Grand random challenge workbook by Phil Gulliver

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?

http://www.grandrandomchallenge.co.uk/

Find GRC at:-


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?


minutes?


minutes?

What is the sum needed to calculate the revolutions in 50

hours?


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?


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 ?


pencils ?


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?


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?


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.


container?


Start here


container?


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


http://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]

mailto:[email protected]

Documents

Grand random challenge workbook by Phil Gulliver