Objective: 

Students will explore the properties of rotations, reflections, and translations by using physical models to represent congruent shapes in multiple ways. They will connect their findings to how computers represent data in various forms, from low-level binary to visual models.

Materials Needed: 

• Transparencies

• Graph paper

• Geometry tools (rulers, protractors)

• Printed shapes

• Markers

• Scissors

Steps:

• Introduction: 

  • Students review congruent shapes and the properties that define congruence, such as equal side lengths and angles. 

  • Discuss the concept that data, like these shapes, can be represented in multiple ways. 

  • In this activity, students will use physical models to represent congruent figures and explore how computers translate data from low-level binary (0s and 1s) to understandable formats like images or charts.

• Group Activity: 

  • Students work in pairs, using transparencies and graph paper to represent transformations (rotations, reflections, translations). 

  • Each group will start with a printed shape, use scissors to cut it out, and then represent the same data (shape) in different ways: 1) the original on graph paper, 2) the shape rotated on a transparency, and 3) the shape reflected on another transparency. 

  • Each transformation will be discussed, emphasizing that while the representation (position or orientation) changes, the shape’s congruence remains unchanged.

• Discussion: 

  • After the activity, lead a class discussion on how different representations of the same data (shapes) retain their essential properties, much like how computers translate the same data into multiple forms (e.g., a number, a visual, or binary code). 

  • Relate this to the importance of understanding how data transformations maintain integrity across different formats.

Equity and Access: 

Provide pre-cut shapes for students who need additional support and pair students with varying strengths in geometry to ensure peer collaboration.

Real-World Application: 

Relate this activity to how digital graphics work, where shapes can be rotated, reflected, or translated on a screen, but their original data (size and structure) remains unchanged.

CS Practice(s):

• Developing and Using Abstractions: Students represent congruent shapes through physical transformations, linking this concept to how computers store and display data in different formats.

• Communicating about Computing: Students explain how the transformations they performed maintain the congruence of the shapes, similar to how data can be represented differently while preserving its original meaning.

Standard(s):

• CA CCSS Mathematics 8.G.2

• CA CCSS Mathematics 8.G.3

• CA CS 6-8.DA.8

Objective: 

Students will use GeoGebra to explore transformations (rotations, reflections, translations) and dilations, observing how data (two-dimensional figures) can be represented in different forms. They will connect this to how computers store and manipulate data, representing it in multiple ways.

Materials Needed: 

• Computers with GeoGebra installed or access to an online version

Steps:

• Introduction: 

  • Start with a quick review of transformations (rotations, reflections, translations) and introduce dilations. 

  • Explain that today, students will use GeoGebra to apply these transformations to geometric shapes. Additionally, they will explore how computers handle and represent this data in different ways. 

  • Use the example of how the same geometric shape can be represented as a set of coordinates, a graph, or a visual image.

• Coding Activity: 

  • Each student will open GeoGebra and input a simple two-dimensional shape (e.g., a triangle or square). They will apply rotations, reflections, translations, and dilations, observing how the shape changes visually on the screen. 

  • As they work, students will toggle between the different representations provided by GeoGebra—coordinates of vertices, equations of lines, and the visual display of the shape—seeing how the same data (the shape) can be represented differently.

• Discussion: 

  • After completing their transformations, students will share their screens and discuss how GeoGebra represents their shapes in multiple forms. 

  • Facilitate a discussion on how this process mirrors how computers store data in binary but present it in various human-readable forms, such as images or graphs. 

  • Relate this to data representation in computer graphics and other fields.

Equity and Access: 

Provide step-by-step instructions for students new to GeoGebra and pair students with varying levels of experience to encourage collaboration.

Real-World Application: 

Discuss how digital design tools and software rely on multiple forms of data representation, such as converting an image to pixel coordinates or binary code, while maintaining the core properties of the image or shape.

CS Practice(s):

• Developing and Using Abstractions: Students use GeoGebra to manipulate and represent geometric shapes, observing how the same data (the shape) can be expressed as coordinates, visual graphs, or equations, just like how computers handle and store data in different formats.

• Communicating about Computing: Students explain how their transformations and representations in GeoGebra connect to the way computers manage and present data.

Standard(s):

• CA CCSS Mathematics