Dawn GarritsonMath History & Technology, Task 2December 9, 2017LESSON PLAN TEMPLATE – 2015GENERAL INFORMATIONLesson Title & Subject(s): Pythagorean Theorem: What do you think? Topic or Unit of Study: Geometry, Pythagorean TheoremGrade/Level: Eighth gradeInstructional Setting:The setting for the lesson will be in the math classroom. There will be approximately 20 eighth grade students. They will start the lesson in their desks. Students will work with a partner to collaborate on ideas, solutions, and proof.
With their partner, they will be allowed to move desks to sit together or sit on the floor in the classroom. The Pythagorean Theorem and its history will be on display in the classroom. STANDARDS AND OBJECTIVESMinnesota State Standard: 8.3.
1.3, Solve problems involving right triangles using the Pythagorean Theorem and its converse. Benchmark: Informally justify the Pythagorean Theorem by using measurements, diagrams, and computer software.Common Core Standard: CCSS.MATH.
CONTENT.8.G.
B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.Lesson Objective:Using dynamic geometry software, students and their partner, will explore the Pythagorean Theorem and justify their opinion of if it holds true for all right triangles. Students will be assessed on their collaborative discovery process and visual presentation using the included rubric. Students will need to score 72% (13/18) to pass this assessment. ComponentValue: 1 pointValue: 2 pointsValue: 3 pointsInvestigation of Theorem with dynamic geometryLittle or no investigationSome investigation Extensive investigationExamples of the Pythagorean Theorem holding true, including screenshotsOne or two examples, no proof of its truthThree or four examples, some proof of its truthFive or more examples, thorough proof of its truthOpinion on the truth of the Pythagorean Theorem holding trueLittle to no opinion, little to no evidence to support opinionOpinion stated, some evidence given to support opinionOpinion stated, extensive evidence given to support opinionApplication of a real-world situation for solving a problem based on the Pythagorean TheoremNo applicationIncomplete application, little or no explanationApplication is given and explainedVisual presentationNo visual presentationIncomplete and/or unorganized visual presentationComplete and organized visual presentationCollaborationRefused to work with partner or worked mostly aloneSome work with partnerCooperated with partner to complete project MATERIALS AND RESOURCESInstructional Materials:Algebra textbook (Larson, 2012)Chromebook (computer)GeoGebra website: https://www.geogebra.org/GeoMeter’s Sketchpad website: http://www.
dynamicgeometry.com/Illuminations website: https://illuminations.nctm.org/Activity.aspx?id=6877Illuminations website: https://illuminations.nctm.org/Activity.aspx?id=4211Illuminations website: https://illuminations.
nctm.org/Activity.aspx?id=6376Visuals of Pythagorean TheoremRubric of expectationsResources:A., Van De Walle John, Karen S.
Karp, and Jennifer M. Bay-Williams. Elementary and Middle School Mathematics: Teaching Developmentally.
Boston: Pearson, 2013. Print.Mathematics, education.state.
mn.us/MDE/dse/stds/Math/.Illuminations.nctm.org, illuminations.nctm.org/Activity.
aspx?id=6877.Illuminations.nctm.org, illuminations.
nctm.org/Activity.aspx?id=6376.Illuminations.nctm.org, illuminations.
nctm.org/Activity.aspx?id=4211.”Discover Math with GeoGebra.” GeoGebra – Dynamic Mathematics, www.geogebra.org/.
“Grade 8 » Geometry » Understand and Apply the Pythagorean Theorem. » 7.” Grade 8 » Geometry » Understand and Apply the Pythagorean Theorem. » 7 | Common Core State Standards Initiative, www.
corestandards.org/Math/Content/8/G/B/7/.Larson, Ron. Holt McDougal Larson Algebra 1. Holt McDougal, 2012.
“Welcome to The Geometer’s Sketchpad® Resource Center.” Home – The Geometer’s Sketchpad Resource Center, www.dynamicgeometry.com/.Minnesota State Standards. INSTRUCTIONAL PLANSequence of Instructional Procedure:Student Connections to Previous Learning: (5-10 minutes)Students will need a beginning understanding of the Pythagorean Theorem. They will also need to possess computer fluency to explore their proof and justification of their opinion about whether or not the Pythagorean Theorem holds true for all right triangles.
