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:
Grade level:
Honors or regular:
Geometry
High School
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
Engage:
Learning Experience
Quickly review Pythagorean Theorem.
(assess prior knowledge)
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?
2. What kind of triangles is this for?
3. What is the shortest way to get from
Wal-Mart to Target?
Student Does
Student Activity
Students are listening and answering
questions.
Expected Student Answers
1. c2 = a2 + b2
2. right triangles
3. a straight line
Evaluate
Teacher will make sure students are on task and participating.
Teacher Does
Explore:
Learning Experience(s)
Teacher is walking around to each group
assessing their progress.
Student Does
What the students are doing
Students are working in groups to discover
the distance formula.
Questions
Expected Student Answers
1. What approach are you using to
1. Answer will vary depending on
solve this problem?
group.
Evaluate
The teacher will walk around the room to assess each groups’ progress.
Day 2
Teacher Does
Explain:
Learning Experience(s)
Teacher is listening to students’ ideas.
Calling on different students to give their
opinions.
Questions
Questions will depend on students’
approaches.
Teacher will summarize his/her
approach to help students grasp the
concept.
Teacher’s Approach:
Questions:
1. What is the first thing we have to
do?
2. What formula do you have to use to
find the distance formula?
3. Show different triangles and ask if
the theorem can be applied to them.
4. How do you know to use this
theorem? (Have them say which
sides are a, b, and c.)
Student Does
What the students are doing
Groups are presenting their work.
Students are listening and correcting their
mistakes.
Expected Student Answers
Students will answer depending on the
question.
Expected Student Answers
1. Graph the points.
2. The Pythagorean Theorem.
3. No
4. The intersection made it a right
triangle.
5. What problem do you have using
this?
6. How do you find the side lengths so
you can use the theorem?
7. How do you use this to find the side
length?
8. Call two students to demonstrate
distance between two horizontal or
vertical points.
9. How do you use these and the
Pythagorean Theorem to find the
distance formula?
10. So, what is the distance formula?
5. No side lengths were given.
6. By labeling the points.
(x1, y1)
and (x2, y2)
7. x2-x1 is one side and y2-y1 is the
other.
8. demonstrating distance.
9. By plugging in a=x2-x1, b=y2-y1,
and c is what we are looking for.
10. 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)
If time permits, show students how this
formula relates to the equation for a circle.
Teacher will assign worksheet for
homework extra practice.
What the students are doing
Students are listening and paying attention
to teacher.
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
Engage:
Learning Experience
Reintroduce graph from first day.
Reflect on constructing a perp. line with a
compass to show them the midpoint.
Questions
1. How do you draw a perpendicular
line recalling the lesson on Friday?
(have them explain)
Student Does
Student Activity
Students are listening and answering
questions.
Expected Student Answers
1. With a compass. Students will
explain how.
2. Is there a midpoint on this line?
2. Yes, the point where the perp. line
and the original line intersect.
3. A point half-way between two
points on a line.
4. Slant—rate of change.
3. What is a midpoint?
4. Can anyone define slope?
5. Think about the slope of this line.
Can you find it?
5. Students will get into groups.
Evaluate
Teacher will make sure students are on task and participating.
Teacher Does
Explore:
Learning Experience(s)
Teacher is walking around to each group
assessing their progress.
Student Does
What the students are doing
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.
Questions
Expected Student Answers
1. What approach are you using to
1. Answer will vary depending on
solve this problem?
group.
Evaluate
The teacher will walk around the room to assess each group’s
progress.
Teacher Does
Explain:
Learning Experience(s)
Teacher is listening to students’ ideas.
Calling on different students to give their
opinions.
Questions
Questions will depend on students’
approaches.
Teacher will summarize his/her
approach to help students grasp the
concept.
Student Does
What the students are doing
Groups are presenting their work.
Expected Student Answers
Students will answer depending on the
question.
Students are listening and correcting their
mistakes.
Explain that we rise before we run.
(example of stairs)
Teacher’s Approach:
Expected Student Answers
Questions:
1. Students are paying attention.
1. Teacher will give a real life
example to explain midpoint
concept.
2. What is the formula for the
2. x=(x1+x2)/2 and y=(y1+y2)/2
midpoint?
3. What does the slope tell us?
3. rate of change
4. What is the formula for the slope?
4. (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
Extend / Elaborate:
Learning Experience(s)
Teacher will assign worksheet for
homework extra practice.
Student Does
What the students are doing
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.