Fractions, Decimals, Percentages
Fractions of an amount ? percentage
We can use fractions to help us calculate percentages.
How can we calculate 25% of 80?
We know that 25% is the same as
1 4
.
To
find
1 4
of 80 we divide by 4.
80 ? 4 = 20
25% of 80 is 20.
4 Use your knowledge of fractions to calculate the percentages:
a 25% of 120 is 30
b 50% of 250 is 125
c 20% of 50 is 10
1 2
=
50%
1 4
=
25%
1 3
=
33
1 3
%
1 5
=
20%
1 10
=
10%
3 4
=
75%
Holiday Review - Year Six 1
4
of 120
=
__3_0___
1 2
of 250
=
__1_2_5__
1 5
of 50
= __1_0___
120 ? 4 = __3_0___
250 ? 2 = __1_2_5__
50 ? 5 = __1_0___
d 25% of 16 is 4
e 3313% of 66 is 22
Fractions, Decimals, Percentages:
f 75% of 80 is 60
Calculators are also handy for working out percentages. This is how we calculate 40% of 50:
5 We enter 0 ? 4 0 %
2 0 Our answer appears
5 Use a calculator to find these percentages:
a 20% of 300 mL = 60 mL
b 35% of 280 mL = 98 mL
d 6% of 70 km = 4.2 km
e 25% of 150 mL = 37.5 mL
g 15% of 400 = 60
h 18% of 300 mL = 54 mL
c 15% of 800 kg = 120 kg f 9% of $700 = $63 i 90% of 1 000 = 900
6 The answer is 75. Use a calculator to work out the percentages and tick all the squares that match the answer:
What is 25% of 300?
What is 75% of 100?
What is 10% of 750?
What is 15% of 55?
What is 45% of 180?
What is 35% of 300?
What is 50% of 150?
What is 20% of 375?
Addition
and
SAup2b4ptlyraiGncgtisot3rna:tegies
? addition
Fractions, Decimals
and
Percentages
4 It isSEiRmIEpS ortTaOnPtICto eat healthy foods that aCroepylroigwhti?n 3faPtLeaanrndinsgugar. This table shows nutritional information
of some common foods:
Total fat Sugars
Bowl of Bowl of coco flakes wheat puffs Meat pie
1.2 g
0.7 g
33.8 g
28.3 g
1.6 g
12.3 g
Salad sandwich
9.3 g
5.4 g
Cola drink 0 g 30 g
Fruit juice 0 g 4.9 g
Milkshake 12 g 61 g
a How healthy are the children listed in the table below? Calculate the total amount of fat and sugar consumed by each child for breakfast and recess:
Breakfast
Lunch
Total fat
Total sugar
Sam
Bowl of coco flakes
Meat pie and 1.2 g + 33.8 g
cola drink
= 35 g
28.3 g + 12.3 g + 30 g = 70.6 g
Nate
Bowl of wheat puffs
Meat pie and 0.7 g + 33.8 g + 12 g a milkshake = 46.5 g
1.6 g + 12.3 g + 61 g = 74.9 g
Wil
Bowl of coco flakes
Salad sandwich 1.2 g + 9.3 g + 0 g and cola drink = 10.5 g
28.3 g + 5.4 g + 30 g = 63.7 g
Trey
Bowl of wheat puffs
Salad sandwich 0.7 g + 9.3 g + 0 g and fruit juice = 10 g
1.6 g + 5.4 g + 4.9 g = 11.9 g
b Draw a smiley face next to the healthiest child.
5 Now it's your turn to look at your breakfast choices. Use the packaging or a calorie counter to find the sugar and fats content of your daily breakfasts. Track your breakfasts over a week:
Day
Breakfast
Total fat Total sugar
Holiday Review - Year Six
MultiplicaMtieonntaalnddivDiisviiosnionst:rategies ? inverse operations
As we know, multiplication and division are inverse operations. This means they do the reverse of each other:
8 ? 9 = 72 72 ? 9 = 8
We can use our knowledge of the times tables to help us answer division questions.
