Applying Mathematical Concepts to Real-World Examples Using Mathematics across the Curriculum

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1 Applying Mathematical Concepts to Real-World Examples Using Mathematics across the Curriculum Applying Mathematical Concepts to Real-World Examples

2 Applying Mathematical Concepts to Real-World Examples MONEY MANAGEMENT YEAR GROUP: 9 OR 10 Introduction These units of work for Key Stage 3 pupils show teachers how to apply and reinforce learning from Mathematics across the wider curriculum. They support the development of the Cross-Curricular Skill of Using Mathematics. When using these lessons in class, the Mathematics unit of work should come before the Home Economics unit of work. Mathematics unit This unit focuses on aspects of financial capability, such as budgeting and how to get the best value for money. Pupils gain experience in considering needs and wants. They have opportunities to create a budget, estimate spending and consider the best value for money when shopping. Home Economics unit This unit focuses on further exploration of needs and wants. Mathematics required Prior learning Add and subtract money Interpret a calculator display when solving money problems and correct money notation Estimate prices by rounding Understand negative numbers in the context of money Calculate simple fractions and percentages Taught in this unit How to distinguish between needs and wants How to create and use a budget How to compare costs by using simple proportion Mathematics used in the Home Economics unit Negative numbers in the context of money Budgeting Value for money and simple proportion Estimating Pupils use games and a case study to examine budgeting, needs and wants, and value for money when planning a family meal using the skills and knowledge gained in the Mathematics classroom. 2

3 Applying Mathematical Concepts to Real-World Examples MATHEMATICS UNIT: MONEY MANAGEMENT Introduction/background In this unit of work, pupils will: keep a money diary of personal expenditure; categorise their purchases; distinguish between needs and wants; learn about the role and purpose of a budget; create a budget sheet; use simple proportion to compare costs by comparing like with like; calculate and compare unit costs to find the best value for money; and learn when it is appropriate and inappropriate to buy best value. Knowledge and Understanding Number and Algebra Pupils can: use number skills in the context of money up to 10; add, subtract, multiply and divide whole numbers using a range of mental, written and calculator methods; interpret a calculator display when solving money problems; make choices about spending and value for money; and make informed choices about personal budgeting and spending. The unit is delivered through two lessons: Lesson 1: Money, Money, Money budgeting, with Resource 1 and Worksheets 1a, 1b, and 1c; and Lesson 2: Value for Money best value, with Resources 2a and 2b and Worksheet 2. Using Mathematics focus: Financial Capability Range of levels: 3 5 Requirements Pupils should be enabled to: choose the appropriate materials, equipment and mathematics to use in a particular situation; use mathematical knowledge and concepts accurately; work systematically and check their work; use mathematical understanding and language to ask and answer questions, talk about and discuss ideas and explain ways of working; and develop financial capability. 3

4 Applying Mathematical Concepts to Real-World Examples Unit learning intentions Lesson 1 Pupils are learning: how to evaluate goods and services (needs and wants); how to create a balanced budget; and how to use appropriate mathematical terms when budgeting. Lesson 2 Pupils are learning how to find the best value for goods. Optional resources Whiteboard or cards Markers Other supporting resources Suitable budgeting app Nationwide Education website which includes many budgeting resources AfL opportunities Share the learning intentions with pupils during discussions in the introduction to the lesson. Also negotiate and share appropriate success criteria with pupils. These lessons use the following AfL strategies: effective questioning; formative feedback; and scaffolding reflection by asking for feedback from pupils; and by encouraging peer and self-assessment. Pedagogical approaches The following approaches are embedded within this unit: think, pair and share; sorting activities; and games. Resources Lessons 1 and 2 PowerPoint presentations with associated teacher notes Worksheets 1a, 1b, 1c and 2 Resources 1, 2a and 2b Scissors 4

