Download - Special Scottish Issue || Enterprising Mathematics

Enterprising MathematicsAuthor(s): Clive ChambersSource: Mathematics in School, Vol. 28, No. 1, Special Scottish Issue (Jan., 1999), pp. 5-11Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30211948 .

Accessed: 06/04/2014 16:49

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access toMathematics in School.

http://www.jstor.org

This content downloaded from 213.113.124.134 on Sun, 6 Apr 2014 16:49:39 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=mathas

http://www.jstor.org/stable/30211948?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Enterprising Mathematics

by Clive Chambers

What have the following in common?

T4 Divide this shape into four equal areas. All the pieces must be congruent and each is similar to the large piece. [Outlines and scissors provided. Glue your answer onto the answer grid.] T6 48 can be described as being 'one short of a square' in two ways. Certainly 48 + 1 = 49 = 72. Also (half of 48) + 1 = 25 = 52. Find the next smallest number which is 'one short of a square'.

T9 You look at the coins in your piggy-bank and find that you have L58.29. This amount is made up of an equal number of coins of the realm. You have 67 coins of each value. What coins do you have?

and

Newtyle Secondary School (in Tayside)

As far as Scotland is concerned Enterprising Maths took off in 1989 in Tayside when 26 secondary schools took part in the first event to be held. Newtyle were the winners in 1989 and the questions were some of the first questions they saw. Running this event was a consequence of an article in the Times Educational Supplement which described a similar event held in Rotherham. At the time I was PT Mathematics at Linlathen HS in Dundee. I and one of my colleagues, Glenys Marra, agreed that it was definitely worth a try, and, as they say, we have been involved ever since.

Although the style of some of the contests has changed since those early days, the basic format has remained much the same for the events held in Scotland.

Here is a quick snapshot of the five contests:

Poster Competition Two weeks before the Enterprise Day, participating schools are circulated with some general information about the topic for investigation. Pupils may bring with them any poster- making equipment that they wish and any sources of material that they may have discovered.

Specific questions only appear on the day but the poster may incorporate any material, photographs, drawings, etc. made or collected by the pupils in the 'preceding' two weeks.

Part of a Poster Information Sheet

Plane Tessellations

~i~8e Find some examples from real life

Mathematics in School, January 1999

Team Competition Teams are given about an hour to work as a group on a number of questions of a fairly long and demanding nature. Teams are not expected to answer all the questions-they will have to decide on which questions to attempt and suit- able strategies to go about solving the problems.

Example

Place all the numbers

1,2,3,4,5,6,7,8,9 in the boxes so that

the total of the numbers in

directly connected boxes matches

those in the table.

Box Total vabe of contining the boxes directly the number conmncted to it

1 13

2 20

3 17

4 13

5 25

6 5

7 15

8 8

9 2

Speed Competition In this part each team works for a fixed amount of time at about twelve different stations where the questions are of a more practical nature.

Example

Rearrange the eight pieces to form a chess board

Swiss Competition This event is designed to be as different as possible from the other competitions.

Teams face each other in three head-to-head games with moves being made or answers being given orally.

Example

Make a path from one side of the board to other. Players place one piece in turn. First to make a path wins. You have 4 of

each of these pieces.

Relay Competition This event provides a spectacular climax to the day-teams work in pairs with only one pair having a question at any given time. Each pair has to judge how long to spend on a question before answering correctly or passing, and thus allowing the other pair to receive the next question-definitely a race against time.

Example

Four beetles travel along these routes A goes at 8 metres per hour, B at 11

metres per hour, ...... Who wins?

A B C D

The Poster contest has evolved over the years into more of an investigation. To give the flavour of the Poster Contest here are the information pages for the last four Enterprising Maths Days together with the 'unseen' questions:

5



:.,.y. ZNTZRPIISmNG MATRZMATICS IN SCOTLAND

;::i·i:y i~i~i::.:!:.:· !:iy:y y,y-I-- M

N-y y - "- i~i:iiC:~:-:--:::-::' :----- - -y--y- . ---- y

Volumne

Asrsxgsaf Amy l> ails

91 r4 Howv cn you Rwomr out 6 pinto writh oniy IL ~ Sa 9 pltj" nd a 4 pintju? m IInveptjpte how you vmurid W the volume of a cubo ifyou know thes a urfwa area of wh feco?

