A Random workbook to go with the most random maths challenge ever!
www.grandrandomchallenge.co.uk
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The Grand Random Challenge
Hello Folks
Welcome to the Grand Random Challenge workbook. GRC was devised because I
felt that many people just “didn’t get it” when the word maths was mentioned. I
decided that if I devised some really random questions, then “getting it” was no
longer a problem, mainly because there was nothing to “get”. You own the numbers
in the questions, because you decide what they should be and you own the answer
because the answer depends on what you decide. Somehow this seems much less
scary to many people! Generally the only way to answer a question is to come up
with some reasonable guesses and to do that you need to devise a process of
travelling from things you do know to things that neither you or anybody else knows.
The workbook is complemented by a website, some GRC playing card packs and
you can follow us on Twitter and Facebook.
Visit: www.grandrandomchallenge.co.uk .
Note: Plain text copies of all questions are also available on the website
Please do share your thoughts, questions and solutions and post a comment to the
online post box or tweet us your comments @grchallenge.
Each of the activities in this workbook have been written with varying levels of help.
They start by providing a clear process of getting to an answer and gradually
provide less and less support until you end up with just the question and some space
for working.
The key to answering each question is to wherever possible, keep the numbers
“simple”, keep to common units and don’t get too bogged down with trying to get
an exact answer to something that can never sensibly be that accurate. Be
prepared to justify your answer and the assumptions you have made. Whilst the
questions are “random”, you should still be able to use normal mathematical
conventions when answering them. Therefore you should be able to explain to
somebody else what you have done and why you have chosen to do it that way.
As you look through the workbook you will find that I have also included a number of
other “random” mathematical activities for you to try. These mainly relate to the
correct use of mathematical terminology and link to developing English skills along
the way. There is absolutely no doubt in my mind that the more confident you are
with English, the easier you will find Mathematics.
I hope that you enjoy the Grand Random Challenge and that you find the tasks
helpful in developing your ability with numbers. Why not have a go at the online
competition and maybe win a pack of GRC cards?
Happy Days
Phil Gulliver
Did you know: There are approximately 345 squirts in a gallon of milk?
Find GRC at:-
www.grandrandomchallenge.co.uk
www.facebook.com/grandrandomchallenge
@grchallenge
What does R.P.M. mean?
How many minutes in an hour?
How many revolutions in 10
minutes
How many minutes in 50 hours ?
How many minutes in 10 hours?
How many revolutions in 100
minutes?
How many revolutions in 1000
minutes?
What is the sum needed to calculate the revolutions in 50
hours?
How many revolutions in 50
hours?
How many cuckoo sounds would the clock make each
hour?
How many cuckoo sounds in 24 hours?At what time does
the 50 hours start? This only matters if the cuckoo sounds once for 1 o'clock. Twice for two o'clock etc.
What sum do you need to calculate
the number of sounds?
How many cuckoo sounds would you
hear in 50 hours from that time?
Can you think of a way to check your answer is sensible?
www.grandrandomchallenge.co.uk
Whatdoyouknow?
Whatcanyoufigureout?
Whatcanyouansw
er?
Start here
Whatcanyoucalculate?
How many shavings do you get from 1
pencil? How would you measure the
amount?
What is the formula for working out the
volume of a cubeoid?
What volume of shavings do you get from a single pencil?What units would you use to measure this?
Is it possible to sharpen the whole pencil? You decide
how much
How big is a pencil?How much space
does a shaving take up?
What volume would you get from 10
pencils ?
What volume would you get from 100
pencils ?
What volume would you get from 1000
pencils ?
What volume would you get from
100 000 pencils ?
Check what units you are using
– is it sensible?
What volume would you get from
1 million pencils ?
What are the dimensions of a bag
for life?
What is the volume of a single bag?
Can you fill or overfill a bag for life with
savings? How much of the volume can you actually use for
the shavings?
What sum do you need to do to
calculate how many bags you need?
HOW MANY BAGS DO YOU NEED?
What is your answer?How does it compare
to somebody else's answer to the same
question?
How big is a cow?
What is the maximum depth the water can
be?
