Lesson

The Big Ideas of Understanding by Design 1. UbD is a way of thinking purposefully about curricular planning and school reform, a set of helpful design tools, and design standards -- not a program or recipe. 2. The end goal of UbD is understanding and the ability to transfer learnings – to appropriately connect, make sense of, and use discrete knowledge and skills in context. 3. Evidence of understanding is revealed through performance – when learners transfer knowledge and skills effectively, us- ing one or more “facets” (explain, interpret, apply, shift per- spective, empathize, and self-assess). 4. Educators are coaches of understanding, not mere purveyors of content or activity. 5. Planning is best done ”backward” from the desired results and the transfer tasks that embody the goals. 6. UbD transforms Content Standards and other goals into fo- cused learning targets based on “big ideas” and transfer tasks. 7. Design Standards guide self-assessment and peer reviews of curriculum, instruction, and assessment for quality control. 8. UbD reflects a “continuous improvement” approach to de- sign and learning. The results of our curriculum designs (e.g., assessment results, quality of student work, degree of learner engagement) inform needed adjustments. Understanding by Design Template Understanding by Design This activity serves as a prerequisite to accomplish the standards below. The goal for this activity is for students to be able to fluently switch between writing area as a product and as a sum (and vice versa). This leads to factoring because factoring is going from a sum to a product. Standard __** : MA-HS-5.2.3
 * < Title: ||||||< Intro to Algebra Tiles ||
 * < Subject/Course: ||||||< Algebra 2 ||
 * < Topic: ||||||< Algebra Tiles ||
 * < Grades: ||||||< 11 ||
 * < Designers: ||||||< CPM & Me! ||
 * < Stage 1 - Desired Results ||
 * < Established Goal:[[image:file://localhost/Users/steveswan/Library/Caches/TemporaryItems/msoclip/0clip_image001.png width="27" height="31" caption="G"]]
 * __
 * Students will add, subtract and multiply polynomial expressions; factor polynomial expressions using the greatest common monomial factor and factor quadratic polynomials of the form ax2 + bx + c, when a = 1 and b and c are integers.**

//MA-HS-5.2.4// //Students will factor quadratic polynomials, such as perfect square trinomials and quadratic polynomials of the form when a ≠ 1 and b and c are integers.//


 * __ Benchmarks: __** Algebraic Thinking ||

//Students will understand that...// - How can I write it? || · The two ways to algebraically represent the area of a rectangle (as a product & sum). ||< //Students will be able to....// · Learning Log || Students will be given a bag of algebra tiles to initially get acquainted with them. Students will begin with problem 5-1 where they take a group of tiles and attempt to create a rectangle out of the. Students will ideally come up with different versions of rectangles. As students complete their rectangles they will do a mini-gallery walk and look at others' rectangles. Students will have to explain why all rectangles are acceptable results. They will then have to move on to interpret their rectangle and write the area as a sum & as a product. Students will make the connection that both expressions are equivalent.
 * < Understandings:[[image:file://localhost/Users/steveswan/Library/Caches/TemporaryItems/msoclip/0clip_image002.png width="27" height="31" caption="U"]]
 * Algebra tiles are a concrete representation of area.
 * Algebra tiles represent variables (unknowns). ||< Essential Question: [[image:file://localhost/Users/steveswan/Library/Caches/TemporaryItems/msoclip/0clip_image003.png width="27" height="31" caption="Q"]]
 * < //Students will know...// [[image:file://localhost/Users/steveswan/Library/Caches/TemporaryItems/msoclip/0clip_image004.png width="27" height="31" caption="K"]]
 * Distribute an expression with and without algebra tiles. ||
 * < Stage 2 – Assessment Evidence ||
 * < Performance Task:[[image:file://localhost/Users/steveswan/Library/Caches/TemporaryItems/msoclip/0clip_image006.png width="26" height="30" caption="T"]]
 * Create a video working and explaining how to take a product, represent it with tiles and write it as a sum. ||||< Other Evidence [[image:file://localhost/Users/steveswan/Library/Caches/TemporaryItems/msoclip/0clip_image007.png width="26" height="30" caption="OE"]]
 * < Stage 3 – Learning Plan ||
 * < //Learning Activity://

Students will then apply their knowledge to 5-2 where they are given several expressions and must repeat the exercise over again. They must make a rectangle and write the area as a product and as a sum. As students work through their problems they will be asked to keep in mind what they do or do not understand about the process. In 5-3 they will have to write a Learning Log explaining how they know that the area as a sum & product are equivalent.

The following day (or same period if it is a longer period or students move quickly) students will be working with virtual algebra tiles in the computer lab. http://nlvm.usu.edu/en/nav/frames_asid_189_g_4_t_2.html?open=activities&from=category_g_4_t_2.html Students will use the website to work on a portion of 5-11. Each student will be given a part (an expression of area written as a product). Students will use Smart Recorder to record a video of themselves working this problem on the virtual manipulatives. Students will have a microphone to explain what they are doing and why as they work through their problem. Upon completion of their video they will upload it to You Tube and then embed it into a class wiki page.

Their closure for the lesson with algebra tiles will be to work out 5-13. 5-14 is the Learning Log for this lesson and the students video will take the place of the learning log.

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TASK Breakdown: The goal of the task is to simply introduce students to algebra tiles. It is also to build fluency in creating concrete representations of an algebraic expression. It is designed to assess their understanding of switching between writing area as a sum and a product using algebra tiles. Students will act as a teacher to the rest of the class during their voice thread. The audience is the class. The situation is a class that has not been through CPM Algebra 1 but is in CPM Algebra 2 and needs to learn how to use algebra tiles because later they will be used to develop the concept of factoring. Voice Thread I will be looking for accuracy in their algebraic expressions and a correct description of what they are doing in their voice thread. This is just a copy of the file.
 * G What is the goal of the task? What is it designed to assess?
 * R What real-world role will the student assume as he/she is performing the task?
 * A Who is the audience for the task?
 * S What is the situation that provides the context for the task?
 * P What is the product or performance that is required by the task?
 * S By what standards will the product or performance be judged?
 * Technology Example Employed to Complete the Task

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This is an electronic version of the text that students will have in front of them as they work on this activity.