Rabotna tetratka 5 odd

2nd edition

Name:

Nelson Internat;onalMathemat;cs~XiOOl!x!fll ~

Task done TaskdonePage ./ Page ./

\-2~ Beyond 999 4 0 Ii• Locating decimals on...3Ca number line 24

~~ What is it worth? 5 0 It.Units of length 25 ("""1\..__){~aRounding to 10 or 100 6 (_)

It • Measure in different units 26 r=>;~

~3 Rounding to 1000s 7 0~-~. Measuring scales 27 ("""1

<::.~

Using inverse operations 8 0~. Comparing scales 28 C)

(.2a Order of operations 9 0~2a Counting in steps 29 0\2a Missing operation signs 10 0 '\29 Adding and subtacting

\2.8 0 ~-I'Working in order 11 by counting in groups 30 ',---,

~2-: Are they the same? 12 0 \.2-: Position on a grid 31 r=>:ii'3 .a L__,

". Finish the shapes 13 0 \;.23 Multiplication facts 32 0;r.-

~. Symmetry in polygons 14 0 \29 Division facts 33 0iii-

~. More symmetry 15 0 \-23 Factors 34 "L__"~-~. Symmetry patterns 16 0 \-2-, Divisibility rules 35 r=>('3 L__,

If". Spinning logos 17 0 rlrt Different scales 36 U'" ". National flags 18 0 rlrJ Show choices on

0~:. Classifying triangles 0 a pictogram 3719

~ •• Showing time on(t2a Positive and negative~-

0 numbers 38 Cdifferent clocks 20\29 Temperature changes 39 r=-;

". Holiday activities 0 L_.,21 ~.

~. Looking at parallel lines 40 r-'~. Units of time 22 0 ~

It • Parallel and perpendicular\.2a Making decimals 23 0 41 Clines in real life

Contents

Taskdone Task donePage ./ Page ./

Ii • Angles 42 0 \2a More division 62 r=>~- \...__)

~ • Angles on a straight line 43 0 \-2' The sawmill 63 r--I,.3 \..__j

(2~ Equivalent fractions 44 0 t2~What willyou do with'1i'l3 ("3iOl-the remainder 64 r=>

\.2a \...__)More equivalent fractions 45 0

\2~ -r. Shapes and nets 65 0Improper fractions and\2amixed numbers 46 0 Birdwatching 66 0~-

~aName the fraction 47 0 (..2~ Colour the correctf3proportions 67 I")... 0 '-._/

"l. Perimeter 48<~~Ratio 68 0

". More perimeter and area 49 0 (r2a Recipes and proportions 69 C(r2a Multiplying by 10 and 100 50 0 10-

\-2- Bubble percentages 70 rr>.

~~i"3 L_)

Mulitplying and dividing~~by 10 and 100 51 0 Problems involving

~('~3percentages 71 0

Doubling and halving 52 0 (r2~ Percentages, decimals~~. Reflections 0 a

53 and fractions 72 0It". Translated shapes 54 C) \.2a Equivalent fraction wheels 73 C~.aPairs of decimals that \2a Ordering equivalent

make 1 55 0 fractions 74 0Ct2.., Making lOs 56 0 flrt Likely and unlikely events 75 013\2JJ Decimal puzzles 57 0 \2a Choose your method 76 0r.-~2'" Frequency tables 58 0 '~.aFind the area 77 C",3

Bar line graphs 59 0 t Multiplying decimals 78 0r2a~-More line graphs 60 0 \2('3 Work out the mass 79 C

\.~Mental division strategies 61 0 ...2a Mixed calculations 80 rro- ,__.J

Contents

see Student Book page 6

II Calculate in your head:

a 43 188 + 100 4-3288 b 43188 + 1000 - 4-4-188c 43 188 + 10000 53188 d 43188 100 - 4-3088e 43 188 1000 4-2188 f 43188 10000 331889 34347 + 200 34- 54-7 h 34347 + 2000 3634-7• 34347 + 20000 54- 34-7 • 34347 200 34- 14-7I Jk 34347 2000 3234-7 I 34347 20000 14-34-7m 20000 + 100 - 20100 n 30000 + 1000 31000o 50000 + 10000 60000 p 20000 100 Ig gOOq 30000 1000 - 2g000 r 50000 10000 4-0000

Number Ten thousand Thousands Hundreds Tens Units10000s 1000s 100s lOs ls

12350 • • • ••• • • • • •

58016 ••••• •••• • • •••••••••22483 •• •• • ••• • ••• • ••••••18095 • •••• ••••• ••••••••• ••••73812 ••••••• ••• • ••• • • •••••82743 •••• •• ••••••• • ••• • ••••••69741 •••••• • •••• • •••••• •••• •••••12694 • •• •••••• • •••• ••••• •••93621 ••••• ••• •••••• • • •••••21762 •• • ••••••• •••••• ••

o Complete the chart. Draw dots to represent thenumber for each place value. The first one has beendone for you.

Beyond 999

Write in words what each underlined digit is worth.

0 125609 D 125609

six hundred nine uni ts

D 58463 II 58463

six tens four hundred

0 58463 D 752186

itfty ihou.sa.n,d. itfty ihou.sa.n,d.

II 752186 II 752186

eigh.t tens seven, hundred th.ouscnd

0 837612 IE 627141

th.irt~ thousand six h.u.n,d.red.thou.send

m 766431 179487

four h.u.n,d.red. one h.u.n,d.red. thousand

H.Th T.Th Th H T U

1 2 5 6 0 9

The digit 5 is worth five thousand because of its positionin the number.

122609

What is it worth?

IIA newspaper reported that 1300 people attended a cricket match.

a If this number was rounded to the nearest 10,what is the smallest and greatestnumber of people who could have attended? 12Cf5/12CfCf

b If this number was rounded to the nearest 100,what is the smallest and greatestnumber of people who could have attended. 1250/134-Cf

c Tell your partner how you worked out your answers. Discussion.see Student Book page 9

Number To the nearest 10 To the nearest 100

369 370 4-00

481 4-80 500

1402 14-00 14-00

8492 84-CfO 8500

6445 64-50 64-00

2569 2570 2600

1385 13CfO 14-00

8884 8880 8CfOO

5495 5500 5500

7783 7780 7800

(2~ G;?)258

256244 241

(2~259

o Circle the numbers that round to250 when they are rounded to thenearest ten.

II Circle the numbers that round to1500 to the nearest 100. 1569 1416

1575 1590

D1439

Roundeach number to the nearest10 and to the nearest 100.

Rounding to 10 or 100

...........5000

40001790

58235459

7000 -r---=61=29:-- ....................___6-95---=5

3125l------H- 3000

1250800

9160

8000 """';'---C7500

2263

8350 2863

1000

9000 .__+--_-+-!-8978

Round each number to its nearest thousand.

Join it to its nearest thousand with a line.

The first one has been done for you.

Rounding to 10005


tru.efalse

1656 .;-Ci - 18lt-228 x 6 - 13lt-lt-

184 x 9 = 16561344 -;-6 = 228

false

7 x 25lt- - 778

778 -;- 254 = 7

true

25 x 13 - 325

325 -;- 13 = 25

true

A2 x 8 - 5Ci36

5936 -i- 8 = 742

true

true

3664- + 1086 = 4-750

false

522 - 3lt-lt- - 178

178 + 344 = 52298 -;- 4 = 21

IJ

o

o fJYou can use a calculator to help you.

True

_--_divideinverse

_--_ subtract

multiply

add

15 x 3 = 45

45 -;- 3 = 15

inverse

For each number sentence, check whether it is true orfalse. Write the inverse number operation to check. Thenwrite true or false. The first one has been done for you.

