Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Unit 04: Geometr: Coordinate Plane, Graphing Transformations, and Perspectives (9 das) Possible Lesson 0 (6 das) Possible Lesson 0 ( das) POSSIBLE LESSON 0 (6 das) This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson b supplementing with districtapproved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is onl a recommendation, and districts ma modif the time frame to meet students needs. To better understand how our district is implementing CSCOPE lessons, please contact our child s teacher. (For our convenience, please find linked the TEA Commissioner s List of State Board of Education Approved Instructional Resources and Midccle State Adopted Instructional Materials.) Lesson Snopsis: Students plot integers and positive rational numbers on the coordinate plane and identif the quadrant in which the point lies. Students transform figures on the coordinate grid described as a translation or a reflection. TEKS: The Teas Essential Knowledge and Skills (TEKS) listed below are the standards adopted b the State Board of Education, which are required b Teas law. An standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit. The TEKS are available on the Teas Education Agenc website at http://www.tea.state.t.us/inde.asp?id=648 7.7 Geometr and spatial reasoning.. The student uses coordinate geometr to describe location on a plane. The student is epected to: 7.7A Locate and name points on a coordinate plane using ordered pairs of integers. Supporting Standard 7.7B Graph reflections across the horizontal or vertical ais and graph translations on a coordinate plane. Readiness Standard Underling Processes and Mathematical Tools TEKS: 7.4 Underling processes and mathematical tools.. The student communicates about mathematics through informal and mathematical page of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das language, representations, and models. The student is epected to: 7.4A Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, phsical, or algebraic mathematical models. Performance Indicator(s): Grade7 Unit04 PI0 Graph and label a set of ordered pairs of integers that will create a figure on a coordinate plane. Reflect the figure over the horizontal or vertical ais. Graph a translation of the figure. In writing, describe how to locate and name the ordered pairs of the image, and identif the quadrant in which it lies. Sample Performance Indicator: Given the points A (-, ), B (-5, 6), and C (-6, ), plot and label the points on a coordinate plane. Graph a reflection across the -ais and label the vertices of the image with prime notation. Net, translate the original figure 7 units down and units to the right, and again label the vertices of the image with prime notation. On the coordinate plane, locate and name the ordered pairs of each image, and identif the quadrants in which the lie. Write a journal entr describing how the vertices were transformed in each of the new images. Standard(s): 7.7A, 7.7B, 7.4A ELPS ELPS.c.5B, ELPS.c.5G Ke Understanding(s): Each quadrant on the coordinate plane is described b the signs of the - and -values of an ordered pair. The order and signs of the coordinates in an ordered pair communicate the location of a point on the coordinate plane. Translations and reflections of shapes can be described and named in terms of coordinates or directions and units. When a figure is transformed on a coordinate grid, the transformation can be described as a translation or reflection. Misconception(s): Some students ma think the order of the coordinates in an ordered pair is not significant. Each coordinate represents the number of units in a specific direction (: left or right, : up or down) and together describe a specific location or point. Some students ma think the quadrants are numbered clockwise instead of counter-clockwise. Some students ma think that Quadrant II should be Quadrant I. page of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Some students ma think a translation or a reflection does not create a congruent image. However, when the transformation is performed, the image is congruent to the original figure. Vocabular of Instructions: coordinate sstem quadrant reflection transformation translation Materials: map pencil ( red, blue, black) ( set per student) wa paper or patt paper (-inch square) (6 per student) graph paper ( sheet per student) math journal ( per student) paper (white) ( sheets per 4 students) Attachments: All attachments associated with this lesson are referenced in the bod of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer kes are available in the district site and are not accessible on the public website. Integers and the Coordinate Plane KEY Integers and the Coordinate Plane It s a Match KEY It s a Match Sherr s Town KEY Sherr s Town page of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Transformers KEY Transformers Summar of Transformations KEY Summar of Transformations Transformations Practice KEY Transformations Practice M Own Transformations KEY M Own Transformations GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificit as well as addressing the Performance Indicators associated with each unit. District personnel ma create original lessons using the Content Creator in the Tools Tab. All originall authored lessons can be saved in the M CSCOPE Tab within the M Content area. Suggested Da Suggested Instructional Procedures Notes for Teacher Topics: Coordinate plane Integers Spiraling Review ATTACHMENTS Engage Students use prior eperiences to locate and name integers on a coordinate plane and review the components of the coordinate plane. Teacher Resource: Integers and the Coordinate Plane KEY ( per teacher) Teacher Resource: Integers and the Coordinate page 4 