Transformations: Translation Written by: Coryn Wilson Warren, Ohio

Instructor Notes Subject Area(s): Math – Geometry and Spatial Sense Grade level: 8 Lesson Length: about 40 minutes Synopsis: This lesson begins with an introduction/pre-assessment of a unit on transformations. After the pre-assessment it concentrates specifically on translations. This PowerPoint is meant to be used along with classroom notes. Objective/goals: Students will be able to translate a point and a figure on the coordinate plane. Students will also be able to write a rule for a given translation.

Instructor Notes Standards: Students will draw the results of translations, reflections, rotations, and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g. lengths of sides remain the same under translations Pre-requisite skills: Students must know how to plot points and determine ordered pairs of points within a Cartesian graph. TurningPoint functions: Standard question slides Materials: Classroom notes handout (attached), Mathematics Course 3 (Prentice Hall) *Instructional delivery notes can be found in the notes section of the slide.

References Initial PowerPoint found online at the link www.tech.ccps.org/downloads/Symmetry,%20Rotation,%20Translation,%20Reflection.ppt Charles, R., Branch-Boyd, J., Illingworth, M., & Mills, D. (2004). Mathematics Course 3. Upper Saddle River, New Jersey: Pearson Prentice Hall.

Translation Symmetry Rotation Reflection Dilation

Let’s see how much you remember about these terms. The next few slides will have questions for you to answer based on what you remember about these concepts. Just do your best to remember, this is not for a grade…yet.

is an example of… Rotation Translation Reflection Dilation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

This is an example of a … Rotation Translation Reflection Dilation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

This is an example of a … Rotation Translation Dilation Symmetry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

How many lines of symmetry does the letter X have? 1 2 3 4 none 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

This is an example of a… Rotation Reflection Translation Dilation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Let’s check how you did! Press F12

Transformation A change in the position, size or shape of a figure. Picture taken from Prentice Hall, Mathematics Course 3

Image The figure that you get after a transformation. Picture taken from Prentice Hall, Mathematics Course 3

The action of sliding a figure in any direction. Translation (Slide) The action of sliding a figure in any direction.

Click the Octagon to see Translation. The act of sliding a figure in any direction.

Ex.1: Translating a Point Translate point B(2,-1) up three units and to the right 4 units. What are the coordinates of its image, B’? Have students complete additional problems from your math text or supplementary resources. Picture taken from Prentice Hall, Mathematics Course 3 The coordinates of B’ are (6, 2)

Ex.2: Translating a Figure Translate ΔDEF to the right 6 units and down 3 units. Have students complete additional problems from your math text or supplementary resources. Picture taken from Prentice Hall, Mathematics Course 3

Ex.3: Describing a Translation Write a rule to describe the translation from the black triangle to the blue triangle. Each point has moved 4 units to the right and 2 units down. How does this move affect each x-coordinate and y-coordinate? Picture taken from Prentice Hall, Mathematics Course 3

Describing a Translation Use arrow notation to write a rule for a translation Have students complete additional problems from your math text or supplementary resources. The rule is: (x, y)→(x + 4, y – 2) Picture taken from Prentice Hall, Mathematics Course 3

Independent Practice Check Your Understanding! Try completing some problems on your own. Ask me for help if you get stuck! Then compare your answers to the overhead. Have students complete additional problems from your math text or supplementary resources.

Let’s see what you learned! Closure Let’s see what you learned!

A synonym for the word translation is… Flip Slide Change Shrink 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 :10 Answer Now

All of the following properties of a figure remain the same when a translation is performed except? The length of the sides The shape of the figure The coordinates of the vertex points The number of lines of symmetry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 :10 Answer Now

Point A(-3, 6) is translated left 2 units and down 2 units Point A(-3, 6) is translated left 2 units and down 2 units. What are the coordinates of the image after the translation? A’(-1, 4) A’(-1, 8) A’(-5, 8) A’(-5, 4) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 :10 Answer Now