Lesson Plan 2: Mathematics

I. Overview of the lesson:

A. Date of lesson: Thursday, April 7, 2011

B. Expected Length: 50 minutes

C: Name: Kirsten Gehm

D: Mathematics – Algebra I/Trigonometry – High School

II. Big Idea:

Standard – 2.10.A1.A: Solve problems involving from the Pythagorean Theorem.

III. Essential Question(s):

How are the students going to use this theorem in life? Why is this going to be needed? In what ways will they be able to apply the theorem?

IV. Pennsylvania State Standards/Eligible Content:

Subject Area 2 – Mathematics

Standard Area 2.10 – Trigonometry

Course 2.10.A1: Algebra I

Standard 2.10.A1.A – Solve problems involving from the Pythagorean Theorem.

V / VI. General Objectives / Behavioral Objectives:

A. The students will recognize the theorem as well as memorize it.

B. They will identify the different components to theorem.

C. Students will apply to theorem mathematically and apply their new knowledge of the Theorem.

D. The students will discover different elements in our society where the theorem is evident.

E. The students will be able construct the different steps used to solve the problems given.

F. Students should be able to conclude the different measurements to the sides of a triangle using the Pythagorean Theorem.

 

VII. Instructional Materials:

Toy car

String

Notebook

Rulers

Worksheet

VIII. Vocabulary:

Words associated with right triangles

Right triangle

Hypotenuse

Base

Leg

Square

Square roots

Right angle

Pythagorean Theorem – calculating the length of the hypotenuse of a right triangle

IX: Instructional Procedures:

A / B. Introduction /Motivation:

I will start by proposing three different questions to the class by using a Smartboard if available. If one isn’t available, I will use white boards or an iClicker.

Question 1: Where do you see triangles in the real world?

   - sailboats, bridges, instruments, clips, quilts, floor tiles

Question 2: What words are used to describe triangles?

   - equilateral (all sides equal), isosceles (2 sides equal), scalene (no sides equal)

   - right angles, acute angles, obtuse angles

   - base, leg, hypotenuse, 30-60-90 or 45-45-90(measurements of angles)

Question 3: What types of triangles do you see in these images? (shows different images of every day scenarios and the students will search for them) Are some more common than others? Why?

This will all motivate the students to be able to see why we need to learn this for everyday life. We will then define a right triangle, leg, and hypotenuse. We will go through the right triangle and identify a, b, and c. Before breaking into groups we will apply the Pythagorean Theorem to solve for a hypotenuse of a right triangle and to solve or a missing leg or base.

 

C. Development:

1. After the introduction questions and activity, we will break up into small groups. Each group will have pieces of string of various lengths. All groups will set up their station along a wall within the class room or by a leg of a desk.

2. The students will then tape all of the different strings on the wall. The bottom of the strings must be on the flush with the ground.

3. Students will then attach the toy car to the end of their string. Students will then “drive” the car as far as they can. This will stretch the string and create a right angle.

4. Students will then have to measure the string (the leg), and how far the car “drove” (the base). Students will draw the triangle on the worksheet and record the measurements of both legs.

5. From these measurements, they will then use the Pythagorean Theorem (a2 + b2 = c2) to calculate the hypotenuse (string length).  

6. The students will continue this process until all the strings have been used and stretched.

7. They will then us the ruler to measure the actual string. This will be used to check their own work with the theorem.

8. Students will then come back into a group to discuss the different triangles that were created by comparing/contrasting the triangles.

 

D. Strategies for diverse learners

(1) Use mixed-ability groups which allows students to learn from one another (i.e. either small or whole group participation)

(2) Incorporating drawing of what figures should look like. This allows students to test the Pythagorean Theorem.

(3) Use guided questioning and discussion to help students articulate the relationship between the sides of the triangle (base and leg) and the hypotenuse.

(4)  Engaging students in small groups by using the car toy to make a right triangle and be able to physically touch and create the right triangle.

E. Summary and Closure:

Students are asked to identify different types of triangles and where they are located and how they are used in the world. They will need to identify the different parts to a right triangle and recite the Pythagorean Theorem onto a white board or I will make it into a voting style game. All students will write that they think  the theorem is and we will pick them all out to make sure they are all a^2+b^2=c^2.

F. Assignment:

The students must finish their write from the problem on the board. I then want the students to go home and bring two everyday objects that they can use in class. We then will be able connect right triangles to everyday life for the next lesson.

X. Assessment:

A. Formative

a. As the students are working on their different projects, I will be asking the questions: “Can students identify the legs and hypotenuse in a right triangle?”

“Do students understand that the hypotenuse is the longest side of the triangle no matter what size the triangle is?”

“Were the students able to apply the Pythagorean Theorem and solve for the hypotenuse or which side is missing?”

b. I will document the students progress by walking around and taking notes on stickers. These stickers will be side the size of an I.D and I will able to jot down notes and then put then in the specific students portfolio.

 

B. Summative

I will put a drawing of a right triangle on the board and give them the measurements of the both the leg and base of the triangle. The students will then have to use the Pythagorean Theorem to solve for the hypotenuse. Students will do a write-up of the problem and the solutions. I will assess their write up by using a rubric. After a night of practice with homework, I will give a quiz four question quiz just to assess that they both understanding of the theorem as well as how to apply it.

XI. Reflection & Self-Evaluation:

A. What worked?

B. What did not work?

C. How can the lesson be improved?

XII. Suggested Instructional Strategies:

To begin the lesson, we will start with an engaged class. Everyone will have to be involved in the class discussion. Everyone would be active in the discussion. I want to be use a system where every uses white boards or even iClicker where I can give them multiple-choice questions to choose from. Then the class would be broken into cooperative groups. Through this process, I would be embedding scaffolding by walking around to each group and observing and supporting students who need more assistance. During the time I am walking around I will also be assessing the students by asking questions to each group.

 



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