The Root of the Problem - WordPress.com · Smile 2151 The Root of the Problem You will need Smile...

Smile 2151

The Root of the ProblemYou will need Smile Worksheet 21 51 a.

This cube is made from 8 centicubes.

Each edge length is 2cm. Its volume is 8cm3 .

To calculate the volume, 2cm x 2cm x 2cm = 8cm3 .

"Two cubed" is written 23. 23 = 8

1. Complete the values 1 3 to 103 in Table 1.

The volume of this cube is 64cm3

4cm x 4cm x 4cm = 64cm3 so the edge length is 4cm.

The cube root of 64 is 4.

"The cube root of 64" is written ^64.

*> <*

2. Complete the values ^1 to \1000 in Table 2.

Use your worksheet to answer these questions.

3. What is the volume of a cube with edge length

a) 6cm?

b) 5cm?

c) 9cm?

4. What is the edge length on a cube with volume

a) 27cm3?

b) 512cm3?

c) 343cm3?

Turn over

To estimate the volume of a cube with an edge length of 5.2 cm you can use Table 1 of your worksheet.

5.2 is near to 5 so a good estimate of the volume of a cube with edge length 5.2cm would be about 145cm3.

Using a calculator 5.2 x 5.2 x 5.2 = 140.608 which to the nearest whole number is 141 so the estimate was close.

Use your worksheet to estimate:

5. The volume of a cube with edge length a) 7.9cmb) 8.5cmc) 3.3cm

6. The edge length of a cube with volume a) 370cm3

b) 920cm3c) 36cm3 A

Use a calculator to see how close your estimates were.

©RBKC SMILE 1994.

Smile Worksheet 21 51 a

The Root of the ProblemTable 1Number | (edge length) |

1 |

2 j

3 j

4 j

5 !

Cube (volume)___ ___

23

33

43

53

1x1x1= 1

2x2x2= 8

3x3x3 =

=

=s

6 |

7 I = =

8 |83

8x8x8= 512

9 j

10 J 103 =

Table 2Cube Root I i _ p__

ft I =

?27 | =

I =

I =

I =

I =

?512 | =

| =

Number

1

2

8

fiooo | = | 10© RBKC SMILE 2001

The Root of the ProblemTable 1Number f (edge length) |

1 j

2 |

3 [

4 |>?

5 I

Cube (volume)...-«._ -.

23

33

43

53

1x1x1= 1

2x2x2= 8

3x3x3 =

=

=

6 |

7 j =

8 j8 3

8x8x8= 512i

9 !10 | 103 =

Smile Worksheet 2151 a

I I Cube Root § Number

' ll I = | 1

?8 | =

?27 | =

I =

| =

I =

| =

^512 | =

| =

fiooo | =

2

8

10

© RBKC SMILE 2001

Smile 2152

An activity for 2 or more.

This activity is about the probability of a spinner landing on one of three colours: red, blue and green.

This spinner is:

mosf likely'to land on a blue /ess likely1o land on a red

impossible to land on a green.

Match the Spinner Cards to the Probability Lines,

Certain T

- red

Impossible . . green

- blue

This pack contains 10 Spinner cards and 10 Probability lines.

Spinner Cards

HOW LIKELY?

Smile 2152a

These cards and those from Smile 2152b should be cut out and kept in the envelope Smile 2152.

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1

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•red

- green

-blue

•

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Impossible . .

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•

- green

• blue, red•

• m j

Smile Worksheet 2153

£1 Search

If you enjoyed this you may like to make up a similar puzzle for someone else.

© RBKC SMILE 2001

Oum L)iSmile 2154

iceYou will need six dice and the number cards from Smile Cut-out sheet 2154a.

The aim Is to make numbers, using the scores of the six dice and +, -, x, •*• and brackets ().

5 x

x

10

= 35

= 35

-35

= 35

are

©RBKC SMILE 1994.

Smile Cut-out sheet 2154a

Number Cards <

36_________

81

18-]

7

I

12J.

100r

137

I

40

19

49

10j

-C?

