Lesson plan

In this lesson, students will learn the key concepts of reflections and what they are. They will then work through an exploratory reflections activity where they will discover what changes about an ordered pair when it is reflected over an axis. You can expect this lesson to take one `45`-minute class period.

Grade 8

Transformations

8.G.A.3

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Students will be able to recognize and perform reflections of points and polygons.

- Teacher slideshow
- Exploratory activity
- Online Practice

We can start students off by asking them to think about what this arrow would look like when reflected over the line. You can ask a volunteer to come up to the board to draw what they think. Ask the class if they agree or disagree with what the student drew. Students can raise their hands and offer their opinions.

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After a short discussion, you can show students the next slide, with the reflected image:

Prompt students to think more closely about what makes this arrow a reflected image of the other. You can ask a series of questions that can lead to discussion. Here are a few examples of questions you’ll want to ask and eventually answer:

- Are the two shapes congruent?
- Is the reflected arrow a mirror image of the original arrow?
- Is the reflected arrow the same distance from the line as the original arrow?

Discussing student responses to these questions will allow students to think more clearly about how to reflect an image, and what specific qualities change or stay the same.

There are a few more examples in the slide deck. Continue having students come to the board to draw the reflected images and have discussions with the class. The answers are all provided within the slideshow!

After the introduction, students will have a better understanding of what a reflection does. The __exploratory activity__ will have them look more closely at reflections on the coordinate plane. Since you’ve already discussed that a reflected image is the same distance away from the line as the original image, this activity will be easy for them to get started on!

You can have students work individually or in pairs. As they work through the activity, they will reflect coordinate points on a graph, and discover how those reflections affect the ordered pairs.

Discuss student answers from the exploratory activity. Here are some points that are likely to be raised:

- There is always a line over which an image is reflected - this is the “Line of Reflection”
- A reflected point is the same distance away from the line as the original point
- When a point is reflected over the `x`-axis, the `y`-value changes but the `x`-value stays the same. And the other way around when a point is reflected over the `y`-axis - Discuss why that happens.

Now it’s time for some independent practice! You can assign a ByteLearn online practice to your class using the link below. Students will get immediate feedback and step-by-step help if they need it. Set a due date and allow students to finish the assignment for homework. Once complete, you’ll see detailed reports of students who may need additional support, students who are ready for a challenge, and other interesting insights!

Reflections Practice

Problem 1 of 5

<p> Point `U` is reflected over the `y`-axis to create Point `V`.</p><p> Plot Point `V`.</p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><InteractiveGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 15, "x_interval": 1, "y_interval": 1, "y_label": "" },"points": [ { "id": 1, "x": 2, "y": 2, "label": "U", "is_interactive": false, "show_point": true, "label_color": "black", "color": "black" }, { "id": 2, "is_interactive": true, "label_color": "blue", "color": "blue", "label": "V" } ], "mode": "POINT", "total_interactive_inputs": 1 }'></InteractiveGraph ></selectivedisplay>

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