smile numbered set 28:2011-2059 - wordpress.com ends of a running track are semi-circles of radius...

cSmile 2013

UQJ to

Circumference = n x DiameterYou may have a button marked © on your calculator. A reasonable approximation for it (pi) is 3.14.

1. The radius of the earth is about 6 400km. How far is it around the equator?

2. How much further does a cyclist go if she keeps to the outside edge of the track rather than the inside?

3. The hour hand of a clock is 5cm long and the minute hand is 10cm long.

a) How far does the tip of the hour hand move each day?

b) How far does the tip of the minute hand move each day?

Turn over

-3//V/ "'ISi * 4 iv8& ?•*£;/ / ' //!\- ;-S?. o

4. The ends of a running track are semi-circles of radius 40m. One complete lap is 400m.

How long are the straights?

©1992RBKCSMIL

Smile 2016.

A 3 digit problem

Here are some different ways of making the number 24 using the digit 4.

4! + 4 - 4 =

4! + V4 -

4! x 4 * 4 =

019C2nBKC SMILE

Fair PlayThis is a game for 2 players.

You will need a dice and counters.

Smile 2017

Each player starts with 9 counters.

Roll the dice. (It does not matter who.)

£VENnumbe

I'll take ^ of \^

your counters. I

(I'll take all the

I 01223 numbers.

Carry on until one player has all the counters, te the game fair?You may need to play about 20 games to find out. Record your results.

Describe and explain what happens.

Roll the dice again.

I'll take 3 of

your counters.

01992RBKCSMIL

Smile 201

1W0

1) Copy and complete this table for = x2 .

iSiSii+5

+4

+3

+2

+1

0-1

-2

-3

-4

-5

+25

+4

0

+1

+16

Draw axes with x values from -5 to +5 and then plot the curve of y = x2 .

Describe your graph,

2) Complete the table= x2 +2.

Draw this curve on the same diagram,

Describe your graph,

+5+4

+27

+18

3) What happens to curves of the form y = x2 + c if c is a negative number?

© 1992 RBKC SMILE

Smile Worksheet 2011

Power MatchCut out the 12 squares and match them in pairs. The number for all the blank boxes is the same. What is it? &?

4D

[_

32

j_

10

...

3°

3x

x5

_l

8

I

9

6

16

——————————

)

i

© RBKC SMILE 2001

i

Smile Worksheet 201 £

Power MatchCut out the 12 squares and match them in pairs. The number for all the blank boxes is the same. What is it? £0

4D

32

[_

10

*j I

3x

x5

_j

8

1

9

---------

6

.n

16

~l

© RBKC SMILE 200

Smile Worksheet 202(

High Powered MatchingCut out the 1 2 squares and match them in pairs. The number for all the blank boxes is the same. What is it? 9&\

997+

---------

24-

r~

3000

r

9

i

3x 10D

3D+3

x 10

_|

2°

i

ii — i 2

2 2X X

9D+ 271

,n

1 —— I 5

3

>


High Powered MatchingCut out the 1 2 squares and match them in pairs. The number for all the blank boxes is the same. What is it? Jfo

997+

---------

24-

3000

r

9

i

3x 10°

3D+3

x 10

j

2D

I

I

I —— I 2

-I

2 2x x

---------

9D+ 271

~1

1 —— I 5

FEWEST KEYSSmile 2022

You may find it more interesting if you work on this activity with someone else.

Do these calculations on a scientific calculator pressing as few keys as possible.

Record your key presses on Worksheet 2022a.

2.55.2 + 3.6

b) (5.81 + 4.6) x (4.1 +3.62)

C) (4.2+ 3.8)+ (2.6-1.34)

CHALLENGECan you do this in 10 presses of the keys?

Your methods should give these answers.

a) 0.2840909b) 80.3652c) 6.3492063d) 0.6428571e) 0.0025188

Smile Worksheet 2022a

Use one box per press.

© RBKC SMILE 2001


Alphabet Symmetry• Put each letter into a box.

Does it have a horizontal line of symmetry?

Does it have a vertical line of symmetry?

Does it have a vertical line of symmetry?

Diagonal line of symmetry?.

Diagonal line of symmetry?

Diagonal line of symmetry?.

Diagonal line of symmetry''

) [Half turn rotational] [ ^symmetry? J I symmetry?

Half turn rotational symmetry?






Half turn rotational

• Why are most boxes empty? ; Vfot/ may like to design a similar sorting diagram for the numbers 0- 9.

© RBKC SMILE 2001

<D§ o:

| CD N C

-./'

Airline passengers may take a certain amount of luggage free of charge. Extra luggage has to be paid for.

