Introduction

Overview

The ‘Product Wars’ case study explores the use of maths in a business context. Learners assume the role of apprentices in a soft drinks company and are invited to coordinate the launch a new range of smoothie drinks, e.g. carrying out market research, creating smoothie recipes and designing the packaging. The case study has been specially designed to encourage KS3 learners to engage with maths and to develop their skills of thinking, reasoning and problem solving. It also contains opportunities for teachers to promote group discussion and presentations within their maths lessons.

The case study is mainly ICT-based and makes use of PDF and spreadsheet files, and a web-based app for presenting videos and feedback. It has been primarily designed for use in an ICT suite (the 2021 version could be used with laptops, Chromebooks and most mobile devices) although opportunities exist to adapt the materials for use in other circumstances, e.g. on a whiteboard in a maths room or as a series of paper-based activities.

Mathematical Content

Taken as a whole, the case study addresses several areas of the revised KS3 Programme of Study for Mathematics, particularly number, geometry, measure and statistics, the key concepts of competence, creativity and the applications and implications of maths and the key processes of representing, analysing, interpreting, evaluating, communicating and reflecting. It is important to note, however, that the three main activities within the case study are distinct from each other and therefore address different areas. Note that a detailed summary of how each individual activity links to the KS3 Programme of Study for Mathematics can be found in the accompanying lesson plans.

Across the case study, a certain level of prior knowledge and understanding is required varying according to the difficulty level selected. In activity 1, for instance, it is assumed that learners are able to construct a variety of statistical charts and graphs and can calculate averages and other measures of spread. In activity 2, it is assumed that learners are at least able to calculate a percentage of a particular quantity. Finally, in activity 3, it is assumed that learners are at least able to calculate the volume of a cuboid.

Organisation & Pedagogy

This case study contains differentiated materials and is suitable for use with most pupils in Year 7, Year 8 and Year 9. The materials can also be adapted for use in other circumstances, e.g. with lower ability learners, if so required.

Learners should be arranged in small groups to maximise the opportunities for collaboration and discussion. The materials can be adapted, however, for use in other circumstances, e.g. with individuals or whole classes, if so required.

The teacher is encouraged to adopt a facilitator role, introducing the chosen activity at the start of each lesson, circulating between learner groups offering appropriate levels of guidance if required and drawing the learning together at the end of each session. The accompanying teacher notes provide more detailed guidance on how to get the best out of the case study including examples of suitable questioning techniques. More general guidance on how to organise and coordinate problem-solving activities such as this can be found in the accompanying Bowland professional development materials.

Follow-up homework tasks have been included with each activity to help consolidate and extend the learning that will have taken place in class.

Resources

A set of teacher notes, a detailed lesson plan and a range of differentiated learner worksheets are supplied for use with each of the activities. These can be accessed by clicking on the buttons shown above and provide advice and guidance on how to make best use of the case study.

Activities 1 and 2 are intended to be completed using spreadsheet software - template files are provided in .xls format which should work with most spreadsheet packages.

A downloadable offline version of the whole package is also available from the Bowland Maths website

A facility for downloading and printing PDF worksheets will be required. Please note that some of the worksheets contain nets drawn accuratelt to scale - when printing these please check the print options in your PDF viewer and ensure that the scale is set to 100%. Check these worksheets with a ruler before using them.

Notes on the 2021 version

These materials were originally published in 2008, but were made unusable by the withdrawal of Flash player in 2020. The Flash portions have now been replaced, and the materials should work on any up-to-date web browser. An attempt has also been made to make the materials usable on mobile devices. Apart from that, the activities and worksheets are substantially unchanged, and the teachers notes still refer to the 2008 National Curriculum.

Since the original version had become effectively unusable the new version has been released with minimal testing - please contact us with any problems.

There have been some minor changes to the way the materials are arranged. Just a couple of things that might trip you up if you are used to the old version:

• On the 'Pupil Start' screen, each Activity now has its own menu page that includes the links to the appropriate briefing video and 'Chat' feedback link.
• On the 'Teacher Start' screen, you will still be treated to random videos of the office antics of Brad King - hit the 'Show/Hide Brad' button to remove this distraction while still being able to play the main videos
• The Activity 3 'which net' quizzes now run in the browser and end with the pupil being presented with a PDF link for just the cut-out-and build net template.
• As with the old version, when printing out worksheets, check that 'scale' setting in your software's print dialogue is set to '100%' and not something like 'fit to page', or the diagrams and nets will not be printed to scale.
• The feedback feature incorporating Brad King's Apprentice-inspired put-downs has been hidden by default, since it might be …unhelpful if taken out of context by someone using the materials without teacher support. See here for details of how to turn it back on.

Product Wars Activity 1: Market Research

These activities are designed for 60-minute lessons. You may need to adapt the materials for use in longer or shorter lessons.