If the cow mdft and com" fib thef A 0

If the Inv I It n;UW a mundc the x- &xK a ow of evoluton I Whallt other odkbd can you form? CE Canyou make a cubs "PO

j Odfj I ~ r1sw~ sacki; we 5 Jay= deep

bow mmM Crawls we

.vile trcuwo?

A 9dUi who" a urne Is murnerically qual to Its surface are Is called "aqare'% Invaetlqatt&

toNT ILrwwOwwIw AT'fHATIAZB EN AYBiuw ·;scommi

DISSECTIONS How many" p decer no you nw to cut the squars Into to make the G re k C ro s s

,. -- --

Can you turn the crescent Into the One*k Cros?

St IB

What can you make wtth a 5 pece ungram wt

A HkWAd moAMI turrlhS a

t Italnglo Into a pamlelop a

1`C square igo,

vs 0 %P W-A

N L';~L V) .~B,

ll~ Iim w f ad Ofteag* sew

Questions on the day

1

2

3

4

A water tank in the shape of a cuboid has a base area of 6 sq. feet and water is lying in it to a depth of 5 inches. A 1 foot solid metal cube is placed in the tank. How much does the water rise? (12 inches = 1 foot).

2 bushels = 1 strike 3 bushels = 1 sack 4 bushels = 1 coomb How many strikes in a last? 8 bushels = 1 quarter How many loads in a last? 36 bushels = 1 chaldron 80 bushels = 1 last 5 quarters = 1 load

A soup manufacturer wishes to supply tins of soup to supermarkets in cartons which contain 48 tins. What size of carton should he use if he wants to use as little cardboard as possible?

14cm

-9cm-

A magician has a sphere which fits exactly into a cylinder as part of a magic trick. Which has the greater surface area, the sphere or the cylinder?

-20 cm

Question 1 Diagram 1 shows a standard 7-piece tangram drawn from a square of side 12 cm. What is the area of the parallelogram?

Question 2 Diagram 2 shows a '2-piece' tangram drawn from a rectangle. Use the sheet of outlines to cut each rectangle into its own pieces and then reassemble the two pieces to make as many different 3-sided or 4-sided shapes as you can.

Question 3a Diagram 3 shows a rectangle measuring 9cm by 4cm. The following instructions show how to dissect this rectangle so that the pieces can be reassembled into a square.

F A B

I D E D C

Find A, 6cm from B. Draw AC Find D, 6cm from E Draw DG where DG is parallel to CB Cut along AC and DG Reassemble into a square

Question 3b Now try a similar procedure for the 16cm by 9cm rectangle.

6 Mathematics in School, January 1999



1997 ENTERPRISING MATHEMATICS IN TAYSIDE -------------- ~t~-~] ~IOIQ~

RE POTELAR POONTETDRA REGULAR POLYH EDRA

Pho.nic So.h :why wM atwy ty Phlatonic sclMs

and how many tmse? WhMt do their nets ok IIke?

vo ,=ro2 y %"

.y

I

. " 4 ,y.L

boS*1 TheWac BE( poslecadsts I:~of aCd caa bao

song h tang 7 eahedruna o d d

NOd r

Wbicb wowwr NAM vu r aft

* The MIN& BM onebwL of a cubial bam

Itus mebme * The hardest part of th puse in to At thw largest erteebod etrahadra in Ltn bab.

bee of 0 Try mnauki a model w&t a cube of aid@ 5 undis and a SWhM * What

t ll

197 ENTERPRISING MATHEMATICS IN SCOTLAND Anva cowma Dwnqo oy coin rem & ormra COUIwl Nwown COB"* )wa~a~lx*Lw~p· rrrearafq·

posTR cOlrTST

EUCLID

WHAT IX[ACTLY WKRE IUCLID'sII EL.lMINTST

TLi~ ;I

Z 41 I

CIO 4e A8~"A

rze. 44 VCN4~

we ot uH~dod based on oi- at" of the aim Oi. What in the onnectio bdo sm th ingtheof thM oam of th hree shapes?

