The Tree House Inside Jack’s Beanstalk

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Inside Jack’s beanstalk, up on one of the highest branches, was a tree house that had a mouse. It really was quite cold inside, but it made a great place where the crows could hide. One day, Jack got a ladder, to see if he could reach the top … he almost fell off once or twice – he thought the wind would never stop. Whenever Jack wanted to hide away from the world, he climbed upto the beanstalk and inside a blanket curled. Sometimes Jack even took a flask of coffee, to keep him warm inside the branches of the tree, which despite the cockroaches, had peace and tranquility. Usually, Jack took a picnic of jam sandwiches which he munched for tea around about half past three. He shared his biscuits with a squirrel. He also carried a map and a telescope, so that from up in his beanstalk, he could see half of the Wirral ! Whilst beneath Farmer Giles was busy sowing, Jack’s beanstalk kept of growing … Jack liked his tree house – away from the hustle and bustle of the rabbit warren below, high in the branches, life was a little more slow. Until, that is, one morning, whilst Jack was snoring, he heard a loud “THUMP” and a very noisy roaring. He woke up with quite a start and drew the curtains of the treehouse apart. Outside, in the wind fastly blowing, a multi – coloured kite, was toing and fro – ing. When Jack looked far down, from the treehouse, on the ground, was a small boy holding a piece of string, spinning around and around. Apparently, the kite been blown off course – although the boy hung on and was dragged through the gorse. Jack tried to set the kite free, he reached from the door of his beanstalk’s tree house, almost toppling down from the tree ! It was hopeless – the kite was completely stuck – none of his animal friends in the beanstalk could help, though the kite was pecked by the rook. Since he couldn’t get his kite back, the boy waved goodbye to his kite and to Jack in the shack. The kite remained in the leaves, blowing all Summer in the breeze that blew through the treehouse eaves. Over the following months, Jack’s beanstalk grew and grew and grew. Throughout the Autumn, the wind blew and blew and blew. Soon, where the kite was, Jack didn’t have a clue. He even forgot it was there at all, until, in the fall, the young boy decided to call. He asked Jack for his kite back. But the beanstalk was so leafy and tall, the kite was difficult to locate – Jack said that only once all the leaves had fallen from the beanstalk in Winter might it possibly be seen, and that he would have to wait. Can you help at all ?

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High As A Kite

Take a look at the following pictures of the kite that landed on the branches of Jack’s beanstalk. Write a algebraic mathematical formula to show your working out. Note the size of the ladder. If each rung is 25 cm high,

a) How high is the ladder ? (r)

b) How high is the kite ? (z)

c) How much higher is the top of the beanstalk than the kite ? (y)

d) How much further does Jack have to climb on the ladder to reach the

top of the beanstalk ? (x)

Question 1

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Height of the Ladder           Height of the Beanstalk         Height of the Kite

(9r) (6r = 1.5 m) (2r)

Example – a) 9r = 9 x 25 = 150 cm = 1.5 m

b) 2 r = 2 x 25 = 50 cm = 0.5 m

c) 6 r – 2 r = 4 r = 4 x 25 = 100 cm = 1m

d) If x = further distance, b = beanstalk and one rung = r = 25 cm, x = 9r – (b = 6r), therefore, x = (9 x 25) – 150 = 225 – 150 = 75 cm = 0.75 m

Question 2

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Question 3

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Question 4

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Height of Height of Height of

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Question 6

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Question 7

Height of Height of Height of

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Question 8

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Question 9

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Question 10

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Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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* Teacher’s note – this exercise can be used to show how in algebraic equations, all parts add to to one whole i.e. a = b + c + d. It may be helpful to present answers as a table.

© Jacqueline Richards 2007

When a = height of the ladder, b = height of the kite, c = distance from the kite to the top of the beanstalk, d = distance from the top of the beanstalk to the top of the ladder

Answers :

2. a) 12 r b) 4r c) 3r d) 3 r

3. a) 9r b) 4r c) 4r d) r

4. a) 11r b) 3r c) 4r d) 4r

5. a) 5r b) 2r c) r d) 2r

6. a) 4r b) 2r c) r d) r

7. a) 9r b) 4r c) 4r d) r

8. a) 13r b) 2r c) 4r d) 7r

9. a) 9r b) 3r c) 2r d) 4r

10. a) 14r b) r c) r d) 2r

11. a) 8r b) 4r c) 2r d) 2r

12. a) 10r b) 2r c) 2r d) 6r

13. a) 18r b) 8r c) 5r d) 5r

14. a) 21r b) 10r c) 5r d) 6r

15. a) 17r b) 10r c) 5r d) 2r

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