# Collaborative Lesson Planning Template

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Collaborative Lesson Planning Template

Team Members
   Sarah Mensching - Kearns Jr. High
   Cathie Lauterborn – Kearns Jr. High
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Part I: Selecting a Mathematical Task
What are the mathematical goals, objectives, and purpose for the lesson?
o What should students know and be able to do as a result of this lesson?
o To what standards / expectations / evidence does this lesson align?
Goals and Objectives:
1. Students will be able to apply the Pythagorean Theorem to find the missing side of a right
triangle.
2. Students will be able to summarize the Pythagorean Theorem using key vocabulary terms.
Standard:
1. 1.2d Calculate the measures of the sides of a right triangle using the Pythagorean Theorem

In what ways does the task build on students’ prior knowledge?
o What definitions, concepts, or ideas do students need to know for the task?
o How will you address any prerequisites that are missing from students’ backgrounds?
o What questions will you ask to help students access their prior knowledge?
The Pythagorean Theorem builds upon knowledge about right triangles, squares and square roots,
and how to solve equations.
1. Students need to know about squares and square roots and that they are inverse operations.
2. Students need to know how to solve equations for a specified variable.
3. Students need to know how to round decimals and simplify square roots.
4. Prerequisite knowledge about squares and square roots will be addressed in the warm-up
activity. Any other missing information will be dealt with on an individual student basis.
5. Questions:
a. What is the opposite of squaring a number?
b. How do we take the square root of a number?
c. What is a right triangle?

What are all the ways the task can be solved?
o What errors might students make? What are the areas of difficulty in the task?
o What misconceptions might students have?
o Which of the methods do you think your students will use?
The Pythagorean Theorem can be learned a variety of ways. Besides just straight lecture, there are
many web based activities, manipulatives, paper and pencil activities with graph paper, diagrams,
and real life examples available to help students learn the theorem. A variety of activities along with
connecting it to real life examples is what we think are best.

Errors:
1. Some students will misidentify the hypotenuse and legs of the right triangle
2. Some students will multiply by 2 instead of squaring a number.
3. Some students will divide by 2 instead of taking the square root of the number.
Areas of Difficulty:
1. Identifying the hypotenuse.
2. Solving for one of the legs instead of the hypotenuse.
3. Connecting the Pythagorean with real life models.
4. Visualizing and diagramming the concept.

Misconceptions:
1. Multiplying by 2 instead of squaring the numbers.
2. Students may assume that they can use the theorem on all triangles
3. Students may leave the negative answer of the square root as an answer.

Methods:
Students will be asked to use a visual method as an introductory task. Students will probably use the
basic algorithm of the theorem to solve problems along with perhaps diagramming the information to
correctly identify the legs and the hypotenuse of the right triangle. To reinforce the algorithm, there
are many web based activities that are fun and engaging to students. The notes that they take in
class will also reinforce the process.
Collaborative Lesson Planning Template

What particular challenges might the task present to students, especially struggling students
or ELL students?
o How will you address these challenges?
o Which strategies would be a good match to both the mathematics goal and students’
needs?
Challenges:
1. Vocabulary is always a big issue with ELL students and struggling readers.
2. Diagramming a problem
3. Connecting the theorem to real life.

How will you address these challenges?
1. Explicit instruction on vocabulary.
2. Frayer model on the specific vocabulary.
3. Model the diagramming process, verbally and on the board. Give several examples.
4. Use resources available to connect to real life such as YouTube videos and PowerPoint
presentation where you see distance problems in real life. Make it fun.
5. Consistent use of vocabulary by teacher.

Strategies:
1. All of the above

What are the expectations for students as they work/complete the task?
o What resources or tools will they use in their work?
o How will they work – groups, independent? How long?
o If they work in groups, in what ways will they be partnered?
o What evidence will I accept that students know the mathematical goal of the lesson?
We expect our students to work in pairs and independently to solve problems using the Pythagorean
Theorem. We expect out students to ask questions when we they do not understand something. We
expect our students to connect what we did previously in solving equations and squares and square
roots. We expect our students to observe already established classroom rules and procedures as
they work on the activities and take notes.

Resources:
Calculators, manipulatives for triangle activity, Frayer model, Cornell notes, textbooks, computer

Grouping:
Students will work in pairs for the triangle activity and independently during notetaking.

