MathsClass

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.

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!

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.