Tag Archives: ratio

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.

301. How much is my sandwich?

A visual discussion starter for you:


These three pots of sandwich filling cost £1 each. The flavours are egg mayo, chicken & bacon and cheese & onion.
How much would the 182g chicken filling cost if it weighed the same as the others?
The large pots contain 5 servings and the small pot contains 3 servings – are they the same size serving?

If you zoom in on the picture you could generate your own questions based on the nutritional information eg calories per serving.

You could extend this to the snacks in students’ bags. Are they as healthy as they think?

261. Revision Egg Hunt

It’s beginning to look a lot like Easter … scrawny plastic chicks and over-priced chocolate eggs everywhere! This little ‘egg’ of an idea was totally inspired by some lovely Tweeters who mentioned ways to use empty plastic eggs.


I bought these two-part plastic eggs from a local craft shop. They are available from lots of places on the high street and online. My pack has 30 eggs in six different colours. You may be able to see that I’ve numbered the top and bottom of each shell – just to avoid arguments.

Now, I used these eggs for revision with my GCSE class. Each colour represents a different topic. There are 30 questions and the answers are the numbers 1 to 30. I hid the eggs in our main hall due to the unpredictable nature of the British weather. You could hide them inside or outside the classroom and give a prize to the person/group who correctly completes the most questions. Points could be deducted for trying to sabotage other groups. If you don’t feel that adventurous or it’s impossible to go outside, you could copy the questions and do this as a desktop activity.

Sometimes we get tunnel-vision on the focus for passing exams. We keep the ‘fun’ stuff for younger pupils. This revision activity is a treat for my hard-working students in KS4. They aren’t the easiest of topics, but they are perfect for students working at GCSE grade C and above.

1-5 Expanding & factorising quadratics
6-10  Ratio & Proportion
11-15  Straight line graphs (y=mx+c)
16-20  Simultaneous Equations
21-25  Shape problems
26-30 Factors & Multiples

You can download the questions here: Easter revision 30Q
You can download the solution here: Easter revision 30Q Solutions

I was surprised to get feedback from this activity from a form teacher, who said their students had arrived at registration bouncing and saying how much they had enjoyed the lesson!

223. Let them eat custard!

This post isn’t a resource, more of a source of ideas. We tell students that maths is about problem solving, but how many problems are fictitious?

Here is a problem, taken directly from ‘real life’ when a friend was making custard on sunday evening.

The question
Do you think the instructions are wrong?

Does 2.75 litres of water seem right? Use the whole packet? How much is in the packet?

The problem

The custard powder had been bought from the wholesalers. It was such good value because it was a catering pack.

  • If the pack weighs 605g, how much would you need for one portion?
  • How much water would you need?
  • How could you decide if 55ml was a decent size portion?
  • How many pint jugs would the fifty-five 55ml portions fill?

If you have access to a wholesaler or talk nicely to the canteen, you will be surprised how much proportion work you can find in catering size value packs

By the way, my friend did a couple of calculations and a bit of estimating resulting in a large, but tasty, bowl of custard.

201. BBC Crispies

There was an interesting discussion on the BBC Breakfast programme this morning about the exchange of maths teaching ideas between British and Chinese teachers.

The guests on the sofa were from the NCETM and a serving Head of Maths. There was mention of the innovative ideas used to teach Maths in Britain – including some of mine. I’m not being presumptive, I happen to know that Head of Maths – in fact some of his ideas are on this site (JDs Tree Diagrams). So just in case you missed Breakfast, here is some Cake.


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.


  • Cocktail sticks
  • Pink and white marshmallows

Step 1


Ask your class to connect the marshmallows together


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

Add on another marshmallow


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!

35. Ratio that is good enough to eat

I originally did this activity for a class that I taught twice in a day, but it would work equally well on sequential days.

Recipe cards labelled A, B, C, D
Microwave or friendly food tech teacher who will lend you their room
Rice Crispies (or Cornflakes)
Bowls & spoons
Oven glove
Cake cases

If you haven’t guessed from the equipment list, you are making chocolate rice crispie cakes to investigate ratio.


Before you start
You need to have at least 4 different recipe cards. Two of them should have the same ratio of chocolate to cereal, but in different quantities. I had one as double the other. The other two should have common errors eg adding rather than multiplying to increase.

The messy part.

Make the rice crispie cakes and leave them to set. You should make sure each set of cakes is labelled with the recipe letter.

This is the fun part. Taste testing in the second lesson – they will be keen to get started.

Each pupil tries each recipe and comments on how they taste. Depending on your recipes, one should be too dry, one should be too chocolatey* and two should be identical. You can then look at the recipes to explain this by comparing quantities and introducing ratio.

*Some will say you cannot have too much chocolate, but if you use Mars bars the high sugar content means they go rock hard if there is not enough cereal. So hard in fact that two boys decided to eat a whole cake each because no one else wanted them and they were quiet for more than ten minutes!

You’re being watched…
I first did this activity 10 years ago when I knew I was being watched by my Head of Department in the tasting/discussion section. The class were a bouncy low ability Y9 group.

They loved it, my HoD loved it and it’s never let me down as a lesson concept since.