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Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?

Oh for the Mathematics of Yesteryear

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy?

Tray Bake

Age 11 to 14 Challenge Level:

cakesYour class has been asked to raise money for charity, so you decide to sell small cakes at break. Each person is going to make as many cakes as they can.  However, the recipe you have is for a tray bake which will cut up into 12 cakes - some people say they can't do that many, others want to do a lot more.  

  • How are you going to scale the recipe for different numbers of cakes? 

Then you have to decide how much you will charge for the cakes.  Clearly you need to cover the cost of ingredients, and you want to make a decent profit for the charity.

  • From this set of cards, find a mauve card for 12 cakes, a turquoise card with the recipe for 12 cakes and a green card with the cost of ingredients of 12 cakes, and lay them out in a group in the centre of the table.
  • Now sort the rest of the cards into groups - in each group you should have one turquoise recipe card, one mauve card for the number of cakes and one green card for the cost of ingredients.  Put each group of cards separately on the table.
  • Use the arrow cards to show the relationships between different group.  You may also wish to use blank arrows for your own relationships between cards.

When you're satisfied you've sorted all the first set of cards and found connections between them, use these two sets of additional cards (set 1, set 2) and arrows to extend the activity.