5 Applying Mathematical Concepts to Real-World Examples Teacher notes Lesson 1 You will find useful videos on the Nationwide Education website that you could use to introduce this lesson. Using the PowerPoint presentation, lead the pupils to discuss where their money is going. Ask them to think about how they can keep track of it and how best to plan their spending and saving. Set the pupils a homework task of keeping a money diary (see Worksheet 1a) for at least one week. They should write down every purchase, including even the smallest expense, from their own money or money their parents have given them for a haircut, school lunch etc. After the specified time, ask the pupils to look at their money diaries and categorise their expenses, for example clothing, food, entertainment, health and beauty, school supplies and other. Explain to the pupils that there are two types of budget record: 1. a plan that shows the expected income and expenditure over a week, month or year; and 2. a continuous record of real income and expenditure. Explain to the pupils that we can use both types. We can predict what we are likely to earn and spend and then record our actual income and expenditure. Comparing the plan and the record can help us to see where to make changes in the future. Ask the pupils to draw up a budget or spending plan for a given length of time, for example one month. They can do this on paper (see Worksheet 1c), in a spreadsheet (they could create their own Excel spreadsheet or download a template) or using an app (there are a lot of free money tracking apps available, such as Wally, Money Lover or Money Manager). Discuss potential cutbacks on spending; pupils can do this in pairs. Discuss needs and wants. Brainstorm with the pupils to create a list of things they need and a list of things they want. Highlight things that fall into both categories, for example food is a need but cake is a want. In groups, ask the pupils to cut out the pictures in Worksheet 1b and sort them into needs and wants on a Carroll diagram. Discuss with the class the needs and wants using slide 9. Pupils can explain to the class why they put each item in the different categories. The rest of the PowerPoint presentation focuses on budgets. 5

6 Applying Mathematical Concepts to Real-World Examples Teacher notes Lesson 2 Use the PowerPoint presentation to discuss with the pupils some of the deals that attract customers into shops and tempt them to spend more money. For the Deal or No Deal and Deal A or Deal B game, put the pupils into groups of three or four. Give them a whiteboard and a marker or cards (see Resources 2a and 2b) to hold up for their choices. Show slides 6 10 one at a time and ask the groups to write Deal or No Deal on the whiteboard or hold up the relevant card. For slides 11 16, ask the pupils to work out which is the best deal and write Deal A or Deal B on the whiteboard or hold up the relevant card. During or after the game, discuss with the pupils the need to compare like with like and unit cost. Explain different ways of comparing like with like, for example using simple proportion, doubling or dividing down to give price per 100 g or price per item. Discuss with the pupils why it is not always right to buy the best value item. Give pupils Worksheet 2: Best Value or similar work. 6

7 Applying Mathematical Concepts to Real-World Examples HOME ECONOMICS UNIT: MAKE YOUR MONEY GO FURTHER Introduction/background In Mathematics, pupils have been taught about needs and wants, budgeting and value for money. They have been taught how to draw up a budget. Using this knowledge, pupils will look at a case study that covers debt, budgets and value for money. In this unit of work, pupils will: distinguish between needs and wants; prioritise needs and wants; create a budget; estimate and calculate spending; and practice shopping wisely within a budget. This unit is delivered through one lesson: Lesson 1: Make Your Money Go Further budgeting, with Resource 1 and Worksheets 1a and 1b. Knowledge and Understanding Number and Algebra Pupils can: use number skills in the context of money up to 10; estimate answers to calculations and approximate by rounding; add, subtract, multiply and divide whole numbers using a range of mental, written and calculator methods; understand and use simple percentages; interpret a calculator display when solving money problems; make choices about spending and value for money; and make informed choices about personal budgeting and spending. Using Mathematics focus: Financial Capability Range of levels: 3 5 Requirements Pupils should be enabled to: choose the appropriate materials, equipment and mathematics to use in a particular situation; use mathematical knowledge and concepts accurately; work systematically and check their work; use mathematical understanding and language to ask and answer questions, talk about and discuss ideas and explain ways of working; and develop financial capability. 7