Why do airlines charge for excess luggage?

Free luggageFirst Class..... Economy Class.

. up to 30kg

. up to 20kg

Air fares from London

:|i^itiiis^(i3|iili||

Addis AbabaBrusselsCairoNairobiNew YorkParisRio de JaneiroRomeSan FranciscoTokyo

i$irsii::£il£tl

1089

95

862

1346

1571

111

1720

406

1774

2284

Ecbribitiy Class

529

95

339

629

510

90

801

171

481

1125

Excess luggage chargeEvery extra kilogram (kg) cx>sts 1% of the First Class fare.

Ngozi is travelling Economy Class to New York.

has 26kg of luggage. 20kg will go free. 6kg has to be paid for.

Each kg costs 1 % of £1571

1% of £1571 = £15.71

6 x £15.71 =£94.26

So Ngozi's excess luggage charge is £94.26

Copy this table and fill it in.P^iger

Ngozi

Pritesh

Paul

Yuen Ling

Chris

Maria

|D^istj^j6^|l|

New York

Rome

Rio de Janeiro

Brussels

Tokyo

Addis Ababa

|Clis^:|i|

Economy

First

Economy

First

Economy

Economy

wapi?e»l§ii luggage26kg

26kg

27kg

41kg

28kg

19kg

Ex^f^l Luggage

6kg

<P$ir$i!»f

£94.26

/Vr^

/Turn over

Luggage charges to Rome.

Copy this table and fill it in.

Is 20kg of luggage enough for most journeys?

Is it worth going over the limit?

Do airlines use a fair way of charging for excess luggage?

Can you think of a fairer way?

£> 1992 RBKC SMILE

SIMILAR TRIANGLESThese are similar triangles,

Smile 2027

in why,

Turn ove

Find three groups of similar triangles, Which triangle is the odd one out?

(The triangles are not drawn to scale.)

&8IS:

© 1992 RBKC SMILE

Smile 2028

Integer Graphs[x] means the integer1 part of x.

This is the largest whole number which is less than or equal to x.

Examples:

[2.73] = 2 [f] = 0 [-3.991—4

Integer graphs can be drawn using mappings.

This is the graph of*——>x.

-4 -3 -2 -1

-2

-3

-4

1234

1. The steps are not connected. Why is this?

Turn over

2. a) Use the graph of * graphs of

M to help you draw

and

b) Generalise your results for |any value of c where |

x ———>- [x] + c |

-4-3-2-1

-2 •

-3

1234

3. a) Compare the graphs of

•*• F" '-L^J

b) Generalise for

4. Compare graphs of the form

and

for different values of m.

01992RBKCSMLE

[x] means the integer part of*.

This is the largest whole number whichis less than or equal to jc.e.g.

[2*1=2

[1ft]-1

[5]-5

If n-0

n =

n = 3

= 0 = 0

-'I 1 - °o

b* 3]= 1=1

so flnl for n = 0,1,2,3,4,5,6,7,

gives the string 0,0,0,1,1,1,2,2,

Similarly

[|njfor n = 0,1,2,3,4,5,6,7,

gives the string 0,0,1,2,2,3,4,4,

Investigate other strings formed in this way.

Smile 2031^

You will need 2 copies of Smile Worksheet 2031 a, each in a different colour, and a large sheet of paper.

You may like to work with a partner.

Look at the Square Spiral* poster or the picture below.

Cut out the squares from theworksheets.Use all the pieces to make asimilar poster.

When you have made the poster, work out how big the next square would be.

What shapes can you see? Can you see any patterns?

poster available from Leapfrogs. © 1992 RBKC SMILE

Spiralling Squares Patterns

Smile Worksheet 2031 a

You will need 4 copies of this worksheet.Each copy should be on a different colour paper.

Cut out all the squares.

rL__4-__ ~i

L "I

L

I I

.L_____|

© RBKC SMILE 2001

Smile 203i

D.I.Y, EarringsKhani and Farkid. are making earrings to sell at the school fair. They are using copper and silver discs with diameters of 1cm, 1.5cm, 2cm, 4cm and 5 cm.

1cm2 of copper costs 1 p.

1 cm2 of silver costs 20p.

Hoops cost 10p a pair.

Area of circle = TC r2( n x radius x radius)

Use the button marked (n) on your calculator.

A reasonable approximation to @ is 3.14.

How much would each pair of these earrings cost to make? Give your answers to the nearest penny. Only round off your answers at the end.

B. C.

E. R

Khani and Farkid want to make a profit of 120% on each pair of earrings.

How much do they need to charge for a pair of the earrings in C?

