LESSON PLAN - Texas State University
LESSON PLAN
Name: Rahul Bhandari
Title of lesson: Distance Formula, Midpoint, & Slope
Length of lesson: Three 50 minute class periods
Description of the class:
Name: Geometry
Grade level: High School
Honors or regular: Honors
TEKS addressed:
(a) Basic understandings.
2) Geometric thinking and spatial reasoning. Spatial reasoning plays a critical role in geometry; shapes and figures provide powerful ways to represent mathematical situations and to express generalizations about space and spatial relationships. Students use geometric thinking to understand mathematical concepts and the relationships among them.
(4) The relationship between geometry, other mathematics, and other disciplines. Geometry can be used to model and represent many mathematical and real-world situations. Students perceive the connection between geometry and the real and mathematical worlds and use geometric ideas, relationships, and properties to solve problems.
(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.
(b) Geometric structure: knowledge and skills and performance descriptions.
(2) The student analyzes geometric relationships in order to make and verify conjectures. Following are performance descriptions.
(A) The student uses constructions to explore attributes of geometric figures and to make conjectures about geometric relationships.
(B) The student makes and verifies conjectures about angles, lines, polygons, circles, and three-dimensional figures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
The Lesson:
I. Overview
The goal of this lesson is to have students determine the distance formula and relate this to the equation of a circle. Students will determine the formulas for midpoint and slope. This will be done through problem-solving.
II. Performance or learner outcomes
The students will be able to: determine the distance formula and be able to relate this to the equation of a circle. Also, students will determine the formulas for midpoint and slope.
III. Resources, materials and supplies needed
Rulers
IV. Supplementary materials, handouts.
Handout for Homework—Attached
Day 1
Five-E Organization
Teacher Does Student Does
|Engage: | |
|Learning Experience |Student Activity |
|Quickly review Pythagorean Theorem. (assess prior knowledge) |Students are listening and answering questions. |
|Set up problem that asks students to find formula for the | |
|shortest distance between 2 points. | |
| | |
| Questions | |
|1. What is the formula for the Pythagorean Theorem? |Expected Student Answers |
|2. What kind of triangles is this for? |c2 = a2 + b2 |
|3. What is the shortest way to get from Wal-Mart to Target? |right triangles |
| |3. a straight line |
| | |
Evaluate
Teacher will make sure students are on task and participating.
Teacher Does Student Does
|Explore: | |
|Learning Experience(s) |What the students are doing |
|Teacher is walking around to each group assessing their progress.|Students are working in groups to discover the distance formula. |
| | |
| Questions |Expected Student Answers |
|1. What approach are you using to solve this problem? |1. Answer will vary depending on group. |
Evaluate
The teacher will walk around the room to assess each groups’ progress.
Day 2
Teacher Does Student Does
|Explain: | |
|Learning Experience(s) |What the students are doing |
|Teacher is listening to students’ ideas. Calling on different | Groups are presenting their work. |
|students to give their opinions. | |
| |Students are listening and correcting their mistakes. |
| | |
|Questions | Expected Student Answers |
|Questions will depend on students’ approaches. |Students will answer depending on the question. |
| | |
|Teacher will summarize his/her approach to help students grasp | |
|the concept. | |
|Teacher’s Approach: | |
|Questions: | |
|What is the first thing we have to do? |Expected Student Answers |
|What formula do you have to use to find the distance formula? |Graph the points. |
|Show different triangles and ask if the theorem can be applied to| |
|them. |The Pythagorean Theorem. |
|How do you know to use this theorem? (Have them say which sides | |
|are a, b, and c.) |No |
|What problem do you have using this? | |
|How do you find the side lengths so you can use the theorem? |The intersection made it a right triangle. |
|How do you use this to find the side length? | |
|Call two students to demonstrate distance between two horizontal |No side lengths were given. |
|or vertical points. | |
|How do you use these and the Pythagorean Theorem to find the |By labeling the points. (x1, y1) and (x2, y2) |
|distance formula? |x2-x1 is one side and y2-y1 is the other. |
|So, what is the distance formula? |demonstrating distance. |
| | |
| | |
| |By plugging in a=x2-x1, b=y2-y1, and c is what we are looking |
| |for. |
| | |
| |c2=(x2-x1)2 + (y2-y1)2 |
Evaluate
The teacher will ask questions to guide the review and the steps to take to find the formula.
Teacher Does Student Does
|Extend / Elaborate: | |
|Learning Experience(s) |What the students are doing |
|If time permits, show students how this formula relates to the |Students are listening and paying attention to teacher. |
|equation for a circle. | |
|Teacher will assign worksheet for homework extra practice. |Students are excited to use the new approach to find out the |
| |distance between two points. |
Evaluate
Each student is looking at the questions and thinking about how they will solve them at home.
Day 3
Five-E Organization
Teacher Does Student Does
|Engage: | |
|Learning Experience |Student Activity |
|Reintroduce graph from first day. |Students are listening and answering questions. |
|Reflect on constructing a perp. line with a compass to show them | |
|the midpoint. | |
| Questions |Expected Student Answers |
|How do you draw a perpendicular line recalling the lesson on |With a compass. Students will explain how. |
|Friday? (have them explain) |Yes, the point where the perp. line and the original line |
|Is there a midpoint on this line? |intersect. |
| |A point half-way between two points on a line. |
|What is a midpoint? |Slant—rate of change. |
| | |
|Can anyone define slope? |Students will get into groups. |
| | |
|Think about the slope of this line. Can you find it? | |
| | |
Evaluate
Teacher will make sure students are on task and participating.
Teacher Does Student Does
|Explore: | |
|Learning Experience(s) |What the students are doing |
|Teacher is walking around to each group assessing their progress.|Students are working in groups to discover the midpoint formula. |
| |Once a group has it, teacher will okay to move on to finding the |
| |slope formula. |
| | |
| | |
| |Expected Student Answers |
|Questions |1. Answer will vary depending on group. |
|1. What approach are you using to solve this problem? | |
Evaluate
The teacher will walk around the room to assess each group’s progress.
Teacher Does Student Does
|Explain: | |
|Learning Experience(s) |What the students are doing |
|Teacher is listening to students’ ideas. Calling on different | Groups are presenting their work. |
|students to give their opinions. | |
| | |
|Questions | |
|Questions will depend on students’ approaches. | Expected Student Answers |
| |Students will answer depending on the question. |
|Teacher will summarize his/her approach to help students grasp | |
|the concept. |Students are listening and correcting their mistakes. |
|Explain that we rise before we run. (example of stairs) | |
| | |
|Teacher’s Approach: | |
|Questions: | |
|Teacher will give a real life example to explain midpoint |Expected Student Answers |
|concept. |Students are paying attention. |
|What is the formula for the midpoint? | |
|What does the slope tell us? | |
|What is the formula for the slope? | |
| |x=(x1+x2)/2 and y=(y1+y2)/2 |
| | |
| |rate of change |
| |(y2-y1)/(x2-x1) |
Evaluate
The teacher will ask questions to guide the review and the steps to take to find the formula.
Teacher Does Student Does
|Extend / Elaborate: | |
|Learning Experience(s) |What the students are doing |
|Teacher will assign worksheet for homework extra practice. |Students are excited to use the new approach to find midpoint and|
| |slope. |
Evaluate
Each student is looking at the questions and thinking about how they will solve them at home.
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