Smile Cut-out sheet 2154a

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1

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Number Cards ci

36

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-4

37

r

40

19

49

10j

i?i

© RBKC SMILE 2001 © RBKC SMILE 2001

Smile 2155 Smile 2155

Visualizing- a group activity

You will need several copies of Worksheet 2155a.

This shape ...

can be seen as:• one isosceles trapezium

and• four congruent, equilateral triangles.

Visualizing- a group activity


This shape ...

can be seen as:• one isosceles trapezium

and• four congruent, equilateral triangles.

But there are many other ways!

• Find a new way of seeing the shape.

• Describe the way you see it to the others in your group. Wait for them to see it that way.

• Use the worksheet to record the way you see it and write the description.



• Describe the way you see it to the others in your group. Wait for them to see it that way.


How many ways can your group find? How many ways can your group find?

© RBKC SMILE Mathematics 2005 © RBKC SMILE Mathematics 2005

Smile 2155

- a gtoup activity


This shape ...

can be seen as one trapezium and four triangles.

r Description

/ trapezium

and

H" triangles.



• Describe the way you see it to the group.Wait for them to see it that way.


How many ways can your group find?

©RBKC SMILE 1994.

Smile Worksheet 2155a

Visualizing Worksheet

Description Description



© RBKC SMILE 2001

Smile 2156

FRACTION SQUARES

Joining midpoints and corners creates a variety of fractions in a square.

3/37-— i —— i -—— i ——& + & + S + S

= 2(1

1) What fractions of the

square are P, Q and 7

\A/hat fractions of the square have been created in the diagrams below?

2)

5) Draw 3 more squares. Create other fractions by joining midpoints and corners.

Q What fractions of this square have been created?

©RBKC SMILE 1994.

Some sums for your mind Smile Worksheet 2157- on activity for two

Use sensible guesswork to match the Questions to the Answers. When you have agreed the results check them with a calculator.

[^

5 30 7

3 7-5

l~<r^

3-5

5-73

57-3

T_3 7 5

3-57

*_

7-53

r

7- (5 -3)

3 -(7+ 5)

(~ m

3-75

\«

3 75 '

i

I/ 1

11 1

J

i

|

-45

^ *-"•

One and a quarter

A bit more than

1 1"2

-6.something

i

2 and a bit

Just over4!

-23

"j

3 1

i

23

About six and a half

-0.something

-1 (T1 -O

i© RBKC SMILE 2001


Turning GreenYou will need: Sorting sheets a and b, scissors and glue.

1. Cut out the rubbish,2. Sort the rubbish into the correct bin.3. When you are sure, stick the rubbish in the bins.

RBKC SMILE 2001


TUrning Green - sorting sheet aClothesfor recycling

Glassfor recycling

Metalfor recycling

© RBKC SMILE 2001

Smile Worksheet 2158b

Turning Green - sorting sheet

Paperfor recycling

© RBKC SMILE 2001

Smile 2159

PSYou will need a set of DIME Tricubes.

Tiroeyb

Four tricubes make

a 3 x 2 x 2 cuboid.

Using two colours, how many different ways can you make a 3x2x2 cuboid?

How can you be sure you have found all the ^different ways?

Explain the system you are using.

Use three colours... ©RBKC SMILE 1994.

You will need Smile cut-out sheet 2160a.

What is half of a half?

• Cut out the from the cut-out sheet.

Smile 2160

Fold it in half.

Match it against the Fraction Ruler below.

of 2 = 4

1234 12 12 12 12

5 6 12 12

12345 10 10 10 10 101234 8888

1 2 6 6

3 6

7 8 12 12

9 12

10 11 12 12 12 12

6 7 8 9 10 10 10 10 10 10

5 6 8 8

4 6

7 8 8 8

5 6 6 6

12345 55555

1 2 4 4

1 3

3 4

2 3

1 2

4 43 32 2

1

Fraction Ruler

Fraction Ruler123456

12 12 12 12 12 1212345

10 10 10 10 101234 8888

1 2 3 666

7 8 9 1C 12 12 12 12678 10 10 10

5 6 8 8

4 6

1234 5555

1 2 4 4

3 4

1 2 3 3

1 2

) 11 12 > 12 12

9 10 10 10

7 8 8 8

5 6 6 6

5 54 43 32 2

1

1. Find g °f 3 by cutting out the 3, folding and matching it against the Fraction Ruler. Record your result.

Find and record

2. of 2 °f 5 4. \ of 1

Now find and record

5- lofl 6. of 1

9. What do you notice about your results?

Find these. You may be able to match your folded fraction against more than one fraction on the Fraction Ruler.

