When Esmerelda the naughty witch flew around the sky,
Everyone watched her from the ground flying high...
Usually she didn't have much bother, on each of her trips,
Casting her spells and doing backwards flips !
But one day, she crashed into a chimney pot,
No wonder her head hurt and her hat was crumpled rather a lot !
Dazzled by the light, she turned left instead of right ...
When all of a sudden her magic pazazzed in mid - flight !
The cat sat on the back, jumped up in fright,
He hadn't had such a bumpy journey since last January's stormy night !
"Ouch !" Esmerelda screeched out in pain,
Dusting off her cloak and trying to get up again ...
For a while, it took her a minute or two,
For her head to stop spinning - then she saw her broomstick had broken in two !
Oopps ! Gadzooks ! What was she to do ?
She had to be back at the cauldron for half past two !
At first she tried a magic spell,
It did nothing, so she tried sellotape as well !
You wouldn't believe the time it took ...
And the broomstick still was bent (and the sellotape - unstuck !)
In the wizard flew, bringing her a pot of glue ...
Soon the broomstick looked like new ! (but the cat was also stuck, too !)
A bit of glue splashed on the floor, sticking the broomstick to the door !
Esmerelda tried to get free (she wanted to make it home for tea !)
Three birds and a crow, suddenly found they too couldn't go ...
Well that's what happens to naughty witches don't you know !
Equation
If Esmerelda's broomstick broke into five pieces, three pieces of broomstick were 20cm long and two pieces were 30cm, can you write this as a mathematical equation and work out the length of the broomstick.
Esmeralda brought a second broomstick that also broke into five pieces. Three of them were 30cm and two were two were 20cm long. Write this as an x and y formula and work out the length of the second broomstick. Compare the two.
Shape
Draw the broomstick. Show the side and an ellipse, the face in a 3d cross section, the vertical and the horizontal.
Solving inequality
On your diagram of the two broomsticks, Mark the middle with 0. Divide the broomstick into negative and positive numbers. If the cat walks a quarter would it be stood in the left or right ? Move the cat to 3/4 of the way along the broomstick, is it in a negative or positive position now ? Is it greater than or less and show this using special symbols. Now finally if the cat takes two more 5cm steps, is it greater or lesser than ? Positive or negative ?
Trigonometry
If Esmerelda leaned the broomstick against the wall in the kitchen, what shape would it make ? What would be the hypotenuse? The adjacent ? The opposite ? Work out the lengths of each using the equation above for both broomstick. Then using the SOHCAHTO A principle show the sin, cos and tan in both broomsticks. Work out the three angles.
The Broomstick's Function
This of the inter-relationship between each of the broomsticks and the pile of soot they sweep up. Think about how each is a variable. X = broomstick. Y = dust. For every 10cm of length, the broomstick magically makes the pile of dust higher by 5cm. Write this as an algebraic formula for each broomstick. Name the variables in this example.
Esmeralda's Action Fractions
1. There were 8 hours of darkness ....Esmerelda flew for half of them....
How many hours did she fly for that night ?
2. Her broomstick snapped into pieces. Show this as a fraction.
3. If her broomstick broke into 3 pieces and the cat was sat on one piece, how much of the broomstick did the cat take up space ?
4. The chimney pot had four pots on it.
Esmeralda smashed one when she crash landed on the roof. What fraction was left ?
5. The sellotape Esmeralda used was 50cm long. She cut off one fifth. 1/5 th. How long is that ?
6. It took Esmeralda 1 hour to glue everything and six times as long for the glue to dry. How long is that ?
7. Esmeralda used up one seventh of the glue - which equals 70 %. If the bottle of glue started off as 100mls, what fraction did she use ?
8. It took Esmeralda twice as long to get home as it did to get to the chimney pot. If it took her 15 minutes to get there, how long did the entire journey take ? What fraction was spent getting back ?
9. Esmeralda had 100 spells in her spell book. To fix the broomstick, she tried one quarter or 1/4 th. How many is that ?
10. Esmeralda crashed again on the way home. The sellotape fell off and each half snapped. How many pieces of broomstick did she now have ?
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