Lesson 3: Transformations

COURSE/LEVEL: 8th grade math

TOPIC: Transformations

GOAL OF LESSON: This lesson would be an introduction to a transformations unit, so I just want the students to get familiar with what transformations are and how shapes move under each kind of transformation.

INSTRUCTIONAL OBJECTIVES: Students Will Be Able To (SWBAT):

Understand the meaning of the word transformation.
Understand what happens to a shape under each kind of transformation.
Start to manipulate shapes when prompted to reflect or rotate them.

NY State Standards for Mathematics:

8.PS.1 Use a variety of strategies to understand new mathematical content and to develop more efficient methods.
8.PS.4 Observe patterns and formulate generalizations.
8.CM.4 Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models and symbols in written and verbal form.
8.CM.10 Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale.
8.CM.11 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing.
8.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations.
8.G.7 Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations).
8.G.8 Draw (for this lesson just visualize with the digital resource) the image of a figure under rotations of 90 and 180 degrees.
8.G.9 Draw (same as above) the image of a figure under a reflection over a given line.

NCTM Standards:

Standard 2: Mathematics as Communication: In grades 5-8, the study of mathematics should include opportunities to communicate so that students can:
- model situations using oral, written, concrete, pictorial, graphical, and algebraic methods.
Standard 4: Mathematical Connections: In grades 5-8, the mathematics curriculum should include the investigation of mathematical connections so that students can:
- explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations.
Standard 8: Patterns and Functions: In grades 5-8, the mathematics curriculum should include explorations of patterns and functions so that students can:
- describe and represent relationships with tables, graphs, and rules.
Standard 12: Geometry: In grades 5-8, the mathematics curriculum should include the study of the geometry of one, two, and three dimensions in a variety of situations so that students can:
- explore transformations of geometric figures.
- represent and solve problems using geometric models.
- understand and apply geometric properties and relationships.

ISTE NETS-S Standards:

1. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
c. Use models and simulations to explore complex systems and issues.
3. Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
a. Plan strategies to guide inquiry.

b. Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
6. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems, and operations.
a. Understand and use technology systems.

b. Select and use applications effectively and productively.

MATERIALS:

Notebooks/Pens/Pencils
Whiteboard w/markers and eraser (if no SMART Board).
Computer with Internet access hooked up to an overhead projector/SMART board.

RATIONALE: The NYS Mathematics Standards state that students should use a variety of strategies to understand new mathematical content, and using a digital resource like the one in this lesson will provide them with a new strategy to understand the new concepts of rotations and reflections. Students will be observing the patterns of objects that are reflected and rotated and noticing how shapes generally move under these transformations. Students will be manipulating objects through the transformations digital resource and learning the new vocabulary of transformations, reflections, and rotations. The ISTE NETS-S state that students should use models and simulations, and the digital resource in this lesson is just that. Students will be using technology and using the application effectively and productively to gain a basic understanding of reflections and rotations in the plane.

PROCEDURES:

Introduction:

1. Tell students that we are going to learn about something that might be only vaguely familiar to them today: transformations in the coordinate plane. We will be focusing on two transformations today: reflections and rotations.
2. Ask if anyone can think of a simple word that means the same thing as “reflect.” (Call on a student – they might know the word “flip.” If no one knows it after calling on a few students and letting them pause for thought, give hints like starting to pronounce the “f,” then say the whole word if they still do not remember.) Give them something to remember this by: flip starts with an “f” and reflect has an “f” in it. Have them write the two words attached like a crossword so that "reflect" goes across, and "flip" goes down, attached to "reflect" by the "f."
3. Ask if anyone can think of a simple word that means the same thing as “rotate.” (Same procedure as above, they should say “spin,” or “turn.”) Again, turn starts with a “t,” and rotate has a “t” in it. Have them write the words in their notebooks again like a crossword so that "rotate" goes across, and "turn" goes down, attached to "rotate" by the "t."

Presentation:

4. Using a projected vertical line (either on the SMART Board, computer projector, or I have even done this with a “dinosaur” projector and transparency sheets) take a triangle (virtual or paper depending on the technology available) and place it on the right hand side of the line. Ask the students to call out as a class where they think the triangle will go if you reflect it over the line. When they call out that it should flip to the left hand side, move the triangle to that position. Repeat this moving in the opposite direction (start on the left) and with a horizontal line. Also try different shapes like rectangles and trapezoids.
5. Go through the same procedure with rotations. This time use two perpendicular lines (an x and y axis, but with no numbers or grid lines). Put a point at the intersection (the origin) to be your point of rotation. Go through the degrees of rotation with the students:
¼ = 90°

½ = 180°

¾ = 270°

1 whole = 360°

Explain to the students that rotations always go counter clockwise if the problem does not specify. Sometimes problems will ask them to rotate counterclockwise, sometimes they will ask them to rotate clockwise. However if it does not say either, it is assumed to be counterclockwise.
6. Now put the shapes (one at a time) on your axes in quadrant I and ask students where it should go under a ¼ or 90° rotation. Do the same for other rotations and shapes.

Application:

7. Tell the students they are going to use our website to complete their homework assignment tonight. Tell them they will go to our site and click the “Homework Assignments” tab and read the directions under the “Homework Assignment 3” bullet. They will play the transtar game and then write a paragraph (using mathematical language – i.e. Rotate, reflect) about how they got the transtars to go through the stargates.

ASSESSMENT: I will check each student’s written paragraph that they email to me for homework.

ASSIGNMENT: Students will play with a transformation game at home: Transformation tool found at: http://www.mangahigh.com/en_us/games/transtar. They will write a short paragraph explaining what they did during the game to get the transtar shapes to rotate or reflect onto the stargate during the game.

Other tools that can be used later in the unit:

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