Review of Essential Skills
from Grade 6
Chapter 1: Factors and Exponents
Place Value
Every digit in a number has a different place value. The location of the
digit determines its place value.
The number 5962 is shown in the place value table below. Notice, for
example, that the place value of the 9 is the tens column.
Thousands
Hundreds
Tens
Ones
5
6
9
2
1. Copy and complete the table.
Ten thousands
1
4
3
Hundreds
Tens
9
2
6
7
Factors
Ms. Zimm has 24 girls in a physical education class. She uses factors of
24 to group them for different exercises. A factor is a number that is used
to make a product.
Here is an organized list for finding all the factors of 24.
Try 1:
Try 2:
Try 3:
Try 4:
Try 5:
Try 6:
1 3 24 5 24
1 and 24 are factors of 24.
2 3 12 5 24
2 and 12 are factors of 24.
3 3 8 5 24
3 and 8 are factors of 24.
4 3 6 5 24
4 and 6 are factors of 24.
5 3 ? 5 24
5 is not a factor of 24.
6 is already known to be a factor of 24.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
2. Find all the factors of each number.
a) 28
b) 32
c) 56
d) 29
e) 39
f) 51
3. Which numbers have 8 as a factor?
a) 30
b) 40
c) 48
d) 54
e) 87
f) 104
4. a) What number do you try first when finding all the factors of 27?
b) What pair of factors do you get?
440 Review of Essential Skills from Grade 6: Chapter 1
NEL
c) What number do you try next?
d) Do you get a factor?
e) Continue until you have all the factors of 27.
Prime and Composite Numbers
A number with only two different factors, 1 and itself, is a prime number.
55531
A number with more than two factors is a composite number.
85432
85831
The number 1 is neither prime nor composite. 1 5 1 3 1
5. Copy and complete the table.
Number
Factors
1
1
2
1, 2
3
1, 3
4
1, 2, 4
Number of factors
Prime or composite
5
6
…
19
20
Operations with Whole Numbers
“The contest winner must first correctly answer a skill-testing question.”
Find the value of 48 4 6 1 2 3 5 2 4.
There are rules for the order of operations.
• Perform any operations within brackets.
• Multiply and divide in order from left to right.
• Then add and subtract in order from left to right.
6. Evaluate.
a) 4 3 24 4 6 2 10 1 5
b) 5 1 8 4 2 2 3
c) 47 2 9 3 2 4 6
48 4 6 1 2 3 5 2 4
58123524
5 8 1 10 2 4
5 14
d) 9 3 12 3 12 4 12
e) 12 1 5 3 3 2 36 4 2
f) 7 1 6 3 3
g) 6 3 5 2 4 4 2
h) 9 2 5 1 4 3 8 2 15 4 3
i) 27 4 3 3 8 2 15 3 4 1 2
7. Copy each statement, and use ,, ., or 5 to make it true.
a) 8 1 7 3 5 ■ 8 3 7 1 5
d) 23 2 12 4 6 ■ 2 1 6 3 3
b) 7 1 2 3 4 ■ 5 3 2 1 6
e) 5 3 5 4 5 ■ 5 4 5 3 5
c) 5 3 9 4 3 ■ 8 1 4 3 8
f) 36 4 12 4 3 ■ 24 4 12 4 2
NEL
Review of Essential Skills from Grade 6: Chapter 1
441
Chapter 2: Ratio, Rate, and Percent
Comparing and Ordering Decimal Numbers
The results for the school 100 m race are shown below.
John
14.30 s
Sam
12.48 s
Henrietta
14.14 s
Christa
13.95 s
Alfred
13.98 s
Henrietta’s time is less than John’s time.
14.14 , 14.30
1 tenth is less than 3 tenths.
Alfred’s time is greater than Christa’s time.
13.98 . 13.95
8 hundredths is greater than 5 hundredths.
1. Copy and complete.
a)
b)
2. Draw a number line 10 cm long.
a) Mark your number line to show 6.0, 6.1, …, 7.0.
b) Use a ruler to mark accurately the point halfway between 6.3
and 6.4.
c) What is the number you marked in part (b)?
