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 Test-taking TIPS

General
• Count the number of pages to make sure that there are no missing
pages.
• Read the instructions carefully so that you know what to do and
how to do it.
• Write neatly.
• Always check your answers and writing after you have completed
the test.
• Skip the questions that you are stuck on and come back to them
after completing the rest of the test.

• Read through the test quickly. Skip the difficult questions and do the easy
ones first.
• Read the question twice before finding the answer.
• Look for keywords in the question. (e.g. “fewer” suggests a subtraction
problem; “share...equally” suggests a division problem)
• Come up with the answer in your head before looking at the possible
answers.
• Read all the four options before deciding which is the correct answer.
• Eliminate the options that you know are incorrect.

2
 Grade 6

• Read the whole question carefully and never make any assumptions about
what the question might be.
• Highlight (i.e. underline / circle) the important information in the question.
• Translate the words into mathematical terms.
• Use drawings to help you better understand the question.
• Break down the problem into several parts and solve them one by one.
• Know exactly what needs to be included in your solution.
• Estimate the answer.
• Before writing out the solution, organize your thoughts.
• For a question that involves measurements,
– make sure the measurements are uniform when solving the problem.
– the measurement in the answer is converted to the unit that is asked.
• Use words to describe what you are calculating.
• Always write a concluding sentence for your solution.
• Check if your answer is reasonable (i.e. Is the answer close to your
estimate?).
• Never leave a question blank. Show your work or write down your
thoughts. Even if you do not get the correct answer, you might get some
marks for your work.

3
 Grade 6 PRACTICE 1
Which of the following is a factor of About how much water is in the jug
72 but not a composite number? below?
36
72
3
4
half a litre
What does the sign below mean? one quarter of a litre
one third of a litre
three quarters of a litre

Katie buys one dress and two tops.

The maximum driving speed is

50 km in 1 h.
The maximum driving speed is
1 km in 50 h.
The driving speed should not be
lower than 50 km/h.
The speed should be at least
50 km in 50 h.

Which is the most appropriate unit How much does she need to pay?
of measurement to describe the area $28
of a beach towel?
$27
cm3
$26
m3
$23
2
km
m2

4
Which number should be placed The graph below shows the number
in the box to make the following of marbles that the children have.
number sentence true?

30 – 24 ÷ 2 + 1 x 4 =

22
7
16
88

Look at the fractions below.

Which sentence is not correct?
11 5 4 12
2 4 3 3 Ted has more marbles than
Tiffany.
Put the fractions in order from
greatest to least. The boys and the girls have the
same number of marbles.
5, 4,11,12
4 3 2 3 Elaine has 6 more marbles than
Bruce.
12 , 4,11 , 5
3 3 2 4 Bruce has 5 more marbles than
1 2 4 5 Ted.
1 ,1 , ,
2 3 3 4
12,11, 4, 5 What comes next?
3 2 3 4

5
 1

In K & M Grocery Store, apples are sold in groups of 3 and oranges are sold in groups
of 5.
If Mrs. Winter buys 26 apples and oranges in all, how many apples does she buy?
How many oranges does she buy?

6
 Grade 6

Uncle Jimmy wants to lay his backyard with sod. Each piece of sod is in the shape of
a rectangle that measures 1 m by 2 m. A drawing of his backyard is shown below.

How many pieces of sod will Uncle Jimmy need to cover his backyard?

7
 Grade 6 PRACTICE 2
Which set of values is represented by The following shape has an order of
the 4 points on the number line? rotational symmetry of 2.

2.81, 2.82, 2.85, 2.90

2.85, 2.91, 2.95, 2.99
2.84, 2.86, 2.90, 2.98
2.90, 2.92, 2.95, 2.99

Which one of the following numbers Flap 1 and flap 5 are already shaded.
is 5.6 when it is rounded to the Which flap(s) should be shaded as
nearest tenth, and is 5.62 when it is well to get an order of rotational
rounded to the nearest hundredth? symmetry of 8?

5.614 3, 7

5.617 2, 4, 6, 8

5.628 2, 6

5.671 2, 3, 4, 6, 7, 8

Look at the pattern.

3, 7, 15, 31, 63...

What comes next?

67
79
114
127

8
Look at the time shown. What is the most appropriate unit to
measure the volume of a swimming
pool?
cm3
m2
m3
mm3
What time will it be after two and a
half hours?
Look at the grid below.
17:38
3:38 p.m.
18:08
6:08 a.m.

What is the volume of the triangular

prism below?

If is moved 3 units down and a few

units right, which one will possibly be
the new coordinates of ?
(3,2)
60 m3
(6,7)
15 m3
20 m3 (8,2)

30 m3 (8,4)

9
 2

Plot the following points on the grid.

A(1,1) B(6,1)
C(8,7) D(3,7)

Join the points to see what quadrilateral is formed. Name and tell the characteristics
of the quadrilateral. Then find its area.

10
 Grade 6

The members of the Environmental Club of Pineway Public School plant trees every
month. They recorded the number of trees they planted in the past 9 months.

What are the mean, median, and mode numbers of trees they planted?
Janet is the president of the club. If she wants to write a letter to the government
to apply for a fund to subsidize the environmental activities, which central tendency
should she use to support her application?

11
 Grade 6 PRACTICE 3
Which of the following should be The area of the parallelogram is
put on the line to make the number 30 cm 2.
sentence true?

24 + ÷ 2 = 27

10 – 4
4+2
18 ÷ 3
32 – 2 What is its height in centimetres?
5 cm
A compass is at an angle of 50˚. 0.5 cm
10 cm
1 cm

Which pattern has this rule?

