Michael+Sigler

Lesson Title: Proving the Pythagorean theorem (55 minute class session)

Related Lessons: Solving problems with exponents and solving 2-step equations

Grade Level: 7th

Unit: Pythagorean theorem

__Lesson Description__: Students will be given a challenging problem; to investigate whether the side opposite the right angle in a right triangle cannot equal the sum of the squares of the remaining sides. Students will be placed into groups and each group will construct three triangles using meter sticks and meter tape. After obtaining their measurements, students will check to see if the sum of the squares of the legs of the triangle equals the square of the hypotenuse. After calculations are complete and students present their findings to the class using a document reader or Geometer's Sketchpad and an interactive white board, the class will discuss and create a formula, which is the Pythagorean theorem.

Outcomes:

SWBAT demonstrate taking measurements using the Metric System. SWBAT use prior math knowledge to investigate and state the Pythagorean theorem. SWBAT use technology to solve problems and communicate results of an investigation.

Content Standards:

Understand the relationship between the sides of a right triangle is a2 + b2 = c2 and that this relationship is known as the Pythagorean theorem.

ISTE NETS-S

Communication and collaboration Critical thinking, problem solving, and decision making Technology operations and concepts

Steps of the Lesson

10 minutes Students are given the directions for the lesson and the teacher models how to create and measure different right triangles, using the wall and floor in the classroom, measuring out a triangle just using the floor, and creating triangles using different objects in the room. Students are told to use only a metric ruler and metric tape, and to make sure their triangles are measured in millimeters, and need to be as accurate as possible. Student groups who perform well, meaning they stay on task and are serious about investigating their problem, will be able to go outside to complete another lesson on similar triangles.

10 minutes Student groups create and measure three right triangles and record measurements.

15 - 20 minutes Students calculate the sum of the squares of the legs of their right triangles and compare the sums to the square of the side opposite the right angle, or the hypotenuse. Students have the choice to present their findings to the class using a document reader or imputing their measurements into Geometer's Sketchpad to be displayed on an interactive white board.

10 minutes Class discusses each of the groups findings and derives the Pythagorean theorem, a2 + b2 = c2

5 minutes Students will complete an exit ticket solving for an unknown side of a right triangle using the Pythagorean theorem

Students will use technology by using the document reader or Geometer's Sketchpad and interactive white board to communicate their results.

Accommodations will be made by grouping students by their different strengths. Each group will need students to measure, students to record, students to use the technology, and students to present. Different learning styles will be addressed as content is presented audibly, visually, kinesthetically, and by peers.

Students will be assessed by their exit tickets.

Michael, I think that having students get up out of their seats and meaure acutal right angles in the room will be a great way to involve multiple learning styles. -Chelsea Lewis

Thanks Chelsea!


 * Michael, **
 * I like how you are starting your lesson off by modeling. I feel modeling can have a powerful impact on the students and really get them started on an activity or be a great introduction to a lesson. Are there enough triangles in the classroom for the students to measure different items? I think it's great you are using real world situations, something PBL should target. Great job thinking out the way you will be accomodating the different learning styles. Flexible grouping can always be useful, as well as presenting the content by using different media. I think your lesson sounds great. I hope it works out for you. **


 * Tiffini **

Hi Tiffini,

The triangles I am referring to are ones students will make up by measuring different distances. They can measure out say a 1 meter and a 1 meter leg, then measure the hypotenuse, and then check their mesurements against the Pythagorean theorem. Or, students can measure up and out from a wall, then check the diagonal hypotenuse distance, etc. Thanks for the comment!

-Mike

Michael, I really like how this is a hands-on lesson and your students are measuring triangles on the floor and wall. You also did a great job addressing the various learning styles and MI of your students. --Brett

Daily Lesson Plan Template – Michael Sigler Lesson 2: Using Collaborative Learning Tools 2. Apply mathematics to real-world situations
 * ** Lesson Title ** : Lesson 2 of 3 – Solving Pythagorean theorem story problems || ** Related Lessons ** : Story problem decoding, how to post to a website or blog ||
 * ** Grade: ** 7 || ** Unit ** : Pythagorean theorem ||
 * GOALS ||
 * Content Standards: **
 * 1) Understand the relationship between the sides of a right triangle is a squared plus b squared equals c squared, and that this relationship is known as the Pythagorean theorem.


 * ** ISTE NETS-S **

1) Ensure all students have access to Edmodo.com 2) Rearrange groups as needed based on success from first lesson ||
 * Creativity and innovation
 * √ ** Communication and collaboration
 * √ ** Research and information fluency || ** √ ** Critical thinking, problem-solving, & decision-making
 * Digital citizenship
 * √ ** Technology operations and concepts ||
 * Instructional objective(s): **
 * effectively decode story problems dealing with the Pythagorean theorem
 * collaborate with peers to reach a goal
 * apply knowledge of the Pythagorean theorem to a real-world situation
 * ACTION ||
 * ** Before-class preparation: **
 * During class ||
 * Time || Instructional Activities || Materials & Resources ||
 * 10 min

15 min

15 min

10 min

5 min || 1. Class discussion –review the Pythagorean theorem with the class. Have students give their understanding of the formula, and how and why it works. Explain to the class they will be solving a story problem in groups and will have only 10 minutes to complete their task. The group who does the most thorough job and correctly solves the problem within 10 minutes will be the first group to conduct the next unit on similar triangles outside.

Students are put into groups, given their problem by the teacher, and work for 10 minutes to solve the problem. Time is also built in for teacher to verify their work at the end of their 10 minutes. Students work only on paper, posting their work online only after their work is complete.

Each group logs onto Edmodo.com and posts their problem and work. Each group member takes turns typing in original problem, steps to complete, and final answer. These roles are decided by the group, or by the teacher if necessary.

Each group responds to two other group’s posts. Groups need to state whether they disagree or agree with the solution, and give one positive comment and one suggestion for improvement.

Teacher reveals solutions to problems, each group comments on results. Exit ticket requires students to comment on lesson and rate their comfort level regarding the Pythagorean theorem from 1 to 10. || Interactive white board, regular white board, markers

Story problem, paper, and pencil.

Laptops, access to Edmodo.com

Laptops, access to Edmodo.com

Half-sheets of paper ||
 * MONITOR ||

Teacher will monitor groups during each step of the lesson by coaching groups and keeping groups on task Students will use technology by accessing the Internet and accessing Edmodo.com. Edmodo functions much like Facebook, and students are able to post and respond similar to how Facebook works. Edmodo was chosen as a class website earlier in the year, and all students will have access and experience using Edmodo by the time this lesson is given.
 * EVALUATE AND EXTEND ||

Accommodations will be made by grouping students by their different strengths. Each group will need students to type different parts of the solution. Dictating part of the solution for a peer to type is acceptable. Different learning styles will be addressed as content is presented audibly, visually, kinesthetically, and by peers.

Students will be assessed by their exit tickets.


 * || === References === ||

Mr. Sigler Math. (2012). Edmodo. [|www.edmodo.com]