Multiplying and Dividing by Powers of 10
A calculator was used to multiply and divide by powers of 10. What
patterns are shown below?
2.4 3 100 5 240
2.4 3 10 5 24
2.4 3 1 5 2.4
2.4 3 0.1 5 0.24
2.4 3 0.01 5 0.024
2.4 4 1000 5 0.0024
2.4 4 100 5 0.024
2.4 4 10 5 0.24
2.4 4 1 5 2.4
3. Evaluate.
a) 45 3 10
45 3 0.1
45 3 0.01
45 3 0.001
b) 100 3 32.15
0.1 3 32.15
0.01 3 321.5
0.01 3 3.215
4. Evaluate.
a) 7.3 3 10
b) 33.65 4 10 000
c) 10 000 3 87.56
d) 100 000 3 85.48 g) 425.7 4 10
e) 4.315 3 0.01
h) 9.8 3 1000
f) 0.7462 4 100
i) 76.93 3 0.001
c) 40.32 4 100
4.032 4 100
403.2 4 10
40.32 4 1
442 Review of Essential Skills from Grade 6: Chapter 2
NEL
Ratios
A ratio is a comparison of two numbers. For example, the front gear on
Rob’s bicycle has 46 teeth and the back gear has 18 teeth. The gear ratio
of a bicycle compares the number of teeth on the front gear to the number
of teeth on the back gear.
The gear ratio can be written in three different ways:
46
46 to 18
46 :18
}}
18
The numbers 46 and 18 are the terms of the ratio. The units of the
measurements are not written because they are the same.
5. One of the gear ratios possible for a five-speed bike is 40 :17. How
many teeth are on the front gear? How do you know?
6. Express each ratio in three different ways.
a) 4 out of 9 bicycles are 15-speed bicycles
b) 5 out of 9 bicycles are not 15-speed bicycles
7. There are about 26 students for every teacher in a school. What is the
student-teacher ratio?
Meaning of Percent
In a survey, 54 out of 100 Grade 5 students could name the ten provinces
of Canada. The result can be shown as a fraction or as a decimal number.
54
}} “54 hundredths”
0.54 “54 hundredths”
100
To write this result as a percent, replace “hundredths” with “%.” The
symbol % is read as “percent.”
This means that 54% of the students asked could name the ten provinces
of Canada.
8. Write each ratio as a percent.
83
1
a) }}
b) }}
100
100
c) 50 :100
9. Write each decimal number as a percent.
a) 0.45 b) 0.76 c) 0.40 d) 0.08
e) 0.80
10. Estimate the percent of each shape that is shaded.
a)
b)
NEL
d) 9 out of 100
e) 100 out of 100
f) 0.8
c)
Review of Essential Skills from Grade 6: Chapter 2
443
Fractions and Decimal Numbers as Percents
About }3} of a circle is shaded. What percent of the circle is shaded?
4
First express the fraction as a decimal number. To do this, divide the
numerator by the denominator.
0.75
4q3w.0
w0w
3
}}
4
3
}} 5 0.75 or 75%
4
About 75% of the circle is shaded.
11. Write each decimal number as a percent.
a) 0.08 b) 0.7
c) 0.45 d) 0.37
e) 0.008 f) 0.5543
12. Write each fraction as a decimal number and as a percent.
1
4
1
6
12
5
a) }}
b) }}
c) }}
d) }}
e) }}
f) }}
10
5
2
8
16
8
13. There are 16 boys and 9 girls in a class.
a) What percent of the students are girls?
b) What percent of the students are boys?
Percents as Decimal Numbers and Fractions
12.5% of an iceberg is above the surface of the ocean.
To write the percent as a decimal number or a fraction, replace “%” with
“hundredths.”
12.5% 5 12.5 hundredths
12.5% 5 12.5 hundredths
12.5
5 }}
100
125
5 }}
1000
1
5 }}
8
5 0.125
About 0.125, or }1}, of an iceberg is above the surface of the ocean.
