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Math 6
Unit 2
Lesson 1
Introduction to Integers
Submarines
A submarine can move around in the water at various depths. If the submarine
is below the surface of the sea it is said to be a number of metres below sea
level. If a submarine is on the surface it is at sea level.
25 m above sea level
0m
25 m below sea level
50 m below sea level
75 m below sea level
100 m below sea level
125 m below sea level
150 m below sea level
175 m below sea level
This submarine is 100 metres below sea level.
Math 6
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Math 6
Unit 2
Lesson 1: Introduction to Integers
In mathematics you can express the measures below sea level with a number
called an integer. You will learn how to express numbers that are greater than
and less than 0 using integers.
An integer for the depth of this submarine is: -100 metres.
This is “negative 100 metres” when you read it out loud.
Reflection
If the surface of the sea is “at sea level”, what are
some objects that would be found “above sea level”?
Objectives for this Lesson
In this lesson you will explore the following concepts:
•
•
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Describe numbers on a number line including
negative integers
Describe contexts in which integers are used
Express the opposite of an integer
Math 6
Unit 2
Lesson 1: Introduction to Integers
Integers
The number line shows the amount of money that each student has in their
pocket or owes their parent. A value of -4 represents a debt of $4.
Lian
-7 -6 -5 -4
Zach
Daksha
-3 -2 -1
0
Nina
1
2
Alyssa
3
4
5
Cameron
6
7
The numbers -4 and 6 are integers. The set of integers is expressed as
{…-3, -2, -1, 0, 1, 2, 3 …}. The three dots mean that the set continues in that
direction without end. This set of numbers has no end.
Here is a description of the set of integers.
0 is neither
negative
nor positive.
Negative integers
are less than 0.
-7 -6 -5 -4 -3 -2 -1
The - sign
marks a
negative.
Positive integers
are greater than 0.
0
1
2
3
4
5
6
7
Positive numbers
can be written with or
without a + sign.
• Go online to watch the Notepad Tutor Lesson: Understanding Integers.
Math 6
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Math 6
Unit 2
Lesson 1: Introduction to Integers
Real World Integers
There are real life values that may be expressed as positive and negative
integers. You need to be able to decide if a value is positive or negative for
different contexts.
Example 1
The lowest temperature on record in Canada was 63 degrees Celsius below 0.
It was recorded on February 3, 1947 in Snag, Yukon Territory.
Express the temperature as an integer.
The temperature “63 degrees Celsius below 0” is a value less than 0.
This is a negative integer: -63˚ C
Let’s Explore
Exploration 1: Elevations and Integers
Materials: Unit 2, Lesson 1, Exploration 1 page in your Workbook,
Internet or almanac, Pencil
The elevation of a place is the measure of the distance above or below sea level.
1
Use the Internet or an almanac to find the elevation of three places that are
above sea level.
2. Find three places that are below sea level.
3. Record the name of the place and the elevation of each in the table,
using an integer.
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Math 6
Unit 2
Lesson 1: Introduction to Integers
Opposites of Integers
Every positive and negative integer has an opposite. The opposite of an integer
is found the same distance from 0 on the number line, but on the opposite side
of 0. The opposite of +2 is -2.
2 Units 2 Units
-7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
Example 2
A quarterback is sacked for a loss of 15 yards. Write that distance as an integer.
What is its opposite?
A loss of 15 yards is less than 0: -15 yards
The opposite of -15 yards: +15 yards
Example 3
Name the opposite of each integer.
a. -5
b. +7
c. -12
d. 4
The answers are found by changing the sign. You can express the positive
number with or without the + symbol.
a. +5 or 5
b. -7
c. +12 or 12
d. -4
Math 6
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Math 6
Unit 2
Lesson 1: Introduction to Integers
Let’s Explore
Exploration 2: Exploring Opposites
Materials: Unit 2, Lesson 1, Exploration 2 page in your Workbook, Integer Counters
from the back of this unit in your Workbook, Pencil, Scissors
You can use integer counters to help you understand the relationship between
positive and negative integers. An integer counter with a + represents the
integer +1. An integer counter with a – represents the integer -1.
Cut out and use integer counters to complete the following.
1. Model -10.
2. Model +10.
3. What is the same about the two models?
4. What is different about the two models?
zero pair is found by putting a + integer counter together with a – integer counter.
A
This is called a zero pair because the result of pairing the two is zero.
Zero Pair
+
–
5.How many zero pairs can you make with your models of -10
and +10 together?
6. Create a model of a pair of opposites.
7. Write the values of your opposites.
8. How many zero pairs can you create from your models?
9. What is the value of a zero pair? Explain.
10. Make a model of +5 and -3. How many zero pairs can you make?
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Math 6
Unit 2
Lesson 1: Introduction to Integers
For 11-14: Either record an oral answer or write one in your Workbook.
If recording, follow the recording instructions in your Workbook.
11. Describe the integer counters that are not part of the zero pairs.
12.Choose the word that best completes this statement: A pair of opposites
(always, sometimes, or never) creates the same number of zero pairs.
13. Reflect: What is the sum of a pair of opposites? Explain.
14. Reflect: Which integer does not have an opposite? Explain.
Number Lines
You can use number lines to show the value of integers. Create number lines so
that they will contain all of the values you want to graph. Place a point on the
value that you want to represent.
Example 4
Golfers try to score under par. Draw a number line to show a golfer with a score
of -4 and another with a score of +2.
Draw a number line with at least four marks to the left and right of 0.
Label all values on the number line:
-4
-3
-2
-1
0
1
2
3
4
-1
0
1
2
3
4
Place points at -4 and +2:
-4
Math 6
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Math 6
Unit 2
Lesson 1: Introduction to Integers
Example 5
Place the following set of integers on a number line: {-3, 0, -6, 2, 7}
Draw your number line and make sure that it ranges from -7 to 7:
-7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
3
4
5
6
7
Place points at each value: {-3, 0, -6, 2, 7}
-7 -6 -5 -4 -3 -2 -1
0
1
2
Let’s Practice
• Turn in your Workbook to Unit 2, Lesson 1 and complete 1 to 22.
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