H i 8d a

b

EuMd and the Moo?

,A LA. bbd h nm -SVmto. ...a h = was"toame cnstuct. hen 6sthe Rde r I4

904 A~

Endid brmael dhis anames o e re~clg. Cmn you peo

the oldbta

A cb ito Pt inI I

n b.h is 8 ots the ralte I I

Ilm rd A cubs is to be u into 17 ---her cubw .Why is 6 cuts the abooaute minimum rwird

1 You have to build a solid using an octagon and triangles. Assuming you have triangles of the correct size, what is the smallest number of triangles with which you can build a solid?

2 Which is the only Platonic solid which 'tiles' to make larger versions of itself?

3 What is the smallest number of flat pieces of any shape which can be joined together to form a vertex of a solid?

4 What is the largest number of regular flat shapes which can be joined together to form a vertex of a solid? What is the regular flat shape?

5 A regular pyramid has a base with n edges. For the pyramid write down the number of faces, edges and vertices.

6 A regular prism has a base with n edges. For the prism write down the number of faces, edges and vertices.

7 A cube is truncated by slicing off each corner as shown. What shapes will you need to build this new solid and how many of each will you need?

before

after


1 SOn the triangle (see separate sheet) construct the circumcentre of the triangle. Leave in all construction lines. Draw the circumcircle.