8
14. Copy and complete the table.
Fraction
Decimal number
Percent
0.01
1
}}
10
5%
3
}}
8
0.2
25%
444 Review of Essential Skills from Grade 6: Chapter 2
NEL
Chapter 3: Data Management
Information on a Graph
Depending on the type of graph, some or all of the following information
must be included: a main title, an x-axis title, a y-axis title, a scale or
interval, and a legend.
1. List the information that is missing from this graph.
2. List the points given on the scatter plot shown.
3. Look at the circle graph shown.
a) What is the largest part
of Kevin’s day?
b) What does he spend the
least amount of time
doing?
c) How much more time
does he spend in school
than playing basketball?
NEL
Review of Essential Skills from Grade 6: Chapter 3
445
Range
The range of a set of data is the difference between the maximum value
and the minimum value.
For example, Karen examined the range of the prices of gasoline over a
two-week period. She noticed that the highest price was $0.89 per litre
and the lowest price was $0.71 per litre. The range of the prices was
$0.89 2 $0.71 5 $0.18.
4. Canadian Joanne Malar swam the 200 m individual medley in the
following times. State the range of the swimming times.
Year
Swimming time (s)
1991
1993
1995
1997
1998
139.14
134.35
135.66
136.17
133.26
Mean, Median, and Mode
Canadian diver Alexandre Despatie received the following scores for a
10 m platform dive.
Judge
France
Spain
Canada
Italy
United States
Score
8.5
9.0
9.5
10.0
9.5
To find the mean of a set of data, calculate the
sum of all the pieces of data and divide by the
number of pieces of data.
(8.5 1 9.0 1 9.5 1 10.0 1 9.5) 4 5
5 46.5 4 5
5 9.3
The mean of Despatie’s scores is 9.3.
To find the median of a set of data, order the
data from smallest to largest and then identify
the piece of data that is in the middle.
8.5, 9.0, 9.5, 9.5, 10.0
To find the mode of a set of data, identify the
piece of data that occurs most often.
The score that appears most often is 9.5, so the
mode is 9.5.
The median of Despatie’s scores is 9.5.
5. Despatie received these scores for another 10 m platform dive.
Judge
Canada
Japan
South Africa
Russia
China
Score
9.5
9.0
8.5
9.0
8.5
a) What is the mean of Despatie’s scores?
b) What is the median of Despatie’s scores?
c) What is the mode of Despatie’s scores?
446 Review of Essential Skills from Grade 6: Chapter 3
NEL
Chapter 4: Patterns and Relationships
A calculator can be a helpful tool when exploring
number patterns. You may use a calculator in the
following activities.
Addition Patterns in a Hundreds Chart
Look at the hundreds chart at the right.
1. Put a square box around any four numbers in the hundreds chart. For
example, you could put a square box around 32, 33, 42, and 43.
a) Add the numbers in each diagonal of your box.
b) What do you notice about each sum in part (a)?
c) Repeat parts (a) and (b) for other square boxes around groups of
four numbers. What do you notice?
2. Now place a square box around any group of nine numbers in the
hundreds chart.
a) Find the sum of the numbers in each diagonal. What do you notice?
b) How does your pattern in part (a) compare with any pattern you
saw in question 1?
c) What other patterns do you see?
d) Find the sum of the numbers in the centre column and the centre
row. What do you notice? Is there a pattern?
e) Repeat parts (a) to (d) for other square boxes around groups of
nine numbers in the hundreds chart. Do you need to modify your
patterns based on other discoveries?
3. Predict what addition patterns you might discover if you drew a
square box around any group of 16 numbers in the hundreds chart.
a) Check your predictions by adding.
b) Try other 4-by-4 squares in the hundreds chart to verify your
predictions.
NEL
Review of Essential Skills from Grade 6: Chapter 4
447
4. Suppose that you turned a square so it was in the shape of a diamond
and placed it around any five numbers in the hundreds chart.
a) Predict what addition patterns you might find.
b) Check your predictions by adding numbers in the hundreds chart.
5. Now place a rectangle around any six numbers in the hundreds chart
so that the rectangle covers three numbers in one row and three
numbers in the row directly underneath it.
a) Find all the patterns that you can.
b) Compare your patterns with the patterns of other students in
your class. What do you notice?