Using inverse operations

D Swap with a partner. Work out the answers to yourpartner's calculations. Own. work.

f __e __d __

c __b __a Own. work.

o Make up six calculations of your own. Make sure thereare at least three steps in each one.

Order of operations

0 For each calculation:• circle the part you would do first• underline the bit you would do second• work out the answers.

a {W-2}-3 b835 10

c@-9)x 24-6 66 d 144~ 102

e 10+7-8 5 f€:)-2

9 5-€ 7D 0 h 1573-6+ 2} 0

i€l_@ 0 j 7-€3> 3

k0-17 18-3 6

m4X2-E:}) 0 n 2+2+8 8

oGx~@ 2 p~x@O : 2)7 11 10

q 2XO+5 II r€+~~(; 2D 6

s (99 +22JL11 II t 87([l'6'-14}1 3


D Use <, > or = to make true statements.

a (8 + 7) X 5 > 8 + 7 X 5

b 7 + 2 X 4 < 5 X 2 + 6 Remember:

c 5 X 9 3 < 8 + 4 X 8 > means 'greater than'

d 23 12 6 > 2 + 6 X 3 < means 'less than'

e 5 X 5 5 - 5 5 X 5 = means' equal to'

f 36 12 3 - 24 12 . 2

II Put in the brackets to make these statements true.

a 5 X ( 7 3 ) - 20b 28 (13 6) - 21

c (6 5 ) X 12 - 12

d (38 23) + (17 12 ) - 10

e 48 (12 + 6 X 6) - 1

f (23 18 5 ) X 7 - 0

g (5 X 6) (13 10) - 10h 8 X (7 2 ) - 40

Missing operation signs

0 Put in the operation signs (+, -, +, x) to make thesenumber sentences true. Youmay also need to usebrackets.

a 2 + 3 [J 4 =1 b 2 0 3 4 =2

c 2 [J 3 8 4 =3 d 2 0 3 8 4 =10

e 8 0 3 [J 2 = 22 f 8 0 (3 8 2 ) = 40

g 8 0 3 [J 2 =12 h 8 [J (3 0 2 ) =2

• 8 [J 3 0 2 =10 • 8 G 3 [J 2 =9I J

D Draw a flow diagram (on a separate piece of paper) to Own work.teach someone how to work in the correct order in maths.

e 80 - 5 - 5 - 5 - 5 - 5 - 5 = 80 - (5 + 5 + 5 + 5 + 5 + 5) _t_ru_e. _

f 64 7 2 7 2 7 2 7 2 7 2 7 2 = 64 7 (2 x 2 x 2 x 2 x 2 x 2) _t_ru_e. _

fa.lse.

fa.lse.

true.

true.a (100 + 10) + 2 = 100 + (10 + 2)

b (100 x 10) X 2 = 100 x (lOx 2)

c (100 - 10) - 2 = 100 - (10 - 2)

d (100 7 10) 7 2 = 100 7 (10 72)

D Write whether each statement is true or false.

n 27 - (1 4 - 8) = 21m lOx (6 + 4) = 100

1(6 - 3)x 2 = 6k (7 + 10 - 5) 7 2 = 6

j 12 + 6 7 (7 - 4) = 14i 5 + 2 X (3 + 7) = 25

4) X 5 = 30h (109 (6 + 6) X 3 _ 36

8) - 6 _ 2f (64e (18 + 9) . 3 = 9

4) + 1 _ 6d(20e 20 7 (4 + 1) _ 4

b (16 - 7) X 3 = 27a 9 X (2 + 3) = 45

o The answers to these calculations are correct, butthe brackets have been left out of the problems. Addbrackets to make each number sentence true. Somenumber sentences might not need brackets.

Working in order


D Choose four digits of your own. Use brackets andoperations as in question 2. Use the space below tomake as many different numbers as you can.Choose one of the numbers you have made. Can youmake it in more than one way using the same fourdigits?

Own. work.

II Fill in the operations and brackets to maketrue statements.

a (7 + 3) x 5 4 = 46

b 7 x 3 + 5 4 = 22

c (7 3) x 5 + 4 = 24

d 7 3 x 5 x 4 = 80

e(7 + 3 ) x 5 x 4 = 200

Are they the same?

0 Here are some pairs of expressions.

Write whether each pair gives the same or adifferent result.

a 2 + 3 X 4 and 3 x 4 + 2 same

b 2 X 12 3 and 12 . 3 x 2 sa.me.

c 50 - 25 - 5 and 25 5 - 50 eliffe.rem t

d 25 X 4 - 8 and 8 - 25 x 4 same

e 25 X 4 5 and 5 25 x 4 eliffe.rem t

11 • II • II • •• • • • • • • •

• • • • • • • • • • • • • •• • • • • • • • • • • • • • •• • • • • • • • • • • • • • • •• • • • •• • • • •• • • • • • B • • • • • • • • • • • •• • • • • • • • • • •

• • • • • • •• • • • • •• • • • • • • • • • •

• • • • • • • • • • • •• • • • • • • • • • • •

••••••••••••••••••••••••••

•• •••••

•••••••••••••••••••

Finish the shapesThese shapes are only half-drawn. Own. work.Use the spots to complete the shapes. O· • • • • •Write what shape you have drawn on • • • • •the line under each shape.

• • • • •• • • • •• •


Pen ta.goY\,Square•

Sq.u.a.re (a.ccept rhombus a.s well)

D

II

II

D

oWrite the name of each polygon.Draw at least one line of symmetry on each.

Symmetry in polygons

o

o

II

D

II

o•mirror.

You can check with a mirror. If your line of symmetry iscorrect, you will see the other half of the shape in the

On these shapes, draw any lines of symmetry in differentcolours.

More symmetry


;- ~ --~ --

-, -"""Y-~I\ V

l(:-1-- -I- -- '" ~I--

t I: I I

I 1- ~I +~

1- - +- t- + ~• • • •I--- ~ ~• • • +- + .,_

I, ,

+- 1- + + +- +-I

[ tI--

+ r t i I t+

!

Draw your own symmetrical patterns using these lines ofsymmetry. Own. work.

~ f f-T T r--

l-tt-t r t I ! If'- ',+ n +- - -,+

,t- -0 Tt rI I I I f

c--I ~ 0-'----'

,- ._I.- ---

-- I-- -

I"- - -

I"- -- -

l"-I' liT- .U....~ ~ ~ ~ -,

t~ ~ ~ : +-I , '+ t ~ ~ +- +- ~ 1 t r

;_j_T

~ •

Complete each pattern so it is symmetrical about both linesof symmetry. Own. work.

Symmetry patterns

EJ Design a logo for your class. Decide what order ofrotational symmetry it should have. Draw it here.

Own. work

3 2dc

7

Many common shapes and patterns have rotationalsymmetry.

o What order of symmetry do these have?

a b

Spinning logos

lines 2-==--------order 2-=-------

Thailand

lines 2--==-------order 2-=-------

Batswana

lines 2-==--------order 2-=------

England


lines 4-___:------order 4-_:_------

Switzerland

lines __:_------order~ __

Canada

lines 2-=------order 2-=------

France

D

lines 0---'------order 2-=------

Trinidad and Tobago

II

lines 2--=------order 2-=------

India

II

lines 0--=:.__-----order I-=-------

Australia

DoFor each flag below, write the number of linesof symmetry and order of rotational symmetry.

The flag of Jamaica has two lines of symmetry.If it was lifted and rotated about its centrepoint, it would fit into its own outline intwo different positions. So it has rotationalsymmetry of order 2.

National flags

Second. one is fue odd. one ou t as it is fue only one fua t is acu te angled.