2 Calculate the area of the largest quarter circle (fig. 1).

3 Why is 28 a perfect number? 6

t

4 Draw a typical Euclidean (geometrical) diagram to illustrate (a + 2b)2 = a2 + 4ab + 4b2.

5 A Greek mathematician carried out the following common Euclidean construction. Lines AB (1 unit) and BC (6 units) were drawn; the midpoint (D) of AC was found and the semicircle

~~~c~--- b ---~

drawn. Finally the perpendicular through B was constructed. What did the line BE represent for the Greek mathematician?

6 Most of the largest prime numbers which are known are called Mersenne Primes. These are of the form 2' - 1. One newspaper reported the discovery of one of the Mersenne Primes and stated that p = 131,049. Another newspaper stated that p = 132,049. Which newspaper was definitely wrong and why?

7



Even the rules have changed somewhat. Nowadays we think it best to allow absolutely anyone to be involved in the preparation of the material for the Poster. The Posters them- selves have become much more ambitious and nowadays it is very rare that a poster is left behind unclaimed at the end of an event. The hardest part of the Poster Event is persuading people to act as judges on the day!

In the Team Contest teams have an opportunity of choos- ing from about 16 questions-the more they can do the better! Past experience has taught us not to be too ambitious-a balance of easy questions and some more difficult is important, enabling teams to make some progress in what is, after all, a long day ofmathematics. The majority of the questions do not depend on syllabus knowledge although it has to be assumed that such basic knowledge as circle formulae, prime number properties, solving equations and Pythagoras will all play a part. Unfortunately, many classic problems involve a knowledge of geometry which has sadly declined in the schools' curriculum and hence these have to be avoided. This aside we have always tried to include some 'golden oldies'-often the only opportunity that some pupils will have of meeting them.

1991 A street is numbered consecutively 1,2,3,... up one side and down the other. The Post Office authorities find this imprac- tical and change the numbers to the conventional way with the odd numbered houses on one side of the street and the even numbered houses on the other. House number '2' is opposite house number '1', etc.

In this new arrangement, two houses have the same number as before: houses numbered 1 and 54.

How many houses are there in the street?

1991 Aberdeen, Dundee, Edinburgh and Glasgow compete against each other in Curling. The situation, at a certain point in the season, is given in an incomplete table below:

Aberdeen Dundee Edinburgh Glasgow

Played Won Drawn Lost

x v z

y x v z v

Given that each team plays the others once in a season, how many games has Dundee won so far?

1996 This Golden Oldie was tackled surprisingly well:

Plato's Cubes by Sam Loyd The diagram shows a 'photographic' view of a huge marble cube which is constructed out of a given number of smaller cubes. The monument rests in the centre of a square plaza, which is paved with a single layer of similar small cubic blocks of marble.

The number of small blocks in the monument is equal to the number of small blocks in the plaza and all the small blocks are exactly the same size.

How many small cubic blocks are required to construct the monument?

1996 Many history books illustrate old methods of calculations. This one proved popular:

8

Heron Goes in Circles Heron was a Greek Mathematician who lived round about the 1st Century AD. Some of his work dealt with mensura- tion-that is calculating sides and areas. Here is how he dealt with a circle problem:

Given the sum of the diameter, circumference and area of a circle, to find each of them separately proceed thus:

Let the given sum be 212. Multiply this by 154; the result is 32648. To this add 841 making 33489 whose square root is 183. From this take away 29 leaving 154, whose eleventh part is 14; this will be the diameter of the circle.

If you wish to find the circumference, double the 154 making 308, and take the seventh part, which is 44; this will be the circumference.

To find the area, take the diameter (14) and the circumference (44) away from the sum (212) giving 154.

So diameter = 14, circumference = 44 and area = 154.

If diameter + circumference + area = 1308, use Heron's method to find each one separately.

The Speed Contest was originally just as it is named-a number of short oral questions in a given time limit. After just one year we decided that this should be a practical event. Sta- tions involve anything that is available-from Soma cubes and Tangrams to Polydron, Multilink and Dominoes. The polydron question shown proved too difficult for many teams in the time available-rather disappointing but is this a sign of the times (or rather a sign of the shapes!)?

Other stations are built up from 'scratch':

1991 Materials: Some blank nets of cubes

2 cubes and a felt pen

Question: A calendar is made up of four cubes. The calendar here shows Thursday 16 May.

Complete the middle two dice so that any date can be shown on the calendar.

THUR I 6 May dau 1I

