Reflection of Coordinates

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Objective

SWBAT reflect coordinates.

Big Idea

Students reflect points over the x and y axes.

Do Now

10 minutes

Students previously learned about the coordinate plane and how to plot ordered pairs.  For the Do Now, each student will receive a piece of graph paper and a ruler.

Do Now

Create a coordinate plane and plot:  (-2,4)  (5,-7)  (3,9)  (-6,-6).

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

 

Mini Lesson

15 minutes

Before working on reflecting coordinates, I will have students discuss with their group the meaning of reflection.

What comes to mind when you think of reflections?  What do you think it means to reflect coordinates?

After 5 minutes, students will share out with the class.

Students may offer ideas, such as:

  • reflections are mirror images
  • reflections are opposites
  • reflection means the coordinates should look the same

After students have shared their ideas, I will give them a more formal definition of reflections.

A reflection is a type of transformation. It is a 'flip' of a point over the line of reflection.

Students will be given the Reflections Worksheet (from the NYS Common Core Curriculum).  After explaining how the worksheet should be completed, we will work through the first column together.

The coordinates of S are (5,3).  If we are reflecting it over the x-axis, then which quadrant will it land in?

Students should recognize that it would be in quadrant IV.

Which point is the reflection of S over the x-axis?  

Since the coordinate plane has already been labeled for this example, students should see that M is the reflected point.

What do you notice about the distance between S and the x-axis and the distance between M and the x-axis?

Students should notice that they both have the same distance of 3 units.

We will continue to the reflection of S over the y-axis.

Which quadrant will the reflection of S over the y-axis lie in?  Which point is the reflection of S over the y-axis?

Students have difficulty with the double reflections, so it is important to model and discuss these.

If we reflect S over the x-axis first and then reflect that point over the y-axis, which quadrant will it lie in?

Students should see that it will be in quadrant III.

What point represents this reflection?

The point should be A.

We will then reflect S over the y-axis first and then the x-axis.  Students should notice that you will still end up with point A.

Group Work

10 minutes

I will instruct students to complete the worksheet.  Students should work with their group and discuss their strategy and answers.

Students are homogeneously grouped, based on a previous assessment.  As students work, I will focus on the groups of lower level math students.

After 10 minutes, I will review the answers and any questions with the class.

Lesson Summary

5 minutes

To add another level to students' understanding of reflections, I want students to begin thinking about how the ordered pair was affected.

When you reflected points over the x-axis, did you notice anything about the ordered pair?

Students may notice that the y-coordinate changes to the opposite sign.

When you reflected points over the y-axis, did you notice anything about the ordered pair?

Students may notice that the x-coordinate changes to the opposite sign.

Would you be able to predict the coordinates of a point reflected over the x- or y- axis without plotting it?

What are the coordinates of (6,-5) reflected over the x-axis?