Lesson Plan:
Teacher__Henry Clagett___________________
I.
Grade Level__10_____________
Content and Standards: Pennsylvania State Standard 2.3.G.C: Use properties of
geometric figures and measurement formulas to solve for a missing quantity (e.g., the
measure of a specific angle created by parallel lines and a transversal).
II.
Prerequisites:
a. Students must understand the concept of parallel lines.
b. Students must understand the Vertical Angle Conjecture and the Linear Pairs
Conjecture
III.
Essential Questions (provide a framework)
a. How do angles created by parallel lines and a transversal relate to each other?
IV.
Instructional Objective: Given a set of parallel lines intersected by a transversal
and the measure of an angle created by these lines, students will be able to
determine the measure of all other angles created by these lines.
V.
Instructional Procedures:
At the beginning of class, students will be given a warm-up problem on the
projector. The problem will contain two intersecting lines. The measures of one
of the angles created by these lines will be given and the students will be asked
to find the measures of the remaining three. The teacher will walk around the
room and inspect the work of the students to ensure that the prerequisite skills
assessed by this warm-up task are sufficiently mastered. Allow about 5 minutes
for this warm-up.
Once the warm-up activity has been completed and the teacher is confident that
all students have the necessary prerequisite skills, call attention to the projector.
Using a Geometer’s Sketchpad or other technology, the teacher will have drawn
a set of parallel lines on the screen. Draw a transversal line and explain to the
students what it means for a line to be a transversal. The teacher should then
label all eight of the angles created by these lines with a letter. Provide the
measure of one of these angles and call on students to give the measure of a
different angle on the diagram that forms a set of vertical angles or a linear pair
with the measured angle. Next, pose the question to the students about how the
angles formed by one of the parallel lines are related to those of the other parallel
line. Refer the students to a pair of corresponding angles and ask the students
to think about how a change in one of the angles would affect the other. Give the
students time to think about it and to confer with another student. Call on
students for their predictions before using the Sketchpad to adjust the diagram
and change the size of one of the corresponding angles. Use the perceived
change in the corresponding angle to introduce the Corresponding Angles
Conjecture. Be sure to demonstrate the extremes of the transversal ( m< = 0
degrees and m< = 90 degrees) to fortify the concept.
Repeat this process for Alternate Interior Angles and Alternate Exterior Angles.
The entire teacher-centered instruction period should last no longer than 15
minutes.
To limit the amount of teacher-centered lesson time, the students should then be
given an example problem on the projector to be solved individually or in pairs,
depending on the students’ preferences. The problem should be similar to the
image below, in which the measure of one angle is provided and the students are
asked to find the measure of all other angles. Allow the students 5 minutes to
complete this problem. During this time, the teacher should be walking around
and ensuring that the students understand the concepts correctly.
Go over the problem with the class, calling on students to provide answers and
reasoning for those answers. At this point, if all has gone according to schedule,
provide one or two more practice problems for the students to complete in
groups.
Next, the students should be given a worksheet with additional problems to
complete during the remainder of the period. The worksheet should be split into
sections based on difficulty. Inform the students that they are only asked to
complete the first (most basic) section, but that they should complete the other
sections if they finish early. The remaining 15-20 minutes of the class period
should be devoted to finishing these problems as the teacher walks around and
provides assistance to individuals and small groups as necessary. Any students
who complete the entire worksheet are invited to begin working on their
homework (a similar worksheet that only contains problems from the basic and
intermediate levels).
VI.
Materials and Equipment: A computer with a program such as Geometer’s
Sketchpad and a projector will be used by the teacher to demonstrate the
congruency of various angles. Personal laptop computers may be used by the
students in the same manner, if such technology is available in the classroom. Two
worksheets, one to be completed in class and another to be completed for
homework, will be used during this lesson. Clickers, small white boards, or a similar
material may be used to receive student answers to teacher probes if these materials
are readily available. Naturally, all students will also need a pencil or other writing
implement.
VII.
Assessment/Evaluation: Formative assessment will be conducted by the teacher as
he or she walks around the room while students are solving the problems on the
projector. This allows the teacher to correct any misconceptions before they are
ingrained in the students’ minds. Calling on students to provide their answers to
these problems is also a form of formative assessment. The worksheet completed at
the end of class is a form of summative assessment in that the students’ answers will
demonstrate what they have learned after the teacher-centered lesson is finished;
however, the teacher is still given some time for formative assessment during the
completion of this worksheet, as he or she should be walking around, answering
student questions, and checking to make sure that the problems are being solved
properly. Finally, the brief homework worksheet, which is to be turned in on the
following day, is an example of summative assessment. Additional forms of
summative assessment, such as projects, tests, or even presentations, can be
assigned on future days once the students have had more practice with the topic.
VIII.
VII. Differentiation: Individualized Activities: The worksheet assigned for students
to work on individually contains questions of several levels of difficulty, to account for
the inevitability of different students to understand the concept at different paces.
The first set of problems would contain questions that ask the students to identify
which angles are congruent, and to determine the measure of one or two angles from
a given measure of an angle using one of the conjectures introduced. The second
level of questions might ask students for the measure of all the unknown angles,
thereby requiring the use of all the conjectures introduced, as well as the knowledge
of vertical angles and linear pairs. The third set of problems might provide students
with the measure of two angles, each of which contains a variable, thereby requiring
the students to solve an equation and use their knowledge of the conjectures
introduced to come to the correct answer.
Additional activities can be developed for students of varying comprehension levels.
