Transformations, Congruence, and Symmetry

At the completion of this unit, students will be able to:

1. Use coordinates to describe a translation of a figure.
2. Use coordinates to describe a reflection and rotation of a figure.
3. Determine whether a pair of congruent figures are related by a transformation, reflection, rotation, or some combination of the three.
4. Explore figures that have symmetry and rotational symmetry.
5. Use a variety of objects to solve problems.

Yes

Students will be assessed:

1. Using the 19-1 Translations Quick Check and Practice worksheets to show that the student is able to use coordinates to describe and sketch a translation of a figure.
2. Using the 19-2 Reflections and 19-3 Rotations Quick Check and Practice worksheets to show that the student can use coordinates to describe and sketch a reflection and rotation of a figure.
3. Using the 19-4 Congruence Quick Check and Practice worksheets to show that the student is able to determine whether a pair of congruent figures are related by a transformation, reflection, rotation, or some combinations of the three.
4. Using the 19-5 Symmetry Quick Check and Practice worksheets to show that the student is able to explore figures that have line symmetry and rotational symmetry.
5. Using the 19-6 Problem Solving: Use Objects Quick Check and Practice worksheets to show that the student can use a variet of objects to solve problems.
6. Using the Topic 19 Transformations, Congruence, and Symmetry Multiple Choice Exam and Free-Response Exam to show the student can:
   • Identify and draw a translation. (Questions 1, 6) (Questions 2, 4, 7-8, 12)
   • Identify and draw a reflection and rotation. (Questions 2, 4, 7) (Questions 1,3, 6, 5, 9-10, 11)
   • Identify transformations and congruent figures. (Questions 5, 7, 9) (Questions 13-15)
   • Identify symmetry. (Questions 8, 10) (Question 16)
   • Use objects to solve problems. (Question 3) (Question 17)
7. Using the Topic 19 Perfomance Assessment to assess the students' understanding of the concepts and skills, regarding coordinates and transformations, through a performance-based task.  

80%

During whole group instruction, students will:

1. Take notes from the SMART Board, follow along as the teacher reviews vocabulary words, works example problems, working out the problems on their slates, and then work guided practice questions on translations, pages 464-465 student edition.  The students will also use Teaching Tool 16 (First-Quadrant Grid) to plot a point, then move the point four units to the right and record the new coordinates.  They have just made a translation. 
2. Take notes from the SMART Board, follow along as the teacher introduces vocabulary words, works example problems, working out the problems on their slates, and then work practice questions on reflections and rotations, pages 468-471 of the student edition.  The students will work in pairs, using Teaching Tool 16 (First-Quadrant Grid), to experiment, draw and describe reflections and rotations. 
3. Take notes from the SMART Board, follow along as the teacher introduces new vocabulary, works example problems, working out the problems on their slates, and then work practice problems on pages 472-473 of the student edition.  The students will also work in pairs, using Teaching Tool 12 (Centimeter Grid Paper), to draw a triangle; then they will translate, rotate, or reflect the triangle.  Next, they will pass their papers to the left within their group.  Each student will tell what was done to the triangle on the paper that was passed to them.  Then they will repeat the activity twice more.  Last, they will answer the questions, 1. What have you noticed about the size and shape of the triangle throughout the actitivity?  2. What can you say about triangles whose size and shape are the same? 
4. Take notes from the SMART Board, follow along as the teacher introduces vocabulary, works example problems, working out the problems on their slates, and then work practice problems on symmetry, pages 474-475 student edition.  The students will be given index cards.  The teacher will instruct them to make a simple shape out of the card.  Next, they will use the shape to make a design with two lines of symmetry.  Then they will explain and share their shapes, designs, and how they used their shape.
5. Take notes from the SMART Board, follow along as the teacher introduces vocabulary, works example problems, working out the problems on their slates, and then work practice problems on using objects to solve problems.  Students will work in pairs, using colored shape tiles, to see how many different shapes they can make with different given numbers of tiles.  Each pair will draw and record their shapes.  Then the class will discuss how it is sometimes easier to use objects, rather than drawing pictures, to solve and break down problems. 

During independent work time, students will complete the:

1. 19-1 Translations Quick Check and Practice worksheet.
2. 19-2 Reflections and 19-3 Rotations Quick Check and Practice worksheet.
3. 19-4 Congruence Quick Check and Practice worksheet.
4. 19-5 Symmetry Quick Check and Practice worksheet.
5. 19-6 Problem Solving: Using Objects Quick Check and Practice worksheet.

 

During whole group instruction, the teacher will:

1. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples, introduce vocabulary and provide guided practice problems, providing assistance and feedback as needed on using coordinates to describe and sketch a translation of a figure.
2. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples, introduce vocabulary and provide guided practice problems, providing assistance and feedback as needed on using coordinates to describe and sketch a reflection and rotation of a figure.
3. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples, introduce new vocabulary and provide guided practice problems, providing assistance and feedback as needed on determining whether a pair of congruent figures are related by a transformation, reflection, rotation, or a combination of the three.
4. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples, introduce vocabulary and provide guided practice problems, providing assistance and feedback as needed on exploring and finding figures that have a line of symmetry and rotational symmetry.
5. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples, introduce new vocabulary and provide guided practice problems, providing assistance and feedback as needed on using a variety of objects to solve problems.

While the students complete individual assignments, the teacher will monitor and observe students, giving assistance as needed. 

Scott Foresman enVision Math Series (Teacher and Student)
www.pearsonsuccess.net
SmartBoard
Student Slates/markers
Student Laptops with Internet Connection
Geometric Shape Manipulatives
Index Cards and Scissors
Pull-in Resources (Math Websites)

enVision Math Reteaching Material
Pull-in Resources if needed.

enVision Math Enrichment Activities/Materials
Center Activities

Teacher will make necessary accommodations and modifications for students as needed.