What is the formula to calculate volume
How many drips would it take to fill a container of known
size? You decide which.
How big is a drip?
How many drips per second
How many drips per hour?
What volume of water per day?
What volume of water per year?
What volume of water in 147 years?
How wide does the container need to be
to allow a cow to walk through it? Or how wide is a cow?
Now you have decided on the width and the
maximum height of the container.
What sum do I need to use to calculate the length of the
container to hold all of the water?
What are the dimensions of the
container?
Does your answer seem reasonable?
Start here
Break the question
down into small steps
Make sure you
understand the
language
Look on the internet if
you need to
Ask questions
Find out if necessary
Decide on sensible
units to be working in
Convert units if
needed
Make reasonable
estimations
Find out formulae
you need
What is the formula
for the
circumferance of a
circle ?
Do the sums
Check your answers
Tweet or Post your findings
@grchallenge or
Facebook/
grandrandomchallenge
See how your answer
compares to others
Can you think of a
way to check your
answer is sensible?
www.grandrandomchallenge.co.uk
What do you know?
What can you figure out?
Wh
at c
an
yo
u a
nsw
er?
Start
here
Wh
at can y
ou
calculate?
How many revolutions of a rear
tractor tyre will it take to travel 40,000
mm?
Can you think of a
way to check your
answer is sensible?
www.grandrandomchallenge.co.uk
What do you know?
What can you figure out?
Wh
at c
an
yo
u a
nsw
er?
Start
here
Wh
at can you
calcu
late?
How many revolutions of a rear
tractor tyre will it take to travel 40,000
mm?
D
C
B
A
1 2 3 4 5 6
The co-ordinated tractor?
Draw a 6 x 4 grid and en-ter the co-ordinates of the jigsaw pieces so that the tractor would be properly displayed
How big is a woodpecker?
How many seconds in a minute?
What sum do I need to calculate the
seconds in 1 Day?
How many hours in 3 Days ?
How many minutes in an hour?
How many seconds in 1 Day?
How many seconds in 3 Days?
What sum do I need to calculate the
number of pecks a woodpecker makes
in 3 days?
Will the woodpecker really peck
continuously for 3 days?
You decide – but justify your answer!
How many pecks in 3 days?
What is the distance between the tip of the beak and the
tree trunk?How far will the beak travel for each peck?
How far will the beak travel in 1 second?
How far will the beak travel in 1 hour?
How far will the beak travel in 3 days?
What units should you use?
Start here
2 = 3π (∛ ( XYZ ))
44 + 5h - 3D
Write out the equation using complete sentences
and correct mathematical terminology
70 bricks per metre squared
So how many bricks if 25% of the houses were made out of Jelly Beans?
How big is a cow?
Whatistheformulatocalculatevolume
How big is a drip?
How many drips per hour?
What volume of water per year?
How wide is a cow?Now you have decided on the width and the
maximum height of the container.
What are the dimensions of the
container?
Does your answer seem reasonable?
Start here
What are the dimensions of the
container?
Does your answer seem reasonable?
Start here
Draw a graph - Describe a graph:
Draw a graph that fits the following description, annotate the major points of reference: -
The cabbages were sown in February germinated after a couple of weeks and grew steadily
to start with, but then all of a sudden they got an attack of the “bunny biters”, growth
stabilized for a short while before gently deceasing and bottoming out at 100 grams per day.
Growth rate rose slightly prior to being harvested in late September.
Draw a graph that allows you to accurately use one word or phrase from each of the groups
below to describe it.
Going up
rose
increased
went up
grew
No Change
stayed the same
remained constant
leveled off
stabilized
Up and Down
fluctuated
zig-zagged
fluttered
undulated
Small Changes -
gently
gradually
slightly
steadily
Big Changes –
suddenly
sharply
dramatically
steeply
a lot
Low Points
bottomed out
reached a low
www.grandrandomchallenge.co.uk
Here are a few creative writing tasks that you might like to try either
yourself or with your students. They are quite grand and random!
You are so startled by the conversation you overhear between a
baked bean and a parrot that you walk into a lamppost. When you
recover, all you can remember is that the first word started with PR
and the last word ended with CH. What were they talking about?
