James and the Giant Peach
by Roald Dahl
Maths Ideas
by Suffolk Maths Team
April 2009
Quick ideas:
What is heavier than a peach?
Do peaches float or sink?
If the peach doubles in size every 30 seconds, how tall / heavy/ wide would
it be after 2 minutes, 5 minutes etc? (Start with a regular peach)
The Aunts charge admission to see the peach. They want to be millionaires!
How much do they need to charge? Give the ticket a price, like if the tickets
cost £10 each, how many visitors do they need? If the children have done a
few of these, they could make a table with costs and ticket prices. E.g. if
tickets cost 1p, they need to sell 100,000,000 tickets, If they are 2p, they
need to sell….
Try some data handling. Ask pupils to design a survey. If you could see a
giant peach, how much would you pay?
Chapter 33 Reaching New York.
How long does it take them to get to New York? How far is it? How fast have
they travelled?
How long would it take James to take off all the centipede’s boots?
Create a map of the journey James and his friends make in the peach. Use
the points of the compass to describe the journey.
Event mapping; Create a line graph that reflects the mood of the characters
at different points in the story, for example, level of happiness, tension in
the story…
Look at different editions of the story published at different times. Why are
some books bigger than others?
If you have the edition with illustrations by Quentin Blake, use the group
picture of the creatures to estimate their heights compared to a 10 year old
(James). How many times bigger are they than before the magic happened?
What times tables can you work out using the legs of the creatures?
2x birds,
6x ladybirds
42x centipedes……..this will need some research about the creatures. What
about the 0 x table?
‘In my opinion,’ the earthworm said, ‘the really marvellous thing is to
have no legs at all and be able to walk just the same.’
Chapter 12
The creatures in the Peach have different properties. Some have legs, some
have no legs. It would be useful for the children to sort the creatures
according to their properties, and then apply this skill to numbers or shapes.
Pupils who are swift readers can use the text to jot down properties of the
creatures (including James) as they read through, e.g. has 8 legs, is not
loved by humans, is female….
Venn diagrams:
Sort the creatures using Venn diagrams with set labels like ‘has wings’ ‘has
six legs’ ‘makes music’ etc.
Carroll diagrams;
Is female, not female, or flies, does not fly. How many can they think of?
Decision tree:
Start with the whole set of creatures and generate questions to sort them
into two groups
For example;
Are you
female?
Do you have
wings?
Can you see?
Keep asking questions until all the creatures are sorted into one position. A
computer programme like Flexitree will help, and lets the pupils
concentrate on the questions.
Who am I? Put the name of one of the creatures on a ‘Post it’ and stick it to
a child so they cannot see it but the rest of the class can. Use their
experience of properties to help them identify their creature by asking
questions with a yes/ no answer like ‘Am I an insect?’ ‘Do I make music?’
etc. As there are not many creatures, you could move on to the same with
numbers. Make sure the children have the chance to discuss the properties
of the numbers.
How many legs has Centipede got?
– An investigation into factors
Chapter 12
“‟You have a lot of boots,‟ James murmured.
„I have a lot of legs,‟ the Centipede answered proudly.
„And a lot of feet. One hundred to be exact.‟
„There he goes again!‟ the Earthworm cried, speaking
for the first time. „He simply cannot stop telling lies
about his legs! He doesn‟t have anything like a hundred
of them! He‟s only got forty-two!‟”
Look at the number on Centipede’s
body. What are the factors of that
number?
Each pair of factors will become
Centipede’s legs.
The number itself and 1 are always the
first pair of factors and so they
become Centipede’s antennae.
If the number is a square number (e.g.
16) then the square root (e.g. 4)
becomes the tail.
Can you think of any numbers
that would give Centipede only
two antennae and a tail?
36
1
2
3
18
36
12
9
4
6
Which number would give
Centipede the greatest
number of legs?
Can you complete the Centipedes?
32
12
24
18
49
16
Can you complete the Centipedes?