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures Instructional Procedures:. Displa teacher resource: Integers and the Coordinate Plane and distribute handout: Integers and the Coordinate Plane to each student.. Eplain to students that the horizontal ais is traditionall labeled the -ais and the vertical ais is traditionall labeled the -ais.. Using the displaed teacher resource: Integers and the Coordinate Plane, demonstrate labeling the horizontal and vertical aes as well as the 4 quadrants and the signs of the coordinates in each quadrant. Instruct students to replicate the solutions on their handout: Integers and the Coordinate Plane. Facilitate a class discussion about the coordinate plane. Ask: Notes for Teacher Plane ( per teacher) Handout: Integers and the Coordinate Plane ( per student) How are the horizontal and vertical aes similar? Different? (Both are number lines showing the set of integers. The horizontal ais goes from east to west and the vertical ais goes from north to south. The horizontal ais has the positive integers to the right of 0 and the negative integers to the left of 0. The vertical ais has the positive integers above 0 and the negative integers below 0.) What happens when the horizontal ais intersects with the vertical ais 0? (There are number lines intersecting at 0 with 4 separate regions and we create a wa to show the location of a point with a horizontal and vertical direction.) What is the place called where the horizontal and vertical number lines intersect? (origin) How would the location where the horizontal and vertical number lines intersect be described using an ordered pair? ((0,0)) If ou start in the top right corner of the coordinate plane and label it Quadrant I and page 5 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures move counter-clockwise, how would ou name the other quadrants? (The quadrant in the top left corner is Quadrant II. The quadrant in the bottom left corner is Quadrant III and the quadrant in the bottom right is Quadrant IV.) What is an ordered pair? (A pair of numbers that identif a location on the coordinate plane b giving a horizontal number and vertical number.) What number of the ordered pair is located first? (The first number in the ordered pair is located on the horizontal ais first and then the second number in the ordered pair is located on the vertical ais. The place where the horizontal and vertical numbers come together is the location of the point on the coordinate plane.) What are the signs of the ordered pairs in each quadrant? (Quadrant I signs (+, +), Quadrant II signs (-, +), Quadrant III signs (-,-) and Quadrant IV signs (+, -).) Notes for Teacher 4. Instruct students to plot the point for the ordered pair (.5, ) and label it A on their handout: Integers and the Coordinate Plane. Ask: Which quadrant is point A located in? (Quadrant I) 5. Instruct students to plot the point for the ordered pair (, 4) and label it B on their handout: Integers and the Coordinate Plane. Ask: Which quadrant is point B located in? (Quadrant II) 6. Instruct students to plot the point for the ordered pair (4, ) and label it C on their handout: Integers and the Coordinate Plane. page 6 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures Notes for Teacher Ask: Which quadrant is point C located in? (Quadrant IV) Wh is the listed order of the coordinates of an ordered pair important? (Since there is a horizontal and a vertical number line, there are two numbers and if no order is maintained, ou would not know which number line to use first to plot the point.) 7. Instruct students to plot the point for the ordered pair (, 4) and label it D on their handout: Integers and the Coordinate Plane. Ask: Which quadrant is point D located in? (Quadrant III) How do the signs of the coordinates of the ordered pair determine the location of the point? (The signs indicate in what quadrant the point is located.) Topics: ATTACHMENTS Coordinate plane Integers Eplore/Eplain Students practice graphing ordered pairs of integers on a coordinate plane. Instructional Procedures:. Place students in pairs and distribute handout: It s a Match to each student. Teacher Resource: It s a Match KEY ( per teacher) Handout: It s a Match ( per student) TEACHER NOTE Encourage students to name the direction on the -ais first, as left or right, and then on the -ais, as up or down. This will assist in the development of correctl plotting ordered pairs as (, ). page 7 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures. Instruct student pairs to plot each coordinate and label the coordinate plane. Allow time for students to complete the activit. Monitor and assess students checking for understanding. Facilitate a class discussion about the points. Ask: Notes for Teacher If ou begin at the origin, what instructions would ou give to plot point A? (9 left, 8 up) If ou begin at the origin, what instructions would ou give to plot point D? (6 left, up) Which quadrant would ou be in if ou begin at the origin and move to the right and then up? (Quadrant I) Which quadrant would ou be in if ou begin at the origin and move to the left and then down? (Quadrant III) Which quadrant would ou be in if ou begin at the origin and move to the right and then down? (Quadrant IV) Which quadrant would ou be in if ou begin at the origin and move to the left and then up? (Quadrant II) Topics: ATTACHMENTS Coordinate plane Integers Elaborate Students etend graphing ordered pairs of integers on a coordinate plane. Teacher Resource: Sherr s Town KEY ( per teacher) Handout: Sherr s Town ( per student) Instructional Procedures:. Distribute handout: Sherr s Town to each student. Instruct students to plot the points on the page 8 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures coordinate plane using smbols and pictures to represent the locations. Allow time for students to complete the activit. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. Notes for Teacher Topics: Engage Transformations Students use prior eperiences to review the definitions for translations and reflections. MATERIALS Spiraling Review paper (white) ( sheets per 4 students) Instructional Procedures:. Place students in groups of 4 and distribute sheets of white paper to each group. Instruct groups to create their own definition and eamples of a translation and reflection on each sheet of paper. Allow time for students to generate their definition and eamples. Monitor and assess students to check for understanding. Facilitate a class discussion for students to share their eamples and definitions. Ask: What is a translation? Answers ma var. A transformation frequentl described as a slide; congruence is maintained, as well as the orientation to the original figure; etc. What is a reflection? Answers ma var. A transformation frequentl described as a flip; congruence is maintained and the orientation is a mirror image; etc. Topics: ATTACHMENTS page 9 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures Transformations Eplore/Eplain Students graph translations and reflections on a coordinate plane. Students name the coordinates of each verte of the figure and image. Students describe transformations b writing mathematical epressions using the -coordinate and -coordinate. Instructional Procedures:. Displa teacher resource: Transformers. Distribute 6 -inch squares of wa paper or patt paper, a red, blue, and black map pencil as well as handout: Transformers to each student. Facilitate a class discussion about problem to discuss translations on the coordinate plane. Ask: If quadrilateral ABCD is an isosceles trapezoid, what would be the coordinates for verte D? Eplain. (The coordinates would be (, 5) because is the same length as and.) What do ou need to do to trapezoid ABCD if ou want to translate it 6 units to the left? (Slide each verte of the trapezoid 6 units to the left horizontall.) What are the coordinates of the translated trapezoid A'B'C'D'? (A'( 4, ); B'(, ); C'(, 4); D'( 4, 5)) How does the length of the corresponding line segments in the original figure and the image of the figure compare? (The line segments are the same length. The size of the trapezoid did not change.) What is the distance between each corresponding verte in the original figure and the image? (6 units) What do ou notice about the - and -coordinates of the image compared to the Notes for Teacher Teacher Resource: Transformers KEY ( per teacher) Teacher Resource: Transformers ( per teacher) Handout: Transformers ( per student) Teacher Resource: Summar of Transformations KEY ( per teacher) Teacher Resource: Summar of Transformations ( per teacher) Handout: Summar of Transformations ( per student) MATERIALS wa paper or patt paper (-inch square) (6 per student) map pencil ( red, blue, black) ( set per student) TEACHER NOTE When a figure is reflected or translated, the new figure is referred to as an image. Additionall, the vertices of the image are now referred to as prime (e.g., Figure ABCD is transformed and is now the image A B C D and described as A prime, B prime, C prime, D prime. ). If the image of a figure is transformed again, the vertices of the new image are referred to as double prime (A B C D ). page 0 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures coordinates of the original figure? (The -coordinates staed the same, but the -coordinates changed. New coordinates = original coordinate 6.) How is the wa ou moved the original figure related to what ou do to the - coordinates of the original figure? (I moved to the left 6 units, so I subtract 6 units from each -coordinate of the original figure.). Using the displaed teacher resource: Transformers, facilitate a class discussion about problem 9 to discuss reflections on the coordinate plane. Ask: If quadrilateral ABCD is an isosceles trapezoid, what would be the coordinates for verte D? Eplain. (The coordinates would be (, 5) because is the same length as and.) What do ou need to do to trapezoid ABCD if ou want to reflect it across the -ais? (Trace the -ais, the -ais, and the original trapezoid on patt paper or wa paper. Flip the patt paper or wa paper over the -ais.) What are the coordinates of the reflected trapezoid A'B'C'D'? (A'(, ); B'( 4, ); C'( 4, 4); D'(, 5)) How does the length of the corresponding line segments in the original figure and the image of the figure compare? (The line segments are the same length. The size of the trapezoid did not change.) What is the distance between each corresponding verte in the original figure and the image in relation to the -ais? (The corresponding vertices are the same distance from the -ais.) What do ou notice about the -coordinates and the -coordinates of the image compared to the coordinates of the original figure? (The -coordinates staed the same, Notes for Teacher TEACHER NOTE When describing the results of a translation or a reflection, students will write a description and a mathematical epression about how the coordinates of the original figure are related to the coordinates of the translated or reflected image. This provides review for writing epressions and equations (e.g., A set of coordinates of the original figure are P(, ); Q(4, ); R(4, 4); and S(, 5). If the figure is translated 6 units to the left, the coordinates of the image arep ( 6, ); Q (4 6, ); R (4 6, 4); S ( 6, 5). The epression that would represent translating a figure in the coordinate plane 6 units to the left ma be represented b the ordered pair ( 6, ). State Resources MTR 6 8: Cop Me if You Can! Transformers. MTR 6 8: Eploring Reflections TEACHER NOTE For handout: Transformers and handout: Summar for Transformations, the notation for the opposite of is written as and the opposite of is written as. Students ma not understand this notation. It is page of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures but the -coordinates changed. New -coordinates are the opposite value of the original - coordinate:.) How is the wa ou reflected the original figure related to what ou do to the - coordinates of the original figure? (We flipped the original figure over the -ais where the - coordinates are opposite the value of the -coordinates on the other side of the -ais.) Notes for Teacher recommended students write opposite of in place of the notation and write opposite of in place of the notation. 