LESSON PLAN Sabbath Middle School Grade Level: 8 Title: Square Roots with Cubism Author: Kyle Linford Enduring

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1 LESSON PLAN Sabbath Middle School Grade Level: 8 Title: Square Roots with Cubism Author: Kyle Linford Enduring The students will develop an understanding of finding the length of segments Understanding: using squares and how to utilize square roots by creating cubist artworks. Overview: Objectives: Students will explore and develop their understanding of finding the length of segments using squares and square roots by creating cubist art. After exploring their understanding of square roots and artwork that utilizes rectangular designs, students will develop their understanding with a sequence pattern guide and practice it by creating cubist artwork. After the students have finished this activity, they will analyze their creation for design and correctness, while reflecting on how they can determine this information without the electronic tools. SWBAT: Utilize the square roots to determine unknown side lengths. Calculate square roots of real numbers using calculated area Construct polygons in GeoGebra Utilize GeoGebra to find the area of a polygon Content Standard(s): CCSS.MATH.CONTENT.8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is 2 irrational. Materials: Rulers Markers Poster Paper Colored Pencils Transparencies with Grid Tablets with GeoGebra Vocabulary: Area Square Root Cubism Art Standard(s): VA:Cr1.1.4a Brainstorm multiple approaches to a creative art or design problem. VA:Cr1.1.8a Document early stages of the creative process visually and/or verbally in traditional or new media. VA:Cr1.2.7a Develop criteria to guide making a work of art or design to meet an identified goal. VA:Cr2.1.8a Demonstrate willingness to experiment, innovate, and take risks to pursue ideas, forms, and meanings that emerge in the process of art-making or designing. VA:Cr2.3.8a Select, organize, and design images and words to make visually clear and compelling presentations. Other Resources: tm FROM THE NATIONAL ARTS STANDARDS-- Create: Students create their own design by utilizing squares. Present: Students share their designs and calculations with the class. Respond: Students check for correctness and reflect on how to calculate area without GeoGebra. Connect: Students connect their design to cubist art.

2 Assessment Strategies FORMATIVE: Completion of the during reading activity. SUMMATIVE: Completion of the square root activity. Instructional Activities & Strategies ENGAGE: (20 minutes-2:08pm) The lesson will begin with PreP for a pre-reading activity. Students will be organized into groups based on their seating arrangements. Each group will be asked to brainstorm everything that comes to mind for the topic of square roots and record their ideas on large poster paper. After 2 minutes, the groups will place their posters around the room so the class can see the different group responses. Students are to be questioned where certain ideas came from, and the class will consolidate and categories these ideas. The instructor should record student responses on blank paper projected onto the screen by the ELMO and projector. After the students have explored their understanding of square roots, they will be presented with cubist artworks that utilize square constructions to create images. Students will be asked to identify what they see, what they think of the art pieces, and what questions they have because of them. The class will be guided into discussing the use of polygons and squares to construct these pieces. BUILD: (15 minutes-2:23pm) Students will then be asked to individually hypothesis how they can utilize square roots when working with the squares in the art pieces. The students will then be read a PowerPoint slide of paragraph 1 on page 22 in their workbooks, Looking for Pythagoras. Once read, students will fill out a sequence pattern guide for their during reading activity. The teacher should have students provide answers for the activity after the class has finished. A PowerPoint slide will be shown revealing the sequence pattern as students record their ideas. See the attached handout for more specific instructions. APPLY: (15 minutes-2:38pm) Students will apply their knowledge of the square roots by creating cubist artwork. To do this after reading activity, students will be taking an original image and create it using only squares. Following the handout directions, students are to first think of an appropriate image that they would like to draw and either draw a quick sketch of the normal image or describe it in words. Once the image is determined, the students will begin redrawing it by using only squares in the image. As students work through their designs, they are to determine the side lengths of these squares. To do this, students will use transparencies to identify the dimensions of their designs and recreate these squares on GeoGebra. Using the area feature on the app, students will approximate the area of their design to then determine the side length by taking the square root. Students are to record these lengths down. See the attached activity handouts for each of the specific requirements. Before students begin the activity, the instructor will inform students about the creation and how to utilize the GeoGebra app on the tablets. The exploration of the app should also discuss the individual responsibilities students have with the technology and how to properly operate and treat the technology. The instructor should also present the class with the required rubric for the activity. REFLECT: (5 minutes-2:42pm) The students will review their final product and determine their correctness. Volunteers will be asked to share their designs. They should then connect this design to the topics they brought up during the PreP activity. The instructor will check with students to see if there are any additional edits their lists need and ask them how their creations help demonstrate these concepts. RUBRIC: See attachment. ANY ADDITIONAL INFORMATION The last minute of class will be spent cleaning up and reorganizing the classroom. If time runs low, students will be asked in groups to break from their art activities to start finding some of the areas and side lengths of their squares. Additionally, the tablet usage can be removed from the lesson and supplemented with the transparency grids if necessary.

3 Finding Lengths of Segments Using Squares Name: Part 1 Sequence of Events Task: Write numbers next to each statement to indicate the order in which the steps occur in the reading. Take the square root of the area. Draw a square with the segment as a side. Determine the area of the square. Part 2 Moral Task: Put an X next to the statements supported by the text AND life in general. 1. Appearances are deceiving. 2. Necessity is our strongest weapon. 3. Slow and steady wins the race. 4. One good plan that works is better than a hundred doubtful ones. 5. The gods help them that help themselves.

4 Name: Activity Square Roots with Cubism Task: For this project, you will be creating your own cubist artwork. The design is to be based off of a real life image and can only include squares no rectangles or other polygons are allowed. When you are done with your design, you will find the dimensions of your artwork by finding the side lengths of the squares. STEP 1: Think of an image you would like to make for your cubist work, and sketch or describe it with words below. STEP 2: Recreate your image using only squares. Then find the side lengths of those squares.

5 Math Goals Square Roots with Cubism We should be able to meet all of these statements for the different activities when we are finished. If we can, then we know that we have made great artwork that depicts math! Category Design is Exceptionally Neat and properly utilized Neatness and well designed, relatively but the design Attractiveness neat, and attractive. appears quite attractive. plan. Squares Dimensions Calculations The design utilizes only squares. All dimensions are approximated appropriately. All calculations for the side lengths are done correctly and with proper units. All but 1 of the dimensions are approximated appropriately. All calculations for the side lengths are correct. All but 2 of the dimensions are approximated appropriately. Calculations for the side length are incorrect because of computation error. Appears messy and thrown together in a hurry. Overly simple design. The design does not utilize only squares. More than 3 of the dimensions are approximated inaccurately. Calculations for the side length are incorrect because of error with the concept.

6 Title: Table by a Window (1917) Artist: Jean Metzinger ( ) Movement: Cubism Title: Portrait of Pablo Picasso (1912) Artist: Juan Gris ( ) Movement: Cubism

7 Title: Still Life with a Bottle of Rum (1911) Artist: Pablo Picasso ( ) Movement: Cubism

8 Title: Nude Descending a Staircase No. 2 (1912) Artist: Marcel Duchamp ( ) Movement: Cubist / Futurist