8 Applying Mathematical Concepts to Real-World Examples Unit learning intentions Lesson 1 Pupils are learning: how to evaluate goods and services (needs and wants); how to create a balanced budget; and how to use appropriate mathematical terms when budgeting. AfL opportunities Share the learning intentions with pupils during discussions in the introduction to the lesson. Also negotiate and share appropriate success criteria with pupils. Optional resources Whiteboard or cards Markers Calculators Other supporting resources Suitable budgeting app Nationwide Education website which includes many budgeting resources The lessons use the following AfL strategies: effective questioning; and scaffolding reflection by asking for feedback from pupils; and by encouraging peer and selfassessment. Pedagogical approaches The following approaches are embedded within this unit: games; think, pair and share; class discussion; case study; and diamond ranking. Resources Lesson 1 PowerPoint presentation with associated teacher notes Worksheets 1a and 1b Resource 1 Dried beans 8

9 Applying Mathematical Concepts to Real-World Examples Teacher notes The Bean Game Introduce the concept of budgeting using Worksheet 1a: The Bean Game and the PowerPoint presentation. Put the pupils into pairs and give them 20 beans as pocket money for a month and Worksheet 1a: The Bean Game. There are various items on the worksheet. Each item has a value of beans, for example the occasional professional haircuts cost two beans as they have two boxes. The pupils must decide how they will spend or save their beans this month. As a class, ask the pupils to discuss how they spent their beans and why. Ask them to give reasons for their choices. After the class discussion, explain to the pupils that there is a shortage of beans and they will only get 13 beans next month. Ask the pupils, in pairs, to decide what changes they will make and where they will cut back on spending. As a class, discuss how pupils decided what they would do without. Ask if any of the pupils thought about using beans they had saved the previous month. It would be beneficial to have class discussions throughout the activity. A natural break for discussion might occur when prioritising Darren s items. This break will allow pupils to share and discuss ideas. Point out that different people have different priorities. Pupils may require help and guidance to draw up a budget sheet for Darren. For consistency, pupils should do this in the way they were taught in Mathematics, either on paper, in a spreadsheet or using an app. Part 2 focuses on Ciara planning a meal and shopping wisely. Discuss with the pupils value for money and quantities needed to minimise waste. Pupils will make a shopping list and then select the items from the Grocery Price List (Resource 1). There is more than one way to do this and the class should discuss this afterwards. This will give pupils the opportunity to explain why they have chosen to buy particular quantities of items. Case Study Ask the pupils, in pairs, to work through the case study about Darren and Ciara (Worksheet 1b). Part 1 focuses on Darren s poor management of his finances. Pupils will calculate Darren s expenditure and debt. They will discuss needs and wants, prioritise spending and draw up a four-week budget. Pupils working at a lower level may require support to calculate Darren s income and expenditure. More able pupils can prioritise spending using diamond ranking. 9

10 Resource 1: Key Words KEY WORDS Income Money you receive from pocket money, presents, jobs or interest on savings. Expenditure Money you spend on things you need (such as food) and things you want (such as meals in restaurants). Budget An estimate of income and expenditure for a specific length of time. Many different types of people and groups have budgets, including individuals, families, companies and governments. 10

11 Worksheet 1a: Expense Tracking Money Diary Date Description Category Cost Total: 11

12 12 Heat Food Chocolate Air Computer game Shelter Ice cream Shoes Clothing Lots of shoes Books Bicycle Cut out the pictures below and sort them into Needs and Wants. Car Glasses Watch Water Television Fizzy drink Medicine Electricity Worksheet 1b: Needs and Wants

13 Worksheet 1b: Needs and Wants Needs Things we must have to stay alive. 13

14 Worksheet 1b: Needs and Wants Wants Things we don t need but would like to have. 14

15 Worksheet 1c: Budget Sheet Income Amount Total: Expenditure Cost Total: 15

16 Resource 2a: Deal or No Deal DEAL 16

17 Resource 2a: Deal or No Deal NO DEAL 17

18 Resource 2b: Deal A or Deal B DEAL A 18

19 Resource 2b: Deal A or Deal B DEAL B 19

20 Worksheet 2: Best Value Circle the items below that provide the best value. Oranges: 5 for 1.20 Oranges: 10 for 2.50 Cereal: 1 kg for 2.20 Cereal: 500 g for 1.20 Soap: 42p each Soap: 1.70 for 4 Potatoes: 3 kg for 87p Potatoes: 5 kg for 1.46 Cheese: 500 g for 2 Cheese: 200 g for 75p Toilet rolls: 4.50 for 9 Toilet rolls: 5.50 for 12 Question In real life, why would you not always choose the goods with the best value? 20