4. Place students in pairs. Instruct student pairs to complete the remainder of handout: Transformers. Allow time for students to complete the activit. Monitor and assess students to check for understanding. 5. Displa teacher resource: Summar of Transformations and distribute handout: Summar of Transformations to each student. Facilitate a class discussion to summarize translations and reflections. Ask: What can ou summarize about the -coordinates when ou translate a figure up? (Add the number of units translated up to the original -coordinate.) What can ou summarize about the -coordinates when ou translate a figure down? (Subtract the number of units translated down from the original -coordinate.) What can ou summarize about the -coordinates when ou translate a figure right? (Add the number of units translated right to the original -coordinate.) What can ou summarize about the -coordinates when ou translate a figure left? (Subtract the number of units translated left from the original -coordinate.) What can ou summarize about the -coordinates when ou reflect a figure across the -ais? (Take the opposite of the original -coordinate to get the value of the new -coordinate.) What can ou summarize about the -coordinates when ou reflect a figure across the -ais? (Take the opposite of the original -coordinate to get the value of the new -coordinate.) page of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures Notes for Teacher 4 Topics: Transformations Eplore/Eplain Spiraling Review ATTACHMENTS Students etend knowledge of translations and reflections. Instructional Procedures:. Place students in pairs and distribute the handout: Transformations Practice. Instruct students to complete the handout. Allow time for students to complete the activit. Monitor and assess students checking for understanding. Facilitate small group discussions about translations and reflections, as needed. Ask: Teacher Resource: Transformations Practice KEY ( per teacher) Handout: Transformations Practice ( per student) What happens to the -coordinate when an image is translated up? (Add the number of units the image is translated up to the -coordinate.) What happens to the -coordinate when an image is translated left? (Subtract the number of units the image is translated left from the -coordinate.) What happens to the coordinates when an image is reflected across the -ais? (The - coordinates remain the same and we take the opposite of the -coordinates.) What happens to the coordinates when an image is reflected across the -ais? (The - coordinates remain the same and we take the opposite of the -coordinates.) 5 Topics: page of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Transformations Elaborate Suggested Instructional Procedures Spiraling Review ATTACHMENTS Notes for Teacher Students continue to eplore translations and reflections in real-life problem situations. Instructional Procedures: Teacher Resource: M Own Transformations KEY ( per teacher) Handout: M Own Transformations ( per student). Distribute handout: M Own Transformations to each student. Instruct students to label each ais and quadrant of the coordinate plane, plot 5 points in Quadrant I, connect the points to form a figure, reflect the figure over either ais, and identif the vertices of the image. Allow time for students to complete the activit.. Place students in pairs. Instruct student pairs to echange handout: M Own Transformations with their partner and describe the reflection on their partner s coordinate plane. Allow time for students to complete their descriptions. Monitor and assess students to check for understanding.. Instruct students to repeat this process for translations on page of handout: M Own Transformations. 6 Evaluate Instructional Procedures:. Assess student understanding of related concepts and processes b using the Performance Indicator(s) aligned to this lesson. Performance Indicator(s): MATERIALS math journal ( per student) graph paper ( sheet per student) TEACHER NOTE Graph paper ma be used to help students create a page 4 of 48
Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Suggested Da Suggested Instructional Procedures Grade7 Unit04 PI0 Graph and label a set of ordered pairs of integers that will create a figure on a coordinate plane. Reflect the figure over the horizontal or vertical ais. Graph a translation of the figure. In writing, describe how to locate and name the ordered pairs of the image, and identif the quadrant in which it lies. Sample Performance Indicator: Notes for Teacher coordinate plane to plot points for the Performance Indicator. Given the points A (-, ), B (-5, 6), and C (-6, ), plot and label the points on a coordinate plane. Graph a reflection across the -ais and label the vertices of the image with prime notation. Net, translate the original figure 7 units down and units to the right, and again label the vertices of the image with prime notation. On the coordinate plane, locate and name the ordered pairs of each image, and identif the quadrants in which the lie. Write a journal entr describing how the vertices were transformed in each of the new images. Standard(s): 7.7A, 7.7B, 7.4A ELPS ELPS.c.5B, ELPS.c.5G 04/0/ page 5 of 48