While students are completing the worksheet to the best of their ability, the teacher
can pull aside any struggling students and provide them with additional instruction.
These lessons can focus solely on one of the conjectures introduced in the lesson
and, when possible, the use of the students’ knowledge of vertical angles and linear
pairs to derive the others. These students could also be given pegboards and rubber
bands to simulate the same demonstration that the teacher performed on the
projector. If the teacher is aware that there are students who will understand the
lesson very easily (or have already learned the material), additional tasks can be
developed for these students that relate to the more difficult topics in math that they
will learn later this year (such as, in the most basic case, consecutive interior angles)
or in future math classes. The teacher can determine beforehand which of these
activities will be necessary based on the students in their class; however, having all
these activities prepared beforehand can be beneficial.
IX.
Technology: A Geometer's Sketchpad or similar computer program will be used in
by the teacher in conjunction with a projector to demonstrate the relationship
between the various angles created by parallel lines and a transversal. If individual
student laptops are available in the classroom, the students can use such a program
individually to better understand the concept; although this may be a better method of
instruction, it requires technology that many classrooms do not have.
X.
Self-Assessment Self-assessment will be conducted in largely the same way as
student assessment. As the teacher calls on students to provide answers, walks
around the room to provide assistance, and performs general observations, it will
become evident to the teacher how successful the lesson has been. If the majority of
students are incapable of solving the problems in pairs or the basic worksheet
problems, then the lesson should be revisited. If only a few students are having
difficulty with the concept, then the lesson would seem to have been mostly
successful; additional accommodations and differentiation of instruction may simply
need to be made for those few students.
It is impossible to determine for certain whether or not one has planned for a lesson
sufficiently before the lesson has taken place. The goal of teaching is for students to learn, and
until we have determined whether or not learning has taken place, we cannot say that our lesson
plan was successful. However, I feel that my planning and preparation skills meet the standards
of Domain 1 of Danielson’s Framework for Teaching. Knowledge of content and pedagogy is
demonstrated through the inclusion of a list of prerequisite skills, each of which will be called
upon by the teacher during the lesson. Also, the structure of the lesson plan demonstrates a
“gradual release,” in which the teacher instructs the students directly, followed by a group activity
with teacher assistance, followed by an individual activity; this format has been found to be
successful in teaching.
Knowledge of students is demonstrated through the options and differentiated activities
available through this lesson plan. For example, students are allowed to work in groups if they
are more socially inclined, but may work independently if they feel that they work better that way.
Problems are assigned in sections of varying difficulty to account for students who may work
more slowly or more quickly than others. The teacher can state, for example, that students need
only complete the first section, (or the first and second) which ensures that struggling students
need not complete the most difficult work while also allowing advanced students the resources for
strengthening their understanding of this concept and related ones. Finally, resources such as
the Geometer’s sketchpad or pegboards with rubber bands are available for use based on the
students’ interests and learning preferences.
The ability to set instructional outcomes is demonstrated in that the instructional objective
is aligned with the lesson standards and content. The objective is written as a complete
objective; that is, it is written in terms of what the students will be capable of doing after this
lesson is completed. The objective is also written in terms that students of this level should, in
general, be able to understand. Students may be unfamiliar with the word ‘transversal,’ but these
are introduced at the very start of the lesson. Multiple strategies for instructing diverse learners
are used in this lesson plan to help ensure that all students are capable of meeting the lesson
objective.
Knowledge of resources is demonstrated through the variety of resources chosen for this
lesson. Technology, such as a Geometer’s sketchpad, projector, and even individual student
laptops (where available); worksheets; and other materials, such as a pegboard and rubber
bands are all used to ensure that the students receive the best learning experience possible.
These resources are all materials that are either traditionally used in this subject to strong
success or are designed specifically for use in such a classroom setting. The ability of the
teacher to use these resources appropriately and skillfully cannot entirely be proven through this
lesson plan, but the description of how said resources will be used should demonstrate some
knowledge of their capabilities and relevance.
The ability to design coherent instruction is demonstrated within this lesson plan. As
mentioned above, the “gradual release” strategy is a well-documented instructional strategy that
has met with great success. The instructional method used in this lesson is a combination of
direct instruction (which, while traditional, is an effective way of teaching) and exploration on the
part of the students (which helps ensure that the content makes a lasting impression in the
students’ minds. The materials and resources used in the lesson are all very educational, and
the lesson encourages higher level thinking skills. The warm-up activity used at the beginning of
the lesson activates prior knowledge that the students can use to help them learn the new
material. It is not certain that the instructional methods described here will work for every class
(and certainly not for every student), but research suggests that these methods are at least
coherent.
Finally, the ability to design student assessment is demonstrated through the use of both
formative and summative assessment. Formative assessment is the most important type of
assessment in that it allows the teacher to correct any misconceptions during the lesson, when
the focus of the student is still on that topic and not on another concept (as summative
assessment tends to do). Teacher observations of individual student efforts are the best type of
formative assessment because the teacher receives direct feedback about the individual
student’s ability to complete the instructional objective. He or she is then able to immediately
attempt to make corrections. Assessments received from groups of students do not ensure that
each student understands the concept; therefore, individual formative assessment is best.
However, summative assessment is also useful to determine whether the lesson as a whole was
successful; the teacher can then decide whether or not further time must be spent on this topic.
This lesson plan contains summative assessments for this purpose. Whether the assessments
are designed appropriately for this lesson is impossible to tell without employing this lesson plan
and knowing the exact nature of the class and its students; however, I believe that this lesson
plan demonstrates my ability to design lessons with appropriate assessment in mind.