It takes a combine harvester 9 seconds to harvest enough wheat to make 70 loaves of bread
In 1386, a pig in France was executed by public hanging for the murder of a child
A Random workbook to go with the most random maths challenge ever!
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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
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@grchallenge
What do you know?
What does R.P.M. mean?
Start here
What can you calculate?
How many minutes in an hour?
How many minutes in 50 hours ?
How many minutes in 10 hours?
How many revolutions in 10 minutes
How many revolutions in 100 minutes?
Can you think of a way to check your answer is sensible?
How many revolutions in 1000 minutes? How many cuckoo sounds would you hear in 50 hours from that time? What is the sum needed to calculate the revolutions in 50 hours? What sum do you need to calculate the number of sounds?
What can you answer?
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.
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How many cuckoo sounds in 24 hours?
How many revolutions in 50 hours?
How many cuckoo sounds would the clock make each hour?
What can you figure out?
What is the formula for working out the volume of a cubeoid?
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?
How many shavings do you get from 1 pencil? How would you measure the amount?
HOW MANY BAGS DO YOU NEED? What is your answer? How does it compare to somebody else's answer to the same question?
What volume of shavings do you get from a single pencil? What units would you use to measure this?
What volume would you get from 10 pencils ?
What volume would you get from 100 pencils ? What sum do you need to do to calculate how many bags you need? What volume would you get from 1000 pencils ? Can you fill or overfill a bag for life with savings? How much of the volume can you actually use for the shavings?
What volume would you get from 100 000 pencils ? What are the dimensions of a bag for life?
Check what units you are using – is it sensible?
What is the volume of a single bag? What volume would you get from 1 million pencils ?
How many drips would it take to fill a container of known size? You decide which.
What is the maximum depth the water can be?
How big is a cow?
Start here
How big is a drip?
What is the formula to calculate volume
How many drips per second
Does your answer seem reasonable?
How many drips per hour? What are the dimensions of the container?
What volume of water per day? What sum do I need to use to calculate the length of the container to hold all of the water?
Now you have decided on the width and the maximum height of the container.
How wide does the container need to be to allow a cow to walk through it? Or how wide is a cow?
What volume of water per year?
What volume of water in 147 years?
What do you know?
Break the question down into small steps
Start here
What can you calculate?
Make sure you understand the language
Ask questions
Find out if necessary
Look on the internet if you need to
Decide on sensible units to be working in
Can you think of a way to check your answer is sensible?
How many revolutions of a rear tractor tyre will it take to travel 40,000 mm?
Convert units if needed See how your answer compares to others
Make reasonable estimations
Tweet or Post your findings @grchallenge or Facebook/ grandrandomchallenge
Find out formulae you need Do the sums
What can you answer?
Check your answers What is the formula for the circumferance of a circle ?
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What can you figure out?
What do you know? What can you calculate?
Start here
Can you think of a way to check your answer is sensible?
How many revolutions of a rear tractor tyre will it take to travel 40,000 mm?
What can you answer?
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What can you figure out?
The co-ordinated tractor?
D
C
B
A
1
2
3
4
5
6
Draw a 6 x 4 grid and enter the co-ordinates of the jigsaw pieces so that the tractor would be properly displayed
How many seconds in a minute?
How big is a woodpecker?
Start here
How many hours in 3 Days ?
How many minutes in an hour?
How far will the beak travel in 3 days? What units should you use?
What sum do I need to calculate the seconds in 1 Day?
How many seconds in 1 Day?
How many seconds in 3 Days? How far will the beak travel in 1 hour? What sum do I need to calculate the number of pecks a woodpecker makes in 3 days? How far will the beak travel in 1 second?
What is the distance between the tip of the beak and the tree trunk?
Will the woodpecker really peck continuously for 3 days? You decide – but justify your answer!
How far will the beak travel for each peck? How many pecks in 3 days?
Write out the equation using complete sentences and correct mathematical terminology
2
= 3Ď€ 44
(∛ + 5h - 3D
( XYZ ))
70 bricks per metre squared So how many bricks if 25% of the houses were made out of Jelly Beans?