Introduction

In this activity, pupils are invited to carry out a survey to gather information about smoothie drinks. This activity will help pupils to prepare for the other activities in this case study. This activity is is mainly ICT-based and makes use of PDF and spreadsheet files, and a web-based app for presenting videos and feedback. It has been primarily designed for use in an ICT suite (the 2021 version could be used with laptops, Chromebooks and most mobile devices) although opportunities exist to adapt the materials for use in other circumstances, e.g. on a whiteboard in a maths room or as a series of paper-based activities. It is suggested that pupils work together in pairs or small groups to encourage appropriate levels of participation and discussion.

The activity contains 3 options offering varying degrees of challenge. Different groups within your class can work on different options. Alternatively, you may prefer to ensure each group has a mix of pupils. This will help to create appropriate conditions for peer support.

These different options are as follows:

• Option A: Pupils are presented with a pre-defined questionnaire and a data sheet containing a batch of preprepared sample data. Pupils are asked to process the sample data and to analyse the patterns and trends found within. This option is considered appropriate for learners working at level – level 4 of the National Curriculum.
• Option B: Pupils are presented with a pre-defined questionnaire and a blank data sheet. Pupils are asked to carry out a survey using the questionnaire with other pupils to complete their data sheet. Pupils are then asked to process their data and to analyse the patterns and trends found within. This option is considered appropriate for learners working at level – level 6 of the National Curriculum.
• Option C: Pupils are presented with a blank questionnaire outline and a blank data sheet. Pupils are asked to complete the questionnaire then carry out a survey with other pupils using their questionnaire to fill in the data sheet. Pupils are then asked to process their data and to analyse the patterns and trends found within. This option is considered appropriate for learners working at or above level of the National Curriculum.

Objectives

• Pupils will collect data.
• Pupils will represent data using a range of measures, diagrams and charts.

Resources

• Pupils will need a copy of the appropriate form(s) of the questionnaire.
• You will need a projector for the start and end of the lesson.
• Pupils will need paper and basic materials to construct their graphs and create their presentations. This may include graph paper, pairs of compasses, colouring pencils, sugar paper, scissors and glue.
• Pupils may require access to computers if they are going to use computer-generated graphs and charts instead. They will also need access to computers to access the feedback tool so they can evaluate how well they did on the task.

Delivering The Case Study

The activity can be used as a tool for teaching, for revision or for consolidating and extending pupil understanding.

There are 4 phases to the task:

1. Introducing the use of questionnaires

• Play the introductory Brad King video for this activity.
• Take time to introduce the appropriate form(s) of the questionnaire, e.g. discussing the issues surrounding questionnaire design.
• You may also wish to discuss basic sampling techniques, e.g. highlighting the need for pupils to ask a balance of both males and females.

2. Data collection

• Pupils should be given the appropriate form(s) of the questionnaire.
• If you have chosen Option A, pupils will use a pre-defined questionnaire and some pre-prepared data.
• If you have chosen Option B, pupils will use a pre-defined questionnaire with twenty people gathering opinions and recording responses on a blank data sheet.
• If you have chosen Option C, pupils will create their own questionnaire on a blank questionnaire outline then use their questionnaire with twenty people gathering opinions and recording responses on a blank data sheet.

3. Analysing and representing the data

• Pupils should be asked to analyse their data using averages and measures of spread, where appropriate.
• Pupils should be asked to produce a summary of their findings, representing their data using bar charts, pie charts and histograms as appropriate.
• You may wish to use some of the graphs in the Misrepresenting Data presentation toremind pupils of the key points when constructing graphs and charts.

4. Presenting their findings to the group

• Either to the whole class or in small working groups.

Homework Suggestions

Pupils should be asked to complete their summary of the data in order to present back to the class during the next session. Alternatively, pupils could be asked to write up an evaluation of the activity.

Product Wars Activity 2: Ultimate Smoothie

These activities are designed for 60-minute lessons. You may need to adapt the materials for use in longer or shorter lessons.

Introduction

In this activity, pupils are asked to create a range of smoothies choosing from a list of potential ingredients. They are then asked to complete a nutrition label for each smoothie and, in some instances, are invited to compare their smoothies, e.g. with Guideline Daily Amount figures.

This activity is is mainly ICT-based and makes use of PDF and spreadsheet files, and a web-based app for presenting videos and feedback. It has been primarily designed for use in an ICT suite (the 2021 version could be used with laptops, Chromebooks and most mobile devices) although opportunities exist to adapt the materials for use in other circumstances, e.g. on a whiteboard in a maths room or as a series of paper-based activities. It is suggested that pupils work together in pairs or small groups to encourage appropriate levels of participation and discussion.

The activity contains 3 options offering varying degrees of challenge. Different pupil pairs or groups within a class can work at different options. Alternatively, you may prefer to ensure each group has a mix of pupils. This will help to create appropriate conditions for peer support.

