1. Comparing Integers
Lesson 1.1.1

2. Comparing Integers 1.1.1 California Standard: What it means for you:
Lesson
1.1.1
Comparing Integers
California Standard:
Number Sense 1.1
Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
What it means for you:
You’ll be able to arrange positive and negative numbers on the number line, and you’ll learn about different types of numbers.
Key words:
natural number
whole number
integer
origin
number line
greater than
less than

3. Lesson
1.1.1
Comparing Integers
This Lesson is about some of the different kinds of numbers you need to use, and how you can use the number line to put them in order.
The number line shows whether numbers are greater than or less than each other.

4. Comparing Integers 1.1.1 The Number Line Shows the Order of Numbers
Lesson
1.1.1
Comparing Integers
The Number Line Shows the Order of Numbers
The number line is a useful diagram that shows how numbers are ordered.
0 is called the origin
Numbers to the left of 0 are negative.
Numbers to the right of 0 are positive.

5. Lesson
1.1.1
Comparing Integers
Example 1
Arrange the numbers 2, 8, and 12 on the number line.
Solution 2 8 12
To place 2 on the number line, count to the right of 0 by 2 steps.
To place 8 on the number line, count to the right of 0 by 8 steps.
To place 12 on the number line, count to the right of 0 by 12 steps.
Solution follows…

6. Comparing Integers 1.1.1 Don’t Forget
Lesson
1.1.1
Comparing Integers
Don’t Forget
You always count in steps from 0, but if it’s a negative number then remember to count to the left.

7. Lesson
1.1.1
Comparing Integers
Example 2
Arrange the numbers –3, –5, 3, and 7 on the number line.
Solution –5 –3 3 7
To place –3 on the number line, count to the left of 0 by 3 steps.
To place –5 on the number line, count to the left of 0 by 5 steps.
To place 3 on the number line, count to the right of 0 by 3 steps.
To place 7 on the number line, count to the right of 0 by 7 steps.
Solution follows…

8. Comparing Integers 1.1.1 Guided Practice
Lesson
1.1.1
Comparing Integers
Guided Practice
1. Arrange the numbers 3, 4, –1, and 8 on the number line. –1 3 4 8
Solution follows…

9. Comparing Integers 1.1.1 Guided Practice Origin
Lesson
1.1.1
Comparing Integers
Guided Practice
Origin
Say which side of the origin the numbers in Exercises 2–5 would go on.
2. – –1
the left
the right
the right
the left
Solution follows…

10. Comparing Integers 1.1.1 The Number Line Lets You Compare Numbers
Lesson
1.1.1
Comparing Integers
The Number Line Lets You Compare Numbers
If two numbers are plotted on the number line, then the number to the left is less than the number to the right. –3 4
You could also say that the number to the right is greater than the number to the left.
There are two important symbols used to order and compare two numbers. The symbol > means “greater than” and the symbol < means “less than.”

11. Lesson
1.1.1
Comparing Integers
Example 3
By placing them on the number line, show that 1 is greater than –4.
Solution –4 1
To place 1 on the number line, count to the right of 0 by 1 step.
To place –4 on the number line, count to the left of 0 by 4 steps.
1 is to the right of –4, so 1 > –4.
Solution follows…

12. Comparing Integers 1.1.1 Guided Practice
Lesson
1.1.1
Comparing Integers
Guided Practice
In Exercises 6–8 fill in each box with the correct < or > symbol, then say which number in each Exercise is greater.
, so is greater.
, so is greater.
8. – , so is greater.
> 7
< 3
< 10
Solution follows…

13. Comparing Integers 1.1.1 Guided Practice
Lesson
1.1.1
Comparing Integers
Guided Practice
In Exercises 9–11 fill in each box with the correct < or > symbol, then say which number in each Exercise is greater.
9. – , so is greater.
10. – –11, so is greater.
11. – , so is greater.
<
> –9
< 1
Solution follows…

14. Lesson
1.1.1
Comparing Integers
Whole and Natural Numbers Are Types of Integers
You’ve already been dealing with different types of numbers on the number line — now it’s time to learn their names.
Natural numbers are also called counting numbers because they’re the numbers used to count with — 1, 2, 3, and so on.
Whole numbers are like the natural numbers except that they include the number zero.
Integers include all the natural numbers, the negative versions of them, and zero.

15. Lesson
1.1.1
Comparing Integers
Example 4
Describe the following numbers as natural, whole, or integer. There may be more than one answer for each. –3
Solution
1. 1 is greater than zero so it is a natural number. All natural numbers are also whole numbers and integers.
2. 0 is not a natural number, but it is a whole number. As it is a whole number it is also an integer.
3. –3 is less than zero so it is not a natural number and not a whole number. But it is an integer.
Solution follows…

16. Comparing Integers 1.1.1 Guided Practice
Lesson
1.1.1
Comparing Integers
Guided Practice
Describe each number as a natural number, a whole number, or an integer. There may be more than one answer for each.
12. 7
13. –9
14. –400
15. 1
16. 55
integer, natural number, whole number
integer
integer
integer, natural number, whole number
integer, natural number, whole number
Solution follows…

17. Comparing Integers 1.1.1 Guided Practice
Lesson
1.1.1
Comparing Integers
Guided Practice
Describe each number as a natural number, a whole number, or an integer. There may be more than one answer for each.
17. 0
18. 26
19. –16
20. –32
integer, whole number
integer, natural number, whole number
integer
integer
not an integer, natural number, or whole number
Solution follows…

18. Comparing Integers 1.1.1 Independent Practice
Lesson
1.1.1
Comparing Integers
Independent Practice
1. Place 3, 1, 5, and –2 on a number line. –2 1 3 5
Answer each of Exercises 2–9 as true or false.
2. 4 < > –40
4. 0 < – –1 > –2
6. 4 > – is a positive number.
8. Whole numbers can be negative.
9. All integers are whole numbers.
true
true
false
true
true
false
false
false
Solution follows…

19. Comparing Integers 1.1.1 Independent Practice
Lesson
1.1.1
Comparing Integers
Independent Practice
10. Hector is thinking of a number that is a whole number but is not a natural number. What number is Hector thinking of?
Use this number line to help answer Exercises 11–13.
11. How many natural numbers are between –3 and 5?
12. How many whole numbers are between –3 and 5?
13. How many integers are between –3 and 5? 4 5 7
Solution follows…

20. Comparing Integers 1.1.1 Round Up
Lesson
1.1.1
Comparing Integers
Round Up
Thinking in terms of the number line is a good way to compare integers so you can say which is greater than the other.
It also helps you to understand what happens when you add positive and negative numbers, which is all part of the next Lesson.