6. Create a pattern of your own based on the numbers in the hundreds
chart. Show your pattern to other students in your class, and verify to
them that your pattern works in all cases.
Multiplication Patterns
7. Put a square box around any four numbers in the hundreds chart. For
example, you could put a square box around 32, 33, 42, and 43.
a) Multiply the numbers in each diagonal of your box. Then
subtract the smaller number from the larger number.
b) What do you notice about your difference in part (a)?
c) Repeat parts (a) and (b) for other square boxes around groups of
four numbers. What do you notice?
8. Now place a square box around any group of nine numbers in the
hundreds chart.
a) Multiply the numbers in the opposite corners of your box. Find
the difference between the two products.
b) Multiply the three numbers in each of the diagonals of your box.
Find the difference of the two products.
c) Divide your answer in part (b) by your answer in part (a). What
do you notice?
d) Repeat parts (a) to (c) for other square boxes around groups of
nine numbers in the hundreds chart. Do you need to modify your
patterns based on other discoveries?
9. Create a pattern of your own based on the numbers in the hundreds
chart. Show your pattern to other students in your class, and verify to
them that your pattern works in all cases.
448 Review of Essential Skills from Grade 6: Chapter 4
NEL
Chapter 5: 2-D Measurement
Converting between Units
To convert between units, you can multiply or divide by powers of 10.
To convert 5 km to metres, you need to know that 1 km 5 1000 m.
5 km 5 5 3 1000 m
5 5000 m
To convert 12 cm to metres, you need to know that 100 cm 5 1 m.
12 cm 5 12 4 100 or 0.12 m
1. Copy and complete the table. The first row is done for you. What
patterns can help you complete the table?
Millimetres
(mm)
4 800
Centimetres
(cm)
Decimetres
(dm)
480
48
Metres
(m)
Kilometres
(km)
4.8
0.0048
90 000
2
8000
3
76 400
Perimeter
What is the distance around this figure?
Perimeter 5 7 cm 1 16 cm 1 10 cm 1 4 cm 1 3 cm 1 12 cm
5 52 cm
2. Find the perimeter of each shape.
a)
b)
NEL
c)
d)
Review of Essential Skills from Grade 6: Chapter 5
449
Area of a Rectangle
The amount of surface that a region occupies is the area of the region.
Area is measured in square units.
Find the area of this rectangle.
Find the area of this square.
Area 5 length 3 width
58m33m
5 24 m2
Area 5 length 3 width
5 9 cm 3 9 cm
5 81 cm2
3. Find the area of each shape.
a)
e)
b)
f)
c)
g)
d)
Area of a Parallelogram
Finding the area of a parallelogram is similar to finding the area of a
rectangle.
450 Review of Essential Skills from Grade 6: Chapter 5
NEL
The area of the rectangle and the area of the parallelogram are the same.
The area of the parallelogram is found as follows:
Area 5 base length 3 height
5 7 cm 3 4 cm
5 28 cm2
4. Find the area of each parallelogram.
c)
a)
d)
b)
Area of a Triangle
The area of a triangle is half the area of a parallelogram.
The area of this triangle is found as follows:
Area 5 0.5 3 base length 3 height
5 0.5 3 3 cm 3 4 cm
5 6 cm2
5. Find the area of each triangle.
b)
a)
NEL
c)
Review of Essential Skills from Grade 6: Chapter 5
451
Chapter 6: Addition and Subtraction of Integers
Positive and Negative Numbers
13 is a positive number.
11, 12, 13, 14, … are all positive numbers.
These numbers can also be written as 1, 2, 3, 4, … without the 1 sign.
23 is a negative number.
21, 22, 23, 24, … are all negative numbers.
When writing a negative number, the negative (2) sign is always shown.
