Minaya+UbD


 * Understanding By Design Lesson Template**

Students will learn how the distance formula can be used to detemine the length of a segment in a coordinate plane. |||| How might a smaller scale example help the “larger picture?” How do you think the Pythagorean Theorem could help a contractor in his/her designs? How might experts have used the distance formula when creating objects? Is it important to simplify triangles by doing pythagorean triples? || Students will figure out lengths of triangle sides. Students will find the distance between two coordinate points. Students will || Students will know… |||||| ** Skills ** Students will be able to… || Students will recognize pythagorean triples and be able to find lengths of triangle legs using nothing but mental math. Students will know that squaring square root numbers makes the problems simpler. |||||| Students will be able to use maps to find the distance between cities. Students will be able to find the length of missing segments on different shapes that containg sides and triangles. || · Granite tops in bathrooms and kitchen · Slate roof · Brick exterior · Vaulted ceilings · Central A/C · Pool || Once the class project is finished the students will then proceed to review what they have learned and realize how and why they have needed to put it into perspective for their project. The project will count as 50% of their test grade. The other 50% will be graded on the written part of the test which will include classifying triangles, angle measures of triangles, isosceles and equilateral triangles and the pythagorean theorem and distance formula.
 * **Title of Lesson** |||| Understanding the Pythagorean Theorem and the Distance Formula || **Grade Level** |||| High School ||
 * **Curriculum Area** |||| Math – Geometry || **Time Frame** |||| 7 Days ||
 * **Developed By** |||||||||| O’Mar C. Minaya ||
 * ** Identify Desired Results (Stage 1) ** ||
 * ** Content Standards ** ||
 * ** 4.2A1 Use geometric models to represent real-world situations and objects and to solve problems using those models. **
 * 4.2C1 Use coordinate geometry to represent and verify properties of lines. **
 * 4.2E1 Use techniques of indirect measurement to represent and solve problems. ** ||
 * ** Understandings ** |||||| ** Essential Question(s) ** ||
 * ** Overarching Understanding ** |||| ** Overarching ** || **Topical** ||
 * Students will learn that it is possible to find the measure of the third leg of a triangle without having to physically measure it.
 * ** Related Misconceptions ** ||
 * Students will see that the distance formula and the pythagorean theorem are actually two similar formulas with one common goal, however, the distance formula is used with coordinates. ||
 * ** Knowledge **
 * Students will see the resemblance between the lengths of triangle segments and perfect squares.
 * ** Assessment Evidence (Stage 2) ** ||
 * ** Performance Task Description ** ||
 * **Goal** |||||||||| To construct a house. ||
 * **Role** |||||||||| You are a contractor that is trying to get a contract to build a house. ||
 * **Audience** |||||||||| Your target is a homeowner that wants to remodel his home. ||
 * **Situation** |||||||||| The homeowner has decided to remodel his entire house completely. You must convince the homeowner that your design is very cost effectcive, has a very modern feel and could be done just as fast as the conventional way. ||
 * **Product/Performance** |||||||||| You must design a house that looks contemporary, however is cost effective to build and has many modern ammenities. The house should keep a large backyard and include a deck, porch, fire place, and attached 2 car garage. ||
 * **Standards** |||||||||| House must include:
 * ** Other Evidence ** ||
 * Students will first be taught the distance formula and the pythagorean theorem. Then students will be quizzed on the subject. All students in class must demonstrate knowledge of mastering both of these formulas in order to be able to proceed with the class project.

