### 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?

##### Stage: 2 Challenge Level:

Mollie of St.Michael's C.of.E Primary School, Sandhurst, laid out her method very carefully:

Firstly I needed to work out all the actual prices for all the items at Gary's Groceries:

Chocobiscuits= 94p- 50%= 47p
Oven Chips= £1.60 - 25%= £1.20
Crisps= £1.20 - 35% = 70p
Lemonade= 55p - 20% = 44p
Sausages= £1.85 - 40% = £1.11

Secondly Ihad to work out how much was saved on each item:

Chocobiscuits= 47p
Oven Chips= 40p
Crisps= 42p
Sausages= 74p

Mrs Lydford's groups of Balgowan Primary School then found the cost of the shopping list at each store:

Gary's Groceries= 2 x 44p + 1 x 78p + 3 x 111p + 1 x 120p = 619p = £6.19

Fiona's Food's= 2 x 43p + 1 x 99p + 3 x 104p + 1 x 155p = 650p = £6.52

Paul's Provision's= 1 x 90p (using buy one get one free) + 1 x 159 + 2 x 204 (two bought at buy one get one free, the third bought at full price) + 1 x 249p = 906p = £9.06

Gary's Groceries would be the cheapest place to buy the whole shopping list, at £6.19, compared with £6.52 at Fiona's Foods and £9.06 at Peter's Provisions, but it would be even cheaper to shop around, buying lemonade and sausages at Fiona's Foods, crisps and chips at Gary's Groceries for a total of £5.96.

We thought the disadvantages of doing it this way would be that we would use more time and petrol.

- it might take different times to get to each of the shops.
- the shop might not have the type you want.
- the shop might be surrounded by more houses so be more popular and therefore have less stock.

Then Mrs Lydford's groups found some different ways not to go over their allotted £10.70 budget for the party food, by first working out which was the cheapest place to buy each item:

For the party, we found 8 ways of buying the food for under £10.70 by shopping around.

First we bought all the items in the cheapest places:
sausages=£4.08 at peter's
chips=£2.40 at Gary's
crisps=£1.56 at Peter's
biscuits=84p at Fiona's
Total-£10.60

Next we substituted items which were close in price to make different totals, still under £10.70.
Change lemonade to Gary's - new total £10.64
Change lemonade to Peter's - new total £10.68
Change chips to Peter's - new total -£10.69
Change crisps to Peter's - new total - £10.63
Change biscuits to Peter's - new total - £10.65
Change biscuits to Gary's - new total - £10.70
Change lemonade to Gary's and crisps to Peter's - new total - £10.67.

Finally, Mollie answered the last part of our question:

Buy one get one free is the same as 50 % off as you are getting double for the money in both situations. Hoever 50% off Ithink is better because you can decide whether to buy two lots where as with buy one get one free you might not use them within the sell by date.

If none of the supermarkets had a special promotion, I would shop at Fiona's, because she sells smaller packages but she charges less for them, so you can use them by the sell by date.