Math



PythagoreanExplorer curriculum.suite101.com/article.cfm/ the_pythagorean_theorem pythagoreantheoremwordproblems.php
 * **Lesson Title** || The ABCs of Geometry: A Pythagorean Theorem Lesson. ||
 * =**Grade/Content Area**= || === This lesson is for an 8th grade Mathematics classroom. === ||
 * =**Context of the Lesson**= || This lesson will cover calculations and problem solving using the Pythagorean Theorem to reinforce its use in the real world. It is part of a unit based on discovery. ||
 * ** Objectives and GLE’s/ **** GSE **** ’s ** || The students will be able to solve problems and calculate the sides of a right triangle using the Pythagorean Theorem and special right triangles. (M(G&M)-8-2) Students will also demonstrate an understanding of the relation between squares of numbers and square roots (M(N&O)-8-2). ||
 * ** Opportunities to Learn ** || **Materials:**
 * Overhead projector
 * Dry erase markers
 * Transparencies
 * Crayola markers
 * Scotch tape
 * Measuring tape
 * Homework worksheets
 * Poster Boards
 * Online resources
 * 1) http://www.shodor.org/interactivate/activities/
 * 1) http://middle-school-
 * 1) http://www.yourteacher.com/geometry/

The materials listed above are tools to conduct the lessons and resources for students to use in their own homes. I will use the overhead to activate prior knowledge and to employ the modeling portion of my lesson. I will make the online resources available for students to explore while doing their homework and journal entries.


 * Differentiated instruction:**

Throughout the unit, students will have worked individually, with a partner, in groups, and as a class. I have provided a variety of problems to meet their needs. ELL students and students with the IEP will be dispersed throughout the groups. The needs of all kinds of learners will be addressed:

__Visual__- Students will be asked to do problems on poster board which will cater to those that are visual learners. __Interpersonal__- Group work is a part of the lesson which will cater to those that are interpersonal learners. __Intrapersonal__- Journals and individual homework assignments are given which will cater to those that are intrapersonal learners. __Linguistic__- Group presentations of their Pythagorean Theorem problem will cater to those that are linguistic learners. __Bodily/Kinesthetic__- The group activity and movement throughout the classroom will cater to those that are kinesthetic learners. __Naturalistic__- A variety of Pythagorean Theorem problems in nature will be provided which will cater to those that are naturalistic learners. __Mathematical__- The calculations of the Pythagorean Theorem throughout the lesson will be great for the mathematical learners.

To support struggling students, I will ask them to read the problem aloud and write down all the information they know. Once they have written down everything they know about the topic and the problem, I will help them organize it into the KWL chart and fill in the gaps.


 * Technology integration:**

I will be using an overhead projector to activate prior knowledge and in the modeling portion of my lesson. The rest of the lesson will be hands on in order to engage the students. However, students will be encouraged to use the internet for research in answering the journal prompt. A sheet with a list of online resources will be provided. || ** Instructional Procedures ** || **__Day 1:__** Students will learn about the history of the Pythagorean Theorem and how to prove it. · I will begin the lesson with the story of Pythagoras and his work as a mathematician. This will lead to the discovery of the Pythagorean Theorem and how it was used in ancient Egypt. · On the board, I will model for students how to construct a right triangle and test the theorem by measuring the sides and using squares with those measurements. · Students will be placed in groups and given different sized triangle cut outs with which they will also test the Pythagorean Theorem.

__Homework__: Construct a right triangle of any size and test the theorem.

· I will begin the lesson by probing the student’s findings in their homework. We will correct any mistakes. Then, we will discuss vocabulary terms such as leg and hypotenuse. · After activating their prior knowledge, I will model how to find the missing side of a triangle. I will show a variety of examples solving for either a, b, or c. · I will place sample problems on the projector and students will be assigned to one problem which they will try individually. Students will then take turns approaching the board and presenting their solution to the class. We will continue until every student has had a turn to show their work to the class and everyone must agree on the solution before we move onto the next problem.
 * __Day 2:__** Students will learn how to calculate the missing side of a right triangle using the theorem.

