Aunt Sally's hat cupboard was full of interesting caps. In fact, her caps did amazing things. When she wore her Easter bonnet, the Sun came out and flowers started to grow. When she put on her woolly Winter hat, everything turned into snow. Aunt Sally liked her all her hats, but the one she tended to prefer, was the magical maths hat, made out of magical fur. You wouldn't believe what she could do, when wearing her hats, things multiplied by two ! The cupboard door was soon so large, that Aunty Sally could use it as a barge and charge. Aunt Sally had lot of maths jobs around the house, so she put on her magical furry maths hat (although she looked like a mouse !). She wanted to measure the size of the hall ... wearing her furry maths hat, it was easy to see, how furry maths magic makes things treble by three. Aunt Sally couldn't decide, whether to add, subtract, multiply or divide. She put on her maths hat and easy as A B C, everything in the hat cupboard started to spin magically and mathematically. In the kitchen, Aunt Sally wanted to bake a cake, but she really had no idea how much sugar the recipe would take. But as soon as she put her hat on, the cake was quickly tastily done. Although, Aunt Sally's furry maths hat just about covered her ears (she hadn't done this much maths homework in years !).

 1. If Aunt Sally's hat had a diameter of 25 cm, work out the dimension of the radius and circumference of the hat, using the formula for working out the distance of a arc.

 2. When Aunt Sally's hat was rolled into three, it measured 7 cm wide. How wide is normally ?

 3. Aunt Sally knit a hat. Three centimetres required one quarter of a ball of wool. If the hat was 21 cm wide, how much wool did she need ?

 4. Aunt Sally dropped her hat in a well that measured 500 m deep. She noticed that steps lead down, but still it was only 20% towards the hat. How long did the rope need to be, therefore ?

 5. As Aunt Sally put her hat on a hatstand, she knocked off 50% of the 12 hats. How many were left ?

 6. Aunt Sally's hat shrank in the wash ! It was 60 cm high but reduced in size by one fifth. How big did it then become ?

 7. Aunt Sally was 175 cm tall, but wearing her hat, she increased by 10 cm - how high did she then become ?

 8. Aunt Sally's hat cost £1.25, how much change did she receive from £10.00 ?

 9. In the hat cupboard, Aunt Sally's hat span to the floor at a speed of 20 cm / 3 seconds. How long did he take to reach the ground, 3 m lower ? Give your answer in seconds and minutes.

 10. Aunt Sally wanted to open a hat shop. She bought 150 hat boxes, but when she looked, she only had enough hats to fill 90% of them - how many is that ? How many boxes, therefore, were empty ?

 Top Hat

Can you spot Aunt Sally's hat inside these words ?

hatter

chat

shatter

hatch

chatter

elephant

halt

hate

heart

haunted

that

haughty

health

what

shattered

chattering

thatch

chatty

© Jacqueline Richards 2007

Answers :

1. If circumference = 4 arc then arc = r x degrees = 4(12.5 x 90) = 4 500

2. 21 cm

3. 1 3 / 4 balls

4. Total distance - steps = 500 - (500 / 100 x 20 = 100) = 400 m ;

5. 6

6. 60 - (60 / 5 = 12) = 48 cm

7. 185 cm

8. £8.75

9. 3 (3 x 100 / 20 = 15) = 45 seconds; 0.75 mins

10. a) 150 / 100 x 90 = 135 b) 15