Tlurd one is od.d.one ou t as it is th.e only one th.a t is not isosceles

Second triangle is odd. one ou t as it is fue only one fua t is e.a._u.ilateral

Th.ird. triangle is odd one out as it is obtu.se-angled. (not righ.t-anglecl)

o Write a sentence saying why the coloured one does notfit with the others in the set. Some possibleanswers are:

o Colour the odd triangle out in each set. You may needto measure the sides and angles to help you decidewhich one is the odd one out. 0 ..Lwn won.

Classifying triangles


• •five to eleven at night I ••,

• •twenty-five to five in the afternoon

quarter to one in the afternoon

quarter past four in the afternoon

half past ten at night

seveno'clock in the morning

· ..quarter to eight at night

• •three 0/clock in the afternoon

lr .1-11-11:1 • 1_11_1

· ..half past eight in the morning

1-11-1 • -11-11_11:1 • :11_1

In words

The first three have been done for you.

Complete the chart to give the times in words, as a.m.and p.m., and in 24-hour notation. Remember that24-hour time always uses four digits.

Showing time on different clocks


. ..-

Ju.do 10:00 - 11:30 OR Archery 10:00 - 11:30T a.rget sh,ootin,g 08:4-5 - 0C!:4-5Su.rfin,g 06:35 - 08:35Th,ree ac tivi ties rnaximurn:

D Write down how many of the five on your list you would beable to do in one day. Explain how you worked out your answer.

Pa.in,tin,g 0C!:30 - 12:00T a.f'get sh,ootin,g 08:4-5 - 0C!:4-5RLdin,g08:30 - 10:00

Archery 10:00 - 11:30Su.rfin,g 06:35 - 08:35.ludo 10:00 - 11:30HLkin.g06:00 - OC!:OO

o Choose five different activities from the list. Write thestart and finish time for each one. Use 24-hour time.

Start time Activity Length of time in hours

6.00 a.m. Hiking 3

6.35 a.m. Surfing 2

8.30 a.m. Riding 1~

8.45 a.m. Target shooting 1

9.30 a.m. Painting 2~

10 a.m. Judo 1~

10 a.m. Archery 1~

12 noon Lunch 1

On a holiday camp, there is a very full programme ofactivities to choose from. These are the activities on offerin the morning:

Holiday activities


D How many days in?

a 1 week 6 days 13b 3 weeks 21c this year plus next year 730 (731 if one of th.e years is a.lea.p year)d the first six months of the year 181(cou.nt th.e actucl d.a.ysper month.)e the last six months of the year 18Lr

b 8 weeks = 56 days

d There are 52 weeks in a year

f 91 days = .!lweeksh 16 weeks is about 4- months

j 1 year = g_ months

I 20 years =24-0months

n 84 months = ]_ years

o Complete.

a There are l_ days in 1 week.

c 35 weeks =~5 days

e 84 days = R weeks

9 175 days = 25 weeks

i 8 months is about 32 weeks

k 5 years = 60 months

m 36 months = j_ years

o 66 months = 5t years

month.

week

h.ou.r

minu.te

second.H 0 U R Q y L

S E L W E E K

B P F X 0 A y

A J Y H C R N

M I N U T E G

M 0 N T H R W

T S E C 0 N 0

a Find the units of time.

b Write them in order from the shortest to the longest.

o There are seven units of time hidden in this wordsearch.

Units of time

Shaded 0.99Unshaded 0.01

Shaded 0.09Unshaded O.CjI

Shaded 0.9Unshaded 0.1..=..:.:..-

Shaded 0.07Unshaded 0.Cj3



Shaded 0.55Unshaded 0.4-5

Shaded 0.05Unshaded 0.Cj5


Shaded 0.9Unshaded 0.1--=.:.:._



Shade each shape to show the decimal fraction.

Write a decimal to show what fraction of the shape is unshaded.Va.riOu.s sha.ctin.a 0' tion.s are possible. Allow th.e stud.en ts to check each. oth.er-'s work.

1- ,

Making decimals


c 2.5 8J 2.9

f 0.33 ~ 0.3e 0.09 ~ 0.1d 0.7 ~ 0.69

II Fill in < or > between each pair of decimals. Use yournumber lines to help you decide.

a 0.3 8J 1 b 0.05 8J 0.5

o O.B 0.5 1.1 0.2 0.7 0.1

II 0.1 1.0 1.5 2.3 4.4 5.B

o 0.55 0.09 0.03 0.33 0.75 0.99

II 21.35 21.39 21.51 21.64 21.69 21.72

21.721.621.521.421.3

21.6<1 21.72, , • I , - "

21.35 21.3<1 21.51 21.64--, , , I' , , ,+, , '-II' , , I , , , , 1-' , , I , , , , I' , '-I'

0.03 0.0<1 0.33 0.55 0.75 0.<1<1111_11111-11111111111111111111111_111111111111111111111+1111111111111111111+11111111111111111111111-1 )o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1 1.0 1.5 2.3 4-.4- 5.8'1_11111111+1111+1111111_11111111111111111111_1111111111111_11"o 1 2 3 456

o

0.1 0.2I '

1.1---- 0.7 0.80.5--

Mark and label each set of decimals on the givennumber lines.

Locating decimals on a number line

Metres Millimetres1 10008 800015 1500027 27000112 112000

Centimetres Millimetres

1 107 7015 15067 670189 18etO

Metres Centimetres1 1009 etOO28 280098 et800150 15000

Kilometres Metres

1 10005 50007.5 750012 12000135 135000

Complete the tables by filling in the equivalentmeasurements.

Units of length


Item In millimetres In centimetres

the length of my thumbnail Own.wort.

~

span of my left hand -

length of my shoe

length of a pair of scissors

length of a pencil

width of this book

height of a coffee mug

length of a stapler

width across a pair of spectacles

length of a belt

Measure each item and write the measurement in twodiHerent ways.

Measure in different units

100g

3S0g

400 grams

It-Ocm

o o1kg

I009~7509/ ikg

7S0g

200

40em2Semo200ml120ml

120mlSOem25cm50ml

SOmlo

1

1.4 litres

---.--21

111

D Draw arrows on each scale to show thegiven measurements.

4S0ml~ litre

o

--+-400

TSOOml-,-1 l

a b 1 I

1 ~

0 159 809 100g

500mlI e

e f 9 or 2l

1 1 1 250ml dI0 lkm 2 2.5km 3.5km 4km or I;. l

0

0 Draw more liquid in each jug to show thegiven measurements.

o The arrows represent measurements on each scale.Estimate what each measurement is. Possible. estima te.s are:

Measuring scales


_5°( _5°(

I j, I I j, I-10 0 10 20 30 40°C -1 0 0

40353030

Oml10o 40 50ml3020

~ It-5ml

It-5mlI j, I

100ml

4kgo3kg2

2.lt-kgj,

2

5m3 44m 23

3.lt-mj,

3.lt-m

I t I

1.2l 1.2lIj, I I I 1--1---II--t.%.....__---II1 2 3 4 5l 0 1 2l

Io

o 400 600g200500go

It-50gIt

45ml

2.4kg

3.4m

1.21

450g

Draw arrows to show where the given amount would showon each scale

Comparing scales

Explain how you answered these questions.

Would he count 198?

Would he count 387?

Stu.d..en.t'5 to discuss th..eproblems in. grou.psWould he count 182?

Pete counts in fives from 132 to 500. Try to answer thesequestions without actually counting.

-30-15o1530lr5I Count back 160In 15s

Count on 205 220 235 250 265 280 2ct5in 15s

Counting in stepsCount on or back in the given steps to complete each set ofnumbers.

When you have finished, use a calculator to check youranswers.

