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TRANSCRIPT
Lesson Title: Introduction to Pythagorean Theorem Grade and Subject: 8th Grade Mathematics
1. Overview, Background & Rationale For Lesson Plan Overview Abstract This lesson introduces the concept of Pythagorean Theorem. Student will
examine the proof and algebraic reasoning behind the Pythagorean Theorem. The Pythagorean theorem is a geometry topic that is taught as part of an overall goal to increase students’ fluency in Mathematics and aiding them in understanding the world in which they live. This specific class has students who are considered struggling readers and a few students are performing below grade level. The lesson will be taught using a Promethean board flipchart, a corresponding booklet with student notes and a brief assessment to close the lesson.
Background, Culture and Context
I teach predominantly African-‐‑American students who are growing up in an urban environment. The culture within the class has been designed to have a balance between rewards and consequences. I am seeking to teach students a method to find the missing side of a right tringle using a theorem that was proven many years ago. In order to do this I have to make the lesson interesting and engaging. I’ve chosen to incorporate a picture book to introduce Unit 3. According to Zimmerman (2012), “What’s Your Angle Pythagoras?’ would be considered a Tier 1 Fundamental Math Picture book because it is directly content related. We are currently behind on the pacing calendar by about three weeks so to save time the lesson will be loosely based on the text and the book will be available for the students to read on their own during homeroom, tutorial, and lunch. The lesson plan is for a 60minute class period and can be the foundation for a 2-‐‑ 3 day exploration of the Pythagorean Theorem.
Reference Zimmerman, Alycia. (2012, November 14). Teaching Math With Picture Books, Part 1. Retrieved from http://www.scholastic.com/teachers/top-‐‑teaching/2012/11/teaching-‐‑math-‐‑picture-‐‑books-‐‑part-‐‑1
Rationale
Builders use the Pythagorean Theorem to help keep right angles and build houses, decks, buildings, and to put windows, doors and floors in. The theorem has practical applications that students can apply this too real life situations once the basics are understood. The students respond positively to rhythmically engaging songs and activities Therefore I have chosen to introduce this lesson with a rap. The lesson elicits prior knowledge of equations, triangles and exponents. King MS students like a good narrative or story line, which is why I kept young Pythagoras, from the text, a common theme throughout the lesson. Coming up to the board and working together in pairs are also activities that appeal to middle school students. Students also have an opportunity to be exposed to proofs, checking math calculations and forming generalizations.
2. Lesson Plan Learning Outcomes And Procedure
Essential Question(s) / Central Focus
} What is the relationship among the lengths of the sides of a right triangle?
} How can the Pythagorean Theorem be used to solve problems? } How can I use the Pythagorean Theorem to find the length of the
hypotenuse of a right triangle? } How do I use the Pythagorean Theorem to find the length of the legs of a
right triangle? Learning Objective(s)
At the end of this lesson, students should know and be able to explain the attributes of a right triangle. They should be able to apply their new found knowledge of the Pythagorean Theorem to a real life scenario in order to correctly answer 3 out of 4 (75%) questions on the final assessment and attempt the challenge problem.
CCGPS or GPS Standard(s)
MCC8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-‐‑world and mathematical problems in two and three dimensions.
Instructional Strategies & Learning Tasks that Support Diverse Student Needs Introduc-‐‑
tion to Lesson 10 minutes
I plan to capture the student’s attention using a picture from the book for the Do Now. I will also use a rap to engage the students in the activity. In the text the picture shows an image of a Pythagorean Theorem proof. The students will get a chance to examine the image, talk with a partner and write down their ideas. They would look for patterns and make observations. After hearing student’s observations I would play the YouTube video of the Pythagorean Theorem rap. It will engage the students as well as introduce key vocabulary terms that the student’s will need to understand the lesson. The image allows students to observe the characteristics of a right triangle without being told directly.
Pythagorean Theorem Rap -‐‑ https://youtu.be/nbopLhP4kpo?t=40s
Body of Lesson
Students will be led through the flipchart by the teacher and follow along by completing the guided notes in the interactive booklet.
1. Students will have a review of radicals, exponents and square root. 2. Student will label the parts of a right triangle and highlight the
hypotenuse with a marker. 3. Students will write the vocabulary words such as hypotenuse, right
triangle, legs and Pythagorean Theorem 4. Students will be introduced to the Pythagorean Theorem and write
down the algebraic formula. 5. Students will identify the hypotenuse on right triangles with different
orientations.