Integers and the Coordinate Plane KEY Unit: 04 Lesson: 0 A Horizontal Ais 0 B. Plot and label the point A to represent the situation a loss of $.. Plot and label the point B to represent the situation an increase of ards. Vertical Ais. Plot and label the point C to represent the situation the diver descended feet below sea level. 4. Plot and label the point D to represent the situation an increase of degrees. D 0 C -ais Quadrant IV (-, +) 9 8 7 Quadrant I (+, +) B 6 5 4 vertical ais A -9-8 -7-6 -5-4 - - origin - 0 - - horizontal ais 4 5 6 7 8 9 -ais C D - -4-5 Quadrant III ( -, -) -6-7 -8 Quadrant IV (+, -) -9 0, TESCCC 08/7/ page of
Integers and the Coordinate Plane Unit: 04 Lesson: 0 Horizontal Ais. Plot and label the point A to represent the situation a loss of $.. Plot and label the point B to represent the situation an increase of ards. Vertical Ais. Plot and label the point C to represent the situation the diver descended feet below sea level. 4. Plot and label the point D to represent the situation an increase of degrees. 9 8 7 6 5 4-9 -8-7 -6-5 -4 - - - 0 4 5 6 7 8 9 - - - -4-5 -6-7 -8-9 0, TESCCC 08/7/ page of
It s a Match KEY Unit: 04 Lesson: 0. Label each quadrant as well as the - and -ais. Take turns reading the coordinates of each ordered pair below and how to plot the ordered pair. The first student will read the coordinates and the second student will give the directions, beginning at the origin, for locating the point on the coordinate plane. Students will alternate reading the coordinates and giving the directions for locating the points. Both students will plot and label the points on the coordinate plane. A ( 9, 8) B (8, 9) C (6, ) D ( 6, ) E ( 6, ) F (0, ) G (, 0) 9 left, 8 up 8 right, 9 down 6 right, up 6 left, up 6 left, down no right, down left, no down -ais A Quadrant II 9 8 7 Quadrant I 6 5 4-9 -8-7 -6 D -5-4 - G - - 0 C 4 5 6 7 8 9 -ais E - - - F -4-5 -6 Quadrant III -7-8 -9 Quadrant IV B 0, TESCCC 08/7/ page of
It s a Match Unit: 04 Lesson: 0. Label each quadrant as well as the - and -ais. Take turns reading the coordinates of each ordered pair below and how to plot the ordered pair. The first student will read the coordinates and the second student will give the directions, beginning at the origin, for locating the point on the coordinate plane. Students will alternate reading the coordinates and giving the directions for locating the points. Both students will plot and label the points on the coordinate plane. A ( 9, 8) B (8, 9) C (6, ) D ( 6, ) E ( 6, ) F (0, ) G (, 0) 9 8 7 6 5 4-9 -8-7 -6-5 -4 - - - 0 4 5 6 7 8 9 - - - -4-5 -6-7 -8-9 0, TESCCC 08/7/ page of
Sherr s Town KEY Unit: 04 Lesson: 0. Sherr s mother asked her to map the places she visits in her town on a coordinate plane. Label the -ais and -ais of the coordinate plane. Plot each point on the coordinate plane with a picture or smbol to represent the places Sherr visits. Create our own ordered pair for a location of our choice. Write the point and location b the blank bullet. Plot and label our point on the coordinate plane. Sherr s home is located at point (5, 7) Sherr s grandma is located at point (, 0) Sherr s school is located at point (-4, 7) Sherr s best friend lives at point (5, 9) The grocer store is at point (-, -8) The movie theater is at point (0, 0) Sherr s aunt lives at point (0, 9 4 ) Sherr s uncle lives at point (-, 0) The park is at (8.5, -4) Answers ma var. -ais 9 8 7 6 5 4-9 -8-7 -6-5 -4 - - - 0 4 5 6 7 8 9 -ais - - - -4-5 -6-7 -8-9 0, TESCCC 08/7/ page of
Sherr s Town Unit: 04 Lesson: 0. Sherr s mother asked her to map the places she visits in her town on a coordinate plane. Label the -ais and -ais of the coordinate plane. Plot each point on the coordinate plane with a picture or smbol to represent the places Sherr visits. Create our own ordered pair for a location of our choice. Write the point and location b the blank bullet. Plot and label our point on the coordinate plane. Sherr s home is located at point (5, 7) Sherr s grandma is located at point (, 0) Sherr s school is located at point (-4, 7) Sherr s best friend lives at point (5, 9) The grocer store is at point (-, -8) The movie theater is at point (0, 0) Sherr s aunt lives at point (0, 9 4 ) Sherr s uncle lives at point (-, 0) The park is at (8.5, -4) 9 8 7 6 5 4-9 -8-7 -6-5 -4 - - - 0 4 5 6 7 8 9 - - - -4-5 -6-7 -8-9 0, TESCCC 08/7/ page of
Transformers KEY Unit: 04 Lesson: 0 For problems and, outline the original figure in blue. Trace the original figure on patt paper or wa paper and translate the original figure. Trace the image of the translation in red.. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, 5 ). Translate trapezoid ABCD 6 units to the left. Label the translated trapezoid A'B'C'D'.. Use the trapezoids in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: D' A' C' B' - - - 0 - - - D A C B Coordinates of Original Figure A(, ) B( 4, ) C( 4, 4) D(, 5) Coordinates of the image A'( 4, ) B'(, ) C'(, 4) D'( 4, 5) (b) How does the length of the corresponding line segments in the original figure and the image compare? The corresponding line segments are the same length. (c) What is the distance between each corresponding verte in the original figure and the image? 6 units. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, 5 ). Translate trapezoid ABCD 5 units down. Label the translated trapezoid A'B'C'D'. 4. Use the trapezoids in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B( 4, ) C( 4, 4) D(, 5) Coordinates of the Image A' (, 4) B' ( 4, ) C' ( 4, ) D' (, 0) (b) How does the length of the corresponding line segments in the original figure and the image compare? The corresponding line segments are the same length. (c) What is the distance between each corresponding verte in the original figure and the image? 5 units 0, TESCCC 08/7/ page of 5
