Jack was out fixing the bird box in the beanstalk one day, when a very lost – looking walker came by his way. The rambler, called John Walker, was so busy talking as the road was forking, he didn’t see the beanstalk, while he was walking. “CRASH !”. With his nose in his map, no wonder he didn’t spot the beanstalk until it went “SNAP !”. Off fell a branch, when the rambler tripped upon a root. John Walker slipped and off flew his boot. “BANG !”. “OUCH !”, Jack cried out in pain, as the rambler’s boot booted him again. “WHALLOP !”. John Walker had been walking so long, that his boots and socks almost walked by themself, the pong was that strong ! “Watch out for that beanstalk !”, Jack issued a warning – he wasn’t the first rambler to almost crash that morning. Soon, all that Jack could see, as the seat of the rambler’s pants as from the brambles, he tried to set himself free. With one foot stuck up in the air, soon, the rambler was cursing everywhere ! John Walker then got out his compass North. But on the way, he dropped it on the woodland floor so the compass didn’t work anymore ! Now he was only able to navigate to the gate – which, of course, for rambling, really isn’t that great ! Hardly surprising, when he stopped for lunch, lunch was late. Then, as ramblers often do, off John Walker set within a minute or two.

The Long & Winding Road

Circle the word “road” inside these words.

**broad**

**road hog**

**roadside**

**slip – road**

**road junction**

**road way**

**roadside**

Can you think of any more ?

Orienteering To The Beanstalk

Divide the class into two teams. Mark on it a suitable location for a beanstalk, then swap maps. Each team writes a set of descriptive directions for the other team to follow to get to the beanstalk from the furthest left – hand corner. Swap maps back. The first team to successfully follow the directions and find the beanstalk wins.

Over The Hill

Circle the word “hill” inside these words.

**chill**

**hill – brow**

**chilly**

**hill – top**

**chiller**

**shilling**

**over the hill**

**hillside**

**chilling**

**shilly shally**

“These Boots Were Made For Walking !”

1. Take a look in an atlas or a map book and write a list of as many place names as you can see which include the word “hill”.

2. What proportion are actually on a hill ?

3. How do you know which places are on a hill or not ? …

John Walker, the rambler called to Jack “Top of the mornin’ to you !”, as he looked at the topography of the hillside …

1. What in geography is topography ?

2. Why is it used ?

3. What, in mathematics, is a graph

4. Giving examples, how might it be used when making mathematical

calculations ?

5. Write a brief description of how graphs work.

6. How many other types of graph can you think of ?

Example – autograph.

Hill Crescents & Gradients

Each of the following algebraic equations, when plotted on a graph depicts a hill with a different gradient (or slope). Solve the algebraic equation then plot the points on graph paper to make five different crescents.

x = 2yx = 4y – 1

x = y + 2

2x = y

3 x = y -1

Write a brief definition of the word “gradient”. How and why are “gradients” used in mathematics ?

© Jacqueline Richards 2008