10. of 11. of 12. of 13. of

14. What do you notice about your results?

15. Work out 2 of s34

©RBKC SMILE 1994.


Folding Fractionscut-out sheet

_____ 2ifeJf^fT??-; -f s i ,: v;l:?i7v?:

, _________ _

...............

3 :'• T-io U¥ £$K 5";%;ivlS;::;;:iiiV ;;ir^ . .lv S i; H: : -V : : ^ : :- i: "'- \ : Y ̂ '.i - ;- ::"-- - : :- •; : _ ^v*****^^

_________________________2|4t:

© RBKC SMILE 2001


Shape names~i

_iB

J

Match each shape with its correct mathematical name and description.

Use a Mathematical Dictionary to check your answers.

Draw a different shape, give its correct mathematical name and write a description.

~l

Descriptions

I This shape has three sides. I It has one right-angle.

This shape has three sides. 1 None of the angles are equal. I It has no right-angle.

-I

"I

~l

~l

J

Mathematical Names

right-angled trapezium

right-angled triangle

isosceles triangle

equilateral triangle

square

scalene triangle

rectangle

This shape has two equal sides. Two of the three angles are equal.

-i

-

-

I All the angles of this shape areI right-angles.I Not all the sides are equal.

I This shape has four sides. I Two sides are parallel. I It has two right-angles.

I This shape has three sides, i The angles are all equal.

"I

I All the sides of this shape areI equal.I All the angles are right-angles.

© RBKC SMILE 2001

Smile 2162

GS You will need Geometry Facts Smile 2163.

These drawings are not to scale.

1. Calculate in degrees the size of the angle marked 'a1 .

2. Calculate the size of the angles marked 'x1 and

3. Calculate the size of the angle marked 'b1 .

Turn over

4- In this diagram what can you say about AB, AC and CD?

Use you answer to help you find the size of:

(i) AACB (ii) zLBAC (iii) Z_ACD

(iv) Z. CAD (v) Z. BAD

6.

Z_TQR = L. PRQ = 60°

Find the size of Z.SPR

5. In this diagrams

LM = MN KL = KNand also

<L LKN = 72°

Find the size of (i) AKML (ii) Z_ KLM

7.

DC = DB

Find i) AADB ii) Z_BAD iii) Z.DBC

©RBKC SMILE 1994.

Smile 2164

There are 180 students in Year 7.

1. This diagram displays the number of girls and boys in the year.

Girls Boys

a) How many girls are there in Year 7?

b) How many boys are there in Year 7?

2. This diagram displays the number of swimmers and non-swimmers.

Swimmers Non-swimmers

a) How many students are swimmers?

b) How many students are non-swimmers?

3. There are 45 students in the choir (135 are not).

Draw a diagram to display this information.

There are 144 students in Year 8

4. This pie chart displays the number of students in Year 8 who play netball, hockey or football.

How many students:a) play netball?b) play hockey?c) play football?

5. This pie chart displays the number of students in Year 8 attending school clubs.

How many students belong to the:a) music club?b) homework club?c) drama club?d) maths club?

6. At lunchtime 12 students go home, 36 students bring a packed lunch, 48 students have school dinners and 48 students go out.

Draw a pie chart to display this information. Add a key to your pie chart.

©RBKC SMILE 1994.

Smile 2166

Matching EquationsThe equation x - y = 2 matches this

graph.

P'here are several methods you can use to check.

Take 2 points on the line, e.g. (4, 2) and (1,-1) and check that they fit the equation.

Re-arrange the equation into the form y = mx + c and look at the gradient and intercept.

Use MicroSMILE program PLOTTER.

Turn over

Here are 12 equations.

