smile 2060 kifbaq - wordpress.com · kifbaq smile 2060 can you make a pattern for this kitbag? you...

KifbaqSmile 2060

Can you make a pattern for this kitbag? You should leave a seam allowance of 2cm.

The length of the strap is four timesthe circumference of the bag.What length of material will you need?

Your cloth is 140cm wide.Lay out your pattern using as little material as possible.

Make a pattern for a pencil case similar in shape to the kitbag whose dimensions are of those of the kitbag. Remember your seam allowance must still be 2cm.

^^^^fliG r^""-'•',' '^V-- '• ^ •• -nW ^'. "V r

Adapted from an activity in MiW Cabbage. ©1993RBKC SMILE

COWMHOURSELF/Investigate the truth of these statements.

Smile 2061

|Try numbers larger than 1• whole numbers• fractions and decimals.

Try numbers smaller than 1• negative numbers• fractions and decimals.

©1993 RBKC SMILE

oSmile 2062

illsGalGulatg the sizii of

pfi tfi| tvyeltfe SiffffisIcfe-iHi:

These are not drawn accurately. Show all your working.

1)

6)

lAld = dN = NIAI

N(6

N

V (8

baEkiOUbB

bi|pijrTif0rerica of semi^circie !s ^0° sfefjdi ntj; on the: sannie arc

ice:thearig atia on the circumference stanp'ing on the same ara

^pjjpliti

<i|uatlrilaferai is 180°.

©1993 RBKC SMILE

ISLAMIC DESIGNS Smile 2063

1. Draw the construction lines faintly.

\\\Z

\in/ \nr

Rub out the pencil lines. Repeat your design.

2.

Rub out the pencil lines. Repeat your design.

Now try some of your own designs.

Intricate geometric designs like these can be found decorating the walls, floors and windows of many buildings in Islamic countries.

These designs were developed because the Islamic religion discourages the making of i iges of lifelike figures. The use of geometric patterning first began in Iran and Iraq in the early 11th century but its use spread elsewhere and can still be seen today in many countries from Spain to India.

RUSSIAN MULTIPLICATIONLook at this method for multiplying

Smile 2064

49 by 423 and 52 by 376.

3 x £7&

7 x J353£

207Z7

.52-

J50¥-ms^-

3 x 6016

I x 72032

19551

Use the same method to multiply other pairs of numbers.

Can you find a "Russian Multiplication" where all but one pair of numbers is crossed out?

How about one where all the numbers are crossed out?

©1993 RBKC SMILE

Smile 2065

An atlas may be useful.

If the earth were shrunk

to the size of a golf ball,

would you be able to feel

the mountains?

• Mount Everest is the highest mountain.• The 'Marianas trench' is the deepest part in the ocean

© 1993 RBKC SMILE

Smile 2067

,|EAN,S

To make one pair of 32" waist jeans

( it takes 1.6m of denim, 0.2m of lining, 230m of thread, 2 labels, 5 studs, 1 zip, and 1 button.

Your factory has just received an order for 5000 dozen pairs.

You have accepted the following prices for the raw materials.

DenimLiningThreadLabelsStudsZipsButtons

£250 per 100m roll £106 per 100m roll £5 per 5000m cone £15 per 1000 £20 per 1000 £12.50 per 100 £3 per 100

A spreadsheet might help.

1. Find a good way of setting out all the information you need:a) to order the correct quantity of all the raw materials you

will want.

b) to calculate the cost of the raw materials for one pair of jeans.

2. a) Denim goes up in price by 5%.How does this affect the cost of one pair of jeans?

b) If there was a 5% increase in one of the raw materials which one would have the greatest effect on the cost of one pair of jeans?

This activity was originally part of the MiW Cabbage Pack. © Crown Copyright 1988. Reproduced by permission of HMSO.

Smile 2069

Turn it MAO !There is a set of four cards with numbers on the front. Sometimes a letter is written on the back. Your friend claims to have discovered something.

Whenever the number

is more than 5. E. is

on the other side.

She puts down the four cards like this.

What is the minimum number of cards you must turn over to check that she is right?

Can you convince someone else?

©1993 RBKC SMILE

Smile 2070

Card Towers

This tower has three levels and is made from 15 cards.

Investigate for different numbers of levels.

The world record is a tower with 61 levels.

How many cards were needed?

How high was it?

©1993 RBKC SMILE

Smile 2071

Half a cuboidYou will need centicubes or multilink.

