Chapter 1: Number Sense Section 1: Integers
Topics in Algebra 1 © 2001 Texas Instruments Teacher Notes 1-6
Number Sense: Integers Teacher Notes
Objectives
•
To illustrate the set of integers in a Venn diagram.
•
To give an overview of the following definitions: the sign of a number, numbers of opposite
sign, and absolute value.
•
To give illustrations of the sets of positive and negative integers, and zero.
•
To review ordering and the additive inverse property.
•
To show examples of addition, subtraction, multiplication, and division of integers.
Math Highlights
This section begins with a Venn diagram and follows with an illustration of the use of integers on
the Fahrenheit and Celsius scales. The temperature equivalencies shown are integer values.
Students are reminded that the absolute value operation is defined as the distance of the number
from zero. Examples of addition, subtraction, multiplication, and division operations are given. A
number line model is used for addition and subtraction. Subtraction uses the
add-the-opposite
rule.
Common Student Errors
Students may have trouble identifying rules, such as the
add-the-opposite
rule for subtraction.
Note:
The number line model for addition and subtraction is shown on the calculator when the Topics in Algebra 1 application is
installed.
Following are some activities to help students construct the rules for multiplication and division.
These activities are not part of the Topics in Algebra 1 application.
Pattern Development for Multiplication and Division
Investigation 1:
What is the product of a positive and negative
number?
Begin by writing the product of two positive numbers, for example,
3
Q
3 = 9. Keep decreasing the second term by 1 to create the sequence
of multiplication values shown to the right. Notice the values on the
right side of the number sentences decrease by 3.
Observation:
The product of a positive and negative number is
negative.
3
Q
3 = 9
3
Q
2 = 6
3
Q
1 = 3
3
Q
0 = 0
3
Q
M
1 =
M
3
3
Q
M
2 =
M
6
3
Q
M
3 =
M
9
. . .
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