You pick up a message in a green bottle that was written by a
Martian. Not understanding it, you take it to the very rare green
spotted translater bird. The bird tells you that the message reads –
alternate words must have 2 vowels all other words must have 1
vowel only.
Write a message back to the Martian that is correct English and
Martian.
150 million years ago a stegosaurus tripped over a thesaurus and the
page opened on mammoth. A police officer trots by on an elephant
and issues a ticket. Who did he issue a ticket to and what was it for?
Hi Claudia
How did your tractor get on at the chiropodists? Did they manage to
untie the liquorice from around the spuffle valve or was the torque
wrench just the wrong size for the wellington boots?
Email me
How, What, Where, When & Why –
Mediterranean market stall
First class letter
Glass of gooseberry juice
Rocking horse
Tweet me @grchallenge
Really!
Describe a graph 2
The following verbs, nouns, adjectives and adverbs may all be used to describe parts of
a graph. Your task is to write accurate descriptions of the graphs provided using
appropriate and accurate terminology.
Expressing the Movement of a Line
VERBS NOUNS ADJECTIVES ADVERBS
Rise (to) a rise Dramatic dramatically
Increase (to) an increase Sharp sharply
Go up to Huge hugely
Grow (to) growth Enormous enormously
Climb (to) a climb Steep steeply
Boom a boom Substantial substantially
Peak (at) (reach) a peak (at) Considerable considerably
Significant significantly
Fall (to) a fall (of) Marked markedly
Decline (to) a decline (of) Moderate moderately
Decrease (to) a decrease (of) Slight slightly
Dip (to) a dip (of) Small
Drop (to) a drop (of) Minimal minimally
Go down (to)
Reduce (to) a reduction (of) Describing the Speed of a Change
A slump
Adjectives Adverbs
Level out a leveling out
No change no change Rapid rapidly
Remain stable (at) Quick quickly
Remain steady (at) Swift swiftly
Stay (at) Sudden suddenly
Stay constant (at) Steady steadily
Maintain the same level
Gradual Slow
Gradually Slowly
On your marks
How many market stall roof stripes can you see in the photograph?
Can you estimate the actual size of these?
The current world record for the 100 metres run in high heels is 14.531 seconds. If all of the white stripes you can see in the photograph of Norwich market were a running track. What speed would an earwig need to be travelling to cover the total distance in the same time of 14.531 seconds?
2 = 3π
4 - 5Y + 3y √
Write out the equation using complete sentences and correct terminology
Race to the bottom
A person in the boat above bails out the water with a thimble at a speed of 30000 full thimbles per second
A person in the boat above bails out the water with a coffee mug at a speed of 17 full mugs per second. Which boat will stay afloat the longest if in a calm sea?
Rhubarb - Rhubarb!
Draw a grid and enter the co-ordinates of the jigsaw pieces so that the picture would be properly displayed
Did you know— The longest recorded flight of a chicken is 13 seconds
Spot the difference help sheet
∑ Sigma – the sum of
± Plus Minus
π Pi (pronounced pie)
√ Square root
Cube root
X2 X squared
X3 X cubed
ab a multiplied by b
a/b a divided by b
= Equals
≠ Not equal to
< Less than
<< Much less than
≤ Less than or equal to
> Greater than
>> Much greater than
≥ Greater than or equal to
Approximately equal to
% Percentage
+ Plus
- Minus
⅞ Fraction – seven eights
Spot the difference
𝑥 =𝑏 ± √𝑏2 − 4𝑎𝑐
2𝑎𝑏
𝑘 =𝑏 − √𝑏3 +−(4𝑎𝑐)
2𝑎𝐵
Task:
Look carefully at the two equations above and using only words write a full
paragraph, using complete sentences to describe the six differences. Use the
help sheet if necessary to ensure that you use the correct terminology.
How many bars of an electric fire are 4
medium sized pigs equivalent to?
How many revolutions of a rear tractor
tyre will it take to travel 40,000mm?
Show mathematically how much grass a
dairy cow can eat.
How much longer will it take a hare
running at full speed to complete 1 circuit
of the San Marino grand prix track
compared to an F1 car?
