Performance+Measures

GRASPS:
G ** oal states the purpose of the task;- The purpose of the task is for the students to learn how these shapes and angles can be applied to everyday real world examples. It is also for the students to be able to measure and crate certain polygons in an effective manner that create a unique quilt. After that they will be able to give a detailed history of quilts and be able to market there own quilt.


 * R ** ole explains student involvement in the scenario- The students involvement in this is they are individual and they will work to create a quilt using certain polygons and patterns. After which they individually research the history of quilts include a write up and a marketing plan for their piece of the quilt. The students will also have a minor yet important role in the making up of the whole class quilt which is a combination of everyones designs.


 * A ** udience identifies the people the students address- The students will be addressing there fellow students in the creation of his or her quilt. The student is addressing the teacher when writing the essay about the quilts. In the marketing of the quilt the student is addressing the “CEOs” of the Quirky Quilts Company (The QQC).


 * S ** ituation explains the scenario- Oh no Quirky Quilts is running out of ideas on how to create new and exciting and of course quirky quilts. They are asking for you to design and create different patterns of quilts. Then to market them to CEO’s of the company to find out which ones they could potentially use in the next line of Quirky Quilt fashion. But of course they need to know that you know a little something about quilts first, so make sure you do your research.


 * P ** roduct is the tangible evidence of student understanding -** The students will have multiple evidence of understanding. Relating to math, the students will have to create a template which has multiple variations of a polygons which will show their knowledge of triangle congruency. The students will also have to identify the angles that are created and how different angles are created. They will do tis by describing why a quilt which is made up all different shapes creates a square quilt. Regarding FACS, the students will have to show their knowledge in how to create a template and use it to make a tessellation quilt. Regarding marketing, the student's marketing plans will be assessed by how well they explain why a quilt costs what it costs. Regarding history and English, the students will be assessed on the knowledge they show on the history of quilts as well as how the history of quilts has to do with how quilts are used today.

S ** tandards/criteria describes how students can complete the task successfully- The students can complete the task successfully by adequate research on the history of quilts. Also by creating a unique design by using the knowledge they already have about parallels and polygons. Then by creating a well developed marketing plan for the marketing of his or her specific quilt and pattern.

Process:
The students will have to use their knowledge of geometry and polygon congruency. The quilts will be interdisciplinary, using math, family and consumer science (FACS), marketing, history, and English.

1) The students will pick 3 or 4 different shapes that will create the overarching design of the quilt this will be the template. The students will have to use their knowledge of parallels, polygons, and triangle congruency to create and aesthetically pleasing design. This is done by using graph paper and making "x"s where a design will map out, using different colors for different fabrics. They will create this template using the tessellation application on the application on [|Tessellation Activity] . The students will have the opportunity to work in class and therefore will not have to have a computer at home. If the students need to take home the project, and don't have a computer at home students can print out what they have worked on in class and then draw the rest of the tessellation, then add it to the computer when they get back to school. Students will be shown how to create this before they are sent off do to it themselves.

2) The template will then be used to make a tessellation quilt, one that has multiple copies of the template they created. The mathematical portion of the project will be scored on 3) Before the students create the quilt they will need to make a budget plan for the fabric intended on using. The students will need to have a template with more then one color and/or texture.

4) The quilt will then be constructed in their FACS classroom. The students should have previous knowledge on how to sew, they will learn more on how to quilt. The students will be graded in their FACS class on the skills they have learned in that class and the one's they are learning.

5) The students will also have to figure out how much the quilt should be sold for, and will have to explain why with the use of Microsoft Excel and Microsoft Word. It is up to the students to determine how the amount will be calculated, some ideas include time put into the quilt, materials used, audience, and so on. With this calculation and description, the students will have to create a marketing plan for a quilt company as a part of their presentation. It is important that the students create a thorough explanation of a budget plan because they will be presenting to a mock CEO of QQC how much they want to sell their quilt for and why their quilt should be chosen. The budget plan will work will in compared to the students actually making the quilt because it will be easy for them to figure out the estimated amount of hours it took them to finish the quilt.

6) If possible, the class will go to the local quilt museum, there are some all over the country. Another option is to have local quilters come in and explain the process of making a quilt and selling quilts. Many quilters probably also have a story about what their reason is for making quilts. They can also share with the class information they have about where quilts are used both now and in history. This will help the students with their project later in the process. If a quilter does come into the class, the teacher can see if he/she wants to come back into the class and act as if he/she is the CEO of QQC. This will make the students feel as if the project is for more then just the teacher. Even if the teacher decides to go on a field trip, they can see if a local quilter wants to come in and have the students present their presentation about their quilt to the local quilter.

7) Quilts have been used in different cultures and the students will have to focus on one aspect of the history of quilts. In addition to creating a quilt, students will have to research quilts in history and write an essay on why quilts were used and what significance they have to the world in which we live in today. This should not be an overview on quilts in history and cultures, but rather a specific explanation concerning one culture and one point in history. Students will also have to compare what they have researched about quilts to the quilts they complete.

8) Students will have to present their quilt and project to a CEO of QQC, trying to sell their quilt to be sold in a store.

