# Distance Between Two Points, Day 1

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## Objective

SWBAT find the distance between two points.

#### Big Idea

Students use absolute value to find the distance between two points.

## Do Now

10 minutes

Students have worked on plotting points on the coordinate plane.  The Do Now serves two purposes: 1.  It will provide students with additional practice.  2.  We will use the coordinates later in the lesson.  Students should be given graph paper and a ruler.  It is important that as students create the coordinate plane to monitor that they are numbering the axes correctly.

Do Now

Create a coordinate plane and plot.

(10,1)(5,1)(5,3)(10,3)

After 5 minutes, I will call students to the board to explain and show how they plotted the coordinates.

## Mini Lesson

30 minutes

*This is a 2 day lesson.  For the first day, we will spend time developing the rules for finding the distance between two points.  The second day, students will work on a group project and there will be a gallery walk.

For this lesson, students will develop the rules for finding the distance between 2 points. Continuing from the Do Now, students will be directed to use their ruler to connect the four points they plotted, forming a rectangle.

How can we find the length of each side or the distance between two points?

Students may suggest counting the boxes to find the length.  They will find that the length is 5 units and the width is 2 units.

Is there another way we find the length and width?  What if we didn't plot the coordinates, how could we have calculated the length and width?

Ex. 1

I will show students the table for example 1.  (see Example 1 - Distance)  With their groups, students will discuss patterns they notice in the table and determine how the numbers in the distance column are calculated.

After 5 minutes, groups will share their ideas with the class.  Most groups will have noticed that if the distances are calculated by subtracting the x coordinates.

Will this always work?

Most students will think that this will always work, because they are not considering all integers.

Ex. 2

For example 2 students will plot (-7,5)  (-2,5)  (-2,-2)  (-7,-2) on their coordinate plane.

I will show students the distance table for example 2. (see Example 2 - Distance) Again, with their groups, students will discuss patterns they notice in the table and determine how the numbers in the distance column are calculated.

After 5 - 7 minutes, groups will share their ideas with the class.  Some groups may have noticed that sometimes you add the coordinates and sometimes you subtract.  I will ask probing questions, to help students develop rules that will always work.

What type of line is formed by the points (-7,5) and (-7,-2)?  What do you notice about the x coordinates of both points?

Students should determine that it's a vertical line and the c coordinates are the same.

Is the same true for the vertical line formed by (-2,5) and (-2,-2)?

Students should notice that the x coordinates are the same.

How did you determine the distance was calculated for these points?

Some groups may have determined that you add the y coordinates.  Some groups may have realized that you have to find the absolute value of the y coordinates before you add.

What type of line is formed by the points (-7,-2) and (-2,-2)?  What do you notice about the y coordinates of both points?

Students should determine that it's a horizontal line and the y coordinates are the same.

Is the same true for the horizontal line formed by (-7,5) and (-2,5)?

Students should notice that the y coordinates are the same.

How did you determine the distance was calculated for these points?

Again, most groups may have determined that they needed to subtract the x coordinates.  However some groups may realize that you have to find the absolute value of the x coordinates before you subtract.

This will lead us to the rules for finding the distances between two points.

If the x- or y- coordinates are both positive or both negative, subtract their absolute values.

If the x- or y- coordinates are opposite signs, add their absolute values.

## 3-2-1 Exit Ticket

5 minutes

Before moving on to the second day of the lesson, it is important for me to know my students' understanding of this concept.  Each student will receive an index card on which to complete the exit ticket.

They will receive the following prompts:

3 things you still want to know about graphing on the coordinate plane

2 things you want help on or are confused about

1 thing about graphing on the coordinate plane you would be able to help someone else with