This question appeared in various guises in both the Team and the Station contests and was poorly done!

1996 It's kids stuff.., well is it?

SThe first diagram shows your basic building piece: an equilateral triangle of side unit length.

a. The second diagram shows a tetrahedron with a base side length of 1 unit. This small tetrahedron is your basic building block. Build some of these. [Your supervisor will want to see at least one].




b. The third diagram shows a tetrahedron of base side length 2 units. If you try to build this using only the basic building blocks you will find it will not work! How many basic building blocks can you use? What other single solid will you need to complete diagram 3? Build one of these other solids and keep it to show the supervisor.

c. If you want to build a tetrahedron of base side length 3 units, how many basic building blocks will you need and how many of the other solids will you need? [You do not have enough triangles to build this one!]

On the other hand, this rather 'old-fashioned' question produced excellent responses.

1992 Materials: two 'solitaire boards'

In solitaire counters (or pegs) are moved and removed as follows. Counters may only move by jumping over an adjacent counter into an empty space. Jumps may only be made horizontally or vertically. The counter which is jumped over is removed.

Example: Here counter 24 jumps to position 44 and counter 34 is removed.

Question: Starting with the Latin Cross in the first figure finish up with the second figure. You must show the intermediate positions.

As previously mentioned, many stations can be constructed using Soma cubes, Tangrams and Multilink, etc. One really difficult assembly is the tetraboloes (illustrated in a Martin Gardner book). All these assembly problems are made out of heavy-weight hardboard and are quite large!

1996 Materials: one set of tetraboloes

Arrange the pieces to fill the jumbo jet outline. Arrange the pieces to fill the wooden tray.

Playing cards also form a vast source of problems:


1991 Materials: one pack of playing cards

Paul Daniels has a deck of eight playing cards (4 Aces and 4 Kings). The deck is placed on the table face down. The top card is placed face up on the table; the next card is placed at the bottom of the deck; the next card is placed face up on the table; and so on. The eight playing cards end up on the table in the following order:

S? v - IV

Question: Demonstrate how this is done to your supervisor.

After a well-earned lunch break teams move into the Swiss competition, probably named from a type of Contract Bridge competition rather than from any geographical context. Teams are ranked on the current scores and then grouped in fours. There are three rounds and each team plays each of the other three teams on a head-to-head basis-one 'seen' game, one 'unseen' game and, finally, one quiz. Past experience has taught us not to make the rules too difficult for the unseen game! It is worth mentioning that the games used need to have a finite number of moves and be completed in about 3 minutes maximum. This is an example of a 'seen' game, i.e. one that can be practised beforehand:

A 'Seen' Game: Rules of the Game One player uses the red pen, the other uses the blue pen. The two players take it in turns to join a pair of adjacent crosses or adjacent dots with a 'straight' line, either vertically or horizontally. Lines do not have to connect with previously drawn lines. One player uses the red pen, the other uses the blue pen. RED starts. The aim of the game is to complete a route in your colour from edge to edge [i.e. dots (red) from top to bottom, crosses (blue) from left to right]. The first person to complete such a route wins the game.

f + + f f + ()

f + + C C +

f + + + + +

+ + + + f +

+ + + + + ~

An 'Unseen' Game: Rules of the Game This game is played on an 8 x 3 grid. Two players take it in turn to mark two Xs (red) or two Os (blue) anywhere on the grid. When 3 Xs or 3 Os appear next to each other in a line draw a line through them. Lines may be horizontal, vertical or diagonal. An X or O may be part of more than one line.

The winner is the player with most lines.

The climax of the day is the Relay Contest. This is very ex- pensive in terms of questions with each Enterprising Event using up about 40 questions. After a hard day's work there needs to be plenty of 'easy' ones to start with:

1991 This figure shows part of the net of a cube. To complete the

9



net another square must be joined to one of the edges. In how many places can this other square be added? Draw them on the large diagram.

1991 Each object represents a different value. The totals for three of the four rows, each of the four columns and the leading diagonal are shown.

What is the total for the first row?

A?

A A 0 318

o A > 333 > I 0 A 347

347 347 333 332 331

but also some real stretchers to sort out the winners.

1996 The number 2,100,010,006 is such that

first digit shows how many Is are used the second digit shows how many 2s are used, etc. the ninth digit shows how many 9s are used the tenth digit shows how many zeroes are used

Write down an 8-digit number which satisfies the conditions:

the first digit shows how many 1s are used the second digit shows how many 2s are used, etc. the seventh digit shows how many 7s are used the eighth digit shows how many zeroes are used

1991 ABCDEFGH What letter is two to the right of the letter immediately to the right of the letter four to the left of the letter two to the right of the letter four to the right of the letter immediately to the left of the letter which comes midway between the letter two to the left of the letter 'C' and the letter three to the left of the letter 'F'?

1995 This question was much better done than anticipated: During the course of the centuries, many abbreviations have been used to denote taking a root. Examples:

1202 Fibonacci RADIX DE 4 ET RADIX DE 13 means 4 + J3

1 2

1572 Bombelli Rq L 20 m 6 p l means 20-6x+ x2

1637 Descartes -q+ qq-p3 means

q q -+ q2 p 3

2 1

(a) What does Rq L 4 p 12 m 3 j mean? (b) What single number is RADIX DE 36 ET RADIX DE

49 equal to?

In 1991 we started the National Event with teams coming from all parts of mainland Scotland. The format remained the same. Perth High School were the first winners of the National Trophy and also the first school to win twice (winning in 1997). The National Event moved to Edinburgh, Glasgow and then back to Tayside where it has remained

10

thanks to the continuing support of Tayside Regional Coun- cil and Northern College, Dundee who have provided the venue. November 1998 saw the last National Event at North- ern College, Dundee; it moves to Edinburgh for 1999 and by the time the Millennium has arrived I hope the National Event has found a new 'home' ...

During the period 1989 to 1998 we organized 14 Enter- prising Mathematics Days, both locally and nationally but 1995 saw the ultimate event-an Enterprising Maths in Eu- rope competition. Teams from Belgium, Holland, Denmark, Finland, Greece, Spain, England and Scotland all joined forces to make up teams consisting of two Scottish pupils together with two 'European' pupils. The teams were hosted by schools in Tayside for a week and took part in many activi- ties as well as the Maths Day which was undoubtedly one of the most successful.

It would be very remiss not to thank all the teachers in Tayside who have helped run the events, especially in the early days. In particular I would like to thank Ian Bryers (former Adviser in Maths, Tayside Region) for his support and enthusiasm when we started to get the event off the ground.

While the event continues at the secondary level, it has also made a move into the Primary Sector. This was initiated by another colleague, Eddie Mullan, PT Maths, Galashiels Academy and has since been run very successfully, both in the Borders and in many other parts of the country including Dundee, where Glenys Marra (Craigie High) is the 'expert'. The Primary Event is organized rather differently with each participating primary school being given a theme and lots of information with which to construct a display. Basically, in- cluded within each display are the answers to a number of questions which each school is asked to provide. Each primary team then has to search out the answers within the other primary displays.

Whenever a competition is run there is only one winner and consequently you have many teams that are not winners. Pupils have to get used to taking part and not winning. We make a conscious effort to reward all those who take part and consequently we do not award some gigantic prize to the winners and just 'thank yous' to the rest.

For the past ten years the Bank of Scotland have given us tremendous support in terms of sponsorship. This has en- abled us not only to provide excellent prizes to the top teams but also something for every contestant. For the last few years every pupil has received a copy of the current Mathematical Fun Calendar-a compendium of 365 or 366! puzzle questions and articles of interest on many areas of mathematics.

Here are five more questions for you to try:

1. The floor of a square room is to be tiled according to the pattern in the diagram. Both white sections are them- selves square and the larger white square has exactly eight more tiles on each side than the smaller one. If 1000 white tiles are needed altogether, how many grey tiles are required?

2. Estimate the volume of a person who is 160 cm tall and who weighs 45 kg.

3. My locker has a padlock with a secret number. The number is a two-digit number. 2, 5 and 9 are factors of my secret number. There are nine other factors (including 1 and the secret number itself). What is my secret number?




4. An old hymn book contains 700 hymns, numbered from 1 to 700. Each Sunday the congregation sing four hymns and the numbers are shown by hanging plates, each con- taining a single digit, on a board. What is the smallest quantity of each numbered plate that is required for com- posing any possible combination of the four hymns, allowing for the fact that the plate for a "6" may be turned upside down to serve as a '9'?

5. The diagram shows a plan view of my house and garden which forms a rectangular plot which is twice as long as it is wide, with each side being a whole number of metres. I have started to erect a fence as shown with posts at each corner. So far I have spent L272. The posts cost L2 each and the fencing cost a whole number of Ls per metre. What is the cost per metre of the fencing?