1. Copy the word. Next to it, write a word with the opposite meaning.
a) increase
c) minus
e) down
g) rise
b) backwards
d) win
f) gain
h) spend
i) below
j) positive
2. What temperature is shown on each thermometer?
a)
c)
e)
b)
d)
f)
3. Which number in each pair of numbers would be to the right on a
number line? Use , or . to make a true statement.
a) 5 or 7
b) 10 or 0
c) 19 or 9
d) 23 or 28
4. Arrange the numbers in each group in order from least to greatest.
a) 12, 3, 9, 0, 18, 5 b) 15, 7, 108, 15, 6, 7
c) 13, 10, 7, 4, 109, 88
5. Evaluate the following expressions. Evaluate as many of them as
you can using mental math.
a) 12 2 5
g) 12 2 5 2 7
m) 5 2 3 1 6 2 2 1 4 1 7 2 13
b) 5 1 9
h) 15 2 8 2 3
n) 12 2 7 2 3 2 2 1 8 2 5 1 1
c) 4 1 3 1 8
i) 9 2 6 2 8
o) 11 2 9 1 7 1 1 2 5 2 3 1 2
d) 7 1 0 1 9 1 4
j) 7 2 3 2 2
p) 4 1 5 2 6 1 10 2 11
e) 5 1 9 2 2
k) 10 2 5 1 3 2 7 1 9 2 2 q) 12 2 5 1 9 2 12 2 3 1 10 2 9
f) 8 1 6 2 12 1 1 l) 3 1 9 2 6 2 2 2 3 1 1
r) 3 1 14 2 12 2 4 1 8 2 7 1 10
452 Review of Essential Skills from Grade 6: Chapter 6
NEL
Chapter 7: 2-D Geometry
Polygon
A polygon is a two-dimensional closed shape that is formed by line
segments.
not a polygon
(not a closed shape)
not a polygon
(not formed with
straight lines)
a polygon
1. Name the shape, and state whether or not it is a polygon.
a)
c)
e)
b)
d)
f)
Angles
An angle is the amount of space between two lines that intersect. An
angle is measured in degrees. A protractor can be used to measure an
angle. For example, /ABC is 45°.
2. Use a protractor to measure each angle.
a)
NEL
b)
c)
d)
Review of Essential Skills from Grade 6: Chapter 7
453
3. Use a protractor to draw each angle.
a) 40°
b) 75°
c) 110°
d) 145°
Types of Angles
Angles of different measurements have different names.
Angle measurement
Name of angle
less than 90°
acute
90°
right
between 90° and 180°
obtuse
180°
straight
between 180° and 360°
reflex
4. What is the name of each angle?
a) 40°
b) 90°
c) 220° d) 180°
e) 14°
f) 95°
Congruent and Similar
Two shapes are congruent if they have the same size and shape. Two
shapes are similar if they have the same shape but are not the same size.
5. Are the following shapes congruent or similar?
a)
c)
b)
d)
Slides, Flips, and Turns
In previous years, you worked with geometric patterns and discovered
how their properties can help you solve problems.
6. Would you slide, flip, or turn the coloured shape to match the
tracing? How do you know?
a)
b)
454 Review of Essential Skills from Grade 6: Chapter 7
c)
NEL
7. Copy and complete the other half of each figure.
a)
c)
b)
8. Copy each diagram onto grid paper. Draw the slide or flip image
indicated.
NEL
a)
d)
b)
e)
c)
f)
Review of Essential Skills from Grade 6: Chapter 7
455
Chapter 8: Variables, Expressions, and Equations
Symbols
Symbols can be used to show information in a more compact form.
Symbols can be used to represent numbers. For example, some companies
use letters to represent their phone numbers to help you remember their
phone numbers.
Look at the keypad on any phone.
1. a) What phone number is represented by 555-SAVE?
b) What type of company might use this number?
2. a) What phone number is represented by 555-TIME?
b) What type of company might use this number?
3. Use the phone number 555-3325.
a) Create a word that could be used to remind you of this number.
b) What type of company might use this number? Give reasons for
your answer.
4. a) Think of your own company. What does it sell? Who are its
customers?
b) What phone number might you want so that you could use it in
an advertisement?
c) Create an advertisement that uses this phone number.
Bar Codes
In many stores, products are labelled with bar codes like the one on the
back of this student textbook. The label is a number of bars, both thin and
thick, that are quickly read by a bar code reader.
5. What do you think a bar code represents?
6. Why do you think stores and companies use bar codes instead of
numbers?