“Increase by adding the same number
to each term.”
20, 18, 16, 14, 12
5, 13, 21, 29, 37
At least how many more degrees do 2, 3, 5, 8, 12
you need to open the compass so
10, 20, 40, 80, 160
that it shows an obtuse angle?
11˚
21˚
31˚
41˚

12
Which shapes have the same area? A report shows that 92% of children
watch TV every day. Which of the
following number is equivalent to
92%?

9.2
92
1000
0.92
0.92
1000

What is the probability that the

pointer will land on red?

A and B
A and C
A, B, and D
B and C

Which set is in order from least to

greatest? 0
2.451, 2.415, 2.154, 2.145 1
3
0.826, 0.862, 0.268, 0.286 1
1.023, 1.203, 1.302, 1.320 4
1
3.097, 3.079, 3.970, 3.790 8

13
 3

Jill has a robot which walks at 8 cm/s at normal speed and 1 cm more in a second
if it is at turbo speed.

How long does it take the robot to walk from the cupboard to the carpet at normal
speed?
How much time will be saved if the robot walks at turbo speed instead?

14
 Grade 6

John makes the rectangle below with a wire.

John uses the same wire to make a square.

What is the side length of the square?
Does the square have the same area as the rectangle? Explain.

15
 Grade 6 PRACTICE 4
Sam can fold two paper planes in a Kenneth draws a ball from the bag
minute. How many paper planes can without looking.
Sam fold in 4 hours?
240
360
480
600

Compare the areas of the two shapes

below.

What is the probability of drawing a

ball that is not “5”?
6
7
1
5
4
5
1
7

What is the sum of the number

sentence below?

Which sentence is true? 999 + 7 + 6 = ?

2
A is larger than B by 3 cm . 999 7

B is larger than A by 3 cm2.

3
A is larger than B by 6 cm2.
8
B is larger than A by 6 cm2.
976
1012

16
What is the sum in expanded form Which fraction represents the shaded
of the number sentence below? part of the shape below?

65.23 + 125.53 =

100 + 9 + 0.7 + 0.06

100 + 90 + 0.7 + 0.6
100 + 9 + 0.07 + 0.6
100 + 90 + 0.7 + 0.06
1
2
If = 6, what is the value of 5
15 + x 2 ÷ 3? 7
5
9 12
6
14 8
16
19 The following record shows the
amount of water drunk by each child
during lunch on a specific day.
Which pattern has the pattern rule
below?
“Subtract half of the previous
term.” A 0.58 L
B 2 L
2, 4, 8, 16, 32 5
64, 32, 16, 8, 4 C 510 mL
50, 48, 46, 44, 42 D half a litre
25, 20, 15, 10, 5
Which child drank the least?
A
B
C
D

17
 4

The table shows the number of toy cars sold by each salesperson.

Make a bar graph to show the data. You may use rounded figures to complete the
bar graph.
If each salesperson earns a commission of $0.70 for each toy car sold, whose
commission is closest to $600?

18
 Grade 6

Abby wants to buy a dozen eggs to make a birthday cake. She compares the costs
of the eggs from two grocery stores and the costs of travelling to these stores.

Which store should she go to buy eggs? What is the total cost?

19
 Grade 6 PRACTICE 5
What is the volume of the triangular The cost of 32 bikes is the same as
block in cubic millimetres? the cost of 128 dolls. If the cost of
each doll is $16, how much is a bike?
$32
$64
$128
$256

Arrange the numbers from greatest

to least.

0.81 200% 2 7 1.875

10
81
810 1.875, 200%, 2 7
10
1620 7
200%, 2 , 1.875
10
200%, 1.875, 2 7
There are 48 boys and 54 girls in 10
Grade 6 of Pineway Public School. 2 7 , 200%, 1.875
What is the ratio of the girls to the 10
boys in simplest form?
What is the 7th term in the number
48:54
pattern?
9:8
475, 440, 405, 370...
27:24
8:9 230
265
295
300

20
Tony is measuring the perimeter of a Which is the top view of the solid
farm using a measuring wheel. below?

The circumference of the wheel is 2 m.

How many full turns will the wheel
make if the perimeter of the farm is
2.2 km?
11
110
1100
11 000

Last year, the highest temperature in

summer was 34˚C, and the lowest
temperature in winter was -20˚C.
What is the difference between the
highest and the lowest temperatures
in ˚C?
14
20 Which number is a factor of 60, but
34 not a factor of 72?

54 4
6
12
15

21
 5

Leo made a spinner with 16 equal sections and numbered each section from 1 to
16.
Leo lets each of his friends choose one of the guesses below before he or she spins
the spinner. If the guess of the player matches the number that the pointer lands
on, he or she gets a prize.

Guess 1: multiples of 4

Guess 2: greater than 10

Guess 3: factors of 10

If you are one of Leo’s friends, which guess will you choose? Explain your choice.

22
 Grade 6

Tom had 69 basketball cards and Jack had 24.

Tom gave some of his cards to Jack and still has 7 more cards than Jack.
How many cards did Tom give Jack? How many cards does each of them have now?

23
 Grade 6 PRACTICE 6
James started driving to Ottawa at There is 4 of a litre of milk in a jar.
5
9:35 a.m. It took him 3 h 30 min to If Sue pours out 250 mL of milk from
get there. What time did he arrive
the jar, how much milk will be left?
in Ottawa?
550 mL
6:05 a.m.
450 mL
12:05 p.m.
250 mL
1:05 p.m.
150 mL
1:25 p.m.

1
The net of a cube is shown below. A survey shows that of the
4
population has less than 5 hours of
sleep a day and 45% has more than
8 hours. What is the portion of the
population that has 5 to 8 hours of
sleep a day?

