Transformation+In+Geometry

Created by : Ms. Strachan Aim: Identifying and describing transformation Strandards: 8.G7, 8. PS.3, 8.CM.10, 8.G.10, 8.PS.6, 8.CM.4, 8.R.11 Materials: Graph paper, and crayons Website Link: http://www.nylearns.org/FileDownloader.aspx?FID=92841-Definiation http://www.nylearns.org/FileDownloader.aspx?FID=92842- Worksheet http://nlvm.usu.edu/en/nav/category_g_3_t_3.html- Interactive website

Powerpoint Presentation: Support Material: Worksheet, Impact 8th Grade, AWSF- Addison Wesley Scott Foresman Grade level: 8th Time Frame: 60 min, 2 days Students will be able to: • Rotate a geometric figure. • Reflect a figure over a line of symmetry. • Translate a figure by sliding it to a different location. • Use dilation by enlarging or reducing the size of a figure without changing its form or shape.

Launch: • Explain to students the activity for the day • Review the definition using website links • Explain to students with examples the following: - In a translation a figure slides up or down, or left or right. No change in shape or size. The location changes. All x and y coordinates of a translated figure change by adding or subtracting.

- In a reflection, a mirror image of the figure is formed across a line called a line of symmetry. No change in size. The orientation of the shape changes. A reflection across the x -axis changes the sign of the y coordinate. A reflection across the y-axis changes the sign of the x-coordinate.

- In a rotation, figure turns around a fixed point, such as the origin. No change in shape, but the orientation and location change. - Rules for rotating a figure about the origin - Rules for 90 degrees rotation- Switch the coordination of each point. Then change the sign of the y coordinate. Ex. A (2,1) to A’ ( 1,-2) - Rotation of 90 degrees counter clockwise- Switch the coordinates of each point. Then change the sign of the x- coordinate. Ex. B (3,1) to B’ (-1,3) - Rotation of 180 degrees- Change the sign of both the x coordinate and the y coordinate. Ex. C (4, 5) ,to C’(-4,-5)

- In dilation, a figure is enlarged or reduced proportionally. No change in shape, but unlike other transformation, the size changes. In dilation all coordinates are divided or multiplied by the same number to find the coordinates of the image.

Explore • Have the students complete the following example in pairs: Rotation practice. Rotate trapezoid ABC D clockwise 90 degrees and 270 degrees and give the vertex coordinates for each. Use the following coordinate A ( 2, 1), B (2,3), C ( 0,4), D (0,0). What is the new coordinate for prime one ABCD at 90 degrees? Prime two ABCD at 270 degrees? • Have the students complete the following: Reflection practice. Triangle ABC has coordinate A (3,5), B (6,1), and C (1,2). Reflect triangle ABC across the x- axis and determine the coordinate of triangle A’B’C’. Set up model on the board so students can see how the rules applies. Triangle ABC RULE (x, -y) Triangle A’B’C’ A (3,5) (3, -5) A’ (3,-5) B ( 6,1) (6,-1) B’ (6,-1) • Now have the students plot and reflect the following STUV across the y-axis. S (-2,4), T (-1, 2), U(-3,0), and V (-4, 2). What do you notice about the x coordinates? S’T’U’V’ x- coordinates are positive.

• Review assignment and have the students complete the following independently. Have the students complete the following: Dilation practice. Use a scale factor of 2 to dilate triangle ABC. Give the coordinates of the dilation. Triangle ABC RULE (2 * x, 2* y) Triangle A’B’C’ A (2,1) (2*2, 2*1) A’ (4,2) B (2,4) C(4,3)

• Use a scale factor to 1/3 to dilate KLMN. Give the coordinates of the new vertices that correspond to KLMN.

KLMN (1/3 *x, 1/3 *y) K’L’M’N’ K(-6,6) (1/3 * -6, 1/3 *6) K’ (-2,2) L M N

• Have the students complete the following. Translation practice. The vertices of a triangle are A ( 2,5), B(4,2), and C(0,2). Give the vertices of triangle ABC translated to the right 4 units and up 2. - On the x- axis, “right “ is a positive direction, so add 4 to each x coordinated. - On the y- axis, “up” is a positive direction, so add 2 to each y-coordinate. Locate points A,B,C and draw triangle ABC.