I Count on156

68 80 ct2 104- 116 128in 12s

I ~ount back 136 2lr 12 0 -12 -2lr -36In 12s

I Count on120

31 lr2 53 6lr 75 86in 11s

I Count back 188 77 66 55 lrlr 33 22In 11s

I Count back 186 75 6lr 53 lr2 31 20In 11s


8999

-7000+ 1-8 -40 -800

r\n1034

-500-3 -4 -50 -30

Mf\n1034 - 587 = 0 lrlr7 9000 - 7848 = 01152

708 746

-300-3 -6 -40

nnf\746 - 349 = 03C17

92

+2

~

+80+10

n184 - 92 = 0Cl2

7122

+ 100 +20 +4

(\(\~+ 1000

1124 + 7122 = o 82lr6

1245

+60 + 10 +6

(\(\(\+800

876 + 1245 = 02121

612

142 + 612 = 0 75lr+ 100

-500-10 -8

{\~708 - 518 = OIClO

77

-3+20

94-77 = 067

3109

+90 + 1+7

(\(\(\3109 + 1098 = 0 lr207

+1000

762

+40 +40 +8+ 1

(\(\(\~+ 100

762 + 189 = 0Cl51

318

+40 +2+5

(\+ 100+100

247 + 318 = 0565

Write the answers to each calculation.

Fill in the missing numbers on each number line.

Adding and subtracting by counting in groups

s


o A(l, 10),8(4,7), C(l, 7) tria.n.gle

0 0(12,10), E(14, 10), F(14, 3) G(12, 3) rec ta.n.gle

0 H(8, 10), 1(11, 7), J(8, 4), K(5, 7) square~

II L(2, 1), M(6, 1), N(6, 3) 0(4, 5), P(2, 3) pentagon.

0 Q(9, 3), R(9, 0), 5(13, 0) triangle

Write the name of each shape.

Draw lines to join them up (in order).

Plot and label each set of points.

00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15xR

1 5

2

4-l

p3

4

8

7 C K -1- -B 2

6 I0

5 I

9

y10 A D--t----e-EPosition on a grid

see Student Book pages 49 and 50

Test 1 Test 2 Test 34 X 5 = 20 2 X 10 = 20 2 X 10 =203 X 8 = 24- 1 X 8 = 8 9 X 9 = 819 X 2 = 18 4x4 = 16 9 X 8 =721x9=Cl 3 X 6 = 18 10 X 9 = ClO4 X 6 = 24- 7 X 10 = 70 4 X 3 =123 X 7 = 21 3 X 9 = 27 5 X 9 =4-52x7=14- 8 x9 = 72 8 X 6 =4-85 X 5 = 25 5 X 3 = 15 5 X 8 =4-02x8=16 9 X 4 = 36 9 X 3 =279 X 3 =27 7 X 5 = 35 6 X 7 =4-26 X 5 = 30 10 X 9 = ClO 5 X 4 =2010 X 7 =70 8 x8 = 64- 1x9=Cl7 X 6 = 4-2 7 X 7 = 4-Cl 8 X 4 = 323 X 9 = 27 9 X 9 = 81 6 X 9 = 54-5 X 8 = 4-0 6 X 8 = 4-8 6 X 7 =4-24x9=36 10 X 6 = 60 7 X 8 =566x6=36 7 X 9 = 63 4 X 9 =365 X 10 =50 9 X 6 = 54- 6 X 5 = 306 X 9 = 54- 8 X 5 = 4-0 6 X 10 =602x3=6 9 X 7 = 63 4 X 9 =36Time: Time: Time:

Time how long it takes you to complete each test.

Write the answers only.

Use these tests to check how well you know your multiplication facts.

Multiplication facts


Test 1 Test 2 Test 31672=8 21 73=7 1274 = 33073 =10 36 7 4 = CJ 32 7 8 = lr247 8 = 3 907 9 = 10 2779 = 327 73 = CJ 2474 = 6 807 8 = 1045 7 5 = CJ 81 79=CJ 64 7 8 = 881 7 9 = CJ 2575 = 5 4878 = 625 7 5 = 5 15 7 3 = 5 4575 = CJ2474=6 64 7 8 = 8 5678 = 748 7 6 = 8 18 7 6 = 3 1272=6507 5 = 10 4276 = 7 28 72 = Ilr7279=8 63 7 7 = CJ 727 8 = CJ4878=6 2074 = 5 357 5 = 7307 6 = 5 4977 = 7 871 =835 7 7 = 5 7279 = 8 3676 =66478 = 8 5075 = 10 1472 = 76379 = 7 5479 = 6 1879=2547 6 = 8 16 7 2 = 8 48 7 6 = 8247 8 = 3 28 7 7 = lr 36 7 9 = lr90 7 10 = CJ 36 7 6 = 6 48 7 6 = 821 73=7 35 7 7 = 5 5479 = 6Time: Time: Time:

Time how long it tokes you to complete each test.

Write the answers only.

Use these tests to check howwell you know your division facts.

Division facts


Factor 1 3 4 5 6 7 8 8

Factor 8 q 8 q 7 7 8 qProduct 8 27 32 45 42 49 64 72

Product 12 18 36 48 30 100 90 81

Factor 1 9 6 6 5 10 9 9

Factor 12 2 6 8 6 10 10 q

D Complete these tables.

~

1 60

2 30

3 20

Lr 15

5 12

6 10

~

1 Lr2

2 21

3 14-

6 7

~

1 36

2 18

3 12

t, q

6 6

3ILr22

7

28

6

~

1 56

2 28

i, 14-

7 8

18

o Find the factor pairs for each number. Write them inthe towers.

Factors

Explain how you decided.

IIAre all numbers that are divisible by 100also divisible by:

a 2 ~e.s b 5 ~e.s c 10 ~e.s

30 @ 35099 30809120 @ 1250 1020 C12 000C2 500) 12050

@@ 480 840 ®®C4880~C8440o)

D Circle all the numbers that are divisible by 100.

43 G® 66 ® 75 ®@9€D<E> 142 188 185 ®@@e® 19 @)@)@)@)®@ 672

®®@ 923 @@GOOO)@ 1099

Colour in the circles if the number is also divisible by 10.

o Circle all the numbers that are divisible by 5.

Divisible by 2 Not divisible by 2

28,16,58,124-,14-8,1120, 17, Ig, 113,2g, 4-5, 109,gOO, 2356, 650, IIgO, Igl, 4-50g, 52014-512

148 1120 900 2356 650 191 1190 4512 4509 5201

12410958452911316192817

o Write the numbers in the box into the correct columnsin the table.

Divisibility rules


Stu.d.en.t'5 own. discussionD Discuss these questions, with a partner.

a Do all three graphs show the same information?

b What makes the graphs look different?

c Which graph do you think gives the most accurate picture of the data? Why?

Store

0 I ~ I ~ 19> ~.$lVlC/) ;:I c '" ~ .~.... J I ~ ,~ 1J(lJ IE~ CLu..~

~

g a.0 ~ ~ if)u, U '"Ii: JStore

~~ 41--Q)

~ 2~=

21--- 1

6Q) 3u'S::::a..

2Graph B4

5

Graph A4

5

~ 3.s::::a..

6,--

6Graph C

o Use the data in the table to complete these bar graphscomparing the prices of the different items.

Store Farmers-R- Fancy Cheop-n- Fresh Specialityus Fruits Fresh Things Fruits

Price per 2.50 4.00 1.00 2.00 6.00kilogram ($)

This table gives the prices per kilogram of bananas at five different stores

Different scales


own. gr-a..ph.

KeyAbseiling

CanoeingWind-surfing

Pony-trekkingParachutingArchery

OrienteeringClimbing

Dinghy sailingWater-skiing

Use this grid to draw the pictogram for your class.