4x = 2y - 8

y - 2x - 4

1 = y -2*

f -*-' La y = 2* + ^

=4

y +4 = 2x

= x - 4y +2

y =

2y =

Here are 3 graphs. Match each equation with one of the graphs.

-

/

2 -

/

/-2 -

^-- --2 -

^

qvj

— 2-

1-

1— -1-

—-2-

o

h-4J

^

— 4.

L-2-

— 1-

1-1-

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^

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— 2-

— 1-^^->

1— _1-

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/

/

;

--— -^

;

/

/2 :

> :

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?

/

/

3 *

— --

-^3 ^

Turn over

[3 Find the equation of this graph in several different forms.

-2 -1 1 2 3

-2

©RBKC SMILE 1994.

Smile 2167

The side of this square card is 21cm to the nearest centimetre.This means that the side length could be anywhere between 20.5cm and 21.5cm.

23cm • • Upper bound21.4,21.49. 21.499.21.4999.. . are all 21 cm to the nearest centimetre.These measurements get nearer and nearer to 21.5cm, so 21.5 cm is the upper bound .of measurements which are corrected to 21cm.

Lower bound20.5cm is the lowest number which would be corrected to 21cm to the nearest centimetre, so 20.5cm is the lower bound of 21cm.

19cm..

The area of the square could range from:

Largest possible area = (21.5 x 21.5) to Smallest possible area = (20.5 x 20.5)= 462.25cm' = 420.25cm'

So the range of area for this square is 42cm2 (462.25cm2 - 420.25cm2 ).

II a) Find the range of area for a square of side 16cm to the ' nearest centimetre.

b) Can you find a connection between the length of the side of this square (to the nearest centimetre) and the range of area?

c) Prove your result for any square.

Turn over.

I! a) Investigate one of these shapes.

ngles

b) Find and prove rules for your chosen shape.

H a) Find rules for shapes measured to the nearest 1/2 cm.

b) Find rules for shapes measured to the nearest x cm.

You might like to look at solids.

©RBKC SMILE 1994.

CalcW

Smile 2168

SMILE MATHEMATICSIsaac Newton Centre for

Professional Developmen108A Lancaster Road

London W11 1QSTel 071-221 8966

This cube has volume of 100cm3 -

What is its edge length?

To answer this you will need to find the cube root of 100.

This is written as >/100.

Edge

Length

1

5

Cube (Volume.)

1 X 1 X 1 = 61

5 x 5 x 5 = /25

_itoo small

too large

"\/TOO is not a whole number.

<f5

t-6

f-7

3-65

*t-5x 1-5x1-5 -91 -125

14x1-6x1-6*91tt6

1-1 x 1-1 * 1-1* J03-323

too small

too small

too large

1. Continue to use a trial and improvement method to find *\/100 as accurately as you can.

2. Use a trial and improvement method to find the edge length of a cube of volume 340cm3 , as accurately as you can.

3. Give a definition of a cube root.

This age pyramid gives information on the population of the UK in 1880 and 1980. It divides the population into six age groups and shows the percentage of the total population in each group.

40 30

UK population by percentage 1880 and 1980

20 10 10 20 30

Percentage of total population

Source: The Body Report- The Observer Magazine 1988.

Copy and complete this table. Check that your percentages in both columns total 100%.

Age

0-14

15-29

30-44

45-59

60-74

75+

Total

1880

36%

26%

/%

1980

m

20%

7Z%

Is it possible to tell from the age pyramid what the actual population was in 1880 or 1980?

Between 1880 and 1980, the 0 -14 age group almost halved as a percentage of the total population - from 36% to 19%.

a) Which age group doubled as a percentage of the population?

b) Which age groups decreased as a percentage of the population between 1880 and 1980?

c) Which age groups increased as a percentage of the population between 1880 and 1980?

This Line graph gives information about the population of the UK from 1840 -1980, by age group (in percentages).

UK population 1840 -1980, by age group (in percentages).