1 Complete these fact families: a 8 ? 3 = 24 24 ? 8 = 3
b 8 ? 4 = 32 32 ? 8 = 4
c 7 ? 6 = 42 42 ? 7 = 6
d 9 ? 3 = 27 27 ? 9 = 3
e 5 ? 5 = 25 25 ? 5 = 5
f 8 ? 12 = 96 96 ? 8 = 12
2 Use your knowledge of multiplication to help you mentally solve these problems. Some will have remainders.
a 36 ? 3 = 12 c 121 ? 11 = 11 e 25 ? 6 = 4 r 1 g 68 ? 11 = 6 r 2
b 63 ? 7 =
9
d 120 ? 10 = 12
f 37 ? 8 = 4 r 5
h 113 ? 12 = 9 r 5
What do we do when there are remainders? We have to guess, check and improve.
27 ? 5 = ?
5 ? 6 = 30 Too high
4 ? 5 = 20 Too low, there are 7 left over
5 ? 5 = 25 There are 2 left over so 27 ? 5 = 5 r 2
3 Try these: a 42 cupcakes are shared evenly amongst you and 7 friends. How many whole cakes does each person receive? 5
b How do you recommend sharing the remainder?
I would cut each cake into eighths or quarters as there are two of them.
c 102 pencils need to be put into packets of 12. How many full packs can be made? How many pencils are left over? 8 r 6
We measure area in square units. For small areas we use square centimetres. 1 cm
1 What is the area of each shaded shape? Each square has an area of 1 cm?.
a
b
c
Area =
4 cm2
Area =
4 cm2
Area =
2 cm2
Coordinates ? plotting coordinates
d
e
f
Holiday Review - Year Six Maps and street directories use coordinates to help us follow routes and find places.
We read coordinates horizontally and then vertically, so the letter comes before the number.
1 Write the letter for each coordinate to work out the riddle and the answer:
Area =
5A cm2B
C AreaD= E 7 cFm2 G
H ArIea = J
Length, Perimeter and Area:
1W
A
EE
U
2 How many different shapes can you make that have an area of 6 cm??
2
I
NN
6K cm2
3
R
FF
TeMacher check.
4
H
D
T
5
S
6
B
Y
Do you need to use whole squares? How could you make an area of 6 cm? using part squares?
Position:
7
O
8
QRiudedslteions
RAindsdwleeranswer
A1, C4, D1, I4, A5
WHAT'S F2, I4
IT
E6, H7, I1, A3 YOUR
E6, H7, I1, A3, A5
YOURS J3, H7, A3, G1 MORE
H2, D1, J3, G1! NAME!
C6, I1, I4
BUT
I4, C4, D1, H2 THAN
E6, H7, I1, A3
YOUR
E6, H7, I1
YOU
Choose another area and see how many of those shapes you can make.
E3, A3, F2, G1, H2, G4, A5 FRIENDS G4, H7?
DO?
G 1 I1, A5, G1
16
ULSeEngth, Perimeter and Area
3
Copyright ? 3P Learning
SERIES TOPIC
2 Plot these points and then connect them to make a 3D shape. Use a ruler.
F1 to C1
F1 to D3
AB C D E F G
C1 to A3
D3 to D5
1
A3 to A5
C1 to C3
A5 to D5
A3 to F3
2
D5 to F3
C3 to A5
3
F3 to F1 4
5
6 G2
SERIES TOPIC
Position
Copyright ? 3P Learning
Holiday Review - Year Six
Geometry:Lines and angles ? classifying angles
An angle is the amount of turn
between the intersection of
two rays (lines).
vertex
angle
Angles are conventionally measured in degrees on a protractor. 360? is a full turn, 180? is a half turn, and 90? is a quarter turn.
360? 0?
Have you heard someone say, "He did a complete 180? on that."? What do you think they meant? What does, "She did a full 360?" mean?
90? 180?
270?
1 Complete the table and use the information to help you to classify the angles below. Use a maths dictionary to help you work out any unknown terms.
right angles are ___9_0_?
acute angles are obtuse angles straight angles
_____l_e_s_s_____ are ___m__o_r_e___ are exactly
than 90?
than 90? and _1_8__0_?
less than _1_8__0_?
reflex angles revolution
are greater than angles are 180? and less exactly _3_6__0_? than _3_6__0_?
a
b
c
acute angle
right angle
obtuse angle
Make sure you check which angle you're meant to be measuring! The little arc tells you here.
d
e
f
reflex angle
obtuse angle
reflex angle
2 Look at the interior angles in this shape. Mark any
R
acute angles with a red arc; obtuse angles with a
blue arc; reflex angles with a green arc; and right
angles with an orange :
O
2 G1
SERIES TOPIC
Geometry
Copyright ? 3P Learning
G G
R
B R
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