# Mathematics in the context of food and drink

In these activities students use a variety of mathematical skills in order to complete the tasks, each set in the context of the production of food and drink.

**Going Bananas, ****Minimise or Maximise** and **What's in Your Bowl**** **contains a number of activities in which students estimate weight and volume, collect data, perform calculations whilst designing smoothies and exploring eating habits. **Food for Thought** is an activity which requires students to use ratios, percentages, fractions, pie charts as students consider what constitutes a healthy diet. **Making a Mocktail **explores ratios when designing cocktails. The resource, **Food**, contains a number of activities requiring the use of a wide range of mathematical skills whilst Keeping the Pizza Hot requires students to model mathematically to find a solution. **Fish Dish **requires time and planning skills. **Fruit Pies **requires students to calculate area and use logical reasoning.** Boxes and Bottles **and **Packaging **are activities requiring students to solve spacial problems using measurement, area and volume. **Growing More **contains three activities all requiring systematic analysis, careful recording and proof.

### Going Bananas

In this Cre8ate maths topic students work out what a portion size looks like, find out whether they are eating enough fruit and vegetables and compare the costs of making and buying smoothies.

In How much is in a portion, students estimate weights of fruit and vegetables then weigh each item and calculate their percentage error.

Five-a-day explores the eating habits of the class, their data is collated and used to compare data handling representations and to estimate means from grouped data.

The smoothie challenge investigates whether they are good value for money and requires students to do calculations involving money, weight and volume.

### Minimise or Supersize

In this resource from Cre8ate maths, students critically compare nutritional measures and calculate their daily energy requirements.

Initially students fill in the worksheet Can we eat what we like, to prompt a whole class discussion about the consequences of a bad diet. They then use the Sugar, salt and fat worksheet, to explore their perceptions of the amounts of these ingredients in a selection of everyday foods.

In Calculating Energy Requirements, pupils use a scientific formula and the Energy requirements fact card, to estimate their energy requirements and compare these to the guidelines for themselves or someone they know.

Working as a Nutritionist requires students to take on the role of a nutritionist and plan suitable lunchtime meals for a family member, a celebrity or a sports person

### What's in Your Bowl?

This Cre8ate maths activity motivates the use of averages, ranges, percentages, bar charts, pie charts, and tables to make comparisons, interpretations and conclusions.

The students can perform the "What is in your bowl?" activities to investigate serving amounts and what is eaten for breakfast. The data collection activities cover estimation and measurement and enable many investigations to be performed: Do boys eat more cereal than girls? What is a typical serving amount? Does bowl diameter affect serving amount? What do pupils eat for breakfast? How healthy are breakfast cereals?

### Food for Thought – The Eat Well Plate

The everyday context of food serves as a vehicle for engaging learners in exploring the mathematical ideas of ratios, percentages, fractions, and pie charts which are useful in their vocational areas. Students are asked to agree the main food groups that might be suitable for a healthy diet and then represent the proportions of each food group mathematically and pictorially.

### Making a Mocktail

This activity aims to engage learners because of its connection to everyday life and the mathematical ideas of measurement and ratio underpin work in vocational areas such as Hairdressing when mixing hair dye and Construction when mixing concrete. This activity requires students to understand and use common measures for volume, use estimation and measurement and understand and use ratios

### Food / Animals

The Food theme, from Century Maths covers decimals, factors and multiples, length and area, number patterns, surveys, percentages, probability, ratio and scale drawing using practical work and practical application of the mathematics.

How much space? - using measuring and logic to determine how to seat people around a dinner table

Packing peaches - using factors and number patterns to investigate different packing designs

Sandwich bar - listing all meal combinations in a logical manner, carrying out a survey to decide what sandwich fillings to use, deciding how much to charge

Remarkable recipes - using proportion to scale recipes

Pick and mix - deciding how much to charge for sweets to make a percentage profit

Planning a party - using information to make decisions in a logical manner to plan an end of term party

Counting your calories - use a spreadsheet and read data from a table to consider the number of calories take in a day

### Keeping the Pizza Hot

This activity requires students to consider the problem of maximising the market available to a pizza shop through the ability to keep a home-delivered pizza warm for longer. Students use a mathematical model to explore the issue that a pizza home delivery business faces in ensuring that the pizza arrives hot! They use mathematical modelling to explore cooling curves for pizzas in different packaging. The model is then used to address the marketing problem faced by the pizza shop.

Students are expected to represent and analyse the problem, including simplifying where needed. The emphasis is on interpreting and evaluating the mathematical models produced and relating them to the original problem in order to improve upon them.

In solving the problem students may use linear equations, formulae analytical, graphical and numerical methods for solving equations and polynomial graphs, units, compound measures and conversions, apply the handling data cycle and use an algebraic interpretation of the real data collected rather than a statistical one.

### Fish Dish

This task requires students to plan when they should start preparing a meal in order to have it ready by a stated time. Students are given a number of job cards. Each card explains what needs to be done, how long the job will take and a condition as to when the job should be completed. Students have to select a way of representing the sequence of jobs using a table or diagram showing times, constraints and which jobs can be done in parallel. Students are to be encouraged work logically towards a result and explore the effects of altering the order of tasks.

Teacher guidance includes concepts which may be discussed with students, examples of probing questions which may be useful and assumptions that students need to make when completing the task.

The assessment guidance consists of a progression table detailing how students may improve in each of the key processes. The resource concludes with a number of examples of students' work, together with comments, probing questions and feedback.

### Fruit Pies

In this task, students are presented with the problem of finding how many circular pie tops and bottoms they can cut from a rectangular sheet of pastry. Students are given the diameter of the top and bottom of the pies, which are different, and the initial size of the sheet of pastry. There is an added twist to this problem as students can take the left over pastry and make a second sheet of pastry from which further tops and bottoms can be cut. Students are required to break down the problem into smaller steps, use logical reasoning, perform accurate calculations and communicate their findings effectively.

### Boxes and Bottles

Boxes and bottles come in all shapes and sizes. These Cre8ate maths activities explore some of the mathematics behind packaging decisions taken by manufacturers, they provide a platform for students to make conjectures and find efficient ways of recording results to justify claims they have made.

In Boxing stock cubes students use 36 multilink cubes to explore the number of different cuboids that can be made with a constant volume.

Exploring nets is the focus of Folding cubes. Here students are challenged to find as many different arrangements of 6 squares as they can. When the pupils have found the 11 nets of a cube they then have to decide which would be the best to use to create boxes to hold eight 1cm cubes of sugar.

In the resource How much does it hold, students order and estimate the capacity of a range of containers, before trying to half fill each of them and check their accuracy with a measuring jug.

### Packaging

This topic explores flat designs which can be folded and used to package food and drink. These Cre8ate maths activities provide rich experience of visualising 3 dimensional shapes from 2 dimensional representations.

In Four Chocolates and It Takes the Biscuit!, studentss will need to measure accurately and construct accurate diagrams. Four Chocolates will draw on and develop their understanding of relationships between linear dimensions and volume.

### Growing More

This rich task from Cre8ate introduces students to a Latin Square, where each row and each column has all the variables once and only once. Students may be aware of Sudoku puzzles which are based on this scenario. They are challenged to find 12 different designs which satisfy the stated conditions for planting three types of rhubarb.

The task then develops to four types of wheat before introducing a Graeco-Latin square, where four crop varieties and four types of fertiliser are arranged in a 4x4 square so that each crop and each fertiliser occurs in each row and column.

All three activities engage the pupils in systematic analysis and the need for careful recording and proof. The resource, Four types of wheat, also draws attention to rotation and reflection.