Transformers KEY Unit: 04 Lesson: 0 For problems 5 and 7, outline the original figure in blue. Trace the original figure on patt paper or wa paper and translate the original figure. Trace the image of the translation in red. 5. Rectangle ABCD is shown on the coordinate grid below. Rectangle ABCD is translated 4 units right and units up. 6. Use the rectangles in problem 5 to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A( 5, 5) B(, 5) C(, ) D( 5, ) D A D' C A' B - - - 0 - - - C' B' Coordinates of the Image A'(, ) B'(, ) C'(, 0) D'(, 0) (b) How does the length of the corresponding line segments in the original figure and the image compare? The corresponding line segments are the same length. (c) Write a description and mathematical epression to represent what was done to the coordinates of the original figure. Moved 4 units right and units up. original (, ) image ( + 4, + ) 7. Parallelogram ABCD was translated from Quadrant IV to Quadrant II. A' B' D' C' - - - 0 - - - A B D C 8. Use the parallelograms in problem 7 to answer questions (a) through (c). (a) Write the coordinates of the original figure and image: Coordinates of Original Figure A(, 4) B(, 5) C( 5, 5) D( 4, 4) Coordinates of the Image A'( 5, 4) B'( 4, ) C'(, ) D'(, 4) (b) How does the length of the corresponding line segments in the original figure and the image compare? The corresponding line segments are the same length. (c) What translations were done to the original figure? Write a description and mathematical epression to represent what was done to the coordinates of the original figure. Moved 7 units left and 8 units up original (, ) image ( 7, + 8) 0, TESCCC 08/7/ page of 5
Transformers KEY Unit: 04 Lesson: 0 For problems 9 and, outline the original figure in blue. Trace the -ais and the -ais and the original figure on patt paper or wa paper and reflect the original figure across the indicated ais. Trace the image of the reflection in red. 9. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, 5 ). Reflect trapezoid ABCD across the -ais. Label the reflected trapezoid A'B'C'D'. 0. Use the trapezoids in problem 9 to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: C' B' D' A' - - - 0 - - - D A C B Coordinates of Original Figure A(, ) B( 4, ) C( 4, 4) D(, 5) Coordinates of the Image A'(, ) B'( 4, ) C'( 4, 4) D'(, 5) (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? The corresponding vertices are same distance from the -ais. (c) How are the coordinates of the image related to the coordinates of the original figure? -coordinates are opposite, - coordinates the same. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, 5 ). Reflect trapezoid ABCD across the -ais. Label the reflected trapezoid A'B'C'D'.. Use the trapezoids in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B( 4, ) C( 4, 4) D(, 5) Coordinates of the Image A' (, ) B' ( 4, ) C' ( 4, 4) D' (, 5) (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? The corresponding vertices are same distance from the -ais. (c) How are the coordinates of the image related to the coordinates of the original figure? -coordinates the same, -coordinates are opposite 0, TESCCC 08/7/ page of 5
Transformers KEY Unit: 04 Lesson: 0 For problems and 5, outline the original figure in blue. Trace the -ais and the -ais and the original figure on patt paper or wa paper and reflect the original figure across the indicated ais. Trace the image of the reflection in red.. Rectangle ABCD is shown on the coordinate grid below. Rectangle ABCD is reflected across the -ais. A' B' 4. Use the rectangles in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A( 5, 5) B(, 5) C(, ) D( 5, ) D' C' Coordinates of the Image A'( 5, 5) B'(, 5) C'(, ) D'( 5, ) D A - - - 0 - C B - - (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? The corresponding vertices are same distance from the -ais. (c) How are the coordinates of the image related to the coordinates of the original figure? -coordinates the same, -coordinates are opposite 5. Parallelogram ABCD was reflected from Quadrant IV to Quadrant III. 6. Use the parallelograms in problem 5 to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure C' D' - - - 0 - - A' B' - A B D C A(, 4) B(, 5) C( 5, 5) D( 4, 4) Coordinates of the Image A'(, 4) B'(, 5) C'( 5, 5) D'( 4, 4) (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? The corresponding vertices are same distance from the -ais. (c) How are the coordinates of the image related to the coordinates of the original figure? -coordinates are opposite, - coordinates the same 0, TESCCC 08/7/ page 4 of 5
Transformers KEY Unit: 04 Lesson: 0 Indicate what transformation (translation or reflection) was done to the original figure ( ABC). Write the coordinates beside each verte of the original figure and the image. Write a description to show the relationship between the coordinates of the original figure and the image. 7. Tpe of Transformation: translation 6 units down 8. Tpe of Transformation: reflection across the -ais Relationship between original figure and image: original (, ) image(, 6) 9. Tpe of Transformation: reflection across the -ais Relationship between original figure and image: original figure (, ) image(, opposite of ) 0. Tpe of Transformation: translation 6 units right Relationship between original figure and image: original (, ) image(opposite of, ) Relationship between original figure and image: original (, ) image( + 6, ) 0, TESCCC 08/7/ page 5 of 5