What is the formula to calculate volume
How big is a cow?
Start here
How big is a drip?
Does your answer seem reasonable?
How many drips per hour? What are the dimensions of the container?
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.
Start here
Does your answer seem reasonable?
What are the dimensions of the container?
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
No Change
rose increased went up grew
Small Changes
gently gradually slightly steadily
stayed the same remained constant leveled off stabilized
Big Changes –
suddenly sharply dramatically steeply a lot
Up and Down
fluctuated zig-zagged fluttered undulated
Low Points
bottomed out reached a low
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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
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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
Rise (to) Increase (to) Go up to Grow (to) Climb (to) Boom Peak (at)
a rise an increase
Fall (to) Decline (to) Decrease (to) Dip (to) Drop (to) Go down (to) Reduce (to)
ADJECTIVES
Dramatic Sharp Huge growth Enormous a climb Steep a boom Substantial (reach) a peak (at) Considerable Significant a fall (of) Marked a decline (of) Moderate a decrease (of) Slight a dip (of) Small a drop (of) Minimal a reduction (of)
ADVERBS dramatically sharply hugely enormously steeply substantially considerably significantly markedly moderately slightly minimally
Describing the Speed of a Change
A slump Level out a leveling out No change no change Remain stable (at) Remain steady (at) Stay (at) Stay constant (at) Maintain the same level
Adjectives
Adverbs
Rapid Quick Swift Sudden Steady Gradual Slow
rapidly quickly swiftly suddenly steadily 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?
Write out the equation using complete sentences and correct terminology
2
= 3Ď€ 4
- 5Y + 3y
√
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 ∑ ± π √
Sigma – the sum of Plus Minus Pi (pronounced pie) Square root Cube root
X2 X3 ab a/b = ≠ < << ≤ > >> ≥
X squared X cubed a multiplied by 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
% + ⅞
Percentage Plus Minus Fraction – seven eights
Spot the difference đ?&#x2018;? Âą â&#x2C6;&#x161;đ?&#x2018;? 2 â&#x2C6;&#x2019; 4đ?&#x2018;&#x17D;đ?&#x2018;? đ?&#x2018;Ľ= 2đ?&#x2018;&#x17D;đ?&#x2018;? đ?&#x2018;? â&#x2C6;&#x2019; â&#x2C6;&#x161;đ?&#x2018;? 3 + â&#x2C6;&#x2019;(4đ?&#x2018;&#x17D;đ?&#x2018;?) đ?&#x2018;&#x2DC;= 2đ?&#x2018;&#x17D;đ??ľ 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?
You drop a fully inflated football from the roof of a barn onto a concrete floor. If the A cow parachutes down into a 1 hectare distance it bounces upwards is filled with field and poo’s. What is the probability of it £20 notes, precisely how long could you dropping in a particular 1metre square? 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 How many sugar beet plants are there in 8 many domestic hot water tanks would that Ha? Is it more or less than the number of fill? 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?
Cine film runs at 30 frames per second. If A trained person can reach a typing speed each frame was taken using a shutter of 80 W.P.M. How long will it take them to speed of 1/125th second, how far could a type the registration numbers of 1200 cars tortoise travel in the total time the shutter if all the numbers are written as words? 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 â&#x20AC;&#x201C; 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 itâ&#x20AC;&#x2122;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 A guinea pig trundles down to the shops in wood at 20 times per second. What is the its exercise wheel. How many revolutions total distance the beak will travel in 3 days per year would you have to maintain on a continuous pecking? 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?
The walls of a 2 storey house are insulated An ant climbs to the top of a telegraph pole using cauliflowers. If these were used to and dives off into a ball pool. How high up make cauliflower cheese. How big would would a sheep have to be if it was to dive the pot need to be to make all of the cheese off from the same proportional height? 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 â&#x20AC;&#x201C; 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.
?
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?
From me two you?
To too's are for? Witch which two choose?
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 comp@grandrandomchallenge.co.uk