Leadership Two Weeks

/ Geometry
Lesson Plan
Teacher:
8th Grade Math Teacher / Grade:
8th Grade
Lesson Title:
Experimenting with Perimeter, Area, Transformations, Congruency and Similarity for Future STEM Career Leaders.
STRANDS
Similarity, Right Triangles, and Trigonometry
Expressing Geometric Properties with Equations
Congruence
LESSON OVERVIEW / Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
The unit will start with a STEM career professional speaking to students about their competitive advantage entering the workplace given their STEM education. Students will take information from their readings in English class and write an essay with central ideas on the changing face of education since the 1900s to STEM in the workplace. Students will review finding perimeter and area of polygons in the different forms in which they can be represented (coordinates, figures, and equations) by using various methods such as the distance formula and Pythagorean’s Theorem. Students will then design a floor plan of their dream home and backyard, scale the drawing, and estimate the costs of putting up fencing and laying down sod given a price list for each of those items. This not only reinforces important Common Core Standards, but also prepares students in planning for their future homes and showing how to estimate costs before purchasing items. This will also prepare students for their scale drawing that will be required with the catapult project. The video clip about the Mercedes Bens Logo and it’s design will lead into the lessons on transformations and tie into the final math component for the State of Stem culminating presentation while tying in the history of mathematics used in business. Students will then experiment with transformations in the plane. Students have had experience with transformations: translations, reflections, rotations, and dilations from Algebra I and Pre-Algebra, and they will be reviewed. Comparisons of transformations will provide the foundation for understanding similarity and congruence, which will also play a part in the culminating presentation requirements. Students will then perform various transformations as requested. Similarity and Congruence will then be visited, first with definitions and following up with discussion questions. These questions are intended to formatively assess prior knowledge and to begin student discussion of similarity versus congruence. Students should be encouraged to answer in their own words and to critique each other’s assessments. This allows students to practice communication of knowledge using language rather than algebraic expressions to demonstrate definitions and the importance of math concepts.
MOTIVATOR / Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature)
Day 1 "Home Quick Planner":
This motivator will utilize the following video clip – “Home Quick Planner” (Appendix A). The students will then discuss what formulas are used to calculate distance, and how these could be used in real world applications.
Day 3 "Motion Geometry":
This motivator will utilize the following video clip – “Motion Geometry” (Appendix F). The students will then discuss how transformations are used in today’s society after watching the informative video. Things will be brought up such as games and digital animation. The students will then debate what kinds of skills and education would be necessary to be a video game designer or creator of digital animation. Teacher will lead the discussion by offering how mathematics is a leading component in programming and animation.
Day 6 “The History of the Mercedes Logo”:
This motivator will utilize the following video clip – “The History of the Mercedes Logo” (Appendix I). The students will discuss pre-image, and how the pre-image of the Mercedes Logo would compare to a rotated image of the same figure. Since they would appear the same, the teacher would explain this gives the Mercedes Logo the property of rotational symmetry. The students will need this knowledge to design their own logo with rotational symmetry for the “State of STEM Presentation” as well as lead into further investigation of transformed figures and their pre-images.
DAY /
Objectives
(I can….) /