21 Resource 1: Grocery Price List Cherry Tomatoes 330 g Baby Plum Tomatoes ( 2.40/kg) Red Onions Loose 0.17 ( 0.79/kg) Iceberg Lettuce 250 g 325 g Save 11p Was 90p Now 79p 0.79 Cherry Tomatoes 1.00 ( 3.08/kg) 250 g 0.53 ( 2.12/kg) Red Onions Red Onions 3 Pack Minimum 385 g 1 Kg 0.75 ( 1.95/kg) Mixed Baby Tomatoes 1.50 ( 6.00/kg) Rosanna Onions 1 Kg Save 25p Was 1.00 Now 75p 1.00 ( 1.00/kg) 0.75 ( 0.75/kg) Sweet Iceberg Lettuce Sweet Iceberg Lettuce 260 g Twin Pack 220 g Mixed Peppers Red Peppers Yellow Peppers Orange Peppers 3 Pack Each Each Each each 0.93 ( 0.31/each) 0.50 ( 0.50/each) 0.50 ( 0.50/kg) ( 0.50/kg)

22 Resource 1: Grocery Price List Chicken Breast Mini Fillets Chicken Breast Fillet Portions Chicken Breast Fillet Portions 500 g per Kg (Typically 625 g) 525 g White Tortilla Wraps 8 Wheat & White Tortilla Wraps 8 Mini Tortilla Wraps Plain 0.90 ( 0.11/each) 1.70 ( 0.21/each) 0.70 ( 0.09/each) Margarine Margarine Unsalted Butter 250 g 500 g 250 g 6 Wheat & White Mini Tortilla Wraps 0.90 ( 0.15/each) 8 Multiseed Tortilla Wraps 0.90 ( 0.11/each) Organic Unsalted Butter 250 g 0.80 ( 3.20/kg) 0.89 ( 1.78/kg) Mixed Sized Value Eggs Medium Free Range Eggs 6 Pack 6 Pack 1.20 ( 4.80/kg) East Anglian Medium Free Range Eggs 1.70 ( 6.80/kg) Mixed Sized Eggs Mixed Sized Value Eggs 6 Pack 15 Pack 6 Pack 0.70 ( 0.12/each) 0.89 ( 0.15/each) 0.89 ( 0.15/each) ( 0.17/each) 1.25 ( 0.08/each)

23 Resource 1: Grocery Price List COCOA POWDER COCOA POWDER COCOA POWDER Cocoa Powder 250 g Organic Cocoa Powder 125 g Fair Trade Cocoa Powder 250 g 1.99 ( 0.80/100g) 2.20 ( 1.76/100g) 2.99 ( 1.20/100g) Icing Sugar 1 Kg Icing Sugar 500 g Royal Icing Sugar 500 g Fondant Icing Sugar 500 g 1.70 ( 1.70/kg) 0.88 ( 1.76/kg) 1.09 ( 2.18/kg) 1.09 ( 2.18/kg) Caster Caster Caster Caster PURE CANE Caster Sugar 1 Kg Caster Sugar 500 g Golden Caster Sugar 1 Kg Caster Sugar 2 Kg Pure Cane Caster Sugar 1 Kg 1.60 ( 1.60/kg) 1.10 ( 2.20/kg) 1.90 ( 1.90/kg) 2.65 ( 1.33/kg) 1.79 ( 1.79/kg) 23