3
4
The area of the net is 24 cm2. What 0.3
is the side length of the cube? 55%
1 cm 0.03
2 cm
4 cm
6 cm

24
Look at the equations. The graph shows the time and
distance travelled in Tom’s journey.
n + 1 = 15
n + 1 + s = 19

What is the value of s?

2
3
4
5

The perimeter of the following

rectangle is 210 cm. How far will Tom travel if he drives
for 6 hours?
450 m
450 000 m
4500 km
45 km
What is the ratio of its length to its
width?
Which number should be placed
699:1 in the box to make the number
sentence true?
12:1
15:14 3.92 – 2 x 1.35 =
6:1
2.591
2.592
1.21
1.22

25
 6

Louise made the triangles below with sticks and modelling clay.

Help her record the number of balls

of modelling clay used in the chart.
Louise says, “I can make a triangle
with 10 layers if I have 2 more balls
of modelling clay.”
How many balls of modelling clay
does she have now?

26
 Grade 6

Draw a triangle with vertices (7,9), (7,14), and (10,14). Then name it A.
Mark the point at (7,9) as P on the grid.

Rotate triangle A 1 clockwise about P. Then name it B.

4
Explain how you would create a picture that has a rotational symmetry of 4 using
triangle A.
Draw the picture on the grid and describe the transformation that you used.

27
 Grade 6 PRACTICE 7
Which of the following is the closest Jack took a train from Toronto to
estimate of the angle? Montreal. The train left at 9:48 a.m.
and arrived at Montreal at 2:03 p.m.
How long did it take Jack to travel
from Toronto to Montreal?
4 h 5 min
3 h 15 min
4 h 15 min
105˚ to 115˚
5 h 15 min
135˚ to 145˚
35˚ to 45˚
Which number matches all the
90˚ to 100˚ descriptions below?
• It is a prime number.
What fraction of the shape is shaded? • It is between 28 and 42.
• The sum of its digits is a composite
number.
• It is a factor of 148.

31
37
41

7 74
8
3
4
6
15
3
8

28
A hiking area has 3 trails. Rotate the shape a quarter turn
clockwise about point M.
Trail Length

A 2.81 km
B 629 m
C 2.098 km

What is the length of the longest trail

expressed in metres?
2098 m
0.281 m
281 m
2810 m What are the new coordinates of A?
(8,0)
What solid can be formed by the net (7,1)
below? (6,2)
(5,3)

Coach Samson wants to rearrange

169 scouts into rows. Each row has
the same number of scouts. Which
way can Coach Samson use to
rearrange the scouts?
9 rows of 16 scouts
rectangular prism 13 rows of 13 scouts
pentagonal prism 16 rows of 9 scouts
hexagonal pyramid 21 rows of 7 scouts
hexagonal prism

29
 7

Jack volunteers to help his teacher make spinners for the school fair. His teacher
made a chart to record details of the spinners and asked Jack to make two of the
three spinners.

Spinner* Red Green Blue

A 1 1 5
8 4 8

B 1 1 3
8 2 8
3 1 1
C
8 2 8

*The player will win a toy if the pointer lands on red or green.

Label the two spinners that Jack has made.

If you play this game, which spinner will you choose to spin?

30
 Grade 6

Look at the fenced rectangular plot in Jenny’s backyard.

Jenny wants to double the length and the width of the existing rectangular plot.
She thinks that the amount of fencing needed will double too. Is she correct?
Jenny then decides to seed her new backyard with grass seeds. If it takes two bags
of grass seeds to cover the old plot, how many bags of grass seeds are needed to
cover the new plot?

31
 Grade 6 PRACTICE 8
A bag of gumballs is shown below. What is the perimeter of the triangle?

*R = Red
B = Blue
G = Green

16.5 cm
18 cm
Which sentence is not true?
19 cm
It is more likely to draw red than
green. 20 cm
Blue has the greatest chance to
be drawn. What is the smallest 4-digit number
Red has less chance to be drawn that can be formed with 0, 1, 3, 6?
than blue.
1306
It is equally likely to draw red and
1036
green.
1006
6310
Joseph walks 7.8 m in 6 s. How fast
does he walk?
0.13 m/s
1.3 cm/s
130 cm/s
13 000 mm/s

32
If Bob drives at 58 km/h for 2 hours Eighteen blocks measuring 4 cm by
and 62 km/h for another hour, how 2 cm by 2 cm fit into the rectangular
far will he travel? prism perfectly.
120 km
186 km
174 km
178 km

Which set of values is represented by

the 4 points on the number line?

What is the volume of the rectangular

prism in cubic centimetres?
72 cm3

1.32, 1.38, 1.4, 1.45 144 cm3

1.31, 1.34, 1.35, 1.4 192 cm3

1.302, 1.309, 1.4, 1.405 288 cm3

1.31, 1.314, 1.315, 1.41

Josephine’s father is 43 years and
4 months old. How old is he in
months?
516
520
47
564

33
 8

Sue has made an input-output machine. When the input number is 9, the output
number is 56.

Write 3 input numbers and find the corresponding output numbers.

Then design a similar machine that works in a reverse direction. Use the same pair
of input and output numbers as above in your design.

34
 Grade 6

Jason is in Town A. He wants to go to Town C through Town B.

Draw a tree diagram to show all the possible routes that Jason can take. Suggest
the shortest route to him.

35
 Grade 6 PRACTICE 9
A food bank collected 360 cans of Which of the following is equivalent
food last month. Sarah helped put to 9 ?
the cans equally into 45 boxes. How 20
many cans are there in each box? 0.018
6 45%
7 4.5%
8 1.8
9

Two bags of candies weigh 2 5 kg

8
A farmer wants to plant trees around 7
and 1 kg. The candies are put into
his farm. The dimensions of his farm 8
are as follows: a jar that weighs 1 kg. What is the
8
weight of a jar of candies in total?

