# 311. Sales starter

Here is a neat little starter photograph (click on the image to enlarge) – get the mini whiteboards at the ready!

Possible questions

• How much money could be saved with the different reductions?
• What are the percentage discounts?
• What is the price as a percentage of the original?
• What is the exchange rate between pounds and euros (using the original prices)?
• What would the sale prices be in Euros?

If you can’t read the data clearly, the prices are: £45, £30, £22.50, £13.50, 70 euros

# 263. Percentages Tick or Trash

To quote a famous DIY company from the UK, this post ‘Does exactly what it says on the tin’!

Image credit: www.ronseal.co.uk

Here is a tick or trash worksheet on percentages, including a couple of tricky ones:

Percentages Tick or Trash inc solution

I usually tick these worksheets until I find a mistake. I then tell the student to have a rethink. Obviously the correct answer is the other option, but the working out will need to be corrected. I also do not tell them how many of the remaining questions are actually correct – they then recheck these before I mark it again.

The only difference with this worksheet is that students have space for working out – no more guessing! The extension task asks students to try and figure out where the wrong (misconception) answers come from – that can be quite tricky and tests their understanding.

# 262. Percentage Building Blocks

A quick reverse percentages resource for you. I explain reverse percentages by using both calculations and diagrams. These resources can be used as a starter activity or as a selective discussion point. The presentations are editable and the pdf is identical to them. I hope they are useful in addressing the reverse percentages misconceptions!

# 210. Most Wanted Percentages

I’ve been looking at how to teach percentage increase and decrease at Key Stage 3. If you can find 20%, you can obviously increase by 20% by adding it on. But does this reinforce the misconception that percentages are an addition, rather than multiplicative, function? I’ve started teaching multipliers for increase and decrease to a wider range of pupils, so it makes sense to introduce the concept earlier. I’ve used finding 120% as a way to increase by 20%. It opens up discussion as to why this works and pupils can form their own ideas on how to decrease.

Image Credit: www.te

To reinforce and practice the idea of increase and decrease by percentages I’ve created some ‘Muppets’ themed Top Trumps cards (not licensed). You can download them here: Muppets Top Trumps (pdf)

There are only eight cards, but you could print out one set per pupil and shuffle them.

# 197. £40.95

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.

# 195. Marshmallow Maths

It’s our first birthday at the MathsSandpit and this post is party themed. Remember a few years ago, when chocolate fountains were the ‘in thing’ at celebrations and parties. The healthy guests stuck to strawberries drenched in chocolate. The unhealthy went for marshmallows on sticks and … well … all I’ll say is Geraldine Granger (Vicar of Dibley – Chocolate Fountain)

I’m trying to decompartmentalise the maths in my students heads. They struggle to see the links between different topics. So I introduced ‘Marshmalllow Maths’ – they were intrigued/hungry as soon as I mentioned it.

Equipment

• Cocktail sticks
• Pink and white marshmallows

Step 1

Step 2

What mathematical characteristics do the marshmallows have? I’ve summarised my classes’ responses below:

Two marshmallows lead to ratio, percentages, fractions, decimals and probability. The links between these topics start to emerge.

Step 3

How have the ratios, fractions, decimals, percentages changed?

Step 4

Make another 1:2 ratio marshmallow, identical to the previous one. How have the mathematical facts changed? In fact although the numbers have changed, the proportions have stayed the same which is proved when you simplify the numbers. Physically you can prove it by stacking the structures on top of each other – from above it looks like the original structure.

At this point I went cross-curricular and discussed the similarities between the marshmallow structure and water (H20). I was going to label the marshmallows with H and O, but my food-colouring pen wasn’t working. My logic was that water always has hydrogen and oxygen in the same ratio – this means we know we can drink it. If the ratio suddenly changed to H2O2, we would be in trouble! As far as I can remember H2O2 is hydrogen peroxide and is better for bleaching than drinking. This actually got the idea across quite well – no-one tried to fudge their ratios.

Step 5

I then allowed the class to make their own simple structures using their own piles of marshmallows. They had to make at least three identical structures, work out the related maths and prove that their numbers could be simplified to the basic form. In doing so they also looked at converting ratios to fractions and also found fractions of amounts.

Step 6

Eat marshmallows (whilst doing some related questions).

Optional: Step 7

Calculate the percentage increase in body mass on results day! It was marshmallows today, a chocolate prize for cracking a code earlier in the week and they say they learn better when they eat. I think it’s all a ploy to scrounge more food … but if it works … maybe fruit next time!

# 146. Sales Fractions

A quick idea for you today:

What is the cheapest each item could have been?

Which of these is the odd one out?

Why is it the odd one out? What discount does it represent? What is this as a decimal or percentage?

Keep your tags the next time you go to the sales – you never know what questions you’ll find.