Students will need to know that 1 2x4 must be accounted for each foot on the perimeter of the house. Students must also realize that the homeowner does not want any room with less than 18 feet diagonally. House lot is 100 ft long by 75 feet wide. Back yard is to be at least 2250 square feet. ||
 * ** Learning Plan (Stage 3) ** ||
 * ** Where are your students headed? Where have they been? How will you make sure the students know where they are going?** |||||||| **Day 1**
 * Engage**: Students will do Pg 189 # 19
 * Objective**: Ch 4.4 Students will learn the Pythagorean Pheorem and the distance formula.
 * Practice**: Students will copy definition of hypotenuse and legs on pg 192 then students will copy the Pythagorean Theorem and the distance formula from the board as I explain them and do extra examples. Then students will do Checkpoints 1-6 Pg 193-194 and volunteers will show their work on the board. For Homework students will do Pg 195 #’s 2-22 even.
 * Evaluate**: Class participation ||
 * **How will you hook students at the beginning of the unit?** |||||||| Day 2
 * Engage**: Students will do Pg 196 # 19 on McDougall Littell book
 * Objective**: Ch 4.4 Students will learn the pythagorean theorem and the distance formula (continued).
 * Practice**: Students will go through their homework answers as I read them out loud. Students will ask questions when they do not fully understand. Then, students will take a quiz on Ch 4.4.
 * Evaluate**: Homework problems and quizzes will be graded. ||
 * **What events will help students experience and explore the big idea and questions in the unit? How will you equip them with needed skills and knowledge?** |||||||| **Day 3**
 * Engage**: Students will do Pg 196 # 21 on McDougall Littell book
 * Objective**: To understand the math involved in designing a house.
 * Practice**: Today students get an overview and begin research on this weeks project. Students will be shown a sample project done by other students the year before. Students will be assigned into groups, and each group is assigned a part of a house. They will make up room sizes and begin to design it’s shape on graph paper.
 * Evaluate**: Design of room including closets doors and windows should be finished. ||
 * **How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?** |||||||| **Day 4**
 * Engage**: Students are to get on computers and explore and document at least 4 different websites (homedepot.com, lowes.com, etc.) where they can purchase the items needed for the room being designed.
 * Objective**: Students will research on prices depending on square footage.
 * Practice**: Students will do research on prices while others from each group finds what is needed and others design the rooms. I will walk around the class and give suggestions on what is needed.
 * Evaluate**: Students will be given credit based on their participation. ||
 * **How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?** |||||||| **Day 5**
 * Engage**: Students are to pull out all material and construction paper.
 * Objective**: Students are to draw similar shapes by converting feet into centimeters.
 * Practice**: Students will transfer their rough drafts onto final drafts on construction paper. Each group will have a different color construction paper to distinguish their work.
 * Evaluate**: Grading will be done on accuracy of scales. ||
 * **How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?** |||||||| **Day 6**
 * Engage**: To finish transfer onto final construction paper.
 * Objective**: To put construction projects together.
 * Practice**: Students will finish the major theme of the house on construction paper by putting all parts of the house together. (Space will be left for the hall ways) The house should look complete with kitchen, bathroom, bedrooms, windows and doors. ||
 * **How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students?** |||||||| **Day 7**
 * Engage**: To finish trimming parts.
 * Objective**: To finish project.
 * Practice**: In order to finish the house fully, all rooms must be adjacent to each other. This means some students rooms will have to be compromised by trimming certain areas or by editing certain parts.
 * Evaluate**: Class participation and willingness to adjust their project for the greater good of the whole picture. ||

From: Wiggins, Grant and J. Mc Tighe. (1998). //__Understanding by Design__//, Association for Supervision and Curriculum Development ISBN # 0-87120-313-8 (ppk)

How was it creating this lesson? It took me a little bit of time to get started, but eventually I just started to generate ideas as to how I would want to run an assessment like this. Things just seemed to flow into place after a while. I find that the lesson plans themselves are not so difficult. It was a bit more tedious to come up with the correct essential question.

What difficulties did you encounter? As stated above my difficulties where in creating essential questions. Then I had to do some research in order to distinguish the differences between understandings and the 2 different types of essential questions. I also had to do some research to distinguish between knowledge and skills. It seems I thought I knew what each was but found it challenging to put on paper.

Did you like the format? I'm not so sure that I like the format. I guess I would have to try the same project with a different template. The last part of this template was a bit confusing. It didn't really have a specific place to put the lesson plans in. Ultimately, having the lesson plans in was a vital part of this UbD.

What are additional questions you now have? The last part of the template had all those questions in the left hand side. I used those as a guide throughout my lesson plans. I answered those questions in my own ways. So my question is: Did we need to answer those questions specifically right next to them?