6th Grade Unit 5: Transformations

Unit Driving Question

How can transformations be applied to real-world situations?

Essential Questions

1. How do transformations affect two-dimensional figures?

2. How can transformations be used to show two-dimensional figures are congruent?

3. How can transformations be used to find lines of symmetry?

Big Ideas

1. Translations, reflections, and rotations can be used to transform a two-dimensional figure.
2. Translations, reflections, and rotations preserve congruency and reflections can be used to find lines of symmetry for a two-dimensional figure.

Useful Websites

The following apps, websites, and smartboard lessons can be used throughout the unit, as needed, during small groups, lessons, to reinforce standards.  They are also useful for students who may need reinforcement, remediation, or differentiation.

1. Virtual Nerd: Virtual Nerd provides video tutorials as a supplemental resource for both students and teachers.

2. Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard so that students may study at their own pace both in and outside of the classroom.

3. Mr.Naussbaum.com: MrNussbaum.com offers interactive games specifically designed to pinpoint one or several essential concepts to make the learning process more interactive and enjoyable.

4. Interactive Sites for Education: These interactive activities work great on your interactive whiteboard, computer, laptop, or Chromebook for whole group or small group instruction or use in the computer lab or at home for individual learning. Most of these activities are Flash-based.  This means that they will NOT work on iPads unless you are running an app that allows Flash to play such as Puffin.  

5. Kahoot: Kahoots are fun, learning games best played in a group setting.  Players answer questions on individual devices (Ex: Chromebook, iPads) while games are displayed on a shared screen (Ex: Smartboard or TV).  Choose a Kahoot to match your desired skill or create your own.

6. Zapzapmath: Zapzapmath has over 150 math lessons designed to incorporate higher order thinking skills in the fields of creation, evaluation, and analysis. This is combined into a game-based system of fun math learning.

7. Mr.Anker Tests: Interactive activities and games for dozens of math skills.  Most of these activities run on Flash.

Launch Task

1 Lesson

• Introduction to Reflections, Translations, and Rotations (Georgia Frameworks): Students investigate reflections, translations, and rotations using applets from the National Library of Virtual Manipulatives.

Big Ideas for Development Lessons

2-3 Weeks (approximately 1 week per big idea)

Big Idea 1: Translations, reflections, and rotations can be used to transform a two-dimensional figure.

Key Resources

1. Naming the Moves (Open Up): In the activity, students complete a card sort to identify translations, reflections, and rotations.  The Cool-Down asks students to identify the transformation for a given figure.

2. Reflecting Reflections (Illustrative Mathematics): In this task, students are asked to reflect a triangle over two lines on a coordinate plane.  The students are also asked what transformation can be used to map the preimage onto the final image formed after the second reflection.

3. Transformations (Open Middle): In the first Open Middle task, students are asked to list three sequences of transformations that take the given pre-image to the image.  The second task has students determine the shortest sequence of transformations needed to take the given pre-image to the image.
4. Transformations (GeoGebra): This applet allows students to investigate how figures can be transformed using translations, reflections, and rotations.

5. Transforming Shapes Collection (Desmos): 

   These activities are designed for students who are studying congruence and transformations of geometric figures in the plane.

Big Idea Probe

• Transformation Probe

Evidence of Understanding 

Recognize and perform translations, reflections, and rotations for two-dimensional figures.

• Predict how translations, reflections, and rotations will transform a two-dimensional figure.

• Use physical models, such as pattern blocks, or graphical models on a coordinate plane, to perform transformations on a two-dimensional figure. The focus should not be placed on how the ordered pairs change when transforming the figure. Instead, use the unit squares of the coordinate plane to transform the figure. For example, when reflecting a figure across the y-axis, determine how far away from the y-axis the figure is by counting the unit squares and create its reflection by counting the same number of unit squares on the opposite side of the y-axis.

• Demonstrate that certain transformations can be obtained using different transformation or a combination of transformations.

Describe a transformation of a two-dimensional figure transformed using translations, reflections, rotations or a combination of these transformations.

• Identify transformations using correct vocabulary: translation, reflection, rotation.

• Discuss the differences between translations, reflections, and rotations.

Big Idea 2: Translations, reflections, and rotations preserve congruency and reflections can be used to find lines of symmetry for a two-dimensional figure.

Key Resources

1. Congruent Polygons (Open Up): In the Warm-Up, students identify triangles that have been translated using tracing paper.  Activity 1 asks students to identify congruent polygons using transformations.  In Activity 2, students take turns explaining to a partner why or why not a pair of polygons are congruent.  Activity 3 has students build quadrilaterals using objects such as toothpicks and pencils and determine if they are congruent using objects such as toothpicks and pencils.  In the Cool-Down, students identify which transformations are needed to prove the given polygons are congruent.

2. Congruence (Open Up): In the Warm-Up, students identify corresponding points for the given trapezoids that are not vertices.  In Activity 1, students determine whether or not the given ovals are congruent using a coordinate plane. Activity 2 provides students with two congruent figures and asks students to determine the lengths of line segments in the figure to show that corresponding line segments of congruent figures have equal lengths.  Activity 3 is an optional activity included in this lesson in which students determine if the two faces shown on a coordinate plane are congruent.  The Cool-Down asks students to determine if the two given ovals are congruent.

3. Finding Lines of Symmetry (Illuminations): In this lesson, students investigate lines of symmetry using geoboards.

    

Big Idea Probe

• Congruency & Lines of Symmetry Probe

Evidence of Understanding

Recognize when two-dimensional figures are congruent.

• Show and describe why translations, reflections, and rotations preserve congruency.

• Use the distance between vertical or horizontal ordered pairs to justify why figures are congruent.

• Prove two-dimensional figures are congruent using translations reflections and rotations.

Identify lines of symmetry for two-dimensional figures.

• Use tools, such as mirrors, to prove a line is a line of symmetry for a two-dimensional figure.

• Describe examples and non-examples of lines of symmetry using correct vocabulary: reflection, vertical, horizontal, diagonal.

•  Explore patterns that may arise from lines of symmetry. (Ex. The number of lines of symmetry will increase by one for a regular polygon as the number of sides increase by one.) 

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment) 

•  Tessellate This (Open Up): In this lesson, students make tessellations and have classmates identify transformations that can be used to create their tessellations.