# Unit Design For Geometric Relationships Developed by Jacqueline Isaacson

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Unit Design

For
Geometric Relationships

Developed by

Jacqueline Isaacson

Marvin L. Winans Academy of Performing Arts

2012

Understanding by Design

Unit Design Worksheet
 Unit Title: Geometric Relationships Subject/Course: Geometry Topic: Circles Grade(s): 10th Staff Name: Jacqueline Isaacson

Stage 2 - Assessment Evidence

Goal: Your task is to show your knowledge of geometric shapes relating to circles by creating a blueprint of a new performing arts school and proposing the new building to board members.
Role: You are part of a team of architects with a strict budget. You need to create a blueprint and proposal of a new creative building. Since it is a performing arts school your design should be very avant-garde and utilize unusual techniques in building structure. Your clients prefer organic shapes and circles to promote a calming, creative atmosphere. Your job is to create a school building that is sound in structure, creative with the use of circles, within the budget, and propose this plan to a board of school members.
Audience: Your target audience is the school board, principal, parents, and high school students.
Situation: The challenge involves creating an 18” x 20” blueprint of the new school and a name for the school. The design must include circles and have a secure structure. Then write a clear proposal explaining why you used the structure you used with the strict budget of \$5,000.
Product: One 18” x 20” blueprint of the new school. One 4 page essay explaining the blueprint, budget usage, and structure of the school. One 5 minute speech on why your school is the one to choose for the project.
Standard: Your blue print, paper, and speech will be judged with a rubric.

Key Criteria: (Rubrics, etc.)
Holistic Rubric:

 Holistic Rubric for (Tests) 4 3 2 1 Student understands the concept with no missed steps and/or confusing rules. Student understands the concept, but missed a step and/or is confusing learned rules. Student work has a lot of errors showing the student has not fully grasped the concept. They are mixing up concepts or rules, and work lacks clarity. Student attempted the problem, but clearly does not understand the concept.

Building A Structure : Analysis of Created Product: Blue Print

Teacher Name:

Student Name:     ________________________________________

 CATEGORY 4 3 2 1 Mathematical computation All instances with geometric computation are correct. Example: If a triangle is inscribed, then all angles depicted are correct. All measurements of perimeter and area are correct, etc. Few errors in mathematical computation. At least 10 errors in mathematical computation. More than 10 errors in mathematical computation. Mathematical usage of tools All drawn geometric shapes have been drawn using geometric construction techniques and tools (compass and straight edge). Shows a clear understanding of how to construct geometric figures. 80% of drawn geometric shapes have been drawn using geometric construction techniques and tools (compass and straight edge). Shows a clear understanding of how to construct geometric figures. 70% of drawn geometric shapes have been drawn using geometric construction techniques and tools (compass and straight edge). Shows a surface level understanding of how to construct geometric figures. 60% or below of drawn geometric shapes have been drawn using geometric construction techniques and tools (compass and straight edge). Shows a shallow understanding of geometric construction. Mathematical usage of geometry on blueprint and in paper. Plans for the structure show a strong understanding of how geometric figures relate to a circle in the correct manner. All mathematical analysis is correct and makes sense. All measurements are correct. Plans for the structure show an understanding of how geometric figures relate to a circle in the correct manner. 80% of mathematical analysis is correct and makes sense. Most measurements are correct. Plans for the structure show little understanding of how geometric figures relate to a circle in the correct manner. 70% of mathematical analysis is correct and makes sense. Many measurements are incorrect. Plans for the structure show very little to no understanding of how geometric figures relate to a circle in the correct manner. 69% or below of mathematical analysis is correct and makes sense. Information Gathering Accurate information taken from several sources in a systematic manner. Accurate information taken from a couple of sources in a systematic manner. Accurate information taken from a couple of sources but not systematically. Information taken from only one source and/or information not accurate.

Computations:
Teacher Name:

Student Name:     ________________________________________

 CATEGORY 4 3 2 1 Mathematical Concepts Explanation shows complete understanding of the mathematical concepts used to solve the problem(s). Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s). Explanation shows some understanding of the mathematical concepts needed to solve the problem(s). Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written. Mathematical Reasoning Uses complex and refined mathematical reasoning. Uses effective mathematical reasoning. Some evidence of mathematical reasoning. Little evidence of mathematical reasoning. Mathematical Errors 90-100% of the steps and solutions have no mathematical errors. Almost all (85-89%) of the steps and solutions have no mathematical errors. Most (75-84%) of the steps and solutions have no mathematical errors. More than 75% of the steps and solutions have mathematical errors. Mathematical Terminology and Notation Correct terminology and notation are always used, making it easy to understand what was done. Correct terminology and notation are usually used, making it fairly easy to understand what was done. Correct terminology and notation are used, but it is sometimes not easy to understand what was done. There is little use, or a lot of inappropriate use, of terminology and notation. Strategy/ Procedures Typically uses an efficient and effective strategy to solve the problem(s). Typically uses an effective strategy to solve the problem(s). Sometimes uses an effective strategy to solve problems, but does not do it consistently. Rarely uses an effective strategy to solve problems.