Design and cost your own earrings using the copper and silver discs,

01992 RBKC SMILE

Smile 2033

Choose ONE of the statements.

Collect some data to show whether it is true or false.

You may like to make a display of your work.

Tall people wear large shoes.

You may like to use a DATABASE.

Likely or unlikely?An activity for a group of 3 or more.

Smile 2034(

You will need a copy of Smile Worksheet 2034a.

Cut out the statements from the worksheet.

Turn over

Talk about the statements.Try to decide in which of the boxes below each statement should go.

Now stick or copy them into boxes in your book.You may prefer to make a display for your classroom wall.

• Look at the statements in the LIKELY box. Which is the most likely? Which is the least likely? Can you put them in order?

• Which statement caused the most disagreement in your group?

• On which statement was it easiest to agree?

You may like to write your own statements.

01992 RBKC SMILE


Likely or unlikely?Cut out the following statements.

You will grow a banana on an apple tree.

-------------

You will see rain today.

t-

It will rain somwhere in Britain today.

You will look out of the window today.

U

Everyone in the class will do their homework this week.

I-

You will look at a clock today.

_____________

You will drink a can of coke or lemonade this week.

r~A spaceship will land in the playground tomorrow.

L

You will enjoy school today.

You will travel home by airplane from school.

L1 ' You will eat chips today.

L_

You will eat fish and chips today.

t~

It will rain in the Sahara desert tomorrow.

You will be older tomorrow then you are today.

You will wake up before 8.00 a.m. tomorrow.

UYou will watch TV at the weekend.

_____

The headteacher will come into your classroom today.

You will get "heads" when you toss a coin.

-

-

-

© RBKC SMILE 2001


Likely or unlikely?Cut out the following statements.

You will grow a banana on an apple tree.

L_

You will see rain today.

-------------

It will rain somwhere in Britain today.

You will look out of the window today.

U

Everyone in the class will do their homework this week.

U

You will look at a clock today.

•• • • ~ ~ ~ - - -

You will drink a can of coke or lemonade this week.

rA spaceship will land in the playground tomorrow.

L

You will enjoy school today.i

rI You will travel home by I airplane from school.LI ' You will eat chips today.

j_

You will eat fish and chips I today.

It will rain in the Sahara desert tomorrow.

You will be older tomorrow then you are today.

You will wake up before 8.00 a.m. tomorrow.

uYou will watch TV at the weekend.

-------------

The headteacher will come into your classroom today.

You will get "heads" when you toss a coin.

-

-

-I

-

© RBKC SMILE 2001


Symmetry CodesYou will need a mirror.

This shape has

4 sides,

and 2 lines

of symmetry.

This shape has code I 4 I 2

This shape has I sides

and I lines of symmetry.

This shape has code

This shape has I sides

and lines of symmetry.

This shape has code I

Draw the lines of symmetry on these shapes and work out their codes.

2)

Code:

3)

Code: D

turn over

4)

Code:

5)

6)

Code:

Code: [

7) Draw and code some more shapes of your own.

© RBKC SMILE 2001

Smile 2l)3l

These designs all use circles, semicircles and quadrants.

In each case, is there more black or more white?

Justify your answers.


3 in 1 MazeYou can only travel horizontally or vertically.Each route runs from the triangle on the top left to the triangle on the bottom right.

1. Can you find a happy route?

2. Can you find a route 3, 3, 4 3, 4 5, 3, 4 5, 6, ...3?

3. Can you find a route that makes green?(You will need to look at the poster before you can answer this.)

© RBKC SMILE 2001

% %

suiaiqojj

»£$;*> **%Vlj ( J / f~\ /***.. £-**jr

1.The price of a CD player in November was £400. On December 1st the price was increased by 15%.

In the January sales the price of the CD player was reduced by 15%.

The sale price was not £400. Why not?

2.

What percentage of the wood is used by rich countries for paper?

Source: Norman Myers (ed) The Gaia Atlas of Planet Management.

3.

Not to scale.

The height of this can is 126.5mm.

If the diameter remains constant what would be the height of a normal size can?

Ti im /~>\/eir

4.

If this trend continues, what percentage of the existing forest will be left in 5 years time?

Show that, 10 years from now, just under half of the tropical forest will have disappeared.

How much will remain after... 50 years

... 100 years?

You may find a spreadsheet useful.

Source: Forest Resources, Food and Agriculture Organisation 1985.

5.

Use this information to calculate the maximum number of cars that could have been illegally parked in London in one day, before wheel clamping was used as a deterent.

Source: Telegraph Weekend Magazine, Sept 24th 1988.

