Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
- demonstrate their understanding of various transformations on polygons in the coordinate plane. This will include reflections, translations, rotations of 90 and 180 degrees, and dilations.
- be able to explain what transformation(s) occurred and how each transformation was done using coordinates.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know how to plot points on the coordinate plane from MAFS.6.G.1.3 - Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
Also, students should enter the lesson with an understanding of the various types of transformations from MAFS.8.G.1.1 - Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines and line segments to line segments of the same length. b. Angles are taken to angles of the same measure, c. Parallel lines are taken to parallel lines.
Students need to have prior knowledge of angle measure, and in particular familiarity with 90 degree and 180 degree angles.
Guiding Questions: What are the guiding questions for this lesson?
How does dilation change the appearance of a figure?
Why do some dilations result in an enlarged figure, and others result in a smaller figure?
How does translation change the graph of a figure?
How do the coordinates of each point change in a translation?
What does it mean to reflect across the x-axis?
What does it mean to reflect across the y-axis?
In what way do the coordinates of a point change in a reflection across the x-axis?
In what way do the coordinates of a point change in a reflection across the y-axis?
How do you rotate an image 90° clockwise?
How do you rotate an image 90° counter-clockwise?
How do you rotate an image 180°?
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will go through the review concepts slides with the students. As each slide is displayed, the teacher will pose the questions provided on each slide for student response. Students should be encouraged to write down their responses before the teacher calls on students for answers. In some cases, the responses that are provided on the slide; they can be revealed for checking and discussion after students have formulated their own individual responses.
Notes for teacher to emphasize, and answers to questions on slides are as follows:
- Slide #2: This slide summarizes the various transformations in visual and verbal form. This is for activating prior knowledge and may help the teacher identify any misconceptions.
- Slide #3:
- Figure 1: Dilation; the original triangle ABC (blue) is enlarged to triangle A'B'C' (red). Comparing corresponding points we can determine the scale factor. A':A = B':B = C':C = 3:2. Since 3:2 = 1.5, the scale factor is greater than 1, and the original figure has been enlarged.
- Figure 2: This can be interpreted in two ways. The teacher should prompt the students to find both of these; it is likely that among the class, students will propose both ways. One way is to use two reflections, either reflect across the x-axis and then reflect that image across the y-axis, or do the reflections in the opposite order. The other way is to make a rotation of 180°. To emphasize this finding, have the students write down the coordinates of each point of both images, and compare the coordinates.
- Figure 3: This is a translation. Ask the students in what way the figure has changed. They should specifically state that its size and shape are unchanged; the figure has been moved to the left 5 and up 3. Ask them how they can verify this by using the coordinates of the pairs of corresponding points.
- Slide #4: This is a rotation. The vertices of the figure have been rotated about the origin in a clockwise direction. Ask the students to write down the coordinates of the corresponding points and explain how the coordinates change in a rotation such as this.
The rest of the PowerPoint will be used as guided practice.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
After the review, the students, with teacher support, will complete the questions on slides 2, 3, 5, 6, 7, 8, 9 and the practice problem on slide 10.
The rest of the power point should be used to work through as guided practice.
- Slide #5: This slide summarizes the various transformations in symbolic form. The teacher should have students record the left side of the slide on their papers, and then work with a partner to tell how a point (x, y) is changed by each case. After students have written down their responses, class discussion may occur, or the teacher may reveal the right side of the slide, and students can check their work. Questions and discussion will enable students to get feedback, and the teacher can assess student understanding and areas where additional explanation is needed.
- Slide #6: Students take a closer look at dilation. They explain the dilation and identify the coordinates of the resulting figure. The teacher may ask for student answers and then reveal the answers on the slide. Students should also identify the dilation factor, how they determined it, and if it indicates enlarging or shrinking the size of the original figure.
- Slide #7: Students practice translations. They should identify and describe the transformation, and describe how each ordered pair has changed.
- Slide #8: Students analyze a reflection across the y-axis. They should be able to respond that the x-coordinates of each point change to the opposite; the y-coordinates do not change. Students then compare this to a reflection across the x-axis. Expected response: the figure will flip down across the x-axis, all x-coordinates stay the same and all y-coordinates change to the opposite.
- Slide #9: Rotation of 180°: Students should respond that both x and y coordinates change to the opposite. This is equivalent to doing two reflections, one across the x-axis, and one across the y-axis.
- Slide #10: This should be printed in advance and distributed to students to complete either individually or with a partner. Allow time for students to give a full response to all three parts. The teacher may call on individuals to explain their responses to each part. Encourage discussion and explore any diverse ideas for validity.
- Slide #11 and #12: These display the details of the project that will serve as a summative assessment. Present this to the class, and then distribute copies (see the Rubric attachment) for each student.
Sample questions to ask students:
- If you are doing a dilation, what kind of result do you expect? When does a dilation result in an enlarged figure? When does a dilation result in a reduced figure? (Sample answers: Same shape figure, but different size. Scale factor greater than 1 causes enlargement. Scale factor less than 1 causes a reduction.)
- Explain how a translation affects a graph. What are the different ways this can occur? (Sample answers: Translations cause the graph to slide horizontally or vertically. The graph can move up or down if the y coordinates are increased or decreased; the graph can move left or right if the x coordinates are decreased or increased.)
- What does it mean to reflect across the x-axis? How does this change the coordinates of each point? What does it mean to reflect across the y-axis? How does this change the coordinates of each point?
- If you are going to do a rotation, why do you need to know if it is clockwise or not?
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will complete the "Transformation project" by referring to the guidelines and rubric in the attached document. The teacher will make sure the students understand the project requirements, and provide class time for students to work on the project. The teacher will provide needed supplies (listed in the Special Materials section) in the classroom. Students will have the rest of the class period today, and one additional class period to work on this. If need be, they can complete the rest of their projects outside of class time.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will refer back to specific slides (#1, 4, and 5) to demonstrate and summarize the key concepts of the lesson.
The transformation project has a rubric that provides a measurement of student understanding and mastery. The teacher will be able to use each student's project score to determine if the student has or has not achieved the objectives of the lesson.
This lesson should be used after direct instruction has been given on transformations. During the review of each transformation, the teacher will pose questions to the class to ascertain the students' understanding. Questions include asking students to define each transformation, describe how each transformation is completed on a graph, and explain the ways the transformed figure compares to the original figure. Slide #5 should be used with the right side initially covered up, so that students can complete the transformation on the ordered pair (x, y) on their own. This is a very important opportunity for the teacher to obtain significant feedback on students' understanding of the concept of each transformation. The teacher will be able to identify areas of misconception and elaborate with further explanation as needed.
Feedback to Students
Students will respond to and discuss the examples and questions that appear in the slide show. Slide 10 provides a comprehensive example for all students to work on either independently or with partners. This example is designed to prompt discussion and analytical thinking about all of types the transformations. Feedback will occur during collaborative work with partners, one-on-one interaction with the teacher, and whole class discussion.