Transformers Unit: 04 Lesson: 0 For problems and, outline the original figure in blue. Trace the original figure on patt paper or wa paper and translate the original figure. Trace the image of the translation in red.. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, ). Translate trapezoid ABCD 6 units to the left. Label the translated trapezoid A'B'C'D'.. Use the trapezoids in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B(, ) C(, ) D(, ) Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) - - - 0 - (b) How does the length of the corresponding line segments in the original figure and the image compare? - - (c) What is the distance between each corresponding verte in the original figure and the image?. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, ). Translate trapezoid ABCD 5 units down. Label the translated trapezoid A'B'C'D'. 4. Use the trapezoids in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B(, ) C(, ) D(, ) - - - 0 - - - Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) (b) How does the length of the corresponding line segments in the original figure and the image compare? (c) What is the distance between each corresponding verte in the original figure and the image? 0, TESCCC 08/7/ page of 5
Transformers Unit: 04 Lesson: 0 For problems 5 and 7, outline the original figure in blue. Trace the original figure on patt paper or wa paper and translate the original figure. Trace the image of the translation in red. 5. Rectangle ABCD is shown on the coordinate grid below. Rectangle ABCD is translated 4 units right and units up. 6. Use the rectangles in problem 5 to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B(, ) C(, ) D(, ) Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) D - - - 0 - C - - (b) How does the length of the corresponding line segments in the original figure and the image compare? (c) Write a description and mathematical epression to represent what was done to the coordinates of the original figure. A B 7. Parallelogram ABCD was translated from Quadrant IV to Quadrant II. 8. Use the parallelograms in problem 7 to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: A' D' Coordinates of Original Figure B' C' - - - 0 - - - A B D C A(, ) B(, ) C(, ) D(, ) Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) (b) How does the length of the corresponding line segments in the original figure and the image compare? (c) What translations were done to the original figure? Write a description and mathematical epression to represent what was done to the coordinates of the original figure. 0, TESCCC 08/7/ page of 5
Transformers Unit: 04 Lesson: 0 For problems 9 and, outline the original figure in blue. Trace the -ais and the -ais and the original figure on patt paper or wa paper and reflect the original figure across the indicated ais. Trace the image of the reflection in red. 9. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, ). Reflect trapezoid ABCD across the -ais. Label the reflected trapezoid A'B'C'D'. 0. Use the trapezoids in problem 9 to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B(, ) C(, ) D(, ) - - - 0 - - - Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? (c) How are the coordinates of the image related to the coordinates of the original figure?. Graph isosceles trapezoid ABCD below: A(, ); B(4, ); C(4, 4); D(, ). Reflect trapezoid ABCD across the -ais. Label the reflected trapezoid A'B'C'D'.. Use the trapezoids in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B(, ) C(, ) D(, ) - - - 0 - - - Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? (c) How are the coordinates of the image related to the coordinates of the original figure? 0, TESCCC 08/7/ page of 5
Transformers Unit: 04 Lesson: 0 For problems and 5, outline the original figure in blue. Trace the -ais and the -ais and the original figure on patt paper or wa paper and reflect the original figure across the indicated ais. Trace the image of the reflection in red.. Rectangle ABCD is shown on the coordinate grid below. Rectangle ABCD is reflected across the -ais. 4. Use the rectangles in problem to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure A(, ) B(, ) C(, ) D(, ) Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) D A - - - 0 - C B - - (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? (c) How are the coordinates of the image related to the coordinates of the original figure? 5. Parallelogram ABCD was reflected from Quadrant IV to Quadrant III. 6. Use the parallelograms in problem 5 to answer questions (a) through (c). (a) Write the coordinates of the original figure and the image: Coordinates of Original Figure C' D' - - - 0 - - A' B' - A B D C A(, ) B(, ) C(, ) D(, ) Coordinates of the Image A'(, ) B'(, ) C'(, ) D'(, ) (b) How is the distance of the vertices from the -ais for the original figure related to the distance of the corresponding vertices for the image? (c) How are the coordinates of the image related to the coordinates of the original figure? 0, TESCCC 08/7/ page 4 of 5
Transformers Unit: 04 Lesson: 0 Indicate what transformation (translation or reflection) was done to the original figure ( ABC). Write the coordinates beside each verte of the original figure and the image. Write a description to show the relationship between the coordinates of the original figure and the image. 7. Tpe of Transformation: A 8. Tpe of Transformation: A B C B C A' - - - 0 - - B' - - - 0 C' - - - - B' C' A' Relationship between original figure and image: 9. Tpe of Transformation: Relationship between original figure and image: 0. Tpe of Transformation: A A' A A' B C C' B' B C B' C' - - - 0 - - - - 0 - - - - - Relationship between original figure and image: Relationship between original figure and image: 0, TESCCC 08/7/ page 5 of 5