01992 RBKC SMILE

Smile 2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

= 2-5

= 04

_4 10

6.15

1. Find other fractions that equal 0 • 4.

These are equivalent fractions.Explain what 'equivalent' means.

(. Find at least 3 fractions equivalent to each of these.

a) b) 3_4

c) _2 3

3. Choose another fraction and find some that are equivalent to it.

C1992 RBKC SMILE

Smile 20

experiment

Use the Q button on a scientific calculator.

On some calculators this may be ff} or a similar notation.

Press

What happens?

Experiment with other values for the two numbers.

© 1992 RBKC SMILE

Smile 2041

Going Scientific1. Do these calculations on a scientific calculator and

record your results.

0.02 x 0.03 0.2 x 0.32x3

20 x 30

2. Continue these sequences and explain how the calculator shows the results.

400 x 200 300 x 500 x 700 500 x 3000 4000x2000 3000 x 5000 x 7000 5000 x 30000

3. Without using a calculator work out

700000 x 2900000

How would your calculator show the result?

e 1992 RBKC SMILE

Smile 2042

and EXE

Use a graphic calculator to generate this sequence(Texas Instruments uses Enter for EXE.)

EXE Ans 1 + I EXE' [iiiiiiiiiiiiiiiiiiiiin

EXE I EXE

and this sequence.

3 I EXE I I Ans 1+14 lEXE 11 EXE I IEXE

What type of sequences do you get?

Try these sequences.

EXE EXE EXE

Arts EXE EXE

Can you describe sequences generated by

EXE lAns EXE I IEXE| I EXE

a EXE I EXE j EXE

for different values of a and b.

Can you describe these sequences?

2 | I Ans EXE

| Ans| !_______—^ Igfa

Try some sequences of the kind

Try to make different types of sequences.Turn over

Try to create the following sequences usingi——1 i——)

the |Ans and I EXE keys.

1,3,5,7,...

4, 2, 0, -2, ...

1, 11,121,1331,

How can you make 1, 0,1,0,1,...?

© 1992 RBKC SMILE

Smile 2043

patterns1 + 1=9 r + ^ = ^T J 2 14 5 2 10

7 3 21

1+1 = 11 7 4 28

Investigate number patterns formed by adding other unit fraction;

How can you check your results?

Can you find a rule for your results ?Turn over

Extend your investigation using non - unit fractions.

e.g. 2 +7

2 +7

2 +7

12

13

14

= 11 or14

= 1321

= 1528

1 +7

1 +7

1 +7

14

24

34

= 1128

= 1828

=

or 2 +5

2 +5

2 +5

23

34

45

= 1615

=

—

Does your rule still work?

Can you find a rule for adding any pair of fractions?

© 1992 RBKC SMILE

Smile 2044

Match the equations to

Explain

01992 RBKC SMILE

Smile 2044bThese cards and those from 2044a and 2044c should be cut out and put in envelope 2044.

t-

u

y

L

4.

X

j

Smile 2044c

These cards and those from 2044a and 2044b should be cut out and put in envelope 2044.

L

Smile 2044a

These cards and those from 2044b and 2044c should be cut out and put in envelope 2044.

U

y = *-

T

y = 4x-2

y = 2x2 + 3x- 4

-I

y =

y = -4^

U

y = 5x-x?

y = - x3 y = 2 -x

y = x?-x

r J

y = 5-2x

y = x_+ 5 J

L

y = x3

,J

Hot and ColdMatch the temperatures below with the letters on the scale.


This thermometer has a Celsius scale (°C).

turn over

Here are some temperatures from around the world, taken on the same day.

Place Temperature

Alice Springs | 38°Ci Delhi | 14°C |

Kingston ) 26°CLondon j 4°C IMoscow -12°C

I New York |. -1°C IBeijingRome

-6°C |8°C |

1. Label the temperatures on this thermometer. (London has been done for you.)

2. In which month of the year do you think these temperatures were taken?

3. Which city is colder, Moscow or Beijing?

4. How much colder is New York than London?

5. Which is colder, -6°C or -10°C?

London (4°C)

RBKC SMILE 2001

Smile 20p"

Pegs in Squares

1) Continue this sequence.

1+3 = 41 +3 + 5 = 9

1+3 + 5 + 7=16

1 2223242


4=4 = 22 (i§ 4 + 12 = 16 = 42

4 + 12 + 20 = 36 = 62


1 = 1 = 12

1 + 8 = 9 = 32 1 + 8 + 16 = 25= 52

Turn over

Smile 2049Unpredictable Patterns?