70

60

50

40

30

20

10

1840 1880 1920

Years

1940 1980

0-14 15-59 60+

Source: The Body Report-The Observer Magazine 1988.

a) Describe the information this line graph shows (the description of the 'Age Pyramid' may help you).

b) What types of people do these three age groups represent?

c) Describe the changes in the percentage of the population in thei) 0-14 age group ii) 15-59 age group iii) 60 + age group.

d) Why might the percentage of the population in the 0 -14 age group be decreasing?

e) Why might the percentage of the population in the 60+ age group be increasing?

f) Looking at the trend in the UK population,i) what can you infer about likely developments in the future? ii) what problems might this cause in the future?

UK population by percentage 1880 and 1980

10 00 10

Percentage of total population20 30 40

In 1880, 62% of the population were aged under 30 (36% + 26%).

a) What percentage of the population were aged 30 or over?

b) What percentage were aged under 30 in 1980?

c) What percentage were aged 30 or over in 1980?

62% of the population were under 30 in 1880. So the majority, over 50%, were probably under 23 years old.

a) Is this a good estimate? Explain your answer.

b) Estimate the age the majority of the population were under in 1980?

Use the data to write about population changes over the last 100 years.

Look at: • the percentage of people aged 0-14. Compare this with other age groups.

• the percentage of people of working age. How did this change between 1880 and 1980?

• the percentage of people aged over 75. How did this change between 1880 and 1980? What reasons can you think of to explain this change?

Smile 21702-1+

This envelope contains: A set of 24 Attribute Cards and a set of 14 Shape Cards.

The rules are on the back of the envelope.

Play the game several times.Which Attribute Cards would you most like to have dealt to you? Which Attribute Cards would you least like to have dealt to you?

Pick one of the shapes.Draw the shape and write its name.Describe the shape using all the Attribute Cards which apply.

Up,2 -

PMffllwM^lHIillS^^^^^W^Ri

iiili^iiiiiiiiiii

© RBKC SMILE 1994.

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Up,Smile 2170a

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These cards and those from Smile 2170b and 2170c should be cut out and kept in the envelope Smile 2170.

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These cards and those from Smile 2170a and 2170c should be cut out and kept in the envelope Smile 2170.

Smile 2170cThese cards and those from Smile 2170a and 2170b should be cut out and kept in the envelope Smile 2170.•v

•

•

I I

ri

Only two sides are

equal.

k

4 right angles.

The diagonals cross at

right-angles.

i

One pair of opposite

angles are equal.

j

3 lines ofsymmetry.

l

One reflex angle.

r

All sides are

different.

I

Only two angles are

equal.

Opposite angles are

equal.

One line of

symmetry.

2 lines ofsymmetry.

Adjacent sides are

equal.

All angles are

equal.

One pair of sides

are parallel.

3 sides.

1

Opposite sides are

equal.

j

Nodiagonals.

T

No lines of

symmetry.

r

One right-angle.

i_H i

All angles are different.

••"

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4 sides.

-i

At leastone

obtuse angle.

4 lines of

symmetry.


Pie Chart MatchCut out the pie charts and percentages and match them to the statements on this table.

Statement

5 in 100 women between 25 and 44 years old live on their own.

Source: General Household Survey 1990

One third of the world's surfaceis land.

(Atlas)

26 out of a pack of 52 playing cards are red.

9 out of ten eggs for sale in Britain come from battery hens.

Source: Compassion in World Fanning 1992.

15 in 100 people in the UK are pensioners.

Source: Keydata 1991-1992.

Just under half of households in Inner London have a car.

Source: Guardian report on 1991 Census.

Two thirds of the water used in the home is flushed down the toilet.

Source: Independent 31/5/92.

By 1 990, a quarter of the petrol delivered to petrol stations each week was unleaded.

Source: Digest of Environmental Protection and Water Statistics 1991.

Approximately 70p in each £1 of Health Spending is used in Hospital Services..

Source: Regional Trends 1992.

Approximately 4 in 5 households do not have a computer.

Source: Keydata 1991-1992.

Pie Chart

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Percentage,^' : i i •

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• ^

66.6%

—H50%

70%

_____!

46%

25%

15%

90%

80%

33.3%

^

© RBKC SMILE 2001

Smile 2172

This envelope contains:;1 playing boardA set of 32 number cards,

for 2 players.

• Share the cards equally. •• ...