24 Worksheet 1a: The Bean Game THE BEAN GAME Food Lunches from home No cost Buy lunch at school 1 2 days each week Buy lunch every day Snacks weekday Snacks weekend Savings Change in piggy bank No cost 5% in bank 10% in bank 15% in bank Clothes Wear existing clothes No cost Buy from high street Buy designer Communications No phone No cost Mobile phone without data Mobile phone with data Personal Care Basic hair products Make-up Occasional professional haircuts Regular professional hairstyling and name brand products Recreation Visiting friends, hiking or cycling No cost Sports and hobbies Music or game downloads Movies Concerts or spectator sports Gifts Make gifts No cost Occasional small gifts Frequent large gifts Charity 24

25 Worksheet 1b: Case Study MUM S BIRTHDAY Think, pair and share With a partner, read the following case study and complete the activities. This is Darren. He is 16 years old and still at school. He has just started a part-time job working at a car wash on Saturdays and earns 30 a week. He also helps his parents around the house (he cuts the grass, cleans the windows and helps with the dishes) and they pay him a further 15 a week. This is Ciara, Darren s sister. Ciara is 13 years old and enjoys cooking and basketball. Darren and Ciara s mum s birthday is next month. Ciara has been saving some of her pocket money so that she can make a special birthday meal for the family. Darren hasn t thought about mum s birthday yet! 25

26 Worksheet 1b: Case Study PART 1 Darren is enjoying having some money to spend. Have a look at his expenditure (spending) last week. Expenditure Cost ( ) Magazine 3.50 Mobile phone top-up Bus fares into town (to work and to meet friends) 5.00 Going out with friends Food lunches and snacks Hair gel and deodorant 5.00 Football practice 5.00 Total expenditure (money spent) 26

27 Worksheet 1b: Case Study Question How much more money is Darren spending than earning? Use the space below to work this out. Darren borrowed this money from Ciara and will need to pay her back. Needs and Wants Needs are things we must have to stay alive, such as food, clothing and shelter. Wants are things we don t need but would like to have. Look at Darren s expenditure. Separate his spending into needs and wants. Needs Wants 27

28 Worksheet 1b: Case Study Using the diamond ranking grid below, help Darren prioritise his spending. Most important Least important 28

29 Worksheet 1b: Case Study Ciara has reminded Darren that it is their mum s birthday next month. He has seen a bracelet costing 28 that he would like to buy for his mum. Darren knows he will need to spend less and save money for the next four weeks if he is going to be able to pay Ciara back and buy the bracelet for his mum. You can use the space below to plan a four-week budget for Darren that will help him achieve this goal. 29

30 Worksheet 1b: Case Study PART 2 Ciara is planning the meal for her family to celebrate their mum s birthday. Ciara wants to make the meal very special and she has saved 15. She has decided to make chicken fajitas with tomato salsa followed by a chocolate Victoria sponge birthday cake. Look at the ingredients lists below, then make a shopping list on the next page. Ciara does not need to buy store cupboard items. These include garlic, pepper, oil, flour, herbs and spices. Ingredients For the tomato salsa 1 small red onion 425 g small tomatoes 2 garlic cloves large handful of fresh coriander leaves freshly ground black pepper For the chicken fajitas 1 tbsp olive oil 1 large red onion 1 red pepper 1 yellow pepper 450 g chicken breast fillets pinch paprika pinch mild chilli powder pinch cumin pinch dried oregano 4 tortilla wraps ½ iceberg lettuce Ingredients For the cake 225 g butter or margarine 225 g caster sugar 4 medium eggs 175 g self-raising flour 50 g cocoa powder For the icing 75 g unsalted butter 175 g icing sugar plus extra to dust 45 g cocoa powder 10 ml warm water 30

31 Worksheet 1b: Case Study My Shopping List 31

32 Worksheet 1b: Case Study Using your shopping list and the Grocery Price List, select the items Ciara should buy. On your shopping list, round the price of the items and estimate the total cost. Is the estimate within Ciara s budget of 15? If not, you will need to change some items. Now calculate the actual cost of the ingredients for the meal in the box below. Can Ciara afford to make the meal? 32