Activity Tally Activity Tally

Abseiling IIII Archery ~ICanoeing ~ II Orienteering ~IWind-surfing ~I Climbing IIIPony-trekking ~ IIII Dinghy sailing ~ IIParachuting III I Water-skiing ~ III

Use this table to record your data.

x = 2 studen ts

KeyAbseiling **Canoeing ***1Wind-surfing ***Pony-trekking ****~Parachuting **Archery ***Orienteering ***Climbing *~Dinghy sailing ***~Water-skiing ****

Use this grid to complete question 1.

Show choices on a pictogram

20

see Student Book page 64-20

10I

oI

-5I

c -15,10, -5, 0, -10-15 -10I I

o

-I II I I

-3I

b -1, -3, -5, -9, 1-C! -5I I

5-5

lrI

1

IoI

-2I

-3I

a 0, -2, 1,4, -3

D Estimate and show where you think each numberwould go on the given number lines. Studen t'5 own.estima tes

a b c d e f 9-16~ -12~ -C! + .t,+ I~ 5+ 8t

I I I I I I I I I I I I I I I I I I I I I I I I I I I-20 -10 0 10

a Ib c d e f-35+ -271+ -15 + -5 ~ 7~ ~ 15+I I I I I I I I I I I I I I I I I I

-40 -30 -20 -10 0 10 20

EJ Write the number shown by each arrow on the number lines.

2821I~7o-7-14-

82-10-16-22-28

15105o-5-10-15

~ ~ ~ ~ 0 2 ~ 6 8 ~ Q ~ ~+5 +5 +5 +5 +5 +5

~~~~~~

+2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2

~~~~~~~~~~~~

o Fill in the missing numbers on each number line.

Positive and negative numbers

9°C colder -iloeAnother 3°C colder -Ilr °e

A drop of - 6°C -IGoeA rise of 8°C lr "C

A rise of 15°C 36°eA decrease of 18°C 3°e

5 degrees warmer 2lr °e22 degrees colder - 3°e

9 degrees colder 3°eAnother 3 degrees colderGoe

4 degrees warmer IGloe12 degrees colder 3°e

°())

I I IW N ~ - N W ~0000000 0

elllllllllllllllllllllllllllllllllill

o()

)

~ ~ ~ - N W ~o 0 0 0 0 000

ellllllllllllljlllllllllllllllllllill

o())

I IW N ~ - N W ~o 0 0 0 0 0 0 0

ellllllllllllllllllllllllllllllllllll

- I

o()

)

~ ~ ~ - N W ~000 0 000 0

ell III 11111 11111 11111 11111 11111 11111 I

- I

n)

I ~, Iw ,~~ - N W ~o 0 0 0 0 000

ellllllllllllllllllllljlllllllllllill

o()

)

I I IW N ~ ~ N W ~o 0 0 0 0 0 0 0

ellllllllllllllllllllllllllllllllllll

- I

Write what the temperature would be if it changed as given.

Colour the thermometers to show the given temperatures.

Temperature changes


• Iii110

Look at these pictures. Tick the ones that have parallel lines.

Looking at parallel lines


Dlscusson

IIWhat can you say about the two angles formed bya pair of perpendicular lines?

b one pair of perpendicular lines.

lEI Draw your own sets of lines:

a one pair of diagonal parallel lines

Own. work

Th.e.yadd u.p to 1800

D What do you notice about the angles formed by aline intersecting parallel lines?

D Write the size of the angles formed between thediagonal bar and the other bars.

220 and 1580

o On this five-barredgate, colour in:

a one pair of horizontalparallel bars green

b one pair of verticalparallel bars red

c the diagonal blue.

Parallel and perpendicular lines in real life


0 Write whether each numbered angle in this drawingis acute, obtuse, or a right angle.

a obtuse b acu teo

e obtuse d acu teo

e acu teo f acu teo

9 obtuse h righ.t• acu teo • obtuseI J

o On the bicycle:

a Find five acute angles. Mark them blue.

b Find three obtuse angles. Mark them green.

e Find four right angles. Mark them red.

these iri.o.n.cje.sform acute M.gles

th~SpolMofth~whuls form.(lCUt.t o.n.cjM

Angles

600

A ]100 BB

A ...JF><_1_S......20.::....._ __ 2_8_0-- B

A ....L.....L B

Use the size of the given angles to calculate the size of theunmarked angle in each diagram.

The line AS is a straight line in each diagram.

Angles on a straight line


a 3 _ 6 ./ b l>~ < c ~< 1 -"5 - 10 2 4 8 4

d 5 > 3 ./ e ~< 1 > f 3 _ 6 ./10 8 8 2 "4 - 8"7 6 ./ h 1 _ 10 ./ I 5 _ 3

9 10 < 8 - 10 8 - "4 <

IIWrite each set of fractions in order from smallest to greatest.3 1 I I I 3a <[ 4 2 t, "2 lr

b 1 9 4 3 3 I t, Cj

2 TO 5 TO 10 2 5 10

C 1 5 3 ~ 3 I 5 32 8 8" 4 8 2 8 lr

d 2 1 1 3 4 I 2 lr I 35 10 2 5 10 10 "5 to "2 "5

e 1 1 1 1 1 I I I I I3" 2 5 10 8 10 8 "5 3' "2

II Tick the statements that are true. Correct anystatements that are false.

®® 5 CD ~ CD 9 ®6 6 10

'i'l CD 5 4 6 4 8 4~5 10 "5 8" 6 10 8

D Circle the fractions that are less than ~.

510

®912

39

®2668"

b ~C ~

4

48"

Circle the fraction that is not equivalent in each set.

CD1a 2

II

C 3 - _Q_<[ - []]

f I_II)"3 - "'6

o Write the equivalent fractions:

Use the circles to help you answer the questions.

Equivalent fractions

5 Ia 10 '2

6 3b 8 4-

4 2C 6 '3

6 3d 10 5

Use the chart to find the simplest equivalent fractionfor each of these:

D In a family of equivalent fractions, the simplestfraction is the one with the lowest numerator anddenominator.

Thirds Quarters Fifths Sixths Eighths Tenths2 3 4 5- - - - - -4 6 8 10

1 1.- - - - -3 6

2 4-- - - -3 6

1 2- - - - -4 8

3 6- - - - '8 -4

1 2- - - - - k)5

- 2 4-- - - -5 o3 6- - - - -5 o

3 4- 5 6 8 o3 4- - '6 8' 105

o Complete this chart of equivalent fractions.

Remember: Equivalent fractions have the same value.

More equivalent fractions


987

8 J. 8':!_2 10

I I I7~5

I I

4~4

ato

6?o

a~

654

5J. 563 8

I I I

Show each mixed number on the number line.

Improper fractions and mixed numbers

0 What fraction of the total set of shapes are:3 1 1

triangles? - . - b small triangles?a 12 l,. 12

1. = 1 i, 1large triangles? 6 d circles? - . -C 12 12 3

2 1 2 1large circles? - . - f small circles? - . 6e 12 6 12

7 3 1not circles? i2 h squares? - .

9 12 l,.

1 8 3• large squares? 12 • not squares? - .

l,.I J 122 1 5

k hexagons? - . I shaded? i212 67 3 1

unshaded? i2 n four-sided? - .m 12 l,.

5 10 squares and hexagons? 12 p unshaded hexagons? i2

o

o

Name the fraction


, r f- , IPossible rectQl1gles Qre.; II

i • •

I I•• •

I •• ••• -• ••I • ••1,"I II I· '" 1.1I I I "'" I II I "'" I f I 1.1I "i I "'" I I:

1··__-r··L··I···1 -I i (Q s tu,Qre ts Ql~o.----------. Q r ctQnglel

..