Summar of Transformations KEY Unit: 04 Lesson: 0 Use the information ou gathered from the handout: Transformers to respond to questions through 8.. How do the lengths of the corresponding line segments in the original figure and the image compare when a translation or a reflection is done? The length of the lines segments in the original figure and the image are the same length.. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated up? Write an epression using the -coordinate and the - coordinate if the original figure is translated 4 units up. Add the number of units translated up to the -coordinate. Original figure (, ) the image(, + 4). How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated down? Write an epression using the -coordinate and the -coordinate if the original figure is translated 4 units down. Subtract the number of units translated down from the -coordinate. Original figure (, ) the image(, 4) 4. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated left? Write an epression using the -coordinate and the - coordinate if the original figure is translated 4 units left. Subtract the number of units translated left from the -coordinate. Original figure (, ) the image( 4, ) 5. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated right? Write an epression using the -coordinate and the -coordinate if the original figure is translated 4 units right. Add the number of units translated right to the -coordinate. Original figure (, ) the image( + 4, ) 6. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated up and left? Write an epression using the -coordinate and the -coordinate if the original figure is translated 4 units up and 4 units left. Subtract the number of units translated left from the -coordinate. Add the number of units translated up to the -coordinate. Original figure (, ) the image( 4, + 4) 7. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is reflected across the -ais? Write an epression using the -coordinate and the -coordinate of the original figure to represent the ordered pairs of the image. -coordinate stas the same and put the opposite of the -coordinate Original figure (, ) the image(, ) 8. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is reflected across the -ais? Write an epression using the -coordinate and the -coordinate of the original figure to represent the ordered pairs of the image. -coordinate stas the same and put the opposite of the -coordinate Original figure (, ) the image(, ) 0, TESCCC 08/7/ page of
Summar of Transformations KEY Unit: 04 Lesson: 0 Graph each transformation using the original figure ( ABC) with the coordinates A(, ); B(, ); C(, 4) as the vertices. Label the corresponding vertices of the image as A', B', and C'. 9. Translation: 6 units left and unit up. C' C 0. Translation: units right and 5 units down. C B' A' - - - 0 - A B - - - 0 - A B C' - - - - A' B'. Reflection across the -ais.. Reflection across the -ais. C C' C - - - 0 - - A A' B B' B' A' - - - 0 - - A B - - C' 0, TESCCC 08/7/ page of
Summar of Transformations KEY Unit: 04 Lesson: 0 Graph each transformation using the original figure ( ABC) with the coordinates A(, ); B(, ); C(, 4) as the vertices. Label the corresponding vertices of the image as A', B', and C'.. Reflection across the -ais and then the -ais. - - - 0 B' C' A' - - - A A' C B B' First Temporar Reflection C' 4. Reflection across the -ais and then the -ais. First Temporar C' Reflection B' - - - 0 B' C' A' A' - - - A C B 5. Complete the table below using the coordinates from problems 9 through 4. Transformation 9. (a) 6 units left, unit up 0. (b) units right, 5 units down. (c) Reflect across -ais. (d) Reflect across -ais. (e) Reflect across -ais and then -ais 4. (f) Reflect across -ais and then -ais Original Figure Coordinates A(, ) B(, ) C(, 4 ) A(, ) B(, ) C(, 4 ) A(, ) B(, ) C(, 4 ) A(, ) B(, ) C(, 4 ) A(, ) B(, ) C(, 4 ) A(, ) B(, ) C(, 4 ) The Image Coordinates A'( 5, ) B'(, ) C'( 4, 5 ) A'(, 4 ) B'( 5, ) C'( 4, ) A'(, ) B'(, ) C'(, 4 ) A'(, ) B'(, ) C'(, 4 ) A'(, ) A'(, ) B'(, ) B'(, ) C'(, 4 ) C'(, 4 ) A'(, ) A'(, ) B'(, ) B'(, ) C'(, 4 ) C'(, 4 ) Mathematical Epression for Coordinates original image (, ) ( 6, + ) original image (, ) ( +, 5) original image (, ) (, ) original image (, ) (, ) original image (, ) (, ) original image (, ) (, ) 0, TESCCC 08/7/ page of
Summar of Transformations Unit: 04 Lesson: 0 Use the information ou gathered from the handout: Transformers to respond to questions through 8.. How do the lengths of the corresponding line segments in the original figure and the image compare when a translation or a reflection is done?. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated up? Write an epression using the -coordinate and the - coordinate if the original figure is translated 4 units up.. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated down? Write an epression using the -coordinate and the -coordinate if the original figure is translated 4 units down. 4. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated left? Write an epression using the -coordinate and the - coordinate if the original figure is translated 4 units left. 5. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated right? Write an epression using the -coordinate and the -coordinate if the original figure is translated 4 units right. 6. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is translated up and left? Write an epression using the -coordinate and the -coordinate if the original figure is translated 4 units up and 4 units left. 7. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is reflected across the -ais? Write an epression using the -coordinate and the -coordinate of the original figure to represent the ordered pairs of the image. 8. How are the -coordinates and -coordinates of the ordered pairs from the original figure affected when the original figure is reflected across the -ais? Write an epression using the -coordinate and the -coordinate of the original figure to represent the ordered pairs of the image. 0, TESCCC 08/7/ page of