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Youngstown City Schools ACCELERATED MATH - - Grade 7 Unit 5B: TRANSFORMATIONS (2 weeks) SYNOPSIS: In this unit, students will be introduced to Transformations and shown how to manipulate shapes through the coordinate plane and algebraically. From here students will expand their knowledge by applying concepts learned to other types of problems and then apply the concepts of this unit to a situation related to an animated movie. STANDARDS 8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length b. Angles are taken to angles of the same measure c. Parallel lines are taken to parallel lines 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8. G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. MATH PRACTICES: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning LITERACY STANDARDS L.2 Communicate using correct mathematical terminology L.4 Listen to and critique peer explanations of reasoning L.5 Justify orally and in writing mathematical reasoning MOTIVATION TEACHER NOTES 1. Discuss Unit standards and preview the Authentic Assessment 2. Provide students with a list of Vocabulary to define that are found in Video Clip: Geometric Transformations from United Streaming. View Video. See Teaching-Learning #1 for Vocabulary. 3. Have students set both personal and academic goals for this Unit (at this point, model and set parameters for goal setting so that students learn how to establish goals that are important and related to the standards of the Unit). Have the students review goals weekly to determine progress or lack of progress. TEACHER NOTES TEACHING-LEARNING 1. Teach vocabulary in context as it comes up in the Unit. Transformations, Rotations (turns), Translations (slides), Reflections (flips), Dilation, Image, Pre-image, Prime, 7/8/2013 YCS Grade 8 Math: Units 4: TRANSFORMATIONS 2013-2014 1 TEACHER NOTES TEACHING-LEARNING Congruent. (8.G.1; 8.G.3) 2. Work through Transformation Lab using Pentominoes or something similar; students manipulate the Pentominoes to achieve Transformations - - Reflection (Flip), Translation (Slide), and Rotation (Turns). Through discussion, students determine which Transformations were modeled. They analyze what is missing (dilation) and how it could be displayed (Talk about the dilation of the eye). (8.G.1; 8.G.3) 3. Teacher provides a quick overview of plotting a point on a coordinate grid to emphasize the four quadrants of the coordinate plane (8.G.3) (L-2; MP-4) 4. FOCUS ON TRANSLATIONS: teacher provides students with Coordinate Grid and the ordered pairs for an arrow. Coordinates are: A (4,3) B (4,6) C (2,6) D (5,9) E (8,6) F (6,6) G (6,3); have students plot pairs and then provide students with a new set of “prime” coordinates (x-5), (y-6) for the same size arrow; have students describe and record the Translation. Students give their partner a description of a Translation. Have group discussion of the geometric properties that change and remain the same as well as Prime Notation. Teacher reviews properties of angles and lines and what makes images congruent and similar. (8.G.1, 8.G.2, 8.G.3, 8.G.4; L- 2, L-4, L-5; MP-3) 5. Have students practice a variety of problems. Resources: Foresman/Wesley Math 3 pages 594 – 604; Glencoe Pre-Algebra pages 506 – 512; www.kutasoftware.com free worksheets on transformations (Choose problems from the worksheets – Do NOT complete worksheets in class.) (MP-1) 6. Once students have written and discussed the Translations, have them write the change Algebraically (i.e., (x, y) -----> (x+4, y - 2). Have students practice a variety of problems. Resources: Foresman/Wesley Math 3 pages 594 – 599; Glencoe Pre-Algebra pages 506 – 512 (Translation problems only). (MP-1, MP-2, MP-4 ) NOTE: for Translations Do points and line first and be sure to include Similar Figures and Congruence Student practice can be done using white boards, Promethean board, centers/stations, and partner work. FORMATIVE ASSESSMENT: Provide the students with paper that has a pre-image and image. They must describe what happened (translation) and then write a hypothesis of a different transformation that could result with the same image from the pre-image. Students should be prepared to share and discuss their reasoning. (MP-1,MP-2, MP-3, MP-6) 7. FOCUS ON REFLECTIONS: Provide students with Coordinate Grid and the same arrow with the same set of coordinates from the Translation activity #4. Give students new Prime Coordinates (-x, y) that will reflect the arrow over the x-axis . Students then describe/record the Reflection and the line of reflection. Teacher then provides new coordinates that will reflect the image over the y-axis . Students then describe / record the reflection and the line of reflection (Double Prime) (x, -y). (8.G.1, 8.G.2, 8.G.3, 8.G.4; L- 2, L-4, L-5; MP-3) NOTE: for Reflections Do points and line first and be sure to include Similar Figures and Congruence 8. Students have a partner discussion about the relationships between the Pre-image / Prime and the Double Prime image. Lead into class discussion that connects back to Translations. (L-2, L-4, L-5) 9. Have students practice with a variety of problems. Resources: Foresmann /Wesley Math 3 pages 594 – 599; Glencoe Pre-Algebra pages 506 – 512 (Reflection problems only) Navigating through Geometry page 103; www.kutasoftware.com free worksheets on transformations (Choose problems from the worksheets – Do NOT have students complete worksheets in class (MP-1) 7/8/2013 YCS