Presentation Procedures for New Information: (15-20 min.)The teacher will revisit previous research done by the class for equations.The teacher will ask students about the concept of the Pythagorean Theorem that was previously introduced.
S/he will chart student responses.The teacher will pose the question: Do you think this is always true? For all triangles? Right triangles? Obtuse triangles? Acute triangles? How do you know that?The teacher will tell students we are going to research this idea. How can we do that? The teacher will prompt students to think about connecting with schema on previous research and justification for their opinion in studying equations, including their use of dynamic software. S/he will start a second chart for students’ responses.Teacher: How could I research and justify my opinion? Where should I look?The teacher will pose the question: When is there a time outside of classroom we could solve a problem with the Pythagorean Theorem? How do you know it will work? Can you prove it?The teacher will direct students to their Google classroom and the current assignment with the rubric (that follows) and links (as seen above in instruction materials) for researching their opinions.The teacher will use an online randomizer to select student partner groups of two for students to collaborate on their opinion and real-world situation.Guided Practice: (25 minutes, then additional class time or student time outside of class) Student groups will explore (either with their partner or individually) the Pythagorean Theorem using online dynamic geometry resources, including but not limited to, GeoGebra, Geometer’s Sketchpad, National Council of Teachers of Mathematics Illuminations website.
Student groups will formulate an opinion on whether the Pythagorean Theorem is always true and begin to justify their understanding. Students will research their opinion and use Geometry software to prove their idea. Students will take what they have learned during their exploration and collaboratively it apply it creatively to a real-world situation in which the Pythagorean Theorem is could be used to solve a problem. The partners will then work together to build a visual presentation that supports their opinions and shows the real-world problem they explored and solved together. Students will present this information visually to their classmates using a gallery walk.As students research and explore how the Pythagorean Theorem works, the teacher will monitor the groups, provide support, and visit with students as they work.
The teacher will use a preformulated set of questions to talk with student groups and check for understanding. The teacher will observe student use of online resources and prompt students’ exploration of the Pythagorean Theorem. S/he will have a class list of groups to record notes about student understanding.
Questions could include the following:What kind of triangle is this? How do you know?Will the Pythagorean Theorem work with this triangle?How do you know?How can you prove that?Is the student showing an understanding of Pythagorean Theorem?Is the student showing an understanding of how to use the technology?Observations of partner work. Are the students working well together? Are the students discussing the next step they need to do?Are the students collaborating?What does your partner think?Do you think there is a different way you solve it?Do you think the Pythagorean Theorem is always true? How can you prove/disprove that opinion?What can you compare this to?Have we done anything like this before?What did you try that did not work?Can you make your explanation clearer?Does that answer the question?Is there another way you can do that?Explain how you did that.Independent Student Practice: (outside classroom time)Will be a continuation of work students have done in class and the completion of the visual presentation that justifies their opinion about the Pythagorean Theorem and ideas.Closing Procedure for initial class period: (5-10 minutes) Students will use the exit ticket system at the end of class as a review and formative assessment. On their ticket, they will be asked to draw or write about one piece of evidence they discovered, one part of the activity that went well, and one thing they have a question about and they are going to research that evening. The exit ticket also supports problem-based learning as it lends itself to students summarizing the main idea of the lesson and extends the lesson to a question they have and are going to answer in the evening.Summative assessment: (35+ minutes in another class period approximately one week later) When completed with the entire project, which will take more than one class period, students will have researched and justified their opinion of the theorem along with a real-world situation they have investigated.
They will complete a visual presentation of their work and the final results. Students will participate in a gallery walk to present their ideas and view their classmates’ displays. This part of the project allows for students to use a variety of exit points when completing their visual presentation.Future relevance: The Pythagorean Theorem will be used to improve critical thinking skills when solving word problems. The Pythagorean Theorem will continue to be studied in subsequent math classes as students work toward graduation.Instructional Strategies: There are multiple pedagogical strategies that will be used in this lesson.
