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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
see Student Book page 12
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
see Student Book page 13
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
see Student Book page 14
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.
• • • • •• • • • •• •
see Student Book page 17
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
see Student Book page 18
;- ~ --~ --
-, -"""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
see Student Book page 19
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
see Student Book page 23
• •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
see Student Book page 231
. ..-
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
see Student Book page 28
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 0.72Unshaded 0.28
Shaded 0.27Unshaded 0.73
Shaded 0.55Unshaded 0.4-5
Shaded 0.05Unshaded 0.Cj5
Shaded 0.5Unshaded 0.5
Shaded 0.9Unshaded 0.1--=.:.:._
Shaded 0.43Unshaded 0.57
Shaded 0.4Unshaded 0.6
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
see Student Book page 30
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
see Student Book page 34
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
see Student Book page 38
_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
see Student Book page 43
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
see Student Book page 471
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
see Student Book pages 49 and 50
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
see Student Book page 54
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
see Student Book page 59
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
see Student Book pages 60 and 61
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
see Student Book page 70
• Iii110
Look at these pictures. Tick the ones that have parallel lines.
Looking at parallel lines
see Student Book page 7141
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
see Student Book page 74
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
see Student Book page 77
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
see Student Book page 78
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
see Student Book page 81
, 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
see Student Book page 84
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
see Student Book page 85
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
see Student Book page 8651
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
see Student Book page 88
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
see Student Book page 94
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
see Student Book page 97
$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
see Student Book page 102
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
see Student Book page 105
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
see Student Book page 10861
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
see Student Book page 109
§] ·~ ~ 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
see Student Book page 110
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
see Student Book page 112
$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?
see Student Book page 1 15
/ -,/ <,
-, // -,
-, /
/ '"
-, /
Use it to make a cube.
Trace and cut out this net.
Shapes and nets
see Student Book page 118
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
see Student Book page 119
~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
see Student Book page 122
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.
see Student Book page 123
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
see Student Book page 124
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
see Student Book page 1241
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
see Student Book page 125
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
see Student Book page 128
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
see Student Book page 128
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
see Student Book page 133
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
see Student Book page 137
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
see Student Book page 14 1
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