Evidence:
1. Exit tickets on language objective.
2. Practice problems
3. Questioning
Collaborative Lesson Planning Template
Steps of the Lesson

Part 1: Set up the Task
How will you introduce students to the activity to
 maintain the cognitive demands of the task?
Teacher Action                                                     Student Reaction / Response
 Instructional / accessibility strategy                           What do you expect will be the
 Higher level / critical thinking questions                       response from students as a
 Reading / vocabulary strategy                                    result of teacher action?
 Formative assessment strategy
 Time allocation

Opening activity:
Triangle Activity (please see attached worksheet)              Students should be able to
discover the theorem
themselves by doing the activity

Higher Level/critical thinking questions:
1. Do you think this works with all triangles?                 1. Most will assume that it does
work with other triangles
2. What is the relationship with a square and the actual       2. The area of a square is that
square of a number?                                         number squared.
3. How is the theorem similar and different to other           3. Multiple responses are
equations                                                   expected.

Vocabulary Strategy:
1. Frayer Model                                                1. We expect a positive
response from our student.
2. Explicit instruction for notes                              2. No response expected

Formative assessment strategy:
1. Questioning                                                 1. We expect our students to
respond to questions.
2. Practice problems                                           2. Some struggling will probably
occur at first especially when
solving for a leg the triangle.
3. Exit tickets                                                3. Students will write out what
the theorem is and explain it at
the end of class.

Time Allocation: Please see attached lesson plan
Collaborative Lesson Planning Template
Steps of the Lesson

Part 2: Exploration
 What higher level / critical thinking questions will you ask?
 How will you ensure students remain engaged in the task?
Teacher Action                                                     Student Reaction / Response
 Instructional / accessibility strategy                           What do you expect will be the
 Higher level / critical thinking questions                       response from students as a
 Reading / vocabulary strategy                                    result of teacher action?
 Formative assessment strategy
 Time allocation

Higher level/critical thinking questions:
Triangle Activity:
1. What do you notice about the area of the legs squared           We expect multiple answers to
and the hypotenuse’s area squared?                              these questions.
2. Why do you think we are making actual squares?
3. Do you see a pattern between the lengths of the legs and
the hypotenuse?
4. What is the relationship between the length of the side
and the square?

Cornell Notes:
1. What is the relationship between the legs of a right             We expect an analyzed detailed
triangle and the hypotenuse?                                     summary on their notes along
2. How do we tell the difference between the legs and the           with higher thinking questions.
hypotenuse?
3. What is the difference between squaring a number a               We engagement while taking
multiplying a number by 2?                                       notes.
4. What is the difference between taking the square root of a
number and dividing by 2?
5. If we know all the lengths of a triangle, can we tell if it is
right triangle?
6. Will this work with other triangles besides right triangles?

Engagement Strategies:
1. For triangle activity, use different color paper for the          100% participation on all
squares to make the activity more visually appealing.             activities.
2. Think-pair-share strategies
3. Computer activities
4. Already understood classroom procedures, expectations,
and consequences.
Collaborative Lesson Planning Template
Steps of the Lesson

Part 3: Share and Discuss
How will you orchestrate the class discussion to accomplish mathematical goals?
 Which solution paths to share and in which order?
 What specific questions will be asked to make sense of mathematical ideas?
Teacher Action                                                   Student Reaction / Response
 Instructional / accessibility strategy                         What do you expect will be the
 Higher level / critical thinking questions                     response from students as a
 Reading / vocabulary strategy                                  result of teacher action?
 Formative assessment strategy
 Time allocation

Class Discussion:
As previous stated, we have multiple higher levels thinking             We expect full participation
questions discusses before, during and after the Triangle activity      according to previously
and during the Cornell notes. Wrapping up the session at the            determined classroom rules and
end of class, we are going to reiterate what should have been           expectations.
learned and clarify any questions at that point.

Solution Paths:
We are using multiple solution paths; diagrams, oral, algebraic         We expect students to be
so that students will have the skills to solve for missing sides of a   familiar with a variety of solution
right triangle.                                                         paths.

Specific Questions:
1. What is the relationship between the legs and the hypotenuse         We expect that our students will
of a right triangle?                                                    be able to answer these
2. Is the theorem specific to right triangles?                          questions.

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