If the distance from one tree to the

next is 5 m, how many trees does the
farmer need?
8
33 kg
14 8
5
16 3 kg
8
78 5
4 kg
8
6
4 kg
8

36
Leo is 7 years old. His age is 2 times What is the name of the triangle
Katie’s plus 1. How old is Katie? below?
3 years old
4 years old
13 years old
15 years old

Christine has 2 strips of ribbon. If

acute isosceles triangle
one is 8.273 m long and the other is
4.876 m longer, how much ribbon obtuse scalene triangle
does she have in all? right scalene triangle
13.149 m obtuse isosceles triangle
11.67 m
18.025 m EasyWrite Pen Factory produces
21.422 m 642 boxes of pens a day. How
many boxes of pens does the
factory produce in 8 weeks if it
Susanna spent $10 on candies, closes on weekends?
$25 on movie tickets, and $15 on
magazines today. The total amount
she spent is 25% of her weekly
income. What is her daily earning if
she works on weekdays only?
$2.50
$150
$250
5136
$40
25 680
30 816
35 952

37
 9

Mrs. Smith recorded the sales of strawberry cakes last year.

Graph the data.

Which months’ sales are higher than the average monthly sales?

38
 Grade 6

Adam is making a net for a 3-dimensional figure.

Draw the missing face to complete the net.
Draw the 3-dimensional figure that is formed by the net on the grid.
Describe the figure to tell about the following:
• number of vertices and edges
• shapes of the faces

39
 Grade 6 PRACTICE 10
Which of the following is equivalent Ken and Pauline made a total of
to 0.4? 192 cookies for fundraising. If the
number of cookies that Ken made is
4 half the number that Pauline made,
100 how many cookies did Ken make?
1
25
2
5
3
5

Mary has made a special drink which

contains 355 mL of iced tea and 1.53 32
L of juice. How much drink has Mary 64
made? 128
256

A regular polygon has a side length

of 6 cm and a perimeter of 30 cm.
What polygon is it?
square
rectangle
pentagon
0.1885 L
hexagon
354.53 mL
1.885 L
5.08 L

40
What is the volume of the solid Which shape has the following
below? characteristics?
• It has 4 sides.
• It has 2 acute angles and 2 obtuse
angles.
• It has one pair of parallel lines
only.

parallelogram

1536 cm3 square

2176 cm3 rhombus

2478 cm3 trapezoid

2560 cm3
About what percent of the shape
below is shaded?
Robert had $50 in quarters. He
spent $4.50 for a bag of chips and
$7.68 for a movie ticket. How many
quarters did he have left?
151
249
755
1245

40%
0.3
33%
50%

41
 10

Each student in Mrs. Duncan’s class draws a triangle. Erica’s and Tina’s triangles are
shown in the circle.

David followed the descriptions

below to draw another triangle.
• ABC = 72˚
• BC = 8 cm
• Join the points A and C.
Draw David’s triangle with the given
line AB.
Which girl’s triangle is similar to
David’s? Explain.

42
 Grade 6

Katie recorded the marks she got on her math quizzes in a chart.

Katie spilled some chocolate milk on the chart by

accident. The spill covered the mark of her second
quiz.

The average mark of her quizzes is 79.

What did Katie get on her second quiz?
Is it possible for Katie to have an average of 85 if she
has one more quiz?

43
 Grade 6 PRACTICE 11
Two spinners are spun at the same Which pattern has the rule below?
time.
“Decrease by subtracting the same
number from each term.”
48, 24, 12, 6, 3
48, 44, 40, 36, 32
48, 46, 50, 48, 52
48, 40, 31, 21, 10

Which sentence is true about the

triangle below?
How many possible outcomes will
there be?
7
9
12
18

Karen has a hobby of collecting

nickels. If Karen’s goal is to have
nickels that are worth $10 000, how
many nickels will there be in her It has an obtuse angle.
collection? It is a right-angle triangle.
20 000 Each angle is 60˚.
50 000 The angles are in different sizes,
100 000 but their sum is 180˚.
200 000

44
Which number are the following Jack draws three vertices of a square
sentences describing? on the Cartesian plane below.
• It is between 33 and 39.
• It is a composite number.
• 5 is not a factor of it.

26
35
36
37

Joe wants to buy a dining set and an

armchair which cost $2992.36 and
$813.57 respectively. The tax for What are the coordinates of the
these items is $532.83. About how missing vertex?
much does Joe need to pay in total? (4,6)
$3100 (5,7)
$3300 (6,7)
$4100 (7,6)
$4300

It is 10:27 a.m. now. What time will

it be after 4 hours 38 minutes?
13:05
3:05 p.m.
16:05
2:05 p.m.

45
 11

Jason uses sixteen 1-cm sticks to make different rectangles. How many different
rectangles can he make?
Which rectangle has the greatest area?
Use diagrams to illustrate your answer.

46
 Grade 6

Mrs. Green had prepared some fruit punch for her family gathering. Each jar
contained 8 cups of fruit punch. Mrs. Green’s son, Johnny, recorded the number
of cups each person drank in the chart below.

How many jars of fruit punch did they drink in all? Express your answer as fraction.

47
 Grade 6 PRACTICE 12
Which of the following is equivalent How many grams of pasta are in one
to 121%? serving if 1.5 kg of pasta can serve 6
people?
12 1 0.25 g
100
0.121 25 g
121 250 g
1000 2500 g
1.21

Which statement best describes the

Ivan has a bag of candies in different transformation from IJK to MLK?
colours:
• 4 red
• 5 green
• 5 blue
• 7 yellow

Ivan took out a red candy from

the bag. If he takes out another
candy without looking, what is the
probability that the candy he picks is
green?