• Take turns to put down 2 cards at a time on the board,

• Cover any 2 numbers so that the sentence stays true.

Two Down11111111- More Than

Smile 2172a

Turn over for Gam© 2

• Leave the cards on the board and continue playing.

• The first person to finish all their cards wins.

• For each game write down the final winning sentence.

^

Two Down Smile 2172a

- More Than

7 is 3 more than 4Turn over for

Two DownSmile 2172b

These cards and those from Smile 2172c should be cut out and kept with the playing board Smile 2172a in the envelope Smile 2172.

11

5

6

1i-----------------

V

5

6

2

3

7

3

2________________

o

7

3

Two Down Smile 2172c

These cards and those from Smile 2172b should be cut out and kept with the playing board Smile 2172a in the envelope Smile 2172.

7>

8

9

1

7t----------------

8

9

4

8

9________________!

2

4

8

9

2

3


The Modes#

The mode is a type of average.The

modeis the

most frequentvalue.

Favourite Colours• Blue

D White

0 Green

D Yellow

m Red

Blue is the most popular colour so blue is the mode.

NameCarolKennyMohammedRaziaHannanIshmae!KimBernadineJackFaisal

Height160cm156cm156cm154cm150cm150cm150cm146cm146cm143cm

Frequency1

2

1

3 -4-

21

The most frequent height is 150cm, so 150cm is the mode.

1. A tally chart has been made to record the letters used in this piece of text taken from William Shakespeare'sMacbeth (Act IV Scene 1).

Complete the chart by filling in the frequencies.

Double, double toil and trouble: Fire, burn; and, cauldron bubble. Fillet of a fenny snake, In the cauldron boil and bake; Eye of newt, and toe of frog, Wool of bat, and tongue of dog, Adder's fork, and blind-worm's sting, Lizard's leg, and howlet's wing For a charm of powerful trouble, Like hell-broth boil and bubble. Double, double toil and trouble: Fire, burn; and, cauldron bubble.

Letter

Tally

Frequency

A

mmmn m

22

B•1-1-

m mi m

24

cfill

4

D•1-1

mil m

22

EMM

m28

F

mm mi14

G-Wf

I

6

H

m

5

I-1

m in

13

J

0

K

llll

L

W-fflrm ,„• m m

MII

Letter

Tally

Frequency

N Q V W

What is the most frequently used letter in this piece of text?

Letter ___ is the mode.urn'over

2. Throw a dice 18 times.

a) Record your results on this tally chart.

Dice Number

1

23456

Tally Frequency

b) Display your results on this pie chart. Complete the key.

Key 12

3

4

5

e

n

c) Which dice score is the mode?.

H 3. Here are the results for Kudeza's matrix.

Card No.

0694;

029413530220175002910623

10691

Test Mark

66

101075

10101010

Which test mark is the mode?.

| 5. Do a survey of yourI! class to find in which| month people werel/; born.

H Use this grid to displayji your results.

Which month is the mode?

4.

Take a handful of centicubes or counters.

Which colour is the mode?

Frequency

-^tV>COJi.OlO>-~JOO<DC

JFMAMJJA'SOND

Months

pi

I

© RBKC SMILE 2001

ypooig OaHSmile 2175

SMILE MATHEMATICSIsaac Newton Centre for

Professional Development108A Lancaster Road

London W11 1QSTel 071-221 8966

Take your pulse for one minute. This is your pulse rate.

To feel your pulse place two fingers here.

1. Find the pulse rate for each member of your class,

a) Record this data in a table.*

'Pulse rate

Tally

No. of pupils

50

II

I

51

0

51

III

3

53

/

/

You will need to collect at least 20 pulse rates. If this is not possible the Answer Book contains data from one year 9 class.

b) Display this information in a bar chart.

5 3o

50 51 52 53Pulse rate

For this set of data:

80, 0, 4, 0, 1, 2, 1, 2, 1, 6, 2, 2, 3, 3, 5, 3, 3, 1, 7, 1, 6, 6,1, 8,10,10, 4, 0,90

The range The difference between the highest and the lowest value (highest value - lowest value).

So the range of this set of values is 90. (90 - 0.)