Make two solids like this.

Fit them together to make a Aboid.

If you had two of each of these solids could you fit them together to make a cuboid?

f? Smile 2072

NEPALNUMBERSThe page illustrated here is from a school mathematics book in Nepal.

r v<m'***4f

fTr^>«^fi«fT»ff5^

fai jJi f-

VO-.Y: M-v.^-V=

* «-¥.,,}*-*«*o-V

IS-v.f^-y, ^ -v= v -v=

^'q^spn

S '^r**-^ f*'.**"^"'"'—>n i?

fSffTT

Vo-Y=^

^-Y=?^

^^Y^^q

*• ,_, . L.

What do you think this mathematics lesson is about?

Can you translate the table of numbers?

Now make a similar table for the number 2.

©1993RBKCSMII

Fibonacci - type Sequences

Smile 2078

1 jfWThis is part of a Fibonacci-type sequence where each number

is the sum of the two previous numbers.

This is part of another Fibonacci-type sequence.

m it

This is part of another Fibonacci-type sequence

SO IS

II

Investigate the possible 'end' numbers for parts of Fibonacci-type sequences.

See over

Leonardo Fibonacci

Leonardo Fibonacci was born about 1175 in Pisa, which was a commercial centre of Italy. His father was a merchant, which probably accounted for Leonardo's early interest in arithmetic. Trips to Egypt, Sicily, Greece and Syria brought him into contact with Eastern and Arabic mathematics and Fibonacci became thoroughly convinced of the practical superiority of the Hindu-Arabic methods of calculation. In 1202 he published his famous work Liber abaci. This book strongly advocated the Hindu-Arabic notation and did much to encourage the introduction of these numerals into Europe. Fibonacci published two other important books: Practica geometicae in 1220 and Liber quadratorum in 1225.

01993 RBKC SMILE

Smile 2079

You will need MicroSMILE program QUAD and copies of Worksheet 2079a.

showing

Turn over

1. Use QUAD to compare the following graphs with the graph of y = x2 .

Note the similarities and differences. Sketch each graph on the worksheet.

a) y = 3;c2b) y = -x2

C) y = (x + 4)2

d) y = (*-l)2e) y = x2 + 2

f) y = x2 -4

2. Use QUAD to help you summarise the effects on the graph of y = x2 for

• different values of a where y = ax2• different values of b where y = (x + b) 2• different values of c where y = x2 + c

You can use the worksheet to illustrate your findings.

3. Use your findings to predict the important features of the graph y = 2(x + 3)2 - 4.

©1993 RBKC SMILE

Smile Worksheet 2079a

A Sketchy Activityy y

y y

y y

© RBKC SMILE 2001

Smile 2081

You will need: cm squared paper tracing paper 2 coloured pens.

•IL

t t

1.

F t

Fill in two of the squares with a start (S) and a finish (F).

Using a coloured pen, draw a complicated path from S to F through the middle of the squares.

2. Using the same colour, add more paths so that every square is visited.

Don't forget to have

• dead ends

• paths that lead back to the start.

tJJ

=11

tt

3. Using a different colour, draw in the walls.

All the grid lines that do not have a path across them become the walls of the

^ maze.

Turn over

4. Take a new sheet of squared paper or a sheet of tracing paper and draw only the walls and S and F.

Now test the maze on a friend. You will need tracing paper to stop your maze being spoilt.

IF

5. Can you make a harder maze?

©1993 RBKC SMILE

Smile 2082

Opposite, Adjacent and HypotenuseYou will need a protractor, scientific calculator and Smile Worksheet 2082a.

adjacent

sure you understand the words opposite, adjacent and hypotenuse.

AB is the side opp05ite the angle 40°.

AC is the side adjacent to the angle 40 C

;BC is the hypotenuse, the side opposite the right-angle.

Draw accurately 3 different right-angled triangles with an angle of 40°.

Measure the three sides of each triangle. Complete the 40° table on the worksheet.

What do you notice?ADraw different right-angled

triangles, 3 with an angle of 20° and 3 with an angle of 60°.

Complete the rest of the worksheet.

Look at all three tables. What do you notice?

For any given angle in a right-angled triangle, the ratio

oppositehypotenuse

is always the same.This is also true for the other two ratios.

These are trigonometric ratios and are called sine, cosine and tangent.

sine 0 = oppositehypotenuse

cosine 0 = adjacent

opposite

hypotenuse

tangent 9 = opposite adjacent

The buttons (sin] (cos) and ftanl on a scientific calculator will give you these ratios.