1 point 1 region

2 points 2 regions

3 points4 regions

4 points 8 regions

What is the maximum number of regions you would expect with 5 points?6 points?

0)raw circles to see if your predictions are correct.

Now what would you expect with 7 points?8 points?

n points?ft 1OO4 DDlfr* CUM C

1. These parallelograms are defined by the vectors p and q.

Smile 2050

a)6 --

5 --

4 •-

3 --

2 --

P -

23456 3456

What are their areas? Try some others.

Turn over

2. In these parallelograms neither vector lies along an axis.

a)6 - -

5 - -

4 --

3 - -

2 --

1 --

b)6 •-

5 --

4 --

3 --

What are their areas? Try some others.

3. Generalise for the area of any parallelogram formed by the vectors p = a\ and q = /c\. b d

©1993 RBKC SMILE

Smile 2051

logYou will need a scientific calculator.

r-^iC^S

^im

Button1. Enter 10 on your calculator.

Press the [log] button.

What is the result?

Repeat for 100,1000... Tabulate your results.

What do you find?

Now do the same to find the log of 5, 50, 500 ...

Describe your results.

2. Use the [logj button on your calculator to tabulate log 1, log 2, ... log 10.

Use your results to calculate a) log 400

b) log 7000

c) log 90

Check your calculations with the [log] button.

Can you predict log 750?

3. By trying different values of x, y and n and by using the (log) button investigate

log x + log y = log ?

log x - log y =

log(xn)

Turn over

4. Use what you have discovered to calculate

a) log 750

b) log 35

c) log 144

Work out log 375 without a calculator. Explain your method.

©1993 RBKC SMILE.

PYTHAGORAS DISSECTIONSmile 2052

Squares P, Q and Rhave been drawn on this right-angled triangle.

Square P iscut into four pieces.

z cm'

i cm

£ cm

jcm

Show how square Q and the four pieces of square P will fit into square R.

Turn over

Here, square Q and the four pieces of square P will fit into square R.

-2 cm-^X

Square P iscut into four pieces.

cm

\ ri I

Z cm

I

cm

cm

cm

cm

Investigate the dissection of square P for right-angled triangles.

Look carefully at the ratio of the dissection.What do you notice about the lines of the dissection?

©1993 RBKC SMILE

Smile 2053^

You might find it helpful to work in a small group.

How many ways can you make 14 by adding 4 odd numbers?

^Check your answers with someone else.

What about 2 odd numbers? 3 odd numbers?

Investigate for different totals.

©1993 RBKC SMILE

Smile 2054

•vv

Ellipses by foldingSmile 2055

You will need circular paper.

Mark a dot inside the circle.

Fold the paper so that the circumference of the circle just touches the dot.

Unfold and draw a line along the fold.

Repeat.

Try putting the dot in different places. What happens when the dot is ... very near the centre of the circle?... very near the circumference? ... equidistant from the centre and circumference?

Surrounding right-angled triangles


Find the area for each square and fill in the table below.

1

2

3

4

5

Area of P Area of Q Area of R

13cm2

What do you notice about the areas of squares P, Q andR?

Without drawing complete the following:

6

7

Area of P

4cm2

17cm2

Area of Q

16cm2

Area of R

26cm2

R

© RBKC SMILE 2001

Smile 2037

3 in 1 Maze There are three routes. You can only travel horizontally or vertically.Each route runs from the triangle on the top left to the triangle on the bottom right.

Smile Worksheet 2037a might help you.

Can you find a happy route?

Can you find a route that makes green?

Can you find a route 3, 3, 4, 3, 4, 5, 3, 4, 5, 6 ... 3?


TiesAn activity for a small group.You will need large sheets of crrr paper.

Ties are made from 3 pieces of cloth cut accurately on the true cross.

• Make a full size pattern for a tie using cm2 paper.

Silk hand-made ties are often made from cloth 1 m wide.

• Explore different layouts of the pieces so that the minimum amount of material is wasted.

• What is the shortest length of plain silk you would need to cut out 4 ties?

• Using patterned material or paper, can you lay out the pieces so that when you cut them out and sew them together, there will be no break in the design?

>- Each smaller square on the pattern represents 1cm of cloth.

\7

© RBKC SMILE 2001

Smile 2059

Drawa4-SET.

How many dominoes?

Turn over

2) Copy and complete this mapping. Domino S£T

Number of dominoes

-> 10

3) Describe in words how to work out the number of dominoes.

4) How many dominoes are there in the 10-SET?

5) How many dominoes are there in the 15-SET?© 1993 RBKC SMILE

smile numbered set 28:2011-2059 - wordpress.com ends of a running track are semi-circles of radius...

Documents