__Homework:__ Worksheet with 20 problems to find a, b, or c.

· I will begin the lesson by going over the homework. Students will work in pairs to correct each other’s work, and then we will review just a few of the problems on the board. · Next, I will present a word problem and model for students how to pull out the information and place it in a KWL chart. I will ask them the following questions for them to think-aloud: a) What is the Pythagorean Theorem? b) Does this problem create a right triangle? c) What information is given to us? d) What is the problem asking for? e) What values can I plug into the theorem? f) What is my solution? · We will also go over special right triangles and how they can be used instead to find a missing side. · Students will be placed in groups of 3-4 and given different word problems to read and solve together. They must complete the same graphic organizer that was modeled and show their work on a poster board then present their case to the class.
 * __Day 3:__** Students will learn how to apply the theorem in problem solving cases and when to use special right triangles.

__Homework:__ Worksheet with 10 word problems.

· Again, I will begin the lesson by going over the homework. Students will work in pairs to correct each other’s work, and then we will review just a few of the problems on the board. · Today, I will demonstrate triangles we can find in the classroom and how to find certain measurements. Students will work in pairs to accurately calculate each other’s height using their shadows and some measuring tape. · At the end of class, students will work individually on a journal prompt which asks them to think about what other real-life cases they can apply the Pythagorean Theorem. If there is time, they can then choose which example to use and begin constructing their own original word problem.
 * __Day 4:__** Students will learn to examine their own environment and apply the theorem.

__Homework:__ Write your own word problem related to the Pythagorean Theorem. || ** Assessment ** || I will assess the students in various ways. I will ask them questions during the modeling portion of the lessons to informally assess their skills and scaffold their understanding. I will also monitor their progress while they are in groups and continue asking questions to deeper their understanding of the Pythagorean Theorem. Informally, they will be assessed through their group KWL chart in class and their journal entries. These informal assessments will measure the literacy objective of the lesson which was for the students to be able to recognize problems which require the Pythagorean Theorem and solve them, and also make their own real-life connections to the theorem.

Formally, students must complete their own chart, sketch, and solution of word problems for homework. The homework problems will be measured on accuracy and effort. Original word problems will also have the same requirements. They must provide a chart and solution for their problem in the same way as the homework handout. Both assessments are graded with the same rubric. They are only required to make one chart for homework assignments in order to activate their prior knowledge and organize their information so that they can solve other problems. These individual formal assessments will measure the content knowledge objective which is that students will be able to solve problems and calculate the sides of a right triangle using the Pythagorean Theorem. ||

Date ** Problem: To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the //nearest// //meter//, how many meters would be saved if it were possible to build a bridge and walk over the pond?
 * Name
 * ** Topic: ** ||
 * ** K **
 * What I Know ** || ** W **
 * What I Want To Know ** || ** L **
 * What I Learned ** ||
 * Sketch: Solution: **

**__ Chart and Solution Rubric __**

** Criteria ** || || ** Exceeds the standard ** || ** Meets the standards ** || ** Approaching the standards ** || ** “What I Know” ** || All prior knowledge of the topic is listed. All information from the problem is given. || Most of the prior knowledge of the topic is listed. Few details are left out from the problem. || About half of the prior knowledge is listed. Half of the information of the problem is given. || ** “What I Want To Know” ** || Identifies what side of the triangle is unknown. Identifies the question asked by the problem. || Identifies what side of the triangle is unknown. Does not pose question. || Does not identify the side of the triangle which is unknown. Poses question asked by problem. || ** “What I Learned” ** || Gives a complete response about the solution of the problem. || Gives a good response with explanation of the solution. || Response is unclear and lacks most key points and information. || ** Sketch/ ** ** Diagram ** || Clear diagram or sketch with some detail from problem. Labels are used. || Clear diagram or sketch. Labels are used. || Inappropriate or unclear diagram. Labels are not used. || ** Solution/ ** ** Mechanics ** || No math errors. || No major math errors or serious flaws in reasoning. || May be some serious math errors or flaws in reasoning. || || ||  ||  ||