7. Do you think each store or company has a different set of bar codes?
Why?
8. Look at the bar code on the back of this textbook. How do you think
each number is represented by each bar? Compare your answer with
other students’ answers.
456 Review of Essential Skills from Grade 6: Chapter 8
NEL
Chapter 9: Fraction Operations
Fractions
A fraction is a part of a whole. The top part of a fraction is called the
numerator. The numerator represents how many parts of the whole there
are. The bottom of a fraction is called the denominator. The denominator
represents how many equal parts the whole is divided into.
The numerator indicates how
many sections of the rectangle
are coloured in.
4
}}
9
The denominator indicates how
many equal sections the whole
rectangle is divided into.
1. Write the fraction that represents each description.
a) a circle divided into 6 sections, with 5 sections coloured in
b) a fraction strip divided into 5 sections, with 2 sections coloured in
c) a 4-by-4 grid, with 7 squares coloured in
d) a pizza cut into 10 slices, with 3 slices eaten
Proper Fractions
A proper fraction is a fraction with a numerator that is smaller than the
denominator. For example, }1} is a proper fraction.
3
Improper Fractions
An improper fraction is a fraction with a numerator that is larger than the
denominator. For example, }11} is an improper fraction.
4
Mixed Numbers
A mixed number is a combination of a whole number and a proper
fraction. For example, 2}1} is a mixed number.
4
To convert a mixed number to an improper fraction, multiply the
denominator by the whole number. Add the result to the numerator to get
the numerator of the improper fraction. The denominator stays the same.
NEL
Review of Essential Skills from Grade 6: Chapter 9
457
1
2(3) 1 1
Convert 3 }1} to an improper fraction: 3}} 5 }}
2
2
2
7
5 }}
2
2. Convert each mixed number to an improper fraction.
1
2
5
3
a) 4}}
b) 7}}
c) 1}}
d) 8}}
3
9
6
5
To convert an improper fraction to a mixed number, divide the numerator
by the denominator. Your whole number answer becomes the whole
number in the mixed number. The remainder becomes the numerator of
the fraction, and the denominator stays the same.
11
3
Convert }11} to a mixed number: }} 5 2}}
4
4
4
3. Convert each improper fraction to a mixed number.
7
16
31
13
a) }}
b) }}
c) }}
d) }}
3
9
5
6
Comparing and Ordering Fractions
Fractions are easily compared if they have the same denominator. If they
do not have the same denominator, follow these steps:
• First find the LCM of the denominators. This number is called the
lowest common denominator (LCD).
• Then write equivalent fractions using the LCD.
For }2} and }4}, the LCM of 3 and 5 is 15.
3
5
10
}}
15
, }112}5 therefore }23} , }45}
4. Which is more?
a) }1} dollar or }1} dollar
b)
2
1
}}
3
4
off or
1
}}
4
the regular price off
c) }1} of a pizza or }1} of a pizza
5
d)
5. Copy and complete the following diagram to
Which is greater?
6
7
apples or 1}} apples
8
3
compare }} and }4}.
4
5
1}3}
4
458 Review of Essential Skills from Grade 6: Chapter 9
NEL
Chapter 10: 3-D Geometry
Polyhedrons
A polyhedron is a three-dimensional shape that is formed by polygons.
Prisms and pyramids are two types of polyhedrons.
Prisms are like stretched polygons.
Pyramids come to a point.
A prism is named according to the
polygon that is its base.
A pyramid is also named according
to the polygon that is its base.
An octagon forms the base of this
prism, so this prism is called an
octagonal prism.
A hexagon forms the base of this
pyramid, so this pyramid is called
a hexagonal pyramid.
1. Name each polyhedron.
a)
b)
c)
e)
d)
f)
A face is a flat surface (polygon) of a polyhedron.
An edge is formed where two of the polygons that
make up a polyhedron meet.
A vertex is formed where two or more edges meet.
(The plural of vertex is vertices).
NEL
Review of Essential Skills from Grade 6: Chapter 10
459
2. State how many faces, edges, and vertices are in each polyhedron
from question 1.