These different options are as follows:

• Option A: Pupils are presented with a list of potential ingredients and are asked to use different ingredients to make 96g of smoothie. They then calculate the percentage of each ingredient to complete a nutrition label for each smoothie. This option is considered appropriate for learners working at level – level 5 of the National Curriculum.
• Option B: Pupils are presented with a list of potential ingredients and are asked to use different ingredients to make 360g of smoothie. They then calculate the number of kcals and the amount of protein, fat and carbohydrate in a g serving to complete a nutrition label for each smoothie. Pupils are then asked to construct a range of graphs comparing the figures for each smoothie. This option is considered appropriate for learners working at level – level 6 of the National Curriculum.
• Option C: Pupils are presented with a list of potential ingredients and are asked to use at least different ingredients to make 980g of smoothie. They then calculate the number of kcals and the amount of protein, fat and carbohydrate in a g serving to complete a nutrition label for each smoothie. Pupils are then asked to construct a range of graphs comparing the figures for each smoothie with some Guideline Daily Amount (GDA) figures. This option is considered appropriate for learners working at or above level of the National Curriculum.

Objectives

• Pupils will use problem-solving skills.
• Pupils will need to calculate percentages.
• Pupils will use ratio and proportion.
• Pupils will draw pie charts of results.

Resources

Pupils will need the following:

• access to computers
• pencil and paper
• copies of the support worksheets for Options A and B
• calculators

Delivering The Case Study

• Pupils should be introduced to the nutritional information given on packaged food.
• Ask your pupils to discuss the best way of providing this information.
• Project the accompanying spreadsheet on to the whiteboard.
• Take some time to introduce the features of the spreadsheet to your pupils.
• In particular, emphasise that pupils will be required to:
  • type the name of the ingredients they want to use in column H
  • enter the amount of each ingredient they want to use in column I
  • input the kcals per g for each ingredient in column J.
• Demonstrate how changing values in one cell can affect the value in other cells. For example, changing the value in cell I will alter the total value in cell I15. Similarly, changing the amount of each ingredient used will result in changes in the cells in column K and in the number of kcals recorded in cell J
• Ask pupils to suggest ways in which they could attempt to reduce the number of kcals per g. Try a number of changes to familiarise pupils with the spreadsheet.
• Allow time for pupils to work within their groups.
• Once they have met the criteria that the smoothie must have fewer than 60kcals per g they should go to the relevant label sheet and enter the number of kcals in the appropriate cell.
• Pupils then use pencil, paper and calculators to find the additional information required on the label, enter the results and print the labels. Help sheets are provided for Option A and Option B. The label print outs can be used for the Package Design activity.
• If time allows, encourage pupils to create up to 4 different smoothies.
• Option C pupils with the necessary spreadsheet knowledge should be encouraged to use the Chart Wizard to draw a pie chart of their results. Others should draw them by hand.
• Pupils could be encouraged to research nutrition on the Internet. Some useful sites are:
  • http://www.nutritiondata.com/
  • http://www.nutrition.gov/
  • http://www.nutrifacts.com/

Homework Suggestions

Pupils could be asked to collect the nutritional information panel from 1, 2 or 3 products and calculate the kcals, protein, fat and carbohydrate in the whole pack.

Most products provide nutritional information for a ‘standard’ serving of x grams. Ask your pupils to weigh out one of their typical ‘helpings’ and compare it to the ‘standard’ serving. Alternatively, pupils could be asked to research the RDA (Recommended Daily Allowance).

Product Wars: Package Design

These activities are designed for 60-minute lessons. You may need to adapt the materials for use in longer or shorter lessons.

Introduction

In this activity, pupils are invited to consider drinks packages before designing and making a container for their smoothie.

This activity is mainly paper based. It has been designed for use with pupils in a maths classroom equipped with a data projector and whiteboard. It is suggested that pupils work together in pairs or small groups to encourage appropriate levels of participation and discussion.

The activity contains 3 options offering varying degrees of challenge. Different pupil pairs or groups within a class can work at different options. Alternatively, you may prefer to ensure each group has a mix of pupils. This will help to create appropriate conditions for peer support.

These different options are as follows:

• Option A: Pupils are presented with a worksheet asking them to decide which diagrams are nets for a cuboid. The main activity asks them to design and make a cuboid container, calculating its volume in cubic millimetres and its capacity in millilitres. A sheet with the net of a cuboid is provided. This option is considered appropriate for learners working at level – level 4 of the National Curriculum.
• Option B: Pupils are presented with a worksheet similar to that in Option A but including nets for containers that are not cuboid. The main activity asks them to design and make a container that is not necessarily cuboid, calculating its volume in cubic millimetres and its capacity in millilitres. A sheet with the net of a container is provided. This option is considered appropriate for pupils working at level – level 6 of the National Curriculum.
• Option C: Pupils are presented with a worksheet asking them to draw 3 nets for an equilateral triangular prism. The main activity asks them to design and make a container of any shape with a capacity of exactly litre. This option is considered appropriate for learners working at or above level of the National Curriculum.

