About these resources - The Prince's Trust

About these resources There are four resource packs:

1: About Time 2: Getting the Best Deal 3: Managing your Money 4: Business Finance

These four everyday maths packs are designed to support young people in dealing with the kind of mathematical problems that arise in everyday life and the world of work. There is some serious and challenging work here, but it is not just ‘more school maths lessons’. Instead, we have focused on relevant examples that young people will recognise the importance of, and we have made the most of opportunities to play with, discuss and make sense of the mathematical content. Who should use them? These resources will be accessible to young people with a wide variety of starting points. The material covered is central to much of the mathematical content from Entry Level 3 to Level 2, and will therefore support young people working at a variety of different levels. How long do they take to complete? Each resource pack will take about two hours, depending on the number of optional activities that are completed. How should they be used? Almost all of the work in the resources is suitable for paired or group approaches and discussion, they can also be used during one-to-one meetings with young people. This is important; young people will come to these sessions with a wide range of experiences, various gaps in their learning, and an assortment of misconceptions. Collaboration and talk will help session leaders and young people identify and address these problems; but it is also important to remember that many young people will feel anxious about mathematics. Collaborative tasks can help to reduce individual anxiety levels, reassuring young people that they are not being tested and judged, and making it more likely that misconceptions and gaps in learning can be identified. The resources can be delivered in any order, in that none of the content is dependent on material covered in other resource packs. However, the overall level of task complexity and independent learning required generally increases through the packs. For this reason, if you are planning to work through all of the resources, you will probably want to do them in numerical order. You do not need to be a maths specialist to use these resources The resources are designed to be delivered by non-specialists. There is no need to prepare a mathematical lecture for any of the resource packs. Instead, you should familiarise yourself with the activities; take time to play the games, and work through the calculations in the same way that the young people will. Ideally, work through the materials with a partner, and discuss any techniques or approaches that you find particularly difficult – or just interesting. Make use of the session leader guidance provided at the start of each

activity. If you can successfully work through each of the activities in a resource pack yourself, you know everything you need to be able to lead the resource with young people. See ‘Mathematical Content’ later in this document for more information about the techniques required in each of the resource packs. Additional materials required We have generally tried to minimise the resources and facilities needed to use these materials. These materials are designed to be portable, so you should have no difficulty using them on or off-site provided that young people have enough space to work and to organise the materials. Although you will certainly need access to calculators, even the cheapest model from

your local discount store will be perfectly adequate. In resource pack 4, you will need access to the Internet to show a couple of video clips. Other than that, the units are generally paper based; you will need access to a printer

or photocopier, pens, pencils, scissors, writing paper and glue.

2: Getting the Best Deal Finding totals and change Calculating percentage increases and decreases Converting between common units Comparing offers on a ‘like for like’ basis This unit includes a much wider range of mathematical content. Much of the material is quite straight forward, although the Guidance Notes include some detailed notes about suggested approaches to some of the trickier techniques (like calculating percentage changes). A variety of approaches to calculation can be used in the activities in this unit: mental arithmetic, written methods or calculator. It is important to encourage an appropriate choice of method: Mental calculation is an important element in developing mathematical confidence and

fluency; the learner who resorts to a calculator to find change from £1 probably has not got a strong grasp of the place value system.

Written calculations have their place, including situations where simple calculations need to be recorded, checked and shared. Informal methods of written calculation (like the number lines in this unit) can be a good way of strengthening fluency in mental arithmetic by reducing the burden on working memory.

Calculators will of course be used for many of the money calculations in this unit. It is important to encourage the habit of checking answers for sense (‘Does this answer seem reasonable?’), as well as rounding calculator answers to sensible levels of accuracy. The calculator should be an aid to mathematical thinking – not a substitute.

Everyday Maths 2 Getting the Best Deal

Main Mathematical Learning This resource covers the following areas of everyday maths:

Finding totals and change Calculating percentage increases and decreases Converting between common units Comparing offers on a ‘like for like’ basis

Why use this resource pack? This resource aims to build young people’s confidence by helping them to practice techniques that can be of clear benefit in their daily lives. The pack starts with some simple work on addition and subtraction with money.

Calculators can be used for this work, but there is also an opportunity here to develop confidence with mental calculation methods. The use of a number line is encouraged throughout the early activities.

The materials goes on to look at percentage increases and decreases; these will be useful later when various sale offers are compared.

Next, we review conversions between metric units. Again, this is in keeping with the theme of ‘getting the best deal’ – as items may be sold using different units, it is important to be able to convert between them.

Finally, we introduce the idea of unit pricing, and use this and the other techniques reviewed in the unit to decide which deals provide the best value for money.

