2.5 Finding the Distance Between Two Numbers - Math 7 CCSS
FlexBooks® 2.0 > CK-12 Interactive Middle School Math 7 - Teacher's Edition > Finding the Distance Between Two Numbers - Math 7 CCSS
Last Modified: Sep 04, 2020
Common Core Standards
Focus Standards: 7.NS.A.1.c
Learning Objectives
Show that the distance between two rational numbers on the number line is the absolute values of their difference.
Solve problems involving finding the difference between two rational numbers in a real-world context.
Agenda
Warm-Up: Diving Deeper10 min
Activity 1: Along the Street20 min
Activity 2: Getting Around Washington DC 15 min
Review Questions5 min
(Students do not see text in purple)
Now that subtraction has been introduced, it is applied to finding the distance between two points in this lesson. The distance between two points will first be introduced as counting units on a number line, but then formalized into a definition with subtraction and absolute value. Review with students that distance is always positive and the definition of absolute value before beginning.
Warm-Up: Diving Deeper
The distance between two points can be defined as the number of units between them. Typically, this means we subtract the values, but what if one point is negative and the other is positive?
Example
Fatima’s friend, Tyler, is more daring than she and when he jumps into the water to scuba dive, he starts from 4 feet above the water, at the back of the boat. After his first jump, he went 7 feet below the water. How many feet did he actually travel?
This interactive shows an application of how negative values are used; in this case, it is how deep a diver dives. Students will see a body of water, a diver on a cliff, boat and some fish. There are also two number lines; the horizontal line ranges from -20 to 5 and the vertical line ranges 5 feet to -20 feet. The horizontal line has a red point that students can click and drag to make the diver dive. While the student moves the point in the negative direction the father down the diver will go. The arrow on the vertical line will travel down with the diver showing the student how many feet down the diver is.
TRY IT
Inline Questions: Students see inline questions here. The questions are formative and have detailed instructional feedback. The questions and correct answers are printed below for your convenience as an instructor.
Which expression tells us the total distance Tyler travels to return to 5 feet above the water from a depth of 15 feet?
|-15 - 5|
|5 -15|
|5 - (-15)|
|-15 - (-5)|
Which expression can we use to find the total distance Tyler traveled?
|4 - (-7)|
4 - 7
|4 - 7|
-7 - 4
If Tyler started 5 feet above the water, jumped, then went 8 feet below the water, which of the following represent the total distance traveled?
|5 - (-8)|
|-8 - (-5)|
|5 - 8|
|-8 - 5|
Tyler is 7 feet below the water's surface and dives another 8 feet down. How can we determine how far below the water's surface he is now?
|-7 - (-8)|
|7 - 8|
|-7 - 8|
|8 - 7|
It is important to remember that when finding the total distance between two points on a number line, you may need to find the absolute value of those distances separately, depending on what the question is asking for.
Emphasize to students that when finding the total distance between two points on a number line, they need to use absolute value. As is the case with #3, you may need to draw a picture showing them that he starts at -7 feet down and goes down another -8 feet. His total distance from the surface is |-7| + |-8| or |-7 - 8|.
Activity 1: Along the Street
Jason lives on the same street as his school, the movie theater, his friend's house and the store. They are all different distances away from his house. Treat Jason's house as the origin, and determine the distance he needs to travel.
This interactive is another application of how negative numbers may be used to show distance traveled. On the number lines there are five places Jason can travel: Jason’s house is the starting point and located at zero. The school is located at -8, the movies are at -5, his friend’s house is at 4 and the store is at 7. Students can move the red point along the number line to the different locations. Above the number line students can see the distance the location is from the starting point (Jason’s house).
TRY IT
Step-by-step explanation:
![Which expression could help you find the distance
between (10, 4) and (-6, 4)?
O [10] + 1-4
O [10](/tpl/images/2073/2513/36ad0.jpg)