+ f.

,, ....

-+-

j I Possible recta.ngLes we: II i • •

I I I •• •I •• ••~

i •• •• ••1······ ........ -o··········.. ·· .. ·· .. ·f······ • ••~ ..... 11······I

I···j···j···········i···,,....- -

-I- 1--------------4• •I I (Qsit u,Qr~ is Ql~o• •..-.-.~~-.-.-.-.-.-.. Q recta.nglel

I,

l.. J

D A rectangle with perimeter 16 cm.

IIA rectangle with perimeter 20 cm.

Draw each of the following shapes.

o A square with perimeter 16 cm.

U A square with perimeter 20 cm.

Perimeter

o What is the area of a square if its perimeter is:

a 20 cm sides are 5 ern. so arec. is 25 an2 b 64 cm sides are 16ern. so aree. is 256 crn.2


a Calculate the length of the rectangle. 13 anb What is the area of this rectangle? C1lan2

not drownaccurately7cm

length

o The perimeter of this rectangle is 40 centimetres.

Eand ---

a Colour two shapes that have a perimeter of 12cm.

b Which two shapes have a perimeter of 14cm? Ac What is the area of Shape B? 7an2d Which has the greater area: Shape A or Shape E? Th.e!1are equal in. arec,

... ____,A B C

+

+

A,

-E

-0

.e --

-1 1 1 I 1

o Here are some shapes on a 1cm grid .

More perimeter and area


Think!

1200l...--_---' x 100 x 10

x 10 x 102300

120a L..-1_12-l

o Work out the missing operations.

c

Multiplying by 10 and 100

o Fill in the missing numbers.

a rX10l 70 rX1l 700 rXl0-j 7000 rXl0-j 70000 I7

b rX10l rX10l r 1°l180 000 I18 180 1800


20100 201

20100

201 20102010

20100

20100

Write the correct numbers in the blocks.

Fill in one of the operations: X 10, X 100, -:- 10 or -:-100in each circle.

Complete this flow diagram.

Multiplying and dividing by 10 and 100


134-

P = 30654

P = 153

108

6767

34-

P = 33617

P = 168

P = 20826

P = 10lt.

15

p = 1'1052

5226 5226

26

14 14

19P =66

38

28 18 18 36 3631 62

P = 132 P =113 P =226

52 6030

19

o The matching sides of the shapes on the right are double the length of those onthe left. Write the missing lengths. Use a calculator to find the perimeter of allthe shapes.

Now:6LrWas $128

oWas $2700Now: 1350

Was $8300Now: 4./50

Was..$B1:t'fo Now: 4-10

~

o Now: \05Was~Now:L,..8

o Super electronics is having a half-price sale. Write thesale price of each item.

Doubling and halving

-1-- "'-I•;~

I; I:t

~~/ -,/ r-,/ " C7'\

~

[7l/ ~~

r\V ~~

----.~-I

I

D

II

D

D

o

Remember: If there is space between the image and themirror line, you need to leave the same amount of spacebetween the reflection and the mirror line.

Image reflection

~ l/1'\ Vr-, V

Draw the reflection of each shape on the other side ofthe dotted line (or mirror line). Notice the equal amountsof space between the image and the mirror line, and thereflection and the mirror line.

Reflections


II Slide this shape forwards7 blocks and up 1 block.

II Translate this shape down5 blocks and forwards 4 blocks.

'- -------'-_,

/ ,'"/ "

D Slide this shape forwards3 blocks.

D Translate this shape back5 blocks.

-,~ ,,i\

\I\.

\ '\

II Slide the square down3 blocks.

o Translate the triangle forwards4 blocks.

Draw each shape translated on the grid according to the instructions.

Translated shapes

0.77 + 0.230.13 + 0.870.17 + 0.830.4- + 0.6

0.5 + 0.5

II List all the numbers that are not crossed out. Next toeach one, write how much you would need to add to itto make 1.

0.8 0.45 0.9 0.65 0.19 0.76 0.05

0.81 0.77 0.15 0.75 0.68 0.5 0.87

0.62 0.49 0.38 0.35 0.32 0.13 0.97

0.25 0.3 0.4 0.58 0.98 0.14 0.51

0.99 0.71 0.59 0.17 0.95 0.79 0.23

0.41 0.2 0.29 0.84 0.24 0.1 0.21

0.4 0.86 0.5 0.41 0.6 0.42 0.65

0.5 0.85 0.03 0.7 0.16 0.01 0.59

o Find pairs of decimals that add up to 1.

As you find each pair, cross out the numbers. Own. work.

Pairs of decimals that make 1


$6.40$1.99

D Each of these items was bought with a $10 note. Howmuch change did each person get?

..---------- ............... _.,

....... ---------- ........ --"'-- _.,,... ... ......... _.,

1.28l

,., 8.071 ....... ,.,---

,... .....'<, _., ....._ _,., '<, ./

...--- --_ -....._ _.,4.991

,----- ... ------_

'<, ./

10em

..------- ... _, -_....._ ./

........ - .. .." -"'-- ..

~---------- ..,....._ ./

2.451....""---------- .._

4.91

o Each barrel can hold 10 litres of water. How muchmore water can each one hold?

8.2em 9.1 em7.1 em

o How much taller does each plant need to grow to be10 cm tall?

Making lOs

0.17 0.16 O.OCJ

0.06 0.14 0.22

O.ICJ 0.12 0.11

1.55 6.1 2.85

4-.8 3.5 2.2

4-.15 O.CJ 5.4-5

3.1 12.2 5.7

CJ.6 7.0 4.4

8.3 1.810.CJ

Grid FGrid EGrid 0

o Grid 0 shows another magic square.

a Find the missing numbers.

b Halve each number and write the answers in Grid E.

c Usethe given number as a starting point to make a decimal magic square in GridF. Each number must have two decimal places.The total of each row, column anddiagonal must be 0.42.

17.1 16.4- 16.CJ

16.6 16.8 17

16.7 17.2 16.5

22.6 21.CJ 22.4-

22.1 22.3 22.5

22.2 22.7 22.0

226 219 224

221 223 225

222 227 220

Grid CGrid BGrid A

In a magic square the sum of each row, each column andeach diagonal is the same.

o Grid A is a magic square with whole numbers.

a Work out the missing number.

b Usethe numbers in the magic square to make a decimal magic square in grid B.Eachdecimal should have one decimal place.

c Subtract 5.5 from each number in the decimal magic square.Write the answers ingrid C. Is it still a magic square? ~es

Decimal puzzles

see Student Book page 10 1

Results Frequency1- 2 03-4 4-5-6 107-8 II9 - 10 8

87666875654

9 10 10 9 9 7 6 3 8 9 10

35678888946

II Use the grouped frequency table to organise this set oftest results.

Shape Tally Frequency

Hearts .J-H1 .J-H1 IIII 14-Stars .J-H1 .J-H1 .J-H1 III 18Rectangles .J-H1 5Moons .J-H1 .J-H1 .J-H1 IIII IgCircles .J-H1 .J-H1 I II

Total 67

o Complete the frequency table to show how many ofeach shape there are in this set.