Triangle A BC RULE (x+4, y+2) Triangle A’B’C’

A (2,5) (2+4, 5+2) A’ (6,7) B (4,2) C (0,2)

Discussion: • Describe how a figure’s coordinate change after the figure is translated to the left on a coordinate grid. • Before drawing a dilation, how can you tell whether it will be an enlargement or a reduction? • How can we summarize the rules that we’ve learnt today?

Homework: Give assignments related to the lesson of the day.

Differentiated Instruction • Interactive lesson: http://nlvm.usu.edu/en/nav/category_g_3_t_3.html- • Grade 8-AWSF pg. 65- Extended response question nstructions: • Suggested HW: Grade 8th- AWSF pgs. 220- 222. Examples. 2 –4, Try it. Excerise 1-7.

Day 2 • Problem of the day: AWSF- Grade 8 pg. 228 short response and extended response pg. 228 pg. 233- extended response pg.227 and 229-232 of Grade 8th. • Suggested Homework pg. 233, pg. 242-244, Impact text pg. 331 problem set A, pg. 338 # 12, 18-20.

Related Standards

Content Strand MST3.08.GE8: Geometry Students will identify and justify geometric relationships, formally and informally. Students will apply transformations and symmetry to analyze problem solving situations. Students will apply coordinate geometry to analyze problem solving situations. Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.

Ms. Strachan School Name Name Class Date

Identifying and Describing Transformation Worksheet

In a translation a figure slides up or down, or left or right. No change in shape or size. The location changes. All x and y coordinates of a translated figure change by adding or subtracting.

 The vertices of a triangle are A ( 2,5), B(4,2), and C(0,2). Give the vertices of triangle ABC translated to the right 4 units and up 2. - On the x- axis, “right “ is a positive direction, so add 4 to each x coordinated. - On the y- axis, “up” is a positive direction, so add 2 to each y-coordinate. Locate points A,B,C and draw triangle ABC.

Triangle A BC RULE (x+4, y+2) Triangle A’B’C’

A (2,5) (2+4, 5+2) A’ (6,7) B (4,2) C (0,2)

In a reflection, a mirror image of the figure is formed across a line called a line of symmetry. No change in size. The orientation of the shape changes. A reflection across the x -axis changes the sign of the y coordinate. A reflection across the y-axis changes the sign of the x-coordinate.

 Triangle ABC has coordinate A (3,5), B (6,1), and C (1,2). Reflect triangle ABC across the x- axis and determine the coordinate of triangle A’B’C’. . Triangle ABC RULE (x, -y) Triangle A’B’C’ A (3,5) (3, -5) A’ (3,-5) B ( 6,1) (6,-1) B’ (6,-1) -Reflect the following STUV across the y-axis. S (-2,4), T (-1, 2), U(-3,0), and V (-4, 2). What do you notice about the x coordinates?

In a rotation, figure turns around a fixed point, such as the origin. No change in shape, but the orientation and location change. - Rules for rotating a figure about the origin - Rules for 90 degrees rotation- Switch the coordination of each point. Then change the sign of the y coordinate. Ex. A (2,1) to A’ ( 1,-2) - Rotation of 90 degrees counter clockwise- Switch the coordinates of each point. Then change the sign of the x- coordinate. Ex. B (3,1) to B’ (-1,3) - Rotation of 180 degrees- Change the sign of both the x coordinate and the y coordinate. Ex. C (4, 5) ,to C’(-4,-5)

 Rotate trapezoid ABC D clockwise 90 degrees and 270 degrees and give the vertex coordinates for each. Use the following coordinate A ( 2, 1), B (2,3), C ( 0,4), D (0,0). What is the new coordinate for prime one ABCD at 90 degrees? Prime two ABCD at 270 degrees?

In dilation, a figure is enlarged or reduced proportionally. No change in shape, but unlike other transformation, the size changes. In dilation all coordinates are divided or multiplied by the same number to find the coordinates of the image.

 Use a scale factor of 2 to dilate triangle ABC. Give the coordinates of the dilation. Triangle ABC RULE (2 * x, 2* y) Triangle A’B’C’ A (2,1) (2*2, 2*1) A’ (4,2) B (2,4) C(4,3)

• Use a scale factor to 1/3 to dilate KLMN. Give the coordinates of the new vertices that correspond to KLMN.

KLMN (1/3 *x, 1/3 *y) K’L’M’N’ K(-6,6) (1/3 * -6, 1/3 *6) K’ (-2,2) L M N