5
Make a 1 turn clockwise about
21 4
5 point K.
20
3 Reflect in line JK.
20 1
Make a turn about point K.
5 2
19 Reflect about point K.

48
The data below shows the number The circle graph below shows the
of babies born in a city each day in number of hours Tommy spends on
the past 5 days. different activities in a day.
21, 90, 17, 83, 79

How many babies were born each

day on average?
54
56
58
62

What is the total surface area of the

rectangular prism below in m2 ?

Tommy sleeps 8 hours a day. Which

section represents the amount of
time he spends on sleeping?
A
B
C
8 D
14
28 Which number below is a factor of
48 50 but not a composite number?
2
7
10
25

49
 12

Ashley drew a polygon on the board. She describes the polygon as follows:
• DAB = 60˚ and DA = 4 cm
• CBA = 60˚ and CB = 4 cm
What is the shape of the polygon ABCD?
Ashley bends a piece of wire to form the shape of polygon ABCD.
How long is the wire?

50
 Grade 6

There are 6 rounds in a game. Look at the scores

that Alan got in the first 4 rounds of the game.
If the mean, median, and mode of the player’s
scores are the same, then the player will win a
prize.
Suggest one set of scores that Alan should get
in the 5th and 6th rounds, so that he can win
a prize.

51
 Grade 6 PRACTICE 13

Which of the following is not Each set of values below shows the
equivalent to 3:5? lengths of the 3 sides of a triangle.
Which set of value is the side length
6:10
of an isosceles triangle?
15:20
3, 4, 5
30:50
2, 3, 2
36:60
5, 5, 5
3, 1, 4
The graph shows the distance that
Mr. Brown travelled on his trip to a
cottage.
Jane practises 3 h of piano on every
4
Monday, and 1 1 h on every Tuesday
2
and Wednesday. How many minutes
does she practise piano each week?

Mr. Brown made a stop for lunch.

When was Mr. Brown having his
lunch?
10:00 – 11:00
10:00 – 12:00 11
4
11:00 – 12:00 33
4
12:00 – 1:00 135

225

52
Tom is 1.78 m tall. Howard is taller The table shows the number of
than Tom but shorter than 2 m. How candies Mary’s robot ate on the 3rd,
tall might Howard be? 4th, 5th, and 6th days last week.
176 cm
184 cm
2.84 m
207 cm

Look at the rectangular carpet.

How many candies did Mary’s robot

eat on the 1st, 2nd, and 7th days?
1 ; 4 ; 49
If the perimeter of the carpet is 1 ; 2 ; 45
460 cm, what is its area in m2? 2 ; 5 ; 47
8 3 ; 6 ; 48
306
1.2 What is the missing number?
4.65 35 – 28 ÷ 7 x = 27

0
1
2
27

53
 13

Jason designs a pattern with a roll of string and records the side length of each
square.

The roll of string is 2.5 m long.

How many layers at most will there be in Jason’s design?

54
 Grade 6

Jessica has asked 25 children about their favourite lunch.

She organized the data and recorded the result in the chart.

Is the result reasonable? Explain.

Assume that the result for “sandwich” is correct. How many children choose
sandwich as their favourite lunch?

55
 Grade 6 PRACTICE 14
Which number are the sentences Sam has 2570 eggs. If each carton
describing? holds a dozen eggs, how many more
eggs are needed to fill up the last
• It is a composite number.
carton?
• It has 4 factors.
2
• The sum of its digits is a prime
number. 8

• It is not a factor of 42. 10

12
21
34
The distance between Judy’s house
36 and Oakfield via Clingtown is 360 km.
48

A 12-g box contains 18 chocolate

bars. If each chocolate bar weighs
117 g, how heavy is a box of chocolate
bar?
2 kg 106 g
Judy arrives at Clingtown by train.
2118 kg If she takes a bus which travels at
2 kg 118 g 55 km/h to finish off the journey,
how long will it take her?
2116 kg
3h
4h
5h
6h

56
Find the area of the L-shape figure Triangle ABC has been transformed
below. to triangle PQR.

20 m2
22 m2
Which one is the correct description
2
24 m of the transformation?
26 m2 rotation of 90˚ clockwise at (0,0)
and reflection about the x-axis

Justin wants to have a sandwich translation to the right by 3 units

for lunch. The food stall serves two and reflection about the y-axis
choices of bread and three choices reflection in the x-axis and
of meat. How many combinations rotation of 180˚ counterclockwise
are there? at (0,0)
3 rotation of 90˚ clockwise at (0,0)
and reflection about the y-axis
4
5
6 Which number is a factor of 96 and
a multiple of 16?
6
24
32
64

57
 14

Susan prepared a gift for Jack’s birthday. Look at the gift box below.

Susan has 1 m2 of wrapping paper. Do you think she has enough wrapping paper
to wrap the gift box? Explain.

58
 Grade 6

John and Mary went strawberry picking yesterday.

John picked 2 baskets of strawberries in 10 minutes and Mary picked 3 baskets in
12 minutes.
Who picked faster?
Each basket of strawberries weighed about 4.2 kg. How many kilograms of
strawberries did they pick in total in one hour?

59
 Grade 6

Which of the following number are Which pattern has this rule: “Increase
the sentences describing? by multiplying the same number to
each term.”?
• It is a prime number.
4, 6, 8, 10, 12
• It is a factor of 52.
6, 12, 18, 24, 30
• It is smaller than 10.
7, 8, 10, 13, 17
2
2, 4, 8, 16, 32
11
13
A block with a square base has a
21 side length of 21 cm and a height
of 10 cm. Mr. Campbell cuts it into
2 identical parts as shown below.
Cliff drew an angle that is 90˚ greater
than the one below.