Frequency tables


8~-1---1----1----1---1~_+---~---1_--~_4--_+--~--+_--~~

12~-1---1----1----1---1~_+---1----1_--~_4--_+--~--+_--~~

161---.---1-_4---1----~--+_--11---*--~--4___4

201---1·--~--4_--1-_4--_+---1---+_--~~---~--4_--+-~~~

241---1·--~--4_--~_4--_+---1---+_--~_4--~--4_--+_~~~

281---+--~--4_--~_4--_+--~--+_--~_4--~--4_--+_~~~

Grid B

2~-I---I---I----~--~-J---~--~~---I---~-+--~--~~

4~-1---1---1----1---~-1·---~--~-~---1---~-+--~--~~

'"QJ~ lOI---~---~---*----~---~-I·---~--I-~---I---~-+--~--~~....oEo 81---1---11---1----1---1~-1----~~1---~---1---~.....8§ 61---1----1---11---1----~--11---1---~--1~-1----~--1---+---~~z

121---1---4---~-1---~~*---+--4---~-1---4_--~_+--4_~

141---4---4---~_+--~--~-+--4_--~-+--4_--~_+--4_~

Use these grids to draw the graphs for Student'sBook page 102.

Grid A

Bar line graphs


876Time

5

20

~17 ~

......v \/

,.. ,\

/ v \- \

100

12Time

32II10

21

22

26

27./ V' "/ lS

vv

28

More line graphs

~ 800.o~ 60'0.....E 40E::lZ

Grid B

Cll....:l15 24....Cll0.E~ 23

Grid A


then by 3 or vice versa.

Students own methods, but should u.n..der-sta.n..dth.a.t you. can divide by 10 and

1:1 Write an instruction for a quick way to divide any number by 30.

b 480 +- 60 = 8

d 720 +- 90 = 8

a 140 +- 20 = 7

c 180 +- 30 = 6

o Now try these:

pla.ce values when you. divide by 10 or- 100.b 100

Discussion...Oieck th.a.t th.e studen ts realise th.a.t th.e digits m.ove one or- twoa 10

D What happens to the digits of any number divided bythe following numbers?

My answer Calculator answer

600 +- 10 Own work.

60 +- 10

1900 +- 100

190 +- 10

4000 +- 100

400 +- 100

o Try to calculate these in your head. Check youranswers with a calculator.

Mental division strategies


§] ·~ ~ EJ ·

~ 0. .. . . .

[2] ·~

[2] 0 · 0 [2]· ·- -

[§J ·~ ill ~

· 0 ill· - · -

5010 14416 24

5 210 63 9810

100

2 21

Use the numbers in the box to correctly complete eachdivision grid.

8 · 0 G. .. .

0 · 0 - 0-

G · 0 '0

In this grid the number sentences can be read from left toright and from top to bottom.

More division


BO pLecesof woocl

II Eight planks of wood were cut into 50 cm lengths.How many pieces of wood did this make?

I.B75m

D A plank was cut into eight equal pieces. Five pieceswere sold. What length of wood was left over?

a 6 pieces, each 250 cm long 3 planks neeclecl, 0 pieces sc:ra.p

b 9 pieces, each 150 cm long 3 planks neeclecl, 3 pLecessc:ra.p, 0.5 m lon9

c 5 pieces, each 120 cm long 2 pLanks neeclecl, 2 pieces sc:ra.p, 0.2 m a.ncl 3.B m lon9

D How many planks would be needed to cut each ofthe following sets of wood?

How many pieces of wood are left over as scrapeach time? How long are the pieces of scrap wood?

fouo-.s0..:.<u.eY.1

d 8 pieces? 62.5 em

c tenths? 50 em

b 2 halves? 250 em

a 4 quarters? 125 em

Planks 5 m long are delivered to the sawmill. The workers cut the planks intodiHerent lengths.

o How long would each piece be incentimetres if they cut a plank into:

The sawmill


$75 .;.5 - $15$75 .;.10 - $7.50$75 + 3 - $25

II Suggest 3 other ways to divide $75 intoequal amounts.

$75 .;.6 - $12.50$75 .;.2 - $37.50

D Two children are wrapping gifts.

a They cut 250 cm of ribbon into 10 pieces.Each piece is 25 crn long.

b How many 20 cm long ribbons canthey cut from a length of 250cm? 12with a. 10empieceleft over-

II $75 is divided equally between 4 people.Each person gets $18.75 .

D A light aircraft flies 457 km using8 barrels of fuel.It travels 57.125 krn kilometresfor each barrel.

o A carpet layer has a huge roll of stair carpet250 m long. He cuts it into 9 m lengths.He gets 27 pieces. with. 7 rn left over-

Solve these problems. Decide whether it is more sensibleto write the remainder as a fraction or leave it as a wholeremainder.

What will you do with the remainder?


/ -,/ <,

-, // -,

-, /

/ '"

-, /

Use it to make a cube.

Trace and cut out this net.

Shapes and nets


a ducks to geese? _IB_t_o_5 _

b ducks to swans? IB to 6 - 3 to I

D If 12 ducks flew away, what would the new ratio beof:

____ 6 swans____ 5 geese

ducks to swans 5 to 1

II If there were 30 ducks, how many geese and swanswere there?

ducks to geese 6 to 1

In a survey of water birds, these were the ratios:

d sparrows to each of the other birds 24- to 2 - 6 to I; 24- to 6 - 4- to I; 24- to 12- 2 to I;24- to 2 - 12to I·24- to I

a starlings to pigeons 12to 4- - 3 to I

b wild geese to starlings 2 to 12- I to 6

c ducks to starlings 6 to 12 - I to 2

o Write down the ratio of:

2 wild geese

24 sparrows

12 starlings

6 ducks

4 pigeons

1 owl.

In an hour a birdwatchersaw these birds:

Birdwatching

~ blue516green

I~ red


~yellow3 red4

iblue

t6 yellow

~ blue

1 red4

~ green

~ green1red4

~ yellow

1red4± yellow

~ blue

~ green1 red2

± blue

~ blue

~ yellow

1red4

~ green

~ blue

~ green

1red4

~ yellow

~ blue~ yellow

Colour each pattern in the given proportions Own wort.

Colour the correct proportions


What is the ratio of:

a conditioner bottles to shampoo bottles? 12b body lotion bottles to bath foam bottles? 1:3

EJ A supermarket sells both products in special packs:

2 bottles of shampoo with 1 free bottle of conditioner.

3 bottles of bath foam with 1 free bottle of lotion.

Own. work.

o List 14 ratios to compare these children.

For example, boys to girls is 6 to 8.


o A class wants to bake 10 cakes. How much of eachingredient will they need?

1000 g margarine (I kg)1500 g sugar (1.5kg)10QQ g self-raising flour (I kg)120_Qg dark chocolate (1.2kg)lli eggs

o If a class has 12 eggs and as much of the otheringredients as they need, how many cakes can theybake? 6-=--------

D What mass of sugar will a class need to make 8 cakes? 1200 9 or- 1.2kg

II One class sells one cake for $8.75. How much moneywill they make if they sell:

a 10 cakes $87.50-l-::..:....:=-= _

b 8 cakes $70.00--'-;.....::..;..::._:;__----

e 25 cakes $218.75....!..:=-..:...;--=------

d 100 cakes? $875.00.....:....;:..__:__:_-=-------

o Sanjay's class sold their cakes for $8 each. If theyraised $232.00, how many cakes did they sell?

Ingredients:

1OOg margarine150g sugar100 g self-raising flour120 g dark chocolate2 eggs

This is the recipe for making one cake.

The students at a school want to make chocolate cakes tosell at the school fete.

Recipes and proportions

o0,' 0 00o 0 0,'000

O 0' 0 00(0 'o 0' 0'o "

000o

oo

o


0 00 0 000 0

00

o oo00

o o

oo

oo 0oo

ooOther ------

Purple _

Yellow _

oooo00

o

oo

o oo00o

oo

o

Red Orange

Green Blue

Grey Black

0 000 0

0 0 0 0

Shade the bubbles different colours. Then write thepercentage of bubbles in each colour. Own. wort.