Objectives

• Pupils will use problem-solving skills.
• Pupils will relate 2-D drawings to 3-D models.
• Pupils will construct accurately using a ruler (and compasses).
• Pupils will find volumes and relate them to capacity.

Resources

Pupils will need the following:

• copies of the nets provided for the appropriate option
• copies of the homework sheet provided for the appropriate option
• card (an A3 sheet will be required for Option C)
• scissors
• glue sticks
• compasses
• rulers.

Delivering The Case Study

• The activity can be used to introduce or revise the idea of a net as a 2-D diagram that can be folded to make a 3-D model.
• Encourage pupils to open up various boxes and containers to find out the net used in their construction before they begin the activity.
• Once pupils have used the net provided they should design and make their own container.
• After they have completed the activity open up a juice container to see how it has been created by folding a rectangular sheet of card.
• Discuss why drink manufacturers would use this design, e.g. rectangles tessellate so many container nets can be cut from a large sheet of card with no waste.
• The activity can be used to revise, or to introduce, volume.
• It should be used to introduce, or reinforce, the connection between volume and capacity. The link with mass can also be stressed, i.e. for water:
  • o mm3 ≡ 1 millilitre
  • o cm3 = 1000 mm3 ≡ 1000 ml =1 centilitre
  • o mm3 = 1000 cm3 ≡ 1000000 ml = 1000 cl = 1 litre
  • o litre of water weighs 1 kilogram
  • o ml of water weighs 1 gram
  • If time allows, pupils can be asked to complete the extension worksheet provided.

Homework Suggestions

Pupils could be asked to produce a packaging display based on examples of packaging collected at home. This should include the dimensions and volumes of the packages used. Alternatively, pupils could be asked to prepare for their presentations next lesson (see below).

Final Presentation Activity

Extend the Product Wars case study by allowing additional lesson time for pupils to create a detailed presentation of their findings across all three activities. Pupils should be directed to deliver their presentations as if to Brad King himself, using mathematical reasoning to present their cases.

Introduce the presentation activity and encourage pupils to identify the success criteria that they think are relevant. These could include, for example, appropriate use of data. Pupils will need to refer back to their records from each activity in order to produce their group reports or displays. Pupils should be encouraged to develop their results:

• calculating any summary statistics
• describing and attempting to explain the patterns within the results, and
• presenting the data using appropriate construction techniques.

Groups could then be asked to present their report or display to the rest of the class. Other pupils could then be invited to peer-evaluate the reports or displays offering suggestions on how they could still be improved relative to the success criteria identified earlier.

Product Wars: Feedback

After having completed an activity, pupils can conduct a simulated online 'chat' with one of the employees at breeze. This tool requires pupils to discuss how well they did on an activity by talking to one of the employees at BREEZE.

There are three employees who will talk about the three separate activities. Each employee will ask pupils questions which they must respond to by typing in free text. Encourage pupils to be honest about how well they thought they did on the task. They must select a ‘smilie’ each time they respond as this will decide how the employee responds to them.

To keep a record of their responses, pupils can select all the text within the instant messenger conversation and copy it into another programme (e.g. Notepad or Microsoft Word). There is a 'Print/Save' option (only available online) that presents a plain text transcript of the chat that is easier to print, copy or save.

The feedback messages here are fairly innane - the idea is for pupils to use this as a 'check list' for self-assessment while maintaining the role play.

'Feedback' from Brad King

When you have completed the case study with your pupils, you can ask Brad King to feed back on how well he thought your pupils did overall.

In the Teacher Start area select the ‘Feedback’ button and then select a rating from 1-5 stars – 1 being bad feedback and 5 being great feedback. You can decide how to rate your whole class or rate groups individually. You could also ask pupils to rate each other based on a number of different criteria, e.g. how well do they think they worked together as a team. The average score will then decide which video you play. Each number rating has a variety of different feedback messages which should ensure that no group receives the same feedback. Use this feature at your discretion.

Welcome to 'Product Wars'

Pupils assume the role of apprentices in a soft drinks company and are invited to create the ultimate range of Smoothie drinks. The class is provided with their objectives as well as resources and support by Brad King, the Managing Director, who models his management style on the likes of Alan Sugar. Pupils work with other employees to carry out market research, develop various mixes for 'smoothies', evaluate them and then design and create the packaging. Video excerpts are used at key points in the lessons to provide support and guidance. Pupils receive feedback via texts from members of the product team and video messages from Brad King himself.

Click here for an introduction to the materials.