There are three main types of average:

Th

Tf

e median The middle value after the values have been arranged in order of size.

0,0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2,3,13,3,4,4,5,6,6, 6, 7,8,10.10,80,90

middle value

ie median of the set of values is 3.

Th

Th

e mode The most frequently occurring value.

0, 0, 0, Illlllllllll 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 6, 6, 7, 8,10,10,80,90

most frequent ,e mode of this set of values is 1.

The mean The sum of all the values divided by the number of values.

0+0+0+1+1+1+1+1+1+2+2+2+2+3+3+3+3+4+4+5+6+6+6+7+8+10+10+80+90 _ 262

The mean of this set

29 29

of values is 9.03 to 2 d.p.

Look at your pulse rate data.

2. a) What is the range ?b) What is the median?c) What is the mode?d) What is the mean?

3. Use your original data to draw two further bar charts:

a) with pulse rates grouped in 5's

Q.3 Q."o

(5

50-5^ 55-5? 60-6H Pulse rate

b) with pulse rates grouped in 10's.

50-5? 60-6? 70-7? Pulse rate

Turn over.

4. Look at your three bar charts.

For each chart, look at the information you have displayed. Can the range, the median, the mode and the mean be found for each chart?

Explain how.

5. Which bar chart gives you the most useful information?

Give your reasons.

©1994 RBKC SMILE.

Smile 2177

Use the graph opposite to answerthe following questions about the projected populations of three regions, North America, Latin America and Europe.

1. Which region had the largest population in 1988?

2. The population of Latin America in 1988 was approximatelyl 430 million. What was the approximate population of North America in 1988?

3. Approximately how many more people were there in Europe than there were in North America in 1988?

4. Look at the graph for the projected population of Latin America.

a) What is the projected population for the year 2000?

b) What is the projected population for the year 2010?

c) What is the projected increase from 2000 to 2020?

5. The populations for the year 2020 are projections. If these trends for 2000 to 2020 continue:

a) What will the projection for each region be in the year 2040?

b) Write a few sentences about the trend in the population for these three regions.

Estimated and Projected Population (minions)

-800

-100

-600

500

Q. O

Q.

100

North America

Latin America

Europe

1990- ZOOO-I I I Z070-i i i1988

ZOZO-I I IYear

Source : 1988 Population Concern.

quietly allows others to do the same.

doesn't mean telling someone the answer.

When you can explain by [I RLKJNCj to someone, then youreally understand.

Working on your own is one way,but "TftllitNQ and sharing ideas

usually helps.

In this classroom

about your work is encouraged.

©RBKC SMILE 1994. Smile 2176

VolumesSmile 2178

You will need Smile Worksheet 2178a and some centimetre cubes.

This is acentimetrecube.

It has a volume of 1 cubic centimetre. (1cm3)

Each layer is made of 6 centimetre cubes.

2 layers make this cuboid.

It is made of 12 centimetre cubes.

It has a volume of 12 cm3.

Each layer is made of 6 centimetre cubes.


What is its volume?

Fill in the table on the worksheet for cuboid B. Cuboid A has been done for you.

Turn over.

Each layer is made of 10 centimetre,cubes.


Fill in the table for cuboid C.

Fill in the fable for cuboid D and cuboid E.

Complete the rest of the worksheet.What do you notice about the numbers in your table?

©RBKC SMILE 1994.


Cuboid

A

B

C

D

E

F

G

H

Number of cubes in one layer

6

6

10

Number of layers

2

5

Total number of cubes

12

Volume

12cm3

Try drawing lines to show the layers on the cuboids [0 [G] and [Hi. •

© RBKC SMILE 2001

Shakes and Adders Smile 2179

A game for 2 players.

• Take turns to roll the 3 dice.

• Add or subtract the three numbers in any way you like. The answers can be positive or negative.

• Cover your answer with a counter.

With these three numbers you could cover:

111 [2 + 4+5] or I-3J [4-2-5] or I 3 1 [2 + 5-4]

[5-4-2] or f-7J [2-5-4] or. . ?

• You may cover only one number in any go.

• Only one counter may be placed on each square

• The winner is the player who covers the most

©1995 RBKC SMILE.

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