Press (Tl fcT) (sin) to get the ratio opposite for the angle of 40'V .' V / \ ' hvnntPniiQPhypotenuse

Check your other results with your calculator.

You can use a trigonometric ratio to work out the length x.

x

sin 55°

6sin 55° = x

Press

55° = 4.9149123

= 4.915 to 3 decimal places.

Turn over

Use your calculator to work out the missing lengths in the following triangles. Give your answers to 3 decimal places.

(Not drawn to scale)1cm

10cm

3cm

10.4cm

Check your answers to 2 of the above, by drawing the triangles accurately.

CHALLENGE!

Find x.

©1993 RBKC SMILE

Opposite, Adjacent and Hypotenuse40°angle

Remember: oppositehypotenuse

Smile Worksheet 2082a means opposite •*• hypotenuse

hypotenuse opposite adjacent oppositehypotenuse

adjacenthypotenuse

opposite adjacent

20°anglehypotenuse opposite adjacent opposite

L hypotenuseadjacenthypotenuse

opposite adjacent

60°anglehypotenuse opposite adjacent opposite

hypotenuseadjacenthypotenuse

opposite adjacent

© RBKC SMILE 2001

Opposite, Adjacent and Hypotenuse Remember: opposite

Smile Worksheet 2082a means opposite •*- hypotenuse

40°angle

20°angle

60°angle

hypotenuse


adjacenthypotenuse

opposite adjacent


adjacenthypotenuse

opposite adjacent


adjacenthypotenuse

opposite adjacent

© RBKC SMILE 2001

o

C/3 3 S"

o CO

ui n

Turn

ove

r

Smile 2084

Polygon Areast ^X

Here are two methods for finding the area of a polygon.

Area = 1 + 2 + 2 + 3 Shaded area = 1 + 2 + Unshaded area = 20 - &

= 12cm2

Copy these shapes on to squared paper.

Choose one of the methods or your own to find the areas of these shapes.

© RBKC SMILE 2001

Smile 2085

These 2 maps are identical apart from their scale.

You may like to use tracing paper.

They have been joined together by pushing a pin through the same place on both maps.

How can you find this point? Explain what you did.

Is it still possible if one of the maps is turned through 180°?

©1993 RBKC SMILE

Smile Worksheet 2088

What's the difference?

are 4 objects: -— potato

Complete the decision tree diagram below, by filling in the names of the objects.

Question\5 It a

vegetable?

QuestionDoes \t have two wheels?

Yes No No

2) Make your 6wn decision tree diagram using these objects.

parrot )( pencil

Think up your own questions.

Question

Question Question

3) Complete this decision tree diagram for 5 objects.

house )( football

turn over


You will need glue and scissors.

Tottenham Court Road

^ Piccadilly ^ Circus

• Cut out the signs below.

• Place them in the correct position on the map and glue them on.

• You might like to make a map of a crossroads near your school and make road signs for it,


Regents Park

Piccadilly Circus

Fold

A Regents T Park

Bond StreetiMarble Arch


Fold

Bond Street Marble Arch

j Piccadilly Circus

-k. Regents ^

Fold

A PiccadillyT /"Srono


Bond Street Marble Arch

Fold

© RBKC SMILE 2001

Black and Red Triable PatternsSmile 2090

1 black triangle. 0 red triangles

Total 1 triangle

A3 black triangles. 1 red triangle.

Total 4 triangles.

How many black triangles? How many red triangles?

What is the total?

Draw more triangle patterns.

What number patterns can you find?

© 1993 RBKC SMILE

Smile 2092

15

= 0.2 17 » 0.142857

i— has 2 non - repeating digits.

•=• has 1 non - repeating digit. o

•£ has 1 non - repeating digit and 1 repeating digit.

•= has 0 non - repeating digits and 6 repeating digits.

We could represent

^ as [ 2; 0 ]

1 as [1;0]w

1 as [1;1] 6 l J

ly as [0;6]

Which fractions are of type [ a; 0 ] ?

Which fractions are of type [ 0; b ] ?

What about type [ a; b ] ?

Can you predict the values of a and b for any denominator?

, iaoo QQkr- CUM c

Smile 2093»"villlC Pattern:

An activity for two people.