The materials provided have been carefully designed to suit a wide range of prior attainment levels. However, it is important to use them selectively. The initial assessment activity is an important tool that will help you decide which activities could be omitted by particular learners, and which ones could be extended. Some of the materials can usefully be adapted and extended; the guidance notes indicate where this is the case. Materials Provided See the Guidance Notes before each activity for advice about using these materials. • Self-Assessment Questionnaire • Starter Activity: • Six Main Learning Tasks:

• Finding Totals • Getting the Right Change • Percentage Increase and Decrease • Units and Conversions • Unit Pricing • Find the Best Offer

• Answers to Exercises • Reference Guide: other materials on the Internet


The Assessment Questionnaire The questionnaire is designed to provide a simple check on prior learning; it can also be used to gauge the progress made during the unit. Ideally, you should work through a copy of the questionnaire with each young person.

Talk through each of the questions, and make a judgement about the their confidence with each topic. Tick one of the boxes below the first row of ‘smiley faces’ for each question, and make any notes that are needed. (The final column can be used to judge progress at the end of the unit.)

Alternatively, you could simply give a copy of the questionnaire to each participant and ask them to fill them in on their own. However, this is only appropriate if participants’ literacy levels are sufficient to allow them to make sense of the questions.

It would be useful to complete the assessment questionnaire before delivering the remaining activities. The questionnaire will give you a better idea of the range of attainment and confidence within the group and will help you to plan your approach.


Assessment Questionnaire Name:

1. I can calculate with money to find totals and change

I had £10. I bought one item costing

£4.10, and two items costing 60p each.

How much money should I

have left?

2. I can work out simple percentage increases and decreases

What is the cost of this item

in the sale?

3. I understand common units and can use them to compare quantities and prices

2.5 metres What length is

this in millimetres

(mm)?

4. I can compare offers and find the best deal

Which of these

is the best offer?

How can you tell?


Starter Activity: Price Match This is a simple matching exercise, which is intended to provide an opportunity for young people to discuss several of the ideas that will feature in the main activities. There are two versions of the activity: Version 1 is a sheet that should be cut up into individual cards. Provide one set of

cards to each pair of learners, and ask them to match the cards into pairs. Version 2 is an adapted version of the same activity, which can be completed by

drawing on the sheet rather than cutting it up. Use this version if space or the young person’s organisational skills make it impractical to use Version 1.

It is important to listen to the discussions that take place as young people carry out this activity, and this should provide useful additional assessment information. In particular, look out for young people who have trouble finding simple totals mentally. These young people will probably benefit from starting with some of the simpler tasks in the main activities that follow.


Starter Activity: Price Match (Version 1) Cut this sheet into individual cards to make a matching game.


Main Activity 1: Finding Totals There are three variations on this activity, in increasing order of difficulty. Sheet 1 involves finding the total of small amounts of money, with totals up to £1. Sheet 2 includes totals up to £10 Sheet 3 includes totals up to £100 Young people should start at an appropriate level – use the information from the initial assessment task to help you decide this. In each case, young people should be encouraged to start with a mental estimate – what seems like a reasonable answer? Each of the sheets starts with an example showing how a number line can be used to support calculation, and it is also possible for young people to use calculators for these tasks. Notice how the level of detail in the printed number lines decreases from Sheet 1 to

Sheet  3. Some young people may benefit from being able to count the marks on the earlier sheets, but the intention should be to support them in progressing to the use of an unlabelled line as a support for mental calculation.


Main Activity 1: Finding Totals, Sheet 1 Example: 35p + 48p.

Question 1. 40p + 50p.




Question 5. 60p + 15p + 9p.

Question 6. 21p + 34p + 26p.


Main Activity 1: Finding Totals, Sheet 2 Example: £2.50 + £4.65

Question 1 Find the total of £3.80 and £2.70 Question 2 What is the sum of £2.60 and £4.55? Question 3 I spend £3.72 and £6.50. How much do I spend altogether? Question 4 Calculate £4.57 + £4.80. Question 5 What is £1.77 + £3.85? Question 6 Find £1.85 + £4.50 + £3.09.


Main Activity 1: Finding Totals, Sheet 3 Example: Find the total of £43.75 and £16.55.

Question 1 Find the total of £40 and £35.50. Question 2 What is the sum of £18.50 and £26.65? Question 3 I spend £42.80 and £37.90. How much do I spend altogether? Question 4 Calculate £27.77 + £24.85. Question 5 What is £24.87 + £66.69? Question 6 Find £14.28 + £42.77 + £25.09.


Main Activity 2: Getting the Right Change Once again, there are three variations on this activity: Sheet 1 involves finding change from £1 Sheet 2 involves finding change from £10 Sheet 3 involves finding change from £100 The use of the number line to support mental calculation is reinforced in this activity. In all of these exercises, we are using the idea of subtraction represented as the difference between two numbers. So, for example, we mark £5.55 on the number line and work out how much more to £10. Notice that we could equally well perform this calculation by starting at £10 and then going back £5.55 to £4.45. As with the previous activity, young people should start at an appropriate level, and

may not need to complete all of the sheets.


