Lesson 3 Student Outcomes
Students understand addition of integers as putting together or counting up, where counting up a negative number of times is counting down.
Students use arrows to show the sum of two integers, p + q, on a number line and to show that the sum is distance |q| from p to the right if q is positive and to the left if q is negative.
Students refer back to the Integer Game to reinforce their understanding of addition.
Lesson 3 Summary
Addition of integers is represented on a number line as “counting up”, where counting up a negative number of times is the same as “counting down.”
Arrows show the sum of two integers on a number line.
The sum is the distance |q| from the p-value (the first addend) to the right if q is positive and to the left if q is negative.
Exercise 1: Addition Using the Integer Game
Example 1: “Counting On” to Express the Sum as Absolute Value on a Number Line
Create a horizontal number line model to represent each of the following expressions. Describe the sum using distance from the p-value along the number line.
a. -5 + 3
b. -6 + (-2)
c. 7 + (-8)
Exercise 3: Writing an Equation Using Verbal Descriptions
Write an equation, and using the number line, create an “arrow” diagram given the following information:
“The p-value is 6, and the sum lies 15 units to the left of the p-value.”
1. Below is a table showing the change in temperature from morning to afternoon for one week.
a. Use the vertical number line to help you complete the table. As an example, the first row is completed for you.
b. Do you agree or disagree with the statement: “A rise of −7°C ” means “a fall of 7°C”? Explain. (Note: No one would ever say, "A rise of −7°C degrees"; however, mathematically speaking, it is an equivalent phrase.)