Lesson Plan : Fun with Rotations

Teacher Name:
 Ms. Rebecca Archer
Grade:
 Grade 7-8
Subject:
 Math

Topic:
 Rotations of Triangles
Content:
 1. Rotation - Moving a geometric figure around a fixed point (also known as the axis). 2. Students should know how to label a graph properly. 3. The class will be taking a fixed object (our object will be a triangle) and move it to different quadrants on their graphs.
Goals:
 1. Students should know and understand what rotation means and be able to apply it in their homework. 2. Students should be able to move a fixed object on a graph onto other area's of the graph given an exact amount to rotate the object.
Objectives:
 1. Students will discuss the importance of accurate measurements; 2. Use their math skills to move an object from a fixed point to another fixed point; and 3. see a resemblance from one rotation to the next.
Materials:
 1. Rulers, one for every student 2. Graphing paper, one for every student 3. pencils, one for every student 4. Maple, mathematics computer program that visual shows (in 3-D or 2-D) what it looks like for an object to rotate around the axis or a fixed point.
Introduction:
 1. I will ask the students to please rise and face the front of the room. I will explain that rotations are always done counter-clockwise, also explaining that it is opposite of the way the clock turns. 2. I will ask the students to close their eyes and then rotate 90 degrees. I will have them open their eyes and see where everyone is. a)I will have them face the front again and repeat the last step but this time have them rotate 180 degrees. b)Repeating the last step, but this time I will have them rotate negative 90 degrees.
Development:
 1. The students, on their paper, and I, on the front board, together will draw a graph with x and y values ranging from negative 15 to positive 15. a) We will label our x and y axis b)I will give the students 3 points to plot on their graph. c)We will connect the 3 points using our rulers to form a triangle. We will put the corresponding coordinates next to the point on the graph and we will also label the 3 points with letters using TED (each letter corresponding to a certain point). 2. We will then take the closest point to the origin and draw a line from that point to the origin. This will be the fixed line that will visually show the students on the graph is moving. 3. I will have the students choose the coordinate closest to the origin and count the number of lines they cross either down or across to get to the origin. The students will then count that same exact number of lines going opposite of what they did rotating the graph 90 degrees (if they couldn't going down then they should count across). ex. if the coordinate was (2,3) they will count, going down, 3 lines and going across 2. While rotating, they will count 3 lines going across and 2 lines up. a)I will have the students label the graph again b)When labeling the coordinates, instead of labeling the graph TED we will label the graph T'E'D' meaning this triangle is a rotation of the first triangle. 4. I will ask "Does anyone see any similarities between the coordinates?" a)if the answer is no, I will then rotate the trianle again 90 degrees. b)if the answer is yes, I will ask them "What is it?" The students should be able to tell me the x and y values switch and depending on what quadrant our graph is in will depend on whether x and y are negative. 5. As a class, we will finish rotating the triangle until it is back in its original position. 6. At the end, I will open up Maple and show the students what a rotating triangle looks like in motion. During homework time, students will be allowed to use Maple and plug in their own coordinates and degrees of rotation and observe what it does.
Practice:
 1. The students will be given a work sheet that has 6 different graphs. Each graph will have a different degree of rotation. They must label the graphs properly. 2. The students will have the opportunity to use Maple to visualize what a rotating triangle looks like and experiment with their own coordinates and degrees of rotation.
Accommodations:
 1. I will be available before and after school to help any student who needs further instruction on how to do the assignment or if there are any other questions 2. Every wednesday for 1 hour after school, there is a group session to accomodate those students who need further help in understanding what we have gone over in class. 3.Students who are done with their homework early, may come to the front of the classroom and grab a sudoku to work on that I will collect everyother monday for a few extra credit points.
Checking For Understanding:
 What I'm looking for: 1. Clear diagram with detail 2. No math errors 3. Shows complete understanding of the questions, mathematical ideas, and processes 4. The students should be able to verbally explain what they have done on their graphs to get from one triangle to the next. 5. Each student will have a one-on-one meeting with the teacher with any questions or concerns they have. We will also go over any homework that was turned in or worked on at that time.
Closure:
 1. We will go over the main concepts of the lesson 2. Graphing and labeling coordinates on a graph 3. Be precise when counting lines 4. Remember to always look at what quadrant your in to know the values of x and y. 5. Next time we will be learning about reflections!
Evaluation:
 1. As a class, I will ask the students what it means to rotate something. 2. We will orally and visually explain how to rotate an object on a graph 3. We will orally and visually be able to explain/show why we label our graphs
Teacher Reflections:
 1. Getting the students involved from the start was helpful 2. TED was a great way to keep the students interested throughout the lesson. 3. There should be more than one example to show the class to give the students more visuals to look at. 4. Hands on learning is extremely helpful. It was clear who followed along on paper, who followed with their eyes and who didn't follow at all.

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