Like the vast majority of questions used, the answers take up little room and are either right or wrong. [On the actual day, these questions have to be marked quickly and so there is

Double arage

House

still to be fenced

little scope for part marks or marking subsequent to an error!] All these answers will fit on a postcard and I shall be delighted to send a copy of a Mathematical Fun Calendar (not neces- sarily the current issue though) to at least the first 5 (correct!) opened after 1 March 1999.

Please send your entries (postcard only), labelled Enter- prising Maths Competition, to me at the address below. F-

Author Clive Chambers, Former Adviser in Mathematics for Tayside Region, Westerlea House, Alyth Road, Blairgowrie PH10 7DY.

Schools TV Programmes for

Spring 1999

TVIM: Puzzle Maths (for 7 to 9 year olds) Mental maths games and puzzles 5 x 15 min progs Tuesdays 10.10-10.25 Repeated Fridays 10.10-10.25

A new 5-part series about mathematical puzzles, problems and games, illustrated through creative graphics, animation and puppet live action. In each programme two lively puppet presenters, Jess and Jake, compete in three five-minute fun mathematical challenges. Viewers are encouraged to participate, use and apply their mathematical skills and solve the problems before the puppets.

The challenges, aimed at 7 to 9 year olds, have been specially cre- ated with the help of the well-known mathematics consultant and erstwhile MiS contributor Dave Kirkby. Key areas within the number, algebra, shape and space aspects of the primary maths curriculum are targeted.

1. Place value and ordering 12 Jan and 15 Jan 2. Adding and subtracting 19 Jan and 22 Jan 3. Multiplication and division 26 Jan and 29 Jan 4. Reasoning about numbers 2 Feb and 5 Feb 5. Shape and space 9 Feb and 12 Feb

TVM: Shape, Space and Measures (for 7 to 11 year olds) Maths from design 5 x 15 min progs Tuesdays 10.10-10.25 Repeated Fridays 10.10-10.25

This series shows us the creative processes which draw on an understanding of shape, space and measures. In each programme, artists and designers reveal their methods of working and show how their designs, drawn from a range of cultures (using traditional methods as well as Computer Aided Design-CAD), depend on maths. Through art and design, pupils are provided with the opportunity to reinforce their mathematical skills and understanding. After watch- ing they can create and investigate their own maths-based designs.

1. Printing Maths (Translation, rotation and repeating patterns) 23 Feb and 26 Feb

2. Weaving Mathematics (Repeating patterns using binary codes) 2 Mar and 5 Mar

3. Tiling Mathematics (Tessellation, mosaics and Escher's tiles) 9 Mar and 12 Mar

4. Folding Mathematics (Pentominos, origami, kirigami and nets) 16 Mar and 19 Mar

5. Reflecting Mathematics (Links with printing, weaving, tiling) 23 Mar and 26 Mar


Eureka!: About Time (for 7 to 11 year olds) 5 x 15 min Topic progs Tuesdays 9.30-9.45 Repeated Fridays 9.30-9.45

What is a millennium? What is a decade? What is time itself? An opportunity for the audience to embark on an exciting trip from Egyptian sundials to Aztec calendars, from tree rings to Stonehenge. Much of the series will be based at the home of World Time, Greenwich Royal Observatory.

1. A Question of Time (What is it we are measuring?) 12 Jan and 15 Jan

2. Solar Time (The sun is also the heartbeat of time) 19 Jan and 22 Jan

3. Measuring Time (Sundials, clocks and calendars) 26 Jan and 29 Jan

4. Time and Nature (Patterns of time in the natural world) 2 Feb and 5 Feb

5. Time and People (Keeping time changes society for ever) 9 Feb and 12 Feb

Enter the Maths Zone (for 11 to 14 year olds) 5 x 15 min progs Fridays 10.45-11.00 Night-time block transmission:-progs 1-5 on Tuesday 27 Apr at 04.00-05.15 progs 6-10 on Wednesday 28 Apr at 04.00-05.15

This new series provides the starting point for imaginative work on key number and algebra concepts within the KS3 curriculum. In each programme three mythical characters engage with each other and the viewers in solving challenges and puzzles related to a particular maths focus. Amazing mathematical facts and figures are inge- niously put forward in each episode.

1. Orders Please (Order of operations) 15 Jan 2. Walking Backwards (Negative numbers) 22 Jan 3. Not All There (Decimals, fractions and percentages) 29 Jan 4. Scaling the Heights (Ratio and scale) 5 Feb 5. Primes and Powers (Patterns on a number grid) 12 Feb 6. Creases Me Up (Number sequences) 26 Feb 7. Keep Your Balance (Manipulating equations) 5 Mar 8. If At First You Don't Succeed ...

(Solving eq'ns by trial and improvement) 19 Mar 9. The Vegetable Plot (Coordinates and graphs) 26 Mar

All these series are supported by a wealth of material ranging from teachers' guides, activity books, information books, net notes, on-line resources and videos. These are all available from:-

Channel 4 Schools, PO Box 100, Warwick CV34 6TZ Tel: 01926 436444 Website: http://www.channel4.com/schools

11



Download - Special Scottish Issue || Enterprising Mathematics

Top Related