What kind of angle did he draw? What is the volume of each part?
acute 1050 cm3
obtuse 2100 cm3
straight 2205 cm3
reflex 4410 cm3

2
A spinner is divided into 5 equal parts A triangle is drawn on the grid as
and it is labelled from 1 to 5. What shown.
is the probability that the pointer will
land on a prime number?
1
5
2
5
3
5
4
5

Which set of values is represented by

the dots on the number line?
The triangle is translated 1 unit to the
left and 2 units down. What are the
new coordinates of point A?
(0,5)
9.32, 9.34, 9.36, 9.39
(0,1)
9.32, 9.35, 9.4, 9.48
(2,1)
9.31, 9.32, 9.41, 9.42
(2,5)
9.33, 9.34, 9.43, 9.45

Which number is equivalent to 5%?

0.5
2
5
0.02
0.05

3
 Look at the equations. Mrs. Winter buys 2 cups of coffee and
a bagel with cream cheese.
c + 3 = 12
Menu
c+d=9
Item Price
What is d?
Coffee $1.45
0
3 Tea $1.50
6 Sandwich $2.85
9 Bagel* $1.75
*$0.75 extra with cream cheese

Put the fractions below from greatest What will be the change if she pays
to least. $10?

3 15 11 7 $4.60
1
1 7 7 4 4 $5.35
$5.40
15 , 11 , 1 3 , 7
7 4 7 4 $6.45

1 3 , 7 , 11 , 15
7 4 4 7
Which of the following is a factor of
11 , 7 , 1 3 , 15
4 4 7 7 52 and a prime number?
11 , 15 , 7 , 1 3 2
4 7 4 7
3
4
26

4
What is the missing number in the Look at the numbers below.
equation below?
2 5
1 52% 1.25
36 – x 3 = 60 ÷ 5 5 2
4 Put them in order from least to
greatest.
8
32 1 2 , 1.25, 5 , 52%
5 2
48
52%, 1.25, 1 2 , 5
5 2

There are 50 guests in a dining hall. 1.25, 5 , 52%, 1 2

2 5
16% of them are children. How
5, 2
many children are there in the dining 1.25, 1 , 52%
2 5
hall?
4 Joe and Leslie start travelling in
6 opposite directions from the same
8 place. Joe is travelling at 40 km/h and
Leslie is travelling at 55 km/h. How
16 far will they be apart after 2 hours?

A birthday cake weighs 1.2 kg. Which

pair of measurements is equivalent to
1.2 kg?
30 km
1200 mg and 120 000 g
95 km
1200 g and 120 000 mg
120 km
1200 g and 1 200 000 mg
190 km
120 g and 12 000 mg

5
 The capacities of 3 bottles of water Jackson is making shapes with
are recorded below. strings. He has made one square
and one rectangle and recorded their
0.82 L 450 mL 0.092 L
perimeters and areas in the chart.
Leo poured the 3 bottles of water into
a jar that has a capacity of 2.4 L. How Rectangle Square
much more water can the jar hold?
Area 12 9
0.21 L (square units)
1.038 L Perimeter
(units)
14 12
1.362 L
1.776 L
Which set of shapes is Jackson’s?

What is the answer in expanded form

to the number sentence below?

21.09 – 14.68 = ?

6 + 0.4 + 0.001
6 + 0.04 + 0.01
6 + 0.4 + 0.01
30 + 5 + 0.7 + 0.07

6
What are the first and the last terms Which statement best describes the
in the number pattern? transformation of figure M to figure N?

, 7, 15, 31, 63,

3 ; 726
3 ; 127
4 ; 126
5 ; 71

The cube below holds 0.8 kg of sand.

Make a 1 turn at (3,8).

4
Make a 1 counterclockwise turn
4
at (8,3).

Reflect in line l.
How many kilograms of sand are
needed to fill the sandbox that Translate 6 units to the left and 6
measures 1.2 m long, 0.5 m wide, units down.
and 0.1 m deep?
20 0.5 L of milk makes 150 chocolate
48 blocks. If Mrs. Collin has 2.5 L of milk,
how many chocolate blocks can she
60
make?
480
30
500
750
7500

7
 Which of the following is a scalene The pictograph below shows the
triangle? number of bags of chips in different
flavours sold in a store yesterday.

Number of Bags of Chips

in Different Flavours Sold

Ketchup

Sour Cream

Barbecue

Cheese

represents 8 bags.

How many bags of chips were sold in

all?
9.5
38
70
76

Laura has a collection of jewels. She

uses 16 of them, which is 25% of her
collection, to decorate her musical
box. How many jewels are there in
Laura’s collection now?
48
36
64
400

8
Sam and George leave their warehouse at the same time to deliver the ordered
items to two different places.
Sam drives at a speed of 72 km/h to City Balas and George drives at a speed of
45 km/h to Brookville.

How far will they be apart after 2 hours?

What is the difference between their arrival times?

9
 There was a jar of 24 chocolate eggs without peanuts. Jack took out 2 chocolate
eggs from the jar and ate them.
Jack’s mom puts a bag of chocolate eggs with peanuts into the jar today. The
probability of drawing a chocolate egg without peanuts is 1 .
3
How many chocolate eggs with peanuts are there in the jar?

10
A wooden rectangular block is cut into two identical triangular prisms.

What is the volume of each triangular prism?

Mr. Campbell wants to paint the triangular prisms red. What is the total surface
area to be painted?

11
 Bonnie drew an isosceles right-angle triangle. The length of the longest side of the
triangle is 8 cm.
She cuts the triangle into 8 identical triangles. What is the area of each small
triangle?
You may draw the triangle on the centimetre grid to work out your answer.

12
Lori has a sticker-making machine. The number of stickers it can make depends on
how much glue she has. The chart below shows their relationship.

