A blog about teaching and learning in a maths classroom.

Double Strength Cordial and Ratio

Monday, 17 January 2011 | 6 Comments

When introducing the topic of ‘ratio’, I use the mixing of cordial as an illustration that most kids get.
The idea of using 1 part of cordial to 4 parts of water makes sense to them – and they get the idea of equivalence when you mix the cordial in a different sized container (I use the examples of using cups to fill a bottle for a picnic, and using buckets to mix a big batch for a party).

Recently Cottee’s Cordial started making their cordial concentrate in 1 L rather than 2 L bottles. Doubling the strength of the concentrate with the instruction, “Just Use Half”. See ‘Products’ on the Cottee’s Cordial web-site.

Rather than explaining how I’m thinking of using this in class – because to be honest, I’m not sure – I’m going to pose a WCYDWT? ala Dan Meyer.

So, what can you do with this? Your suggestions in the comments.

2 L Bottle

(click on images to view larger)
Thumbnail of 2 L bottle front Thumbnail of 2 L bottle back

1 L Bottle

Thumbnail of 1 L bottle front Thumbnail of 1 L bottle back

A set of photos is in the zip file below. High resolution versions are available on Flickr.

Cordial ZIP, 754 KB
This work is licensed under a Creative Commons License (?).

Posted in • Lesson IdeaRatioMediaPhotoWhat can you do with this? | Short URL:


Nordin Zuber on  17 January 11  at  11:49 PM #
Firstly, ditch the home brand cordial - that's an offense against nature. We need to see the fresh healthy looking fruit on the front to feel better about the cordial. I would start with the 2L less concentrated cordial mix. Begin with a taste test of pre-mixed cordial at different concentrations to start the conversation (watch out for diabetics). Form small groups - give them water, cordial concentrate and cups to make their own recipe (have sponges handy). Ask students to describe their optimum recipe mathematically. Then perhaps work out how many drinks their recipe can make with a standard 2L cordial bottle. Work out the cost per glass. Compare student groups - look, taste, colour, maths working out. Group formation could be guided by degree of sweet tooth to get more interesting results. Now consider the extra concentrated 1L bottle. How does their recipe change? Look at the cost of the 1L bottle - work out cost per glass. Compare price difference from 2L bottle. Pose the question: So *why* did Cottees introduce the extra concentrate? Do some maths to make your point. (I can think of at least 5 good reasons each for consumers, for Cottees and for the supermarket). What other consumer goods use similar strategy? (Concentrated dishwashing and laundry powder) Visit the Cottees website - comment on their analysis (could be a homework activity) - could you explain it better? Extension activity: Look at the back of the bottle at the "natural" ingredients and work out how many ml of each of these you get in your made up drink. Perhaps play with the 5% natural fruit juice element? Or how many grams of sugar you are consuming in one glass made to your recipe. How many calories? Extension activity#2: Compare the student optimum recipe to the recommended recipe - for taste, for price, for value. Extension activity#3: Develop a business plan for selling made up cordial using your recipe. What is ratio of cost of goods to price? What is the ratio of cost of goods to profit? All this cordial talk reminds of my favorite Italian restaurant Bill & Toni's in Stanley St, East Sydney - where they plonk a huge bottle of orange cordial on your table when you arrive. Goes remarkably well with spag. bol. - delicious. In fact - I think I'm going to go make up a cordial right now.
Adam Bevan on  18 January 11  at  09:43 AM #
I would start with a discussion about some great TV advertisements from the 80’s and show a couple like Mello Yello [url=][/url], Life Be in It [url=][/url], Mortein [url=][/url], and finally Cottees [url=][/url] . The kids will love the ads and be singing them for days to come. Then I would introduce the downsizing of 2L to 1L and put the question to the class are you getting value for money? How can we find out? I would mention how the same company (Cadbury Schweppes) were responsible for reducing the size of their chocolate blocks from 250g to 200g and keeping the price the same [url=][/url] . So the lesson would involve the children comparing the price and ratio of the old 2L with the price and ratio of the new 1L. Some useless information from a former Cadbury Schweppes employee, ‘Coola’ (lime) is the number one seller. One respondent on this strange Whirlpool forum thinks the old Coola is nothing like the new Coola [url=][/url] . Nordin, you have some great ideas. Cottees only sell the 1L now so it would be hard to test between 2L and 1L. Simon, I really enjoy Dan Meyer’s blog, and think this is a great approach. If the students care about the problem they will care about the solution and the maths that brings them to that solution. Not sure if it is the same for everyone else but if you google ‘2L Cottees Cordial’ comes up as the top search result, I bet Cadbury Schweppes will not be happy about that 
Deb Hogg on  18 January 11  at  10:41 AM #
These previous two comments are such fun! Good job guys! Strange that as soon as product changes and value for money get mentioned, my housewife hat goes on and I think... toilet paper! Could just imagine bringing in different rolls and comparing sizes of sheets and length of rolls and all those other value for money concerns! Now there's a class you would have to have a great relationship with - the class where you can discuss toilet paper!


Simon Job on  19 January 11  at  09:44 PM #
Thanks for the great ideas. @enzuber Home Brand - I like the non-natural flavours of my childhood. I'm a devotee of green snakes, green jelly beans and green frogs. I lament the move to natural flavours 😊 @Adam Bevan, thanks for the ads, my daughter loved them 😊 I use that video about Cadbury packaging when looking at "Surface Area": @Deb Hogg - toilet paper - love it. Best Buy in Year 9/10. One of my first thoughts was looking at the recipe for the new concentrate - 1:9. It just looks wrong. The original recipe is 1:4, the new recipe is double strength, so shouldn't it be 1:8? I look forward to taking all these ideas and putting into a lesson later this year. Thanks.
Peter Gould on  23 January 11  at  02:17 AM #
Your comment: "One of my first thoughts was looking at the recipe for the new concentrate – 1:9. It just looks wrong. The original recipe is 1:4, the new recipe is double strength, so shouldn’t it be 1:8?" I think that you could ask that question of Year 8 or Year 9 as a discussion starter. But be prepared for the misconceptions that will come up and allow time to resolve them. This is potentially quite a nice idea to discuss the difference between ratios and fractions. Comparing 1/5 (original) to 1/10 (new) and what might the 1 in the numerator represent? I would expect to see some drawings in the explanations. I use the 'concentration model' with fractions but I don't think that it is commonly used.
Nan on  09 March 11  at  09:09 AM #
I would be telling the class that the reason Cottees is selling the smaller, more concentrated cordial, is because they are using an artificial sweetener (sucralose) so that they can use less natural sugar. What they don't tell you is that sucralose is a chemical manufactured in a laboratory, it is very close to those chemicals called aspartame, and that aspartame is banned in many countries. They also don't say that sucralose is experimental in nature and they don't yet know what the effects on humans are. Maybe a class in ethics in marketing should be on the agenda.

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Simon Job — eleventh year of teaching maths in a public high school in Western Sydney, Australia.
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