Bubble percentages


b 50% of $5 is $2.50c 1% of $10 is 10 centsa 100% of $5 is _....:t$=5~ _II Work out these amounts.

b A quarter is the same as 25 %.d Three-fifths is the same as 60 %.%.

o Complete the sentences.

a Half is the same as 50 %.c One-tenth is the same as 10

o Shade the correct percentage of each shape.(Hint: Convert the percentage to a fraction and simplify it!)

a 25% b 40% c 75%

o Shade the correct percentage of each lOx 10 square.

a 15% b 20% c 1%

Problems involving percentages


Studen ts own workAllow #tern to check.each other's placemen t ancl to discuss an~ diso-epandes.

100%o

710

99100

45100

3TO

1TO

1:2

D Show where each of these fractions would fit on the0-100% line

Fraction Decimal Percentage

1 0.5 50%:21 0.1 20%10

4 0.Lt. 40%10

7 0.7 701010

2 I 0.02 2%100 - 5017 0.17 17%10017... 0.27 27%100

88 22 0.88 88"/000 - 25q

0.9 ClOlo0l,.5 q

0.45 Lt.5"/000 - 20

6 3 0.6 60%10 - 5

For example, i= 0.5 = 50%.

o Complete the chart.

A number can be written as a fraction, decimal orpercentage.

Percentages, decimals and fractions


Complete these equivalent fraction wheels. Own. work.

Da c

This is a fraction wheel for t. It shows equivalentfractions and decimals. There are other fractions whichcould go on this wheel, for example, ~~,1~ or 15000.

0.5

24

5 1 310 2 6

48

0.5

For example, i= 1 + 4 = 0.25

Remember: To convert a fraction to a decimal, you dividethe numerator by the denominator.

Equivalent fraction wheels


Own. work.

a

c: ~~B. 65. 100

a Write down the highest and lowest value in each set.

Set A 0 and 2Set B 25"/0and 16

Set C Igo a.n.ci 0.66b Calculate the difference between the two values. A· 1.. 4-

c Show the differences on this number line.

II

D Write down two numbers from each set above thathave a sum of 1.

Set A: 10.251+ 1C 1= 1 Set B: 175/01 + 125"/01= 1 Set C: 10.lrl + 160/01 = 1

IgO' os. ~,6010, 0.660.412

_Q_1000.66c 60%

~ 25/0, ~, t, 75/0, 0.8, 1625%120.875%

50% 0, ~ ,0.25,5010,0.7, ~0.7o01

210

34"a 0.25

o Arrange each set of fractions in order from smallest togreatest.

1"2

Tenths 1 2 3 ~ 5 6 7 8 q 1010 iO iO iO 10 10 iJ iO 10 iO

Decimals 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 IPercentages 10"/0 20"/0 30% lrOlo 5010 6010 70% 8010 CJOlo 100%

o Complete this table.

Ordering equivalent fractions

I will eatfruit today

this week

Impossible

Unlikely

Even chance

Likely

Certain

Draw lines to match the events to the correct placeon the scale. Answers will va.ry

Likely and unlikely events


c 925 washers at 9c each. d 8 extension cables at $8.99 each.

$71.g2$83.25

$55g3$1026

o Mr Musa's electric shop orders some electronicequipment. Work out the total cost of each order.

a 9 TV sets at $114 each. b 7 camcorders at $799 each.

f 199 X 9 = 17g1e 497 X 4 = Ig88d 469 X 6 = 2814-

c 155 X 9 = 13g5b 332 x 7 = 2324-a 4 X 239 = g56

o Here are some multiplications. Try and solve themwithout a calculator. Choose your own method.

Choose your method

62m

91 m78m

7Sm

17m

94m

27m

43m3526m219m

82m

Remember Area = length X breadth

Work out the area of each field. Do your working inside thefields.

Find the area


x 2 3 4 5 6 7 8 9

1.1 2.2 3.3 4-.4- 5.5 6.6 7.7 8.8 Cl.Cl

1.8 3.6 5.4- 7.2 Cl 10.8 12.6 14-.4- 16.2

1.7 3.4- 5.1 6.8 8.5 10.2 II.Cl 13.6 15.3

2.3 4-.6 6.Cl Cl.2 11.5 13.8 16.1 18.4- 20.7

2.5 5 7.5 10 12.5 15 17.5 20 22.5

2.9 5.8 8.7 11.6 14-.5 17.4- 20.3 23.2 26.1

3.0 6 Cl 12 15 18 21 24- 27

3.1 6.2 Cl.3 12.4- 15.5 18.6 21.7 24-.8 27.Cl

3.3 6.Cl Cl.Cl 13.2 16.5 ICl.8 23.1 26.4- 2Cl.7

3.7 7.4- ILl 14-.8 18.5 22.2 25.Cl 2Cl.6 33.3

4.5 Cl 13.5 18 22.5 27 31.5 36 4-0.5

4.8 Cl.6 14-.4- ICl.2 24- 28.8 33.6 38.4- 4-3.2

5.9 11.8 17.7 23.6 2Cl.5 35.4- 4-1.3 4-7.2 53.1

7.2 14-.4- 21.6 28.8 36 4-3.2 50.4- 57.6 64-.8

9.6 ICl.2 28.8 38.4- 4-8 57.6 67.2 76.8 86.4-

9.9 ICl.8 2Cl.7 3Cl.6 4-Cl.5 5Cl.4- 6Cl.3 7Cl.2 8Cl.1

Complete this multiplication table.

Multiplying decimals

67.5 kg5 of each item

36.4- kg2 coils of rope + 3 blocks + 5 planks

7 coils of rope

4-4-.8 kg

coil of rope 6.4 kg

3 bog of nails 3.3 kg

bog of nails 1.1 kg

2 of each item 27 kg

2 blocks + 3 bogs of nails

9 planks 25.2kg5 blocks 16kg

Work out the mass of each pile.

The mass of each item is given.

plank 2.8kgblock 3.2kg

Work out the mass


3 of 32 + 3 of 28 - Lr5t.. t..

o Complete these problems. Youwill first need to writethe number sentence, then find the answer.

a Jenny organises a cherry-picking expedition and picnic.The following people confirm they will join her: Maryand her two sisters,James and his four cousins, Leahand her brother and mother. Jenny needs to take onepicnic basket for every two people. How many picnicbaskets must she take? (I + I + 2 + I + Lr + I + 2) 72 - 6 baskets

b Three friends go out for a meal. They add up the itemson the bill and then split the total evenly betweenthem. The items on the bill are as follows: two startersat $6.45 each, three main disheswhich cost $8.99,$7.35 and $10.50, and one dessertwhich costs $9.00.How much must each person pay? (2 x $6.Lr5 + $8.CICI + $7.35 + $10.50 + $CI.OO)

c ClassA has 32 students and ClassB has 28 students. 7 3 - $16.2534 of the students from each class go on the schoolouting. How many students go altogether?

BracketsOfDivisionMultiplicationAdditionSubtraction

Remember BODMAS,to give you the correctorder of operations:

I 32" of 50 + 4" of 100 100

j 4 X 4 + 4 X 4 + 5 X 5 57k

o Complete these mixed operations.

a ~of (200 - 50) 50b (100 + 44) -:- 12 12c (10+4x4)+(17+3x8) 201d 18 -:-3 + 8 x 2 + 25 -:-5 27e ~of 18 + 19 + 20 + 21 6C1

I I 3f 2" of 22 - 2" of 16

g (! of 66) + 55 -:- 11 5Lr.5h 43 + 19 + 15 + 200 -:-2 X 5 577i lOx (16 - 6) 100 I 7 x 30 + 2 x 40 2C10

m ~of 16 + ~of 16 16n (10 + 10 + 10 + 10 + 10 + 10) -:-5

12

Mixed calculations

Education

Rabotna tetratka 5 odd