Amount of Glue (mL) No. of Stickers Made

2 2
4 6
6 10
8 14

If Lori puts 20.4 mL of glue into the machine, how many stickers can sh e make?
Lori has two bottles of glue, one 4 mL and the other 8 mL. Should she put the glue
into the machine at two different times or at the same time? Explain.

13
 There are 80 people in the school playground. 5% of them are teachers and the
rest are children.
There are 60 people in the gymnasium. 0.15 of them are teachers and the rest are
children.
What is the ratio of the number of teachers to all the people in each place? Which
place has a higher ratio?

14
The shape that Flora makes is symmetrical in line d.
Help her complete the shape and write the coordinates of the vertices of the shape.

Make a 1 turn of the shape at (3,4) and write the coordinates of the vertices of
2
the image.

15
 There is a summer sale at Eddie’s Grocery Store. Every customer receives a box of
orange juice for free with the purchase of 2 bags of chips.
Olivia paid $40 for 7 bags of chips at $3.86 each and some boxes of orange juice
at $2 each and recieved $2.98 change.
How many boxes of juice did Olivia get in total?

16
 Grade 6

Practice 1 9. Time needed at normal speed: 216 ÷ 8 = 27

It takes the robot 27 s at normal speed.
1. 3
Time needed at turbo speed: 216 ÷ 9 = 24
2. The maximum driving speed is 50 km in 1
h. Time saved: 27 – 24 = 3
3. m2 3 seconds will be saved.
4. three quarters of a litre 10. Length of wire: (30 + 18) x 2 = 96 (cm)
5. $23 6. 22 Side length of square: 96 ÷ 4 = 24 (cm)
2, 1, 4, 5 The side length of the square is 24 cm.
7. 1 1 Area of the rectangle: 540 cm2
3 2 3 4
8. Bruce has 5 more marbles than Ted. Area of the square: 576 cm2
9. The square does not have the same area as
the rectangle.
10. She buys 6 apples and 20 oranges, or 21
apples and 5 oranges. Practice 4
11. 1. 480
2. B is larger than A by 3 cm2.
Uncle Jimmy will
need 13 pieces 6
3. 4. 8
of sod. 7
5. 100 + 90 + 0.7 + 0.06
6. 19 7. 64, 32, 16, 8, 4
Practice 2 1
8. 9. B
1. 2.84, 2.86, 2.90, 2.98 2
10.
2. 5.617 3. 2, 3, 4, 6, 7, 8
4. 127 5. 18:08
6. 30 m3 7. m3
8. (8,2)
9.

Amy’s commission is closest to $600.

11. P & W: $3.96 + $2.08 = $6.04
Onville: $4.20 + $1.29 = $5.49
It is a parallelogram. A parallelogram has Abby should choose Onville Grocery. The
2 pairs of lines that are equal in length and total cost is $5.49.
parallel to each other. It also has 2 pairs of
equal angles that are opposite to each other. Practice 5
Its area is 30 square units.
10. Mean: 53 trees ; Median: 47 trees ; 1. 810 2. 9:8 3. $64
Mode: 43 trees 4. 2 7 , 200%, 1.875
✃

Janet should use the mean because it is the 10

largest value among the three. 5. 265 6. 1100
7. 54 8.
Practice 3 9. 15
1. 18 ÷ 3 2. 41˚ 10. The probability of matching each guess:
3. 5 cm 4. 5, 13, 21, 29, 37 4 6 4

Guess 1: ; Guess 2: ; Guess 3:
5. A and C 16 16 16
6. 1.023, 1.203, 1.302, 1.320 I will choose Guess 2 because it has the
1 greatest chance of winning a prize.
7. 0.92 8.
8
1
 11. of winning a toy with spinner C is greater
than spinner A.
10.
They share: 69 – 24 – 7 = 38 (cards)
No. of cards Tom gave Jack: 38 ÷ 2 = 19
(cards)
Perimeter of A: 10 m ; Area of A: 6 m2
Tom has: 69 – 19 = 50 (cards)
Perimeter of B: 20 m ; Area of B: 24 m2
Jack has: 24 + 19 = 43 (cards)
Yes, the amount of fencing needed will double.
So Tom has 50 cards and Jack has 43 cards.
The area of the new plot is 4 times the old
one, so 8 bags of grass seeds are needed to
Practice 6 cover the new plot.
1. 1:05 p.m. 2. 2 cm
3. 550 mL 4. 0.3 Practice 8
5. 4 6. 6:1 1. It is more likely to draw red than green.
7. 450 000 m 8. 1.22 2. 130 cm/s 3. 20 cm
9. No. of : 3 ; 6 ; 10 ; 15 4. 1036 5. 178 km
Pattern rule: Start at 3. Add 3 and increase 6. 1.32, 1.38, 1.4, 1.45
the number you add by 1 each time. 7. 288 cm3 8. 520
No. of balls of modelling clay with 10 layers: 9. (Suggested answers)
15 + 6 + 7 + 8 + 9 + 10 + 11 = 66 input: 1 ; output: 24
Louise has 66 – 2 = 64 balls of modelling clay. input: 2 ; output: 28
10. input: 3 ; output: 32
input: 24 ; output: 1
input: 28 ; output: 2
input: 32 ; output: 3
10.

Rotate triangle A 1 clockwise about P and

2
draw the image. Then rotate triangle A
1 The shortest route is via Hwy. 6 and
counterclockwise about P and draw the
4 Hwy. 11 through Town B. It is 350 km long.
image.