Main Activity 2: Getting the Right Change, Sheet 1 Example: I pay for an item costing 45p with a £1 coin. How much change should I get?

Question 1. I have £1 and I spend 65p. How much change?



Question 4. I have £1 and I spend 24p and 37p. How much change?

Question 5. I have 90p and I spend 65p. How much money do I have left?

Question 6. I got 31p change from £1. How much did I spend?


Main Activity 2: Getting the Right Change, Sheet 2 Example: I pay for an item costing £3.87 with a £10 note. How much change should I get?

Question 1 I went to the shop with £10 and spent £5.55. How much change should I have? Question 2 I spent £5.69. How much change from £10? Question 3 I had £10, but I spent £6 and £3.66. How much have I got left? Question 4 I got £7.20 change from £10. How much did I spend? Question 5 I went to the shop with £10. I bought a pen for £1.40 and a drink. I got £7.35 change. How much did the drink cost? Question 6 I bought three identical items and got £2.05 change from £10. How much did each item cost?


Example: I had £100, and bought an item costing £37.85. How much have I got left?

Question 1 I started with £100 and spent £36.50. How much have I got left? Question 2 I had £100 to spend on clothes. I have spent £42.35. How much is left? Question 3 I won £100 in a competition. I spent £65.78; how much is left? Question 4 I have £100 to spend on food in a month. I have already spent £25.87 and £36.55. How much have I got left? Question 5 I went shopping with £100, and I have £44.10 left. How much did I spend? Question 6 I went shopping with £100 to spend. I bought a jumper for £17.50 and two identical belts. I have now got £78.52 left. How much did each of the belts cost?


Main Activity 3: Percentage Increase and Decrease This jigsaw activity is provided in two versions. Version 1 has simple square pieces that need to be cut up and rearranged so that

adjacent edges match – i.e. a calculation is shown alongside its answer. Version 2 has the same calculations and solutions, but is provided with interlocking

pieces, which may help less confident young people to check their answers.

The activity requires young people to calculate the effect of simple percentage changes. Introduce the activity by discussing the importance of this sort of calculation in everyday life, and talk about some of the ways in which they could be carried out. It is often possible to ‘start with 10%’ (which can be worked out mentally), and then add

or subtract multiples of this amount from the original sum as required. For example, to increase £400 by 20%, first work out 10% of £400 (£40) and then add two lots of this amount to the original amount: £40 + £40 = £80. £400 + £80 = £480.

Alternatively, there are various ways to carry out these calculations with a calculator. One simple technique is to use a decimal multiplier: for example to increase an amount by 20%, multiply by 1.2, or to reduce an amount by 5%, multiply by 0.95.

You will find further suggestions for teaching these techniques in the resource guide at the end of this unit. The main idea of this activity is to encourage discussion between young people and to help you to identify and develop the techniques that young people use in attempting to solve the puzzle.


Main Activity 3: Percentage Jigsaw (Version 1) Cut up the sheet to make a jigsaw puzzle.


Main Activity 3: Percentage Jigsaw (Version 2) Cut up the sheet to make a jigsaw puzzle.


Main Activity 4: Units and Conversions This is a simple worksheet about converting between common metric units for mass (weight), length and capacity. Introduce this activity by explaining the importance of ‘comparing like with like’ when trying to find the best deal. As offers may be made using different units, we need to be able to convert between them. The conversions needed here are: Mass (milligrams, grams, kilograms): 1000 mg = 1 g, 1000 g = 1 kg. Length (millimetres, centimetres, metres and kilometres): 1000 mm = 1 m, 100 cm =

1 m, 10 mm = 1 cm, 1000 m = 1 km Capacity (millilitres, cubic centimetres, centilitres, litres): 1 ml = 1 cc, 1000 ml = 1 litre,

100 cl = 1 litre. Note in particular that one millilitre and one cubic centimetre are the same, and that 1000 of either of these will make one litre.

This activity can be made much more engaging and meaningful by providing a range of packages and bottles marked with weights and capacities. Young people could be asked to estimate and compare the weights and capacities of the different containers, and to convert to different units.


Main Activity 4: Converting Units Fill in the missing quantities.


Main Activity 5: Unit Pricing Explain that many stores now provide unit prices as an easy way of comparing the value for money for different goods. The worksheet provides some practice in carrying out this kind of calculation; young people should be encouraged to look out for this kind of information the next time they go shopping. Work through the example at the top of the worksheet to explain how unit pricing

works. It is important to understand that the ‘unit’ involved is likely to be a convenient multiple

like 100 g for example, rather than a standard unit like 1 gram or 1 kilogram.


