the supermarket to buy your favourite shower gel (or other product). It usually costs £2.99. You have three £1 coins ready, when you notice the price has temporarily been reduced to £1.
What is the most money you can save?
Hint: Think of future gain
It’s not the obvious £1.99 saved – that is instant gratification.
It is actually better to buy 3 bottles:
Saving = Actual price x 3 – Reduced price x 3
Saving = £2.99 x 3 – £1 x 3 = £8.97 – £3 = £5.97
If you spent the whole £3 (which is one bottle plus one pence), you get a long term saving which is worth far more, for just 1p more.
Teaching the concept of delayed benefit is rather useful, especially if you are trying to encourage open investigations or looking at time spent on personal revision.
If you offer personal finance as a compulsory part of the curriculum, stop reading now.
‘Pay day loan’ companies have been the subject of several news stories over the last few months. Do they make money from those suffering from financial strife? Are the people who take them out too short-sighted to see the long term impact? Are they bad at Maths?
Personally, I don’t think there is a simple answer to any of it. That is the reason I’ve started including pay day loans when I do percentages with KS4 pupils.
This idea arose when I was revising with older pupils who had the skills to work out percentages, but were struggling to apply them.
I showed them the loan calculator sliders on Wonga.
I asked the class to estimate how much different loans would cost for different numbers of days. They showed their answers on whiteboards. I then showed the actual amount owed and we discussed it.
The questions they came up with and how they justified their choices were brilliant.
If you are always £100 short at the end of the month and continually paid off the loan with interest, what would you owe after a year?
(They spotted that after each month you would need £100, plus an extra months interest etc)
What is the APR? What does APR mean?
(It was 4214% on the day we discussed it)
Why do you pay fees on a loan?
Are pay day loans a bad thing as a one off, emergency solution?
(They were split on their answer to this one)
Some of these questions wouldn’t be relevant in a GCSE, but they are life skills which will hopefully benefit them in the future.
By the way, they were ‘gobsmacked’ when they realised how much interest you pay back on a mortgage and what percentage of your wages go on monthly repayments!
Two cuddly dogs for £10.
Take a closer look …