Research:
Teacher Name:

Student Name:     ________________________________________

 CATEGORY 4 3 2 1 Research Packet Research packet is complete with all parts filled in. Research packet is missing a few parts but have been completed since. Research packet is vague and missing parts. Research is inaccurate or unfinished. Research in packet Research is accurate, clear, and follows format of packet. Research is mostly complete, but has a few inaccuracies. Student used unreliable websites to find information or research is inaccurate. Student’s research is incomplete and unreliable either by using improper websites or making things up.

Oral Presentation Rubric : GRASPS Rubric:

Architecture Project
Teacher Name:

Student Name:     ________________________________________

 CATEGORY 4 3 2 1 Vocabulary Uses vocabulary appropriate for the audience. Extends audience vocabulary by defining words that might be new to most of the audience. Uses vocabulary appropriate for the audience. Includes 1-2 words that might be new to most of the audience, but does not define them. Uses vocabulary appropriate for the audience. Does not include any vocabulary that might be new to the audience. Uses several (5 or more) words or phrases that are not understood by the audience. Time-Limit Presentation is 4-5 minutes long. Presentation is 3 minutes long. Presentation is 2 minutes long. Presentation is less than 2 minutes OR more than 5 minutes. Content Shows a full understanding of the topic, both geometric and economic. Shows a good understanding of the topic, both geometric and economic. Shows a good understanding of parts of the topic, both geometric and economic. Does not seem to understand the topic very well. Evaluates Peers Fills out peer evaluation completely and always gives scores based on the presentation rather than other factors (e.g., person is a close friend). Fills out almost all of the peer evaluation and always gives scores based on the presentation rather than other factors (e.g., person is a close friend). Fills out most of the peer evaluation and always gives scores based on the presentation rather than other factors (e.g., person is a close friend). Fills out most of the peer evaluation but scoring appears to be biased.

Other Evidence:
Journals, rough drafts, vocabulary activity, quizzes, concept maps, observations, daily assignments, textbook, worksheets, prompts on backing up mathematical thought.

BEFORE
Pre-quizzes on vocabulary

The teacher will test the students on vocabulary to see what they know prior to starting the unit.

Brainstorming

The students will brainstorm ideas for their building before beginning the GRASPS project. This will promote critical thinking and problem solving.

Think/pair/ share

Students will think, pair, and share about problems. The teacher will give them feedback on what they will be learning.

DURING
Vocabulary log

Students will keep a running vocabulary log for personal reference.

Questioning

The teacher will ask questions as the students work and learn.

Daily assignments

Daily book and worksheet assignments.

Drawings

Students will practice their constructions with small assignments similar to the GRASPS assignment to check for understanding.

Observations

The teacher will monitor the students’ in-class work and check for understanding.

Quizzes

The teacher will retest the students on vocabulary and information to see if they learned the terms and information that they had not learned before.

AFTER
Posttest GRASPS

GRASPS project on architecture.

Student Review

Students will re-teach parts of the unit as partners to the class to help promote learning.

Describe the assessment/s and state the prompt if applicable. □ F X S

What type of scoring tools will be used for evaluation?

X Analytic rubric □ Checklist

X Holistic rubric □ Answer Key

X Criterion rubric □ Other

 Student Self-Assessment and Reflection: Students will write a few short journal entries to reflect on their work and demonstrate understanding. They will be asked to write about: How do you feel about the unit so far? What is the easiest concept for you to understand, what is the most difficult? Explain a concept in your own words. How does what we learned today relate to real life? How did you do this week? At the end of the project, students will reflect on how much work they have done. They will be expected to give other groups a grade for their work as well. Students will ask themselves: What parts of the project did I contribute to? What could I have done more on? What did I learn from this project? How did the circles make creating the building more difficult? How did the budget make creating the building more difficult? What other subjects did I have to use to complete this project? How will this project and unit help me later on in life? Did performing in front of an audience cause me to pay attention to the information more closely? Did working with a group of peers help me to understand concepts I didn’t understand before? Group project peer analysis questionnaire: What parts did I contribute to, what parts did the others do? Who did not do anything? Who helped you the most when it came to understanding the mathematical analysis? As a group, how did you think you did? Rate your group on a scale of 1-10, with one being the lowest and ten being the highest.