Main Activity 5: Unit Pricing Example: This item costs £5.25 for 250g (‘2.5 lots of 100g’). Divide the price by 2.5 to find the cost for every 100 grams. £5.25 ÷ 2.5 = £2.10.

Fill in the gaps in the table. In some cases, you will need to round your answer on your calculator to give the price per 100g to the nearest penny.

Item Price Size Unit Price

£6.50 350g

£2.55 400g

£9.50 750ml

300g 75p per 100g

250ml £1.20 per 100ml

£5.60 28p per 100g

£12.99 2.5kg

£8.75 1.5kg

900g £4.50 per kg

£9.85 £2.19 per 100ml


Main Activity 6: Find the Best Offer This activity is designed to provide practice in bringing together some of the mathematical techniques used in the previous tasks to decide between alternative offers for comparable products. This task is well suited to paired work.

Start by asking young people to cut the first sheet into individual price labels. As they do so, remind them of the importance of ‘comparing like with like’. They can assume that the pairs of products are of comparable quality, but they need to determine which one offers the best value for money.

They next need to decide which is the best offer for each item, and why. They can stick the labels into the appropriate places in the table on the second

sheet. Encourage them to make some notes to explain their decisions in each case.


Main Activity 6: Find the Best Offer (Sheet 1) These are the price tickets from a set of items on sale at Super Savers supermarket.

These are price tickets for the same items on sale at BestPrice UK.

Your task is to decide which shop offers the best value for each item. You can use the table on Sheet 2 to record your work.


Main Activity 6: Find the Best Offer (Sheet 2) Use the table to record your work. You can write in the details, or cut out the price tickets from Sheet 1, and stick them into the correct places in the table.

Item Best Offer Worst Offer Notes

Butter

Power Pack

Drinks Bottle

Chair

Cooking Oil

A4 Paper

Shower Gel

Batteries


8. Reviewing Progress Return to the questionnaire that was completed at the start of the unit. Work through each of the questions again, asking young people to assess their confidence with each aspect of the material covered, and to reflect on any progress that they have made over the course of the unit. Where necessary, refer young people to some of the additional resources listed in the Reference Guide at the end of this unit.


Answers to Exercises Main Activity 1: Finding Totals

Question Sheet 1 Sheet 2 Sheet 3 1 90p £6.50 £75.50 2 70p £7.15 £45.15 3 63p £10.22 £80.70 4 91p £9.37 £52.62 5 84p £5.62 £91.56 6 81p £9.44 £82.14

Main Activity 2: Getting the Right Change

Question Sheet 1 Sheet 2 Sheet 3 1 35p £4.45 £63.50 2 63p £4.31 £57.65 3 19p 34p £34.22 4 39p £2.80 £37.58 5 25p £1.25 £55.90 6 69p £2.65 £1.99


Main Activity 3: Jigsaw


Answers to Exercises

(Continued) Main Activity 4: Conversions


Answers to Exercises (Continued)

Main Activity 5: Unit Pricing The required answers are shown in bold.

Item Price Size Unit Price

£6.50 350g £1.86 per 100g

£2.55 400g 64p per 100g

£9.50 750ml £1.27 per 100ml

£2.25 300g 75p per 100g

£3.00 250ml £1.20 per 100ml

£5.60 2kg 28p per 100g

£12.99 2.5kg £5.20 per kg

£8.75 1.5kg £5.83 per kg

£4.05 900g £4.50 per kg

£9.85 450ml £2.19 per 100ml


Answers to Exercises (Continued)

Main Activity 6: Find the Best Offer

Item Best Offer Worst Offer Notes Butter

Power Pack

Drinks Bottle

Chair

Cooking Oil

A4 Paper

Shower Gel

Batteries


Reference Guide

The BBC Skillswise website provides a range of assistance with all of the mathematical techniques used in this unit. This page includes advice about using numberlines for calculations.

This government publication provides information for consumers about unit pricing.

There are many online tools supporting conversions between different units.

About the Authors The Prince’s Trust has created these resources in collaboration with UK based charity National Numeracy. Derek Huby Derek is an experienced mathematics teacher, advisor and textbook author. He has worked with a wide range of schools and colleges, local authorities, national agencies, charities and publishers. Derek is currently enjoying working as an independent consultant. Nina Patel After spending many years as a successful mathematics teacher and subject leader, Nina is now sharing her passion for the subject with trainee teachers. Never short of enthusiasm for her subject, she is committed to the idea that ‘maths is everywhere’ and is convinced that, with the right support, everyone can do and enjoy mathematics.

http://www.bbc.co.uk/skillswise/0/

http://www.bbc.co.uk/skillswise/factsheet/ma01line-l1-f-using-a-number-line

https://www.gov.uk/government/publications/unit-pricing-information-for-consumers

http://www.convert-me.com/en/

About these resources - The Prince's Trust

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