Grade 8 Math: Units 4: TRANSFORMATIONS 2013-2014 2 TEACHER NOTES TEACHING-LEARNING FORMATIVE ASSESSMENT: Provide the students with paper that has a pre-image and image. They must describe what happened (reflection) and then write a hypothesis of a different transformation that could result with the same image from the pre-image. Students should be prepared to share and discuss their reasoning. (MP-1, MP-2, MP-3, MP-6) 10. FOCUS ON ROTATIONS: Have students stand at their desks and all face the front of the room. To integrate vocabulary, have students practice rotating clockwise and counter-clockwise 90°, 180°, 270°, 360°, etc. (8.G.1, 8.G.2, 8.G.3, 8.G.4; L-2, L-4, L-5; MP-4) 11. Teacher provides students with a Coordinate Grid and the same arrow and same set of coordinates from the Translation activity (#4). Provide students with patty paper, and have them place this over the Pre-image and trace. Students then rotate patty paper image 90°, 180°, 270°, 360° clockwise and counter-clockwise around the origin. Have class discussions about all of the Rotated Images. (L- 2; MP-4; MP-8) 12. Teacher provides students with new Coordinate Grid and the coordinates for rectangle MNOP. Provide students with coordinates of the rectangle image; then have students describe in words the rotation (clockwise, counter-clockwise, and the amount of degrees). Teacher offers students a Coordinate Grid that has a flag on it and has the students sketch 90°, 180°, 270°, 360° rotation around the origin and discuss the properties that change and those that stay the same - - angles, lines, congruent, similar and orientation. Teacher expands the practice to include other points of origin. (L-2,L-5; MP 4,MP-8) NOTE: for Rotations, Do points and line first and be sure to include Similar Figures and Congruence Rectangle MNOP M (-7,2) N (-7,4) O (-3,4) P (-3,2) Rectangle M’N’O’P’ M’ (-2,-7) N’ (-4, -7) O’ (-4,-3) P’ (-2, -3) 13. Students complete additional practice. Resources: Foresmann/Wesley Math 3 pages 548 – 549; Glencoe Pre-Algebra pages 506 – 512; Glencoe Algebra I pages 197 – 203 (Rotation problems only); Navigating through Geometry pages 104 – 106; www.kutasoftware.com free worksheets on transformations (Choose problems from the worksheets – Do NOT have students complete worksheets in class.) (MP-1) FORMATIVE ASSESSMENT: Provide the students with paper that has a pre-image and image. They must describe what happened (rotation) and then write a hypothesis of a different transformation that could result with the same image from the pre-image. Students should be prepared to share and discuss their reasoning. (MP-1,MP-2,MP-3,MP-6) 14. FOCUS ON DILATIONS: Teacher reviews vocabulary words - - Dilation and Scale Factor - - provide students with Coordinate Grid and the set of coordinates for rectangle ABCD: A (-6,4) B (6,4) C (6,-4) D (-6,-4) and have students draw the shape. Provide students with coordinates for rectangle A’B’C’D’: A’ (-3,2) B’ (3,2) C’ (3,-2) D’ (-3.-2). Students describe / record the change and determine the scale factor. Student pairs discuss the change they described of the dilation then discuss properties that stayed the same and changed (Properties: similar, congruent, angles, sides) NOTE: Review properties of similar figures if needed and be sure to include practice that has the form go from large to small and small to large. (8.G.1, 8.G.2, 8.G.3, 8.G.4; L- 2, L-4, L-5; MP- 3,MP-4,MP-8) 15. Students complete “additional practice. Resources: Foresmann/Wesley Math 3 pages 450 455; Glencoe Pre-Algebra pages 512; Glencoe Algebra I pages 197 – 203 (Dilation problems only); Navigating through Geometry pages 92,107. (MP-1) FORMATIVE ASSESSMENT: use Released Item #11 from the 2007 Math OAA Test 7/8/2013 YCS Grade 8 Math: Units 4: TRANSFORMATIONS 2013-2014 3 TEACHER NOTES TEACHING-LEARNING (Attached: page 4). 16. Use Teaching the Common Core Math Standards with Hands-On Activities, pages 213-214: The Mixed-Up Notes activity. TRADITIONAL ASSESSMENT TEACHER NOTES 1. Paper-pencil test with M-C questions and 2-and 4-point questions 2. CFA as a M-C test AUTHENTIC ASSESSMENT TEACHER NOTES 1. Students evaluate goals they set at beginning of unit. 2. Students use the Coordinate Grid with both an image and pre-image that have been through 3 different transformations. Students are to describe and sketch three different ways to get from the pre-image to the image. At least one description needs to be a sequence of different transformations (e.g., reflection - - rotation - - translation. Students must write a description of how the position changes for each “drawing.” The student descriptions should include which properties stay the same and which change. NOTE: there may be more than one correct answer! (8.G.1, 8.G.2, 8.G.3, 8.G.4; L. 2, L.5; MP.1,MP.6, MP.7, MP.8) 7/8/2013 Teachers will have five different forms of the problem to distribute. (Jan Ross has some pictures that can be used) YCS Grade 8 Math: Units 4: TRANSFORMATIONS 2013-2014 4 Sketch rectangle ABCD centered at the origin to represent a dilation of rectangle PQRS by a scale factor of 1.5 State one characteristic of rectangle PQRS that does not change as a result of the dilation 7/8/2013 YCS Grade 8 Math: Units 4: TRANSFORMATIONS 2013-2014 5 A flag is drawn on a coordinate plane. Y X In your Answer Document, sketch this flag on a coordinate plane. Then rotate the flag 180° about the origin and sketch the flag in its new position. 7/8/2013 YCS Grade 8 Math: Units 4: TRANSFORMATIONS 2013-2014 6