### The Magic Number and the Hepta-tree

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

### Would You Rather?

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

### You Never Get a Six

Charlie thinks that a six comes up less often than the other numbers on the dice. Have a look at the results of the test his class did to see if he was right.

# Are You a Smart Shopper?

## Are You a Smart Shopper?

In my local town there are three supermarkets: Gary's Groceries, Fiona's Foods and Paul's Provisions.

This week they have each got a special deal on some products.

At Gary's Groceries, they are selling items at discount prices.

At Fiona's Foods, you can buy items which have a certain amount free.

At Paul's Provisions, there are some "buy one get one free" deals.

Have a look:

## Paul's Provisions.

If you shopped at Gary's Groceries, how much would you actually pay for each item? So how much money have you saved on each?

• 2 bottles of lemonade (2litre size)
• 1 6 pack of crisps
• 24 sausages
• 1 bag of chips (1.8kg size)

If you bought all the items in one shop, where would be the cheapest?

If you could buy the items from different shops, how would you do it to spend the least amount of money?

Apart from the cost, can you think of any other advantages or disadvantages with buying these items at just one shop?

You have got £10.70 to spend on a party meal for you and nine friends. Here's your shopping list:

• 4 bottles of lemonade (2 litres)
• 4 packs of sausages (8 packs)
• 2 bags of chips (1.8kg)
• 2 bags of crisps (6 packs)
• 2 packs of biscuits (7 packs)

How can you do this so that you don't go over your budget?

How many different ways are there?

Which shop offers best value for money on each item?

What sorts of things do you need to take into account to answer this?

Is the "buy one get one free" deal at Paul's Provisions the same as if they had 50% off?

### Why do this problem?

This activity is particularly good in a number of mathematical aspects of learning:
Using mathematical ideas and methods to solve "real life" problems
Using and understanding vocabulary and notation related to money
Organising and using data
Choosing and using appropriate number operations and calculation strategies
Explaining methods and reasoning
Making and investigating general statements
The maths behind this scene can obviously be differentiated accordingly, from basic practice using coins and exchanging, to applications of addition and subtraction.

### Possible approach

Younger children would enjoy having shops set up in the classroom and being involved in role play. Using empty packets and cartons, along with plastic money or tokens, would be a good way in for many pupils. Another excellent resource would be flyers or leaflets from local supermarkets advertising their offers. (We would have used these ourselves but would get in trouble for copyright reasons!)

### Key questions

This investigation will stimulate a great deal of relevant discussion. Try to make the most of it! With only a small amount of exemplification, the children themselves should be able to suggest different scenarios which may affect where they would shop. This may lead into "what if?" type extensions, initially instigated by you but later by them too.

### Possible extension

At a higher level, a more general approach can be taken, perhaps along the lines of consumer versus retailer benefits. You can open up the investigation further by splitting the class into groups and setting them off on a "shopping project" with certain aims and/or constraints