Planning tool

Students can:

• formulate a mathematical problem to solve within a given context
• assess mathematical-modelling approaches and choose the most efficient process
• interpret results and report findings effectively
• justify and communicate approach, results and conclusions
• identify refinements, receive feedback and reflect on potential next steps.

Some students may:

• struggle to identify a problem from a context (word problem).
• have difficulty in isolating the variables.
• have difficulty in formulating the correct equations or expressions needed to solve a problem.
• struggle in communicating their ideas clearly using the correct mathematical terminology and symbols.

To support students, teachers should use worked examples and guide students through the process. Students need practice and time to develop their thinking and problem-solving skills.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning ratios and ratios of scale.
• We are solving a common problem in the home: adapting recipes for those with allergies and intolerances, as well as political and cultural preferences.

Why are we learning about this?

Being able to be flexible and adaptable in the kitchen is an everyday skill everyone needs. Using a mathematical approach to adapt recipes in cooking makes life easier.

What to do

Problem: you are going to your friend’s house for dinner and you are asked to bring a chocolate cake for dessert, only to find out that one guest is allergic to gluten and another is vegan. You decide to adapt your regular chocolate cake recipe to cater for the food requests. Come up with a plan to adapt your recipe. Use your knowledge of ratios and proportion to make the adapted recipe work. Record your steps so that you can make the same recipe again.

1. Start by writing out your problem and identifying the broad variables you need to consider.

2. Now go deeper and brainstorm your adaptation approach. For example, will you adapt three different recipes or will you research which ingredients need to be eliminated, added or swapped? What quantities do you need to consider? Which ingredients definitely need to remain the same and which need to be changed? Will the cooking time change? What other elements do you need to consider (perhaps the shape of the cake tin, size of the tin and cooking temperature)?

3. Identify your questions and answers and arrange them in a way that makes sense.

4. Testing and evaluating is important, especially in this case. Come up with a plan to test your approach. Will you do a taste test before or after baking? Will you make more than one cake?

5. Use maths and your knowledge of measurement to attain the quantities of the ingredients as correctly as you can. How accurate do you think these need to be? Think about relative error and how accurately you need to measure your ingredients.

6. Make your cake and bake it according to your considerations/model.

7. Evaluate your outcome. Has it baked? Did your cake sink in the middle? Was the overall quantity too much or too little for the pan?

8. What could you do differently? Do you need to start again?

9. Refine your recipe!

10. Ask your friends to tell you about the cake and whether your model was successful. What could you do differently?

Success criteria

• I can exchange quantities of different unit measurements, identify my variables, and make a mathematical model to solve issues of scale and ratios.
• I can evaluate my outcome.