6. Student will work through two examples of solving triangles for the
missing side. One example would involve finding the hypotenuse and the other example will involve finding a leg of the right triangle.
Each step was chosen based on common steps and misconceptions made by students. Students tend to have difficulty correctly labeling the hypotenuse which may affect their use of the formula. Students also think that the hypotenuse is always the missing side resulting in errors when substituting values into the equation. I chose to use an interactive booklet and guided notes so students could focus more on what is being said rather than trying to record everything from the flipchart. Also I’ve highlighted notes that should be written using a pink glow. This way students know if it glows it is something they should know. I have provided support for students who struggle in Mathematic by reviewing key radical concepts before beginning the lesson. This will help reactivate prior knowledge. The lesson will consist of primarily teacher student interaction because the topic is new. However, students are given opportunities to collaborate with a partner during the Do Now activity, the class examples and the final challenge problem. I will use call and response techniques such as “Class Class!” , “Yes, Yes!” to get student’s attention when necessary. The closing activity (formal assessment) will be an individual activity but will be reviewed together as the closure of the lesson. Language supports for academic language will be in the rap introduction, throughout the flipchart and in the constructive response section of the final challenge.
Closure Students will summarize and share what they have learned by answering a four question quiz and helping Pythagoras, from the text find a direct route to Crete from his home. Students will have to explain how they found the distance using their vocabulary words. Students will receive a homework assignment due the following day based on the lesson as well as an extension question.
Learning Supports: Differentiation, Modification(s)and Accommoda-‐‑tion(s)
• Provided guided notes to students. Many are struggling readers and writers. Guided notes relieve the stress of having to record perfect notes while still keeping the students engaged.
• Have students repeat given directions. Students that have issues focusing tend to miss initial directions. This just helps the students stay on task.
• Extra visual and verbal cues and prompts having important information highlighted on the flipchart, scaffolds students to discern important information during the note taking process.
• Take a longer time to go through the lesson in order to maximize understanding. This will eliminate the challenge question but will provide the students with a stronger content knowledge foundation.
Formal and Informal Assessment
Formal Assessment: The formal assessment is the four question task that students are required to turn in during the closure of the lesson. The formal assessment consists of the fundamental concepts of the Pythagorean theorem and can indicate clearly what a student may be struggling with. The information from the assessment can be incorporated into the Do Now off the next lesson to increase understanding. The final challenge requires students to use their knowledge in a real world situation.
https://www.brainingcamp.com/content/pythagorean-‐‑theorem/questions.php (Questions 1-‐‑4) Informal Assessment: Throughout the lesson I will request a show of hands to identify whether or not students are struggling. This allows me to provide immediate changes, repetition or clarification.
3. Resources
Academ
ic Language
Language Functions
• Justify the use of the Pythagorean Theorem to solve for the missing side of a right triangle.
• Argue whether a triangle is a right triangle using the Pythagorean Theorem and the three given sides
• Define the hypotenuse based on the characteristics of a right triangle. Vocabulary The students will demonstrate their understanding of the vocabulary by
labeling a right triangle, using correct terminology when contributing to class discussions and by writing using clear and complete sentences in the constructive response portion of the Final Challenge.
• Pythagorean Theorem • Square • Square root • Legs of a triangle • Hypotenuse • Inverse Operations
Syntax or Discourse
Students will identify the Pythagorean theorem algebraic formula as an equation that can be solved for the unknown using integer properties and inverse operations. Students will be able to create and identify right triangles by the right angle symbol. Symbols such as the radical should be used appropriately as the inverse operation for a number or variable that has been squared.
Materials • Calculators • iPads • Promethean Board • Formal Assessment Worksheet • Homework Worksheet • Interactive Booklet • 2 markers per student
Technology Calculators were used in the closure of the lesson to calculate the square root of numbers that are not perfect squares. The promethean board was used as an interactive tool for students to participate in class discussions during the review of the formal assessment as well as an engagement tool for students to view the Pythagorean Theorem rap. iPads can be integrated into this lesson for the formal assessment to be done online.
Lesson Flipchart – Pythagorean Theorem
INTERACTIVE STUDENT BOOKLET
Formal Assessment
Final Challenge
Name: ___________________________
Date: ________________ Period: _____
Pythagorean Theorem Homework
1. In each of the following problems, highlight the hypotenuse and find the value of x.
a.
x =
________ b.
x = ________
2. Is triangle ABC a right triangle? Justify your reasoning.
34
30
x
5
15
x
Show your work.
A
C
B
9 12
18