Devise a formula to calculate the depth of
water in any object left outside exposed to
the weather.
Use the formula to calculate the depth of
water in a size 8 wellington boot, left
outside for 27 years 45 days.
If the price of pigs were the same as
Nickel, would the value of a bacon pig be
worth more or less than 17% of a beach
hut in Southwold?
How many tonnes of winter wheat could a
grain store measuring 22000mm X 10m X
500cm hold?
A tap is left to drip for 147 years. What is
the smallest rectangular, straight sided
container that would hold all of the water
and still be shallow enough for a cow to
walk through it?
Estimate how long it will take a person
driving a tractor to travel from Norwich to
Carlisle.
How many car tyres will you need to cover
the top of a silage clamp measuring 15m X
5 m with no overlapping?
How many sausages can you produce from
a beef cow, assuming all edible meat is
used?
How many dozen eggs will a hen lay in 3
years 4 months?
What is the volume of air needed to
provide 3 air changes in a monopitch
building measuring 2.5m X 3.6m 2.1m high
at the front and 1.3m high at the rear?
How many party balloons would this
inflate?
How many tonnes of winter barley could
you fit into 13 rear tractor tyres?
How many Swaledale ewes would it take to
counterbalance a tractor on a seesaw?
Would it be quicker to drive my fat lambs
to market from Halvergate marshes to
Bury st Edmunds or take them from
Norwich to Brussels in a Eurofighter?
A cow parachutes down into a 1 hectare
field and poo’s. What is the probability of it
dropping in a particular 1metre square?
You drop a fully inflated football from the
roof of a barn onto a concrete floor. If the
distance it bounces upwards is filled with
£20 notes, precisely how long could you
afford to stay in a hotel charging £1234 per
night?
12 tonnes of grain is stored in a 3.5m
diameter hopper and fills it. Is the hopper
taller than a Ford Mondeo stood upright?
How many Kg of cream would you get from
6 tonnes of Jersey cow milk? How long
would it take the cow to produce this
much?
A 100 acre straight edged field has a
greater perimeter than 30 football pitches
– true or false?
If there was 215,000 litres of water in a
ditch 40m long and 1.5m wide. Would
ducks be able to swim in it?
2 inches of rain falls over a 7 ha field. How
many domestic hot water tanks would that
fill?
How many sugar beet plants are there in 8
Ha? Is it more or less than the number of
days in 0.85 of a century?
How many 3 bedroom semi detached
houses in Great Yarmouth would you have
to sell, to buy all of the potatoes grown in
Norfolk?
How many chickens could you house in a
bus shelter and keep within the welfare
guidelines for floor space allowance?
If the number of grams of dry matter in 25
Kg of silage were minutes, Would it be
longer than a Harry Potter film?
What is the stopping distance of a cow
travelling at 60 knots in wet conditions if
it behaves like a family car?
A mini rod racing car engine runs at
19,000 r.p.m. If a Cuckoo clock rotated at
the same speed, how many Cuckoo sounds
would you hear in 50 hours?
How many ducks could you fit on a
reservoir measuring 30m X 93m allowing
enough room for them all to be holding a
bunch of flowers in their beaks?
A trained person can reach a typing speed
of 80 W.P.M. How long will it take them to
type the registration numbers of 1200 cars
if all the numbers are written as words?
Cine film runs at 30 frames per second. If
each frame was taken using a shutter
speed of 1/125th second, how far could a
tortoise travel in the total time the shutter
is open when shooting a 90min film
The tyres of an adults bicycle are stuffed
with cotton wool. Would the total weight of
this stuffing for 144 bicycles weigh more
than 26 copies of Farmers Weekly?
You make a panorama photograph from
pictures on your phone. If you fill an 8Gb
card with pictures what length of wood do
you need to frame the panorama?
How many strawberries would it take to
make enough jam to fill the estimated
5000 hollow spines on a hedgehog? (hint –
4pints of fruit makes about 4.5lbs of jam)
You want to keep the shavings from
sharpening 1million normal pencils. How
many supermarket bags for life do you
need?
A rat runs up a vertical drainpipe and
keeps going for 90 days non-stop. If that
distance of the pipe were filled with water.