 Stage 3 - Learning Plan Differentiated Instruction: Level C – 90 points (All activities are required) 1. Unit vocabulary list (10 points) 2. “Do Now” unit bell work tracker (2 points a day – 30 points) 3. Daily homework problem sets (5 points a day – 50 total points) Level B – 25 points (Activity one is required, choose one of the next two) 1. Use a compass and protractor to discover how to make inscribed shapes and complete a worksheet. (10 points) 2. Create a series of 5 mini textbooks showing a variety of proofs of inscribed shapes, angles, similar circles, and constructions of all the geometric shapes. Must explain in own words. ( 15 points) 3. Create/complete work packet with a partner. (15 points) Level A – 56 points GRASPS project: create a blueprint for a new school with a given budget Research packet with filled in questions and essays ( 8 points) Written notes showing all work of all mathematical computation (20 points) Fully rendered blueprint (16 points) Oral presentation (12 points) Learning Activities: The end of the unit project asks students to answer the question of, where are we going? They will have to rethink what they have learned and re organize the information to create a blueprint of a new school with a given budget which will deepen understanding of geometry in relation to real life. Students will use geometric tools to understand the construction of geometric objects and why we compute the way we do. They will use a variety of worksheets, inquiry based group work, and choices to tailor to their needs. The teacher will hook students’ interest by giving them choices and projects that use new tools and ideas they have not used before. Students will either create a series of 5 mini textbooks with visual aids that explain the main unit points or complete a work packet with a partner. At the end of the unit, students will present their GRASPS project, reflect on their project, and peer evaluate the projects. Students will be equipped with materials and supplies to complete each learning activity.

 Essential Vocabulary Angles: two rays that share one end-point. Area: any particular extent of space or surface; part. Arc: any unbroken part of the circumference of a circle or other curved line. Bisector: a line or plane that bisects  an angle or line segment. Center: the middle point, as the point within a circle or sphere equally distant from all points of the circumference or surface. Chord: the line segment between two points on a given curve. Circle: a closed plane curve consisting of all points at a given distance from a point within it called the center. Congruent: equal parts. Diameter: a straight line passing through the center of a circle or sphere and meeting the circumference or surface at each end. Equidistant: equally distant. Interior Angles: an angle formed between parallel lines by a third line that intersects them. Inscribe: to draw or delineate (one figure) within another figure so that the inner lies entirely within the boundary of the outer, touching it at as many points as possible. Line Segment: a finite section of a line. Parallel Line: extending in the same direction, equidistant at all points, and never converging or diverging. Perimeter: the border or outer boundary of a two-dimensional figure. Perpendicular Line: meeting a given line or surface at right angles. Proportion: comparative relation between things or magnitudes as to size, quantity, number, etc.; ratio. Pythagorean Theorem: the theorem that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Radius: a straight line extending from the center of a circle or sphere to the circumference or surface. Segment: a part cut off from a figure, especially a circular or spherical one, by a line or plane, as a part of a circular area contained by an arc and its chord or by two parallel lines or planes. Similar: having the same shape; having corresponding sides proportional and corresponding angles equal. Vertical Angle: one of two opposite and equal angles formed by the intersection of two lines.

 Sequencing the Learning MONDAY Pre-quiz: Identify what basic vocabularies are. Identify what the basic geometric shapes are. Complete basic math skills i.e. multiplication, division, and solving for variables Level C: daily assignment TUESDAY Identifying Basic geometric shapes and how they relate to each other. Level C: daily assignment WEDNESDAY Intro to circles Level C: daily assignment THURSDAY Manipulation of/ similarity of circles Level C: daily assignment FRIDAY Manipulation of/ similarity of circles Quiz over week information. Level C: Packet for the week MONDAY Basic proofing knowledge by brainstorming in pairs Level C: daily assignment TUESDAY Proofing of similar circles Think-pair-share activity Level C: daily assignment WEDNESDAY Level B: activity day Inquiry based work sheet by drawing constructions Level C: daily assignment THURSDAY Inscribed circles Level C: daily assignment FRIDAY Quiz Level C: Packet for the week MONDAY Pythagorean theorem with inscribed and non triangles Level C: daily assignment TUESDAY Research on relation to real life day. How to research effectively. Level C: daily assignment WEDNESDAY Level B: choice assignment Work day THURSDAY Level B: choice assignment Work day FRIDAY Level C: Packet for the week Level B: choice assignment due MONDAY Level A GRASPS work day TUESDAY Level A GRASPS work day Research packet due WEDNESDAY Level A GRASPS work day THURSDAY Level A GRASPS work day Mathematical computation work packet due FRIDAY Level A GRASPS work day MONDAY Level A GRASPS work day Complete peer evaluations TUESDAY Presentations Blueprints due WEDNESDAY Presentations THURSDAY Geometric relationships test Unit vocabulary packets due FRIDAY

UBD Unit Design Worksheet / Saginaw Valley State University

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