_ Make a template for your quilt _ Use your template to create a tessellation, using the computer program _ Create a budget plan for the buying of material, making of the quilt, and selling your quilt, ect. (whatever you feel is needed in your budget plan) _ Create your quilt in FACS (this will be created in FACS class, not when you are in math, you will get graded in that class concerning topics in the class) _ ** Write a paper about 2-3 pages in length about a specific culture and period in history when quilts were used. _ Presentation to either the local quilter or to the teacher, either on acting as the CEO of QQC looking to see if they want to buy the quilt.
 * Check List:

**Tessellation** **Budget Plan** **Paper** **Presentation**
 * || 10-9 || 8-7 || 6-5 || 4-3 || 2-1 ||
 * Knowledge of Symmetry in polygons || Constructs a symmetric tessellation || Constructs a mostly symmetric tessellation || Construct a partly symmetric tessellation || Construct a partially symmetric tessellation || Construct an asymmetric tessellation ||
 * Knowledge of Polygon properties || Construct a tessellation demonstrating excellent knowledge of theorems || Construct a tessellation demonstrating good knowledge of theorems || Construct a tessellation demonstrating acceptable knowledge of theorems || Construct a tessellation demonstrating poor knowledge of theorems || Construct a tessellation demonstrating little/no knowledge of theorems ||
 * || 10-9 || 8-7 || 6-5 || 4-3 || 2-1 ||
 * Use of Excel || Shows excellent knowledge and proficiency of the use of Excel || Shows good knowledge and proficiency of the use of Excel || Shows acceptable knowledge and proficiency of the use of Excel || Shows poor knowledge and proficiency of the use of Excel || Did not use Excel ||
 * Explanation of why || Elaborated fully on the derivation of the budget || Elaborated mostly on the derivation of the budget || Elaborated partially on the derivation of the budget || Elaborated poorly on the derivation of the budget || Elaborated didn’t on the derivation of the budget ||
 * || 10-9 || 8-7 || 6-5 || 4-3 || 2-1 ||
 * History and Cultures || Researched all proper history and related cultures of quilts; all documented in desired format || Researched most proper history and related cultures of quilts; all documented in desired format || Researched acceptable proper history and related cultures of quilts; most documented in desired format || Researched poor proper history and related cultures of quilts; some documented in desired format || Researched very little or no proper history and related cultures of quilts; little or none documented in desired format ||
 * Use and Significance || Identified and analyzed all uses and significance of quilts || Identified and analyzed most uses and significance of quilts || Identified and analyzed some uses and significance of quilts || Identified and analyzed little uses and significance of quilts || Didn’t identify or analyze any use or significance of quilts ||
 * || 10-9 || 8-7 || 6-5 || 4-3 || 2-1 ||
 * Rehearsed || Well rehearsed, with smooth delivery || Rehearsed with good delivery || Rehearsed with acceptable delivery || Not rehearsed with acceptable delivery || Not rehearsed, poor delivery ||
 * Knowledge of topic || Demonstrates full knowledge of topic || Demonstrates most knowledge of topic || Demonstrates some knowledge of topic || Demonstrates a little knowledge or topic || Demonstrates no knowledge of topic ||

Informal Assessments:
Directions for teacher- ask one question from questions 1-4. Ask one from questions 5-8. Ask either question 9 or 10. If the student is taking too long on the first round of questions you can skip round two and then go to round 3.
 * Interview

Directions for student- Explain to me in your own words how each theorem or postulate works and why it does. You can draw a picture if you want.

1. Corresponding Angles Postulate- If two lines cut by a transversal are parallel, then corresponding angles are congruent

2. Alternate Interior Angles Theorem- If two lines cut by a transversal are parallel, then alternate interior angles are congruent.

3. Alternate Exterior Angles theorem- If two lines cut by a transversal are parallel, then alternate exterior angles are congruent.

4. Same-side Interior Angles Theorem- If two lines cut by a transversal are parallel, then same-side interior angles are supplementary.

5. Converse of the Corresponding Angles Postulate- if two lines are cut by a transversal in such a way that corresponding angles are congruent, then the two lines are parallel.

6. Converse of the Same-side Interior Angles Theorem- If two lines are cut by transversal in such a way that same-side interior angles are supplementary, then the two lines are parallel.

7. Converse of the Alternate Interior Angles Theorem- If two lines are cut by a transversal in such a way that alternate interior angels are congruent, then the two lines are parallel.

8. Converse of the Alternate Exterior Angles Theorem- If two lines are cut by a transversal in such a way that alternate exterior angles are congruent, then the two lines are parallel.

9. The Parallel Postulate- Given a line and a point not on the line, there is one and only one line that contains the given point and is parallel to the given line.

10. The Exterior Angle Theorem- The measure fo an exterior angle of a triangles in equal to the sum of the measures of the remote interior angles. **

The sum of all the angles on one line are equal to __(fill in the blank)__. What can you say about angels that when added together equal 180˚? Describe, in a sentence, what it means to have angles be complementary. **
 * Example of Exit Ticket Questions:**
 * The sum of all the angles in a triangle are __(fill in the blank)__.

Formal Assessments:
Quiz:
 * NAME _

1. In the following set of triangles are the two triangles congruent, if so explain which postulates or theorem justifies your answer, and if not explain why not.

a.

b.

c.

2. Is there exactly one triangle that can be constructed with the given measurements? If so, identify the postulate that applies. a. Δ RGS: RG=5, GS=12, m< G = 75 __˚__

b. Δ DJE: DJ=5, m< D = 15˚, m< J = 75˚

3. Find x, if possible, if not explain why not. **

1) In the diagram below, ∆AMW≅∆GNL. Complete the following the following statements about congruent:
 * Test:**



Line MN≅ < N≅ _ Line LG≅ _ ∆NGL≅

2) Find x.

3) Which triangles are possible? State why or why not. For ∆ABC AB=7, BC=10, AC=12

For ∆XYZ XY=6, YZ=5, XZ=14

4) Are the following pairs of triangles congruent, if so, why, if not, why not?





5) You are building a window in a building. According to the design specifications, you are to make ΔDOA congruent to ΔDOG. From your construction, you know that line DO is perpendicular to line AG and line OD bisects line AG. Can you conclude that ∆DOA ≅ ∆DOG?



6)Using what you know about angles, lines and triangles, find the measurements of angles 1-9.