The most important part of the lesson is student discovery strategy that is student-lead in their formation of an opinion on the Pythagorean Theorem and their justification of their opinion based on exploring with dynamic geometry software programs online. In this way, students can develop a deeper understanding of the theorem.The lesson begins will direct instruction and review guided by the teacher. The lesson continues with active learning as the students experiment with ideas and integrate the Pythagorean Theorem with their previous learning. Students will explore the Pythagorean Theorem using technology and theorize an opinion of whether this theorem is always true. Another strategy students will use in their learning is working in groups. During this lesson, students will collaborate with a partner to apply this theorem by justifying their opinion and developing a real-world situation and solution.
Finally, students use writing to learn in displaying their learning with a visual presentation to show what they know.Differentiated Instruction Accommodations:English Language Learners (ELL): Review vocabulary and theorem with visual cues. Have a graphic organizer available to guide student exploration and development of presentation.
Also, have visuals steps for use of technology. Ask questions based on student’s level of understanding.Students with Special Needs: Same as above for the English Language Learners. Also, teacher plans to use voice amplifier system for my students with hearing loss. As a teacher, be aware of any student’s individualized education plan and have adjustments prepared as needed.Gifted Students: Encourage students to use technology for more advanced research. Encourage them to create two or three-dimensional model of the theorem, develop another way to prove the theorem. Allow students to formulate their own project, based on their interests, for the Pythagorean Theorem.
Use of Technology:Technology is at the core of this lesson. Students will explore the Pythagorean Theorem using dynamic software specific to geometry. Students will use the software to manipulate and develop an understanding of triangles and the theorem. The software will allow students to quickly draw and find, in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides or as we usually see it: a2 + b2 = c2. Students may also discover that if they do not draw a right angle triangle this theorem no longer holds true.
In doing this, students will deepen their understanding of triangles and the theorem. Students will also use technology to for drawing and computation to eliminate the tedious task of students drawing inaccurate right triangles, spending time measuring lines, and computing squares and then square roots. In doing all these steps to test the accuracy of the theorem students will most frequently make some small mistake that affects their answer. This in turn, leads to student frustration and disengagement from the project. In using the technology student learning is enhanced and broadened.
The use of technology also increases differentiation for students. It allows for a larger segment of students to participate in discovering and learning concepts such as the theorem in this lesson. Students who have learning disabilities can use technology to manipulate triangles and calculation of the Pythagorean Theorem for each triangle.
They may not have as many examples and work at a slower pace but will deepen their understanding of the lesson’s concepts. Advanced students can use technology not only to complement what they already might know but use technology to expand their knowledge but studying more complex figures or the converse of the theorem. This learning and their presentation to classmates would increase student learning for the entire class.Use of the technology not only will be used for the exploration of the Pythagorean Theorem but also a creative way for students to research and compute a solution that uses the Pythagorean Theorem in the real-world. Students will be able to model this situation used the technology resources previously used in this lesson. Student Assessment/Rubrics:Observations: As previously discussed, the teacher will walk around the classroom and monitor students as they work.
S/he will be available to assist students as they work.The teacher will have a class log for questioning students, checking student understanding, and recording information. The teacher will make note of any questions or difficulty a student may have.Formative Assessment:Exit ticket:Draw or write about one piece of evidence you discovered.What is one part of the activity that went well?What is one thing you have a question about and you are going to research tonight?Summative Assessment: Visual PresentationStudents will need to score 13 out of 18 points or 72%.ComponentValue: 1 pointValue: 2 pointsValue: 3 pointsInvestigation of Theorem with dynamic geometryLittle or no investigationSome investigation Extensive investigationExamples of the Pythagorean Theorem holding true, including screenshotsOne or two examples, no proof of its truthThree or four examples, some proof of its truthFive or more examples, thorough proof of its truthOpinion on the truth of the Pythagorean Theorem holding trueLittle to no opinion, little to no evidence to support opinionOpinion stated, some evidence given to support opinionOpinion stated, extensive evidence given to support opinionApplication of a real-world situation for solving a problem based on the Pythagorean TheoremNo applicationIncomplete application, little or no explanationApplication is given and explainedVisual presentationNo visual presentationIncomplete and/or unorganized visual presentationComplete and organized visual presentationCollaborationRefused to work with partner or worked mostly aloneSome work with partnerCooperated with partner to complete project
