Students are given 4 minutes to work independently on the Think About It problems.
I then cold call on students for each question on this page. Students identify that the points are located at (4, 5) and (4, -5). They notice that the points have the same x-coordinate, and that the y-coordinates are opposite of each other.
I want students to use the language of absolute value throughout this lesson, so I ask them to share out more that the pairs have in common. If 2-3 more students share out similarities they have noticed, but have not yet talked about distance from the y-axis, I will guide them to get there. I'll say, "I'm noticing something about distance. What do both points have in common, when we think about distance?"
Once students recognize that the two points have the same distance from the y-axis, so that the y-coordinates have the same absolute value, I will move into the new material for the lesson.
To begin this section of the lesson, I have students help me label the parts of the graph. I have a copy of the INM materials on the document camera, and I ask for students to give me the names of the important pieces. We label the origin, the x- and y-axis, and all four quadrants.
Together, we plot the first point, (4, 5) and label it as Point A. Students annotate the problem by boxing the words 'y-axis.' My expectation is that they always box the axis over which we're rotating, as a small way to help them not reflect over the incorrect axis.
For this first point, (4, 5), I ask students to count how many units it takes to get from the y-axis to the point. I want to spend time on the conceptual idea of reflecting a point, so we don't jump right into simply using the opposite value for the x-coordinate. Once students name that the point is 4 units away from the axis, I tell them that the reflection is going to be the same distance from the y axis but in the opposite direction. We know that the y-axis represents 0, so therefore both points have the same absolute value, or distance from 0. Then we are going to count that same number of units going away from the y-axis and plot and label my point with the coordinate pair (-4, 5).
Once, we've gone through the same process for the other two ordered pairs in this section, I have students turn and talk with their partner about a generalization we can make about reflections. I ask them:
When we reflect a point over the y-axis, what do you notice about the relationship between the x- and y-values of the coordinates of each point?
Students share out, and then I ask for the group to make a conjecture about the relationship of the coordinates when we reflect over the x-axis.
Students work on the Partner Practice problem set for 10 minutes. As they are working, I circulate around the room.
I am looking for:
I am asking pairs:
After the 10 minutes of partner work time, students complete the final check for understanding independently. As a class, we discuss question 14, where students are asked to generalize about any point, (x, y).
After our conversation about the final CFU problem, students work on the Independent Practice problems for 15 minutes. As I am circulating, I am looking for and asking students the same questions that I use for my circulation during partner practice.
At the end of Independent Work time, we discuss Problem_25. First, I have students show me on their fingers which quadrant Nate's house is in. This gives me a quick visual check of how students have done with this problem. The students have to complete a number of reflections to arrive at the location of Nate's house. It is likely that there will be a variety of answers. I call on a student with the correct quadrant shown, and ask that student to convince us that her/his answer is correct. I then give other students the opportunity to add to the response. I want us to build an exemplar oral response together.
Students end class by working on the Exit Ticket independently.