This pattern was drawn on square centimetre dotty paper. It is a tessellation of the shape below.

o Find a, x and y using trigonometry.

o Use your results to write a LOGO program to draw this tessellation.

Turn over.

The following tessellation was drawn on isometric dotty paper.

Use LOGO to reproduce it.

You may prefer to reproduce some other Islamic patterns using LOGO. 'Geometric Concepts in Islamic Art' by L El-Said and A. Parman, may give you some ideas.

©1993 RBKC SMILE


Squares, Cubes and Roots

1. Solve this cross-puzzle.The information below may help.

Across1. square of 44. square of 75. square root of 258. cube root of 89. cube of 11

Down

2. cube of 43. cube root of 276. square of 117. square root of 169

2. Invent a cross-puzzle using squares, cubes and roots of your own. Give it to someone else to solve.

9.

4.

7.

6.

Information

3x3 = 9

6x6 = 36

4 x 4 x 4 - 64

5 x 5 x 5 - 125

9 \e> the square of 3

36 \e the square of 6

64 is the cube of 4

125 is the cube of 5

3 is the square root of 9

6 is the square root of 36

4 is the cube root of 64

5 is the cube root of 125

© RBKC SMILE 2001

You will need Smile 2096, the Fraction Playing Cards. A card game for 4 or more players.

The aim of this game is to collect the Fraction Playing Cards into fraction 'families'.

3This is the 5 fraction 'family'.

35

three fifths

Smile 2097

•quara

Turn over for the rules.

Rules• Deal out all the cards.

• The first player asks any other player for a particular card 'Do you have the three fifths circle?'If the player has the card then she must give it to the first player. The first player has another go. If the player does not have the card, then it is the next player's go.

• When a player gets a set of four equal fractions, she puts them down on the table for the other players to check.

iJMwnu

35

numbtr

®• l»H»

fCT\VAX

clrcli

lit r • • IKIk.

»JOO

threefifths

word

H•nnkf

•qum

:ILE

Smile 2100

tke Test An activity for a small group.

You will need 3 dice.

Here are four statements.

• Discuss each statement.Predict whether they are true or false or is it difficult to say?

• Test each statement out at least 20 times.

• Record your results.

• Discuss your results.Do you still agree your original predictions? Why?

©1993 RBKC SMILE

Smile 2101

You will need a set of Logiblpcks and the 11 Logicards.

This is a game of logic for four players working in pairs. One pair selects three logicards and the other pair has to discover what they are and where they go in the smallest possible number of goes.

©1992 RBKC SMILE

How to play.

All players should read ALL these instructions.

You should have the 11 logicards with RED, GREEN, YELLOW, BLUE, SQUARE, CIRCLE, TRIANGLE, LARGE, SMALL, THICK and THIN printed on one side.

Make sure that you have all looked at the logiblocks and can recognise the above attributes.

First pair

Choose 3 logicards.

DO NOT let the other pair see them. Look at the cards before placing them FACE DOWNWARDS on the 3 spaces provided.

These cards 'name1 the circles that they are next to, e.g. if the logicard says THIN then all shapes placed in that circle must be thin.

You can look at the cards during the game if you forget what you have chosen.

Second Your aim is to find which 3 logicards have pair been chosen.

To do this you need to:• Choose a logiblock.• Ask the first pair to place it on the

correct part of the board.

Remember:Logiblocks placed where 2 CIRCLES OVERLAP,e.g. THIN overlaps BLUE means that all logiblocks inthat space must be thin and blue. Their shape does notmatter.

Sometimes it is impossible to put a logiblock on a space, e.g. if THIN overlaps THICK. You cannot get a shape that is both thick and thin.

Logiblocks placed where 3 CIRCLES OVERLAP, e.g. THIN, BLUE and SQUARE, have to be thin and blue and square. Their size does not matter.

If a logiblock DOES NOT BELONG in any of the circles, place it on the outside of the board.

You are allowed only ONE ATTEMPT to name the logicards after your selected logiblock has been placed on the board.

You should try to use as few logiblocks as possible to name the 3 logicards.

First pair

Do not reveal any of the cards until the other pair have decided correctly on all three.

A possible solution

1. Square

2.-Red

3. Circle

yj

yj yj

yj

Smile 2103

1. What percentage of these squares is shaded?

Turn over.

2. Find a packing arrangement which reduces the shaded area .,,

,,. for different rectangles ... for an infinite plane.

What is the lowest percentage of shaded area that can be achieved?

©1993 RBKC SMILE

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