Practice 9
Practice 7
1. 8 2. 16 3. 45%
3 5
1. 135˚ to 145˚ 2. 4. 4 kg 5. 3 years old 6. 21.422 m
8 8
3. 4 h 15 min 4. 37
7. $40 8. obtuse scalene triangle
5. 2810 m 6. hexagonal prism
9. 25 680
7. (6,2)
10.
8. 13 rows of 13 scouts
9. Left spinner: C ; Right spinner: A
The probability that the pointer will land on
red or green:

Spinner A: 3 ; Spinner C: 7
8 8
I will choose spinner C because the probability

2
 Grade 6

Average monthly sale: 400 strawberry cakes 10.

The months that have monthly sales higher
than average are: April, August, September,
October, and November.
11.
Total number of jars of fruit punch drunk:
1 1
1 + 1 + =2
8 8
The net forms a triangular prism which has 1
6 vertices, 9 edges, 2 triangular faces, and 3 They drank 2 jars of fruit punch in all.
8
rectangular faces.
Practice 12
Practice 10 5
1. 1.21 2. 3. 250 g
20
2 4. Make a 1 turn about point K.
1. 2. 1.885 L 2
5 5. 58 6. 28
3. 64 4. pentagon 7. B 8. 2
5. 2176 cm3 6. 151 9. It is a trapezoid.
7. trapezoid 8. 33% The perimeter of
9. ABCD is 18 cm, so the
wire is 18 cm long.
Erica’s triangle is similar 10. (Suggested answer)
to David’s because the First 4 scores in order: 53, 62, 68, 75
three corresponding Choose 62 to be the median and mode, so
angles are equal. one of the unknowns is 62. Then find the
other unknown so that the mean is 62.
Sum of the first 5 scores: 320
10. Total mark: 79 x 5 = 395 Sum of all the scores: 62 x 6 = 372
Second quiz’s mark: Difference between the two sums: 52
395 – (78 + 85 + 69 + 74) = 89 So, the other unknown is 52.
Katie got 89 marks on her second quiz. The two scores are 52 and 62.
She will need 85 x 6 – 79 x 5 = 115 (marks)
to get an average of 85, which is impossible.
Practice 13
So Katie will not get an average of 85 with
one more quiz. 1. 15:20 2. 11:00 – 12:00
3. 2, 3, 2 4. 225
Practice 11 5. 184 cm 6. 1.2
7. 1 ; 4 ; 49 8. 2
1. 12 2. 200 000
9.
3. 48, 44, 40, 36, 32 4. Each angle is 60˚.
5. 36 6. $4300
7. (6,7) 8. 3:05 p.m.
9. Area in cm2:
A: 7 Amount of string needed for 6 layers: 1.88 m
B: 12 Amount of string needed for 7 layers: 2.8 m
C: 15 So, there are at most 6 layers in Jason’s design.
D: 16 10.
No. The result is not reasonable because the
sum of the data is not 100%.
He can make 4 different rectangles. The The number of children who choose
rectangle with dimensions 4 cm by 4 cm has sandwich is 20% of 25, which is 5.
the greatest area.

3
 Grade 6

Practice 14 29. No. of chocolate eggs without peanuts: 22

No. of all chocolate eggs: 22 x 3 = 66
1. 34 2. 2 kg 118 g
Portion of chocolate eggs with peanuts:
3. 10 4. 4 h
1 – 1 = 2
2
5. 22 m 6. 6
7. rotation of 90˚ clockwise at (0,0) and 3 3
No. of chocolate eggs with peanuts:
reflection about the x-axis
2 44
8. 32 =
3 66
9. Susan has 10 000 cm2 of wrapping paper There are 44 chocolate eggs with peanuts in
and she needs 2700 cm2. Susan has enough the jar.
wrapping paper. 30. The volume of each triangular prism is 4860
10. To pick one basket of strawberries, John cm3. The total surface area to be painted is
needed 5 min and Mary needed 4 min, so 4320 cm2.
Mary picked faster. 31.
John picked 12 baskets and Mary picked 15
baskets in an hour. They picked a total of
27 baskets in an hour which weighed a total
of about 113.4 kg.

Assessment
1. 2 2. reflex The area of each small triangle is 2 cm2.
3. 2, 4, 8, 16, 32 4. 2205 cm3 32. Lori can make 38 stickers with 20 mL of glue.
3 4 mL makes 6 stickers and 8 mL makes 14.
5. 12 mL makes 22 stickers. She should put the
5
6. 9.32, 9.35, 9.4, 9.48 glue into the machine at the same time.
7. (0,1) 8. 0.05 9. 0 33. Ratio in playground:
teachers: all= 4:80 = 1:20
10. 11 , 15 , 7 , 1 3
4 7 4 7 Ratio in gymnasium:
11. $4.60 12. 2 teachers: all= 9:60 = 3:20
13. 8 14. 8 The gymnasium has a higher ratio of teachers.
15. 1200 g and 1 200 000 mg 34.

16. 52%, 1.25, 1 2 , 5

5 2
17. 190 km 18. 1.038 L
19. 6 + 0.4 + 0.01
20.

21. 3 ; 127 22. 48

1
23. Make a 4 counterclockwise turn at (8,3).
24. 750 25. Coordinates of the shape:
(3,2), (1,4), (2,7), (6,3)
Coordinates of the image:
26.48 27. 76
(3,6), (5,4), (4,1), (0,5)
28.Sam travelled in 2 h: 72 x 2 = 144 (km)
George travelled in 2 h: 45 x 2 = 90 (km) 35. Olivia paid $40 – $2.98 = $37.02.
They will be 144 + 90 = 234 (km) apart after 7 bags of chips cost $27.02, so Olivia spent
2 hours. $37.02 – $27.02 = $10 on 5 boxes of orange
Sam needs 3 hours and George needs 4 hours juice. She got 3 boxes of orange juice for
to arrive at their destinations. The difference free, so she has 8 boxes in total.
between their arrival times is 1 hour.