3. State the polygons that form each polyhedron below. The first one is
done for you.
Polyhedron
Polygons
2 triangles
3 rectangles
Nets
A net is a 2-D representation of what a 3-D shape would look like if it
were taken apart and laid out flat.
3-D hexagonal pyramid
net of hexagonal pyramid
4. Draw a net for each polyhedron.
a)
b)
460 Review of Essential Skills from Grade 6: Chapter 10
c)
NEL
Chapter 11: Surface Area and Volume
Volume is the amount of space that is occupied by a 3-D object. Volume
is measured in units cubed. Below are some of the units that are used to
measure volume.
1 cm3 5 1 mL
1000 cm3 5 1 L
1 m3 5 1000 L
1. A 1 cm3 block is shown. Estimate how many 1 cm3 blocks are needed
to fill each object below.
a) a pop can
b) your shoe
c) a box that is the same size as this student textbook
The volume of any rectangular solid can be found as follows:
Volume 5 length 3 width 3 height
2. Find the volume of each rectangular solid.
a) length 6 cm, width 5 cm, height 2 cm
b) dimensions 2.5 m by 5.5 m by 6.0 m
c) dimensions 2.5 cm by 2.5 cm by 4.0 cm
d) length 1.4 m, width 2.3 m, height 5.4 m
e) dimensions 0.3 cm by 0.4 cm by 0.9 cm
3. A rectangular mould for making bricks is 90 mm by 90 mm by 57 mm.
What is the volume of one brick that is made from this mould?
4. A wall is 5 m long, 1 m high, and 19 cm thick. There are 100 blocks
in a cubic metre. How many blocks are in the wall?
5. The Czukars built a swimming pool in their yard. The pool is
10 m long, 5 m wide, and 2 m deep.
a) What is the maximum volume of the pool?
b) The walls and floor of the pool are 15 cm thick. How many
cubic metres of soil were removed to allow for the pool,
including the walls and floor?
c) The depth of the water is only 1.7 m. What volume of water was
in the pool the first time it was filled?
NEL
Review of Essential Skills from Grade 6: Chapter 11
461
Chapter 12: Probability
Possible Outcomes
Possible outcomes are the different events that have a possibility of
occurring.
1. For each spinner, how many different possible outcomes are there?
a)
c)
b)
d)
Tree Diagrams
A tree diagram is a visual representation of the number of outcomes of an
event.
A coin is tossed twice in a row. Use a tree diagram to show how many
different possible outcomes there are.
The last “branch” on the tree diagram shows how many different possible
outcomes there are. In this example, there are four possible outcomes.
2. a) Draw a tree diagram for rolling a die twice in a row.
b) How many possible outcomes are there?
462 Review of Essential Skills from Grade 6: Chapter 12
NEL
Probability
Probability is the measure of how likely an event is to occur.
3. State which of the two events has the greater probability of occurring.
a) rolling a 5 on a die or tossing Heads on a coin
b) winning a national lottery or winning a draw at your school
c) drawing a king from a deck of cards or drawing the 3 of spades
from a deck of cards
d) getting an A on a math test after studying or getting an A on a
math test without studying
4. Order these events from most probable to least probable.
A. The first baby born next year is a girl.
B. The Sun will set today.
C. You will live to be 100 years old.
D. A classmate will live to be 100 years old.
E. Your best friend will live to be 90 years old.
5. Suppose that you have four red cards, three blue cards, and two
white cards in a box.
a) How many possible outcomes are there for selecting a card from
the box?
b) What is the probability of selecting a red card from the box?
c) What is the probability of selecting a blue card from the box?
d) What is the probability of selecting a yellow card from the box?
6. You have 12 blank cards. On each card, you write a different number
from 1 to 12. Find the probability of selecting each number below.
a) the number 1
d) a prime number
b) any number except 5
e) a composite number
c) an odd number
f) a multiple of 3
7. A purse has five loose keys in it. Two keys are house keys, and three
keys are car keys. One key is taken from the purse.
a) What is the probability that the key taken is a house key?
b) What is the probability that the key taken is a car key?
NEL
Review of Essential Skills from Grade 6: Chapter 12
463