32
12
24
18
49
16
Look at the legs, antennae and tails on these
Centipedes. What could the numbers be?
“I’m going to take a long silk string,” James went on
“and I’m going to loop one end of it round a seagull’s
neck. And then I’m going to tie the other end to the
stem of the peach….then I’m going to get another
seagull and do the same thing again, then another and
another -“
Chapter 20
Challenge 1 – Speedy Silkworm?
In the end it took the combined uplift of 502 seagulls to get the
Giant Peach airborne.
Challenge 1
If each seagull needs 50 yards (might need explaining or you could
change to metres if you prefer) of silk for its tether and Silkworm
produces silk at a rate of 10 yards a minute, how long would it take
enough silk to be produced for 502 seagulls?
This could be left as it is, as an open investigation for more able pupils
or it could be simplified by being broken down into smaller steps if
necessary –
How long would it take to produce enough silk for;
…… 1 seagull?
…… 10 Seagulls?
…… 100 Seagulls?
…… 200 Seagulls? etc
This problem will also lead onto the need to convert minutes into hours –
calculators could come into play here if the final total is found initially in
minutes and then converted.
Extensions and simplifications
This problem offers endless possible variations, simply by changing the
number of seagulls needed, the length of the tether needed or the time
Silkworm takes to produce a given quantity.
Challenge 2 – Speedy Sharks?
This is a very similarly structured problem to Challenge 1 but offers a
different context. This time it concerns the amount of time needed by
sharks to polish off the entire Giant Peach.
A shark can eat peach flesh at the rate of 5 kilograms a minute. If
the Giant Peach weighs 10 000 kilograms how long would it take one
shark to eat it all?
How long would it take……
…… 2 sharks?
…… 3 sharks?
…… 4 sharks?
Alternatively, you could pose the investigation in a different way – for
example: - Would 5 sharks be able to eat the entire Giant Peach in
less than 10 hours?
Extensions and simplifications
The example here takes kind numbers – (5kg, 10 000kg and 1 minute) –
varying these will offer lots of potential for extensions.
.
Challenge 3 – The Race Against Time
This is a combination of the previous two challenges and offers the
opportunity for children to work in groups to pursue a longer
investigation.
It could be created as a collaborative learning problem with the
following information written on separate cards for each group.
James needs 50 yards of silk to make a
tether for one seagull.
A shark eats peach flesh at the rate of
5 kilograms a minute.
It takes 502 Seagulls to lift the Giant
Peach up off the surface of the water.
Silkworm can spin silk at the rate of 10
yards a minute.
There are 25 sharks eating the peach.
What happens first – does the Giant Peach
lift off or do the sharks eat it all?
What if there were 26 sharks or 24?
Extensions and simplifications
Again this investigation can easily be varied by changing any of the
numbers.
Another possibility is to ask the children to investigate if they could
change any of the numbers in the statements to create a “dead-heat”.
NB – there is another variable here which you ought to bring to the
attention of the children – the fact that as the sharks eat the peach
flesh, then it becomes lighter so less seagulls will be needed to lift it! –
there is another investigation in there somewhere but we’d suggest
perhaps not for Key stage 2!
‘Put on another seagull, quick!’
‘Quiet everybody! Quiet! Here’s one coming now!’
This was the five hundred and first seagull, and the moment that James
caught it and tethered it to the stem with all the others, the whole
enormous peach suddenly started rising up slowly out of the water.
Chapter 22
James starts counting his seagulls in hundreds, then starts counting in ones
to get the exact number he needs. Ask pupils to apply this to weighing to
the nearest gram, where they would begin using bigger weights, such as
100g, then using tens and ones to be accurate.
How many helium balloons would it take to lift a regular sized peach?
It would take some organisation to get some balloons into the school. Ask
the pupils to feel the ‘lift’ of a balloon. Estimate how many it would take to
lift small objects like a multilink cube.
Less spectacular would be to use one helium balloon and see what it can
lift. Ask groups of pupils to work out how they could use one balloon to
investigate how many they would need to lift a peach. (One way may be to
see how many grams one balloon can lift, and then divide the weight of the
peach by this many grams.)
Can pupils devise a test to see how much a seagull can lift in real life?
Maybe some fish heads attached to weights? We suggest they don’t actually
carry out the test for fear of injury to the birds, but making the plan would
test teamwork and problem solving skills.
Counting back game.
Pupils ‘start’ at 502. They roll dice to count back to zero. Different types of
dice could be used so it does not take too long. For example, if they used
two dice and multiplied the dots together before they subtracted, so a 2
and a 6 means they subtract 12.
Use a tens dice and a ones dice to generate the numbers.
What is special about 502?
Ask pupils to collect interesting facts about 502, like, it is even, it is a
multiple of 2, one of the factors is 251, double it is 1004, It is the area code
for Louisville, Kentucky….
Ladybird Spots investigations
Chapter Twenty –five
‘Well is it really true that I can tell how old a Ladybird is by
counting her spots?’ ‘Oh no, that’s just a children’s story,’ the
Ladybird said. ‘We never change our spots. Some of us, of course,
are born with more spots than others but we never change them’
Arranging the spots on a ladybird
How many different ways can you arrange the spots on a Five-Spotted Ladybird?
I’m a Five-Spotted
Ladybird
Have you have
found all the
possibilities?
possibilities?
Try the same for a Seven-Spotted Ladybird and a Nine-Spotted Ladybird.
How many Ladybirds
Nine-Spotted Ladybird invited some of her other relatives for lunch. There were some
Two-Spotted Ladybirds, Three-Spotted Ladybirds, Five-Spotted Ladybirds and NineSpotted Ladybirds in the family.
When she counted the spots there were a total of 24. Can you work out which Ladybirds
could have been invited?
Here is one set of Ladybirds at lunch
Can you find all the other combinations?
How can you check you have all the possible answers?
James and the Giant Peach
Mathematical activities
TALL BUILDINGS
“James could see the skyscrapers rushing up to meet them at the most awful
speed, and most of them had square flat tops, but the very tallest of them
all had a top that tapered off into a long sharp point – like an enormous silver
needle sticking up into the sky. And it was precisely on to the top of this
needle that the peach fell!”
(James and the Giant Peach, chapter 36)
The Empire State Building was the world's tallest building from 1931 to 1972. It is
1,250 feet (381m) tall.
(Was it the tallest building when Roald Dahl wrote his book?)
Even today the Empire State is still in the top ten of the world’s tallest buildings.
Provide children with the fact sheet on the top ten tallest buildings and ask them
to work in pairs to discover how much taller the Taipei 101 is than the Empire
State.
Highest skyscrapers by architectural detail (top ten)
Rank
Building[A][2]
City
Country
Taipei
Republic
509 1,671
101
of China
m ft
(Taiwan)
2004
People's
Republic of
China
492 1,614
101
m ft
2008[B]
Height
Floors
Built
1
Taipei 101
2
Shanghai World
Financial Center
Shanghai
3=
Petronas Tower 1
Kuala
Lumpur
Malaysia
452 1,483
88
m ft
1998
3=
Petronas Tower 2
Kuala
Lumpur
Malaysia
452 1,483
88
m ft
1998
5
Sears Tower
Chicago
United
States
442 1,451
108
m ft
1973
6
Jin Mao Tower
Shanghai
People's
Republic of
China
421 1,380
88
m ft
1998
7
Two International
Hong
Hong Kong
Finance Centre
Kong SAR
415 1,362
88
m ft
2003
8
People's
Guangzhou Republic of
China
391 1,283
80
m ft
1997
384 1,260
69
m ft
1996
381 1,250
102
m ft
1931
CITIC Plaza
9
Shun Hing Square Shenzhen
People's
Republic of
China
10
Empire State
Building
United
States
New York
City