How many domestic baths could you fill?
It takes 7-8 bunches of grapes to make
750ml of wine. How many individual
grapes would you need to make enough
wine to fill a dumper truck?
A seagull is hopping along the road holding
an ice lolly in it’s beak. How far will it get
before all of the lolly is melted?
You have special permission to print
money on an A4 printer. How long will it
take to print enough money to fill a
lighthouse? What % of a city would that
amount buy?
A blu-ray disc rolls on its edge down an
avenue lined with houses on both sides.
How many revolutions will it take if the
disc travels from house number 13 to
house number 178?
A computer screen needs to show the
entire lyrics of a song on a single line.
What size would the screen need to be
measuring from bottom left to top right?
A woodpecker can pound its beak against
wood at 20 times per second. What is the
total distance the beak will travel in 3 days
continuous pecking?
A guinea pig trundles down to the shops in
its exercise wheel. How many revolutions
per year would you have to maintain on a
bicycle to maintain the same speed?
The construction of Spaghetti Junction on
the M6 took 134 000 M3 of concrete. How
many tins of spaghetti hoops would this
much fill? Would the sauce in this many
tins fill a swimming pool?
A lady rides her bicycle down the street at
a constant speed. If sunflower seeds were
falling through the front basket onto a
seedbed and 80% germinated, how many
seed heads would there be for my
chickens?
How many Christmas geese could you
cover with the down from 275 king sized
duvets?
A fuel tanker is parked next to a
swimming pool. Would it take more time
for a person to fill the tanker with water
from the swimming pool than it would to
walk around the world?
An ant climbs to the top of a telegraph pole
and dives off into a ball pool. How high up
would a sheep have to be if it was to dive
off from the same proportional height?
The walls of a 2 storey house are insulated
using cauliflowers. If these were used to
make cauliflower cheese. How big would
the pot need to be to make all of the cheese
sauce required in a single batch?
4 people row a Thames rowing skiff from
Norwich to London. If the number of
strokes taken for the journey were
lettuces, how many rabbits could you feed
for 7 days?
A hamster jumps on a suitably sized pogo
stick and bounces continuously for 99
years. Would the total distance travelled
be greater than 99 trips up the Eiffel
Tower?
How many 1st class postage stamps could
you fix to a stick of rhubarb without any
overlapping? If the value of the stamps
was equal to the value of the rhubarb,
what is the price of rhubarb per tonne?
A washing line is stretched from Norwich
to New York. How many crows could stand
on it if 7% had their wings outstretched?
On average 1 tonne of paper is made from
17 trees and 1 piece of A4 paper weighs 5
grams. So how many sentences of
handwriting could you fit on the paper
from 23 trees?
It takes 100 tomatoes to make 5 standard
bottles of ketchup. How many tomatoes
would you need to make sufficient ketchup
to fill the 127 mile long Leeds – Liverpool
canal?
Three dimensional noughts and crosses
To win you need three in a row, either horizontally, vertically or diagonally.
How many winning lines can you spot in this photograph?
Look at the picture below, decide on your move and then try to describe your choice and the reasons for it using complete sentences.
?
From me two you?
To too's are for?
Witch which two choose?
Write in sentences to fully explain
what the number or the word
means in each of the examples. Use
further examples if you are able to
help your explanations.
Can you think of any others?
Unscramble the question?
Write a maths challenge using as many words as possible from the scramble below.
GRC COMPETITION
Hello; please "have a go" at our online competition. One lucky winner will receive a pack of Grand Random Challenge cards. You cannot buy these! You could win a near unique gift simply by taking part. Good Luck and thank you for your entry. There are only four things that you need to do :-
1 - On Facebook, Twitter or through the GRC website post box, post your answer and workings out to one of the Grand Random Challenge questions.
2 - Guess the name of the Grand Random Challenge Cow
3 - Answer this question: The number of sheep in the heap multiplied by the number of feet in a mile minus the number of seconds in a short while is the answer that will make me smile. What number do you get?
4 - What is this picture of and in which county is the triangle?
All you need to do is email your four answers to me at the following address [email protected]
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