Materials & Resources

/

Instructional Procedures

/ Differentiated
Instruction /

Assessment

1 / I can use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
I can know precise definitions of angle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and distance along a line. / “Home Quick Planner”
(Appendix A)
Graph paper
Station Work
(Appendix B)
Ruler (or straight edge)
iPad
Calculator
“Need More Support” Station Work
(Appendix C)
“Need More Challenge” Station Work
(Appendix D) / Essential Question(s):
1. What are polygons?
2. How to find the area and perimeter and area of a polygon?
3. How to define angle, perpendicular line, parallel line and line segment based on undefined notions of point, line and distance along a line? / Remediation:
Peer Tutoring
Heterogeneous Grouping
“Need More Support” Stations
Enrichment:
Peer Tutoring
Heterogeneous Grouping
“Need More Challenge” Stations / Formative Assessment:
Opening Writing Assignment
Teacher Observations
Performance Assessment:
Exit Ticket
Summative Assessment:
Work Station calculations with graphs where appropriate
Set:
Teacher will begin by showing the “Home Quick Planner” video clip, then asking students to write down the distance formula, Pythagorean’s Theorem, and name one situation where you may use each formula. How are they similar and can they be used for the same purpose? Teacher will activate discussion regarding distance formulas and their real world applications such as floor plans for homes, determining how to estimate supplies needed for construction, and how knowing perimeter and area of a given location could change the approach to a design.
Teaching Strategy:
1.  Teacher will assign students to heterogeneous groups of 2-4.
2.  Each group will travel to Stations 1-4 (Appendix B) and complete the directions given at each station. All stations are concerning perimeter and area of differently shaped polygons presented in different forms. Groups can pick from three folders at the station: Assigned Work (Appendix B), Need More Challenge, (Appendix D) and Need More Support (Appendix C). Teacher will direct students to the folders that are appropriate given the group ability level.
3.  Have the students complete the stations and regroup for a discussion. Were any of the stations harder than the others? What technique was most effective for calculating the length of each polygon’s side? Would the order in which you complete the stations make a difference?
Summarizing Strategy:
As an exit ticket, have students summarize their findings. Ask what they think their strengths and weaknesses are for finding perimeter and area for given polygons.
2 / I can use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
I can use geometric shapes, their measures, and their properties to describe objects.
I can apply geometric methods to solve design problems. / Graph paper
“Dream Home Design” Handout (Appendix E)
Ruler (or straight edge)
Protractor
iPad
Calculator / Essential Question(s):
1. How to use geometric shapes, their measurements, and their properties to describe objects?
2. How to apply geometric methods to solve design problems? / Remediation:
Have students create floor plans with only 90º angles.
Enrichment:
Have students create at least six angles that are not 90º angles. / Formative Assessment:
Teacher observations of methods used to find area and perimeter.
Performance Assessment:
Ending discussion of methods used by students
Summative Assessment:
Floor Plan drawing with perimeters and areas, along with cost estimates for sod, brick and fencing.
Set:
Begin by asking students about their dream home floor plan. How many bedrooms and bathrooms would you like? Explain that they get to design their own one floor, dream home design. All of this must be put into a plan first, and perimeter and area must be calculated to estimate the total costs in order to estimate the amount of materials to buy and what they may cost.
Teaching Strategy:
1.  Have students design their floor plan design on a coordinate plane. Students should use each of the quadrants and make sure that all vertices are plotted on integer coordinates. Students may have to modify their design slightly in order to transfer the diagram successfully. Allow students access to graph paper, rulers, and protractors for this task.
2.  Ask students to calculate the length of each of the walls and the total perimeter their home’s floor plan design. Have students keep each of these measurements on their “Dream Home Design” handout.
3.  Within the design, have students add a backyard that includes a pool (with straight sides) behind their dream home design. Have students calculate the perimeter of the backyard, the perimeter of their dream pool, and the area of their backyard. Using the area, have students calculate the number of square feet of sod that would need to be purchased.
4.  Ask students to use the provided prices of fence, stone and sod to determine the total cost of all the landscaping materials on the “Dream Home Design” handout.
Summarizing Strategy:
Ask the class to compare costs, and see what caused some floor plans to be more or less expensive than others. Ask students to share their techniques for finding area and perimeter of the spaces they created, and let the class discuss which would be easiest to use and why.
Adapted from: Leinwand, S. (2009). Accessible Mathematics: 10 instructional shifts that raise student achievement. Portsmouth, NH: Heinemann.
3 / I can use geometric descriptions of rigid motions to predict the effect of a given rigid motion on a given figure. / Video “Motion Geometry”
(Appendix F) / Essential Question(s):
How can I use geometric descriptions of rigid motions to predict the effect of a given rigid motion on a given figure? / Remediation:
None
Enrichment:
none / Formative Assessment:
Teacher observations of current knowledge on the subject.
Summative Assessment:
Exit ticket.
½ Project Day – See Unit Plan
The Catapult Project - Writing
Set:
Teacher will begin by showing “Motion Geometry” a video clip on use of transformations in video animation.
Teaching Strategy:
Students and teacher will discuss how transformations are used in today’s society after watching the informative video. Things will be brought up such as games and digital animation. Ask students if they realized that it is all transformations that are programmed that create the look of movement on screen. Spark a debate on what kinds of skills and education would be necessary to be a video game designer or creator of digital animation. Lead the discussion by offering how mathematics is a leading component in programming and animation.”
Summarizing Strategy:
Tell students that after the following project days, they will begin diving into transformations and their properties. As an exit ticket, have them write down 3 things they know about transformations and 2 things they would like to learn.
4
Project Day – See Unit Plan
The Catapult Project – Traditional Design and STEM Design
5
Project Day – See Unit Plan
The Catapult Project – STEM Design
6 / I can articulate the definitions of the transformations: reflection, rotation, and translation.
I can recognize the difference between the examples and non-examples of reflections, rotations, and translations / “Transformation Examples and Non-Examples”
(Appendix G)
“Transformation Identification”
(Appendix H)
“The History of the Mercedes Logo” video clip
(Appendix I)
Graph Paper
Calculator / Essential Question(s):
1.What are the definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments?
2.How to recognize the difference between examples and non-examples of reflections, rotations, and translations? / Remediation:
- Peer Tutoring
- Heterogeneous Grouping
Enrichment:
- Peer Tutoring
- Heterogeneous Grouping / Formative Assessment:
Teacher observations of definitions developed by students for transformations
Performance Assessment:
-Ending discussion of determining the best definitions
- Homework: Ask students to create their own examples of a rotation, reflection, and translation using the definitions they developed in class
Summative Assessment:
-Exit Ticket
Set:
The teacher will ask students to make a list of the different types of transformations that can occur in a plane. The teacher will then show “The History of the Mercedes Logo” (Appendix I) video clip. The students will discuss pre-image, and how the pre-image (the original figure before the transformation) of the Mercedes Logo would compare to a rotated image of the same figure. Since they would appear the same, the teacher would explain this gives the Mercedes Logo the property of rotational symmetry. The students will need this knowledge to design their own logo with rotational symmetry for the “State of STEM Presentation” (See Unit Plan) as well as lead into further investigation of transformed figures and their pre-images.
Teaching Strategy:
Determining the definitions for transformations activity
Create three transformation stations: reflection, rotation, and translation, from the Transformation Examples and Non-examples.
1.  Divide the class into heterogeneous groups of 3-4 and have students look at different examples provided for rotation, reflections, and translations and write their own definitions for those types of translations.
2.  Go through each group and have them provide their definition for each. As a group discuss the definitions, and decide as a class on the nest one. Use this as an opportunity to clear up any misconceptions students may have.
Identifying transformations activity
1.  Have student access the “Transformation Identification” activity.
2.  Have the groups go through each of the transformations and classify them into the appropriate group. Some of the transformations may be classified as more than one transformation.
3.  After completing the “Transformation Identification” activity have students reexamine their definitions. Discuss as a group if the definition is well written or needs to be changed to fit their new findings.
4.  Discuss with students each group’s definitions. Decide which are the best and why.
Summarizing Strategy:
As an exit ticket, ask students how does a reflection, rotation, or translation affect the lines and angles of a transformed figure? Where do you find examples of reflection, rotation, and translation in the real world?
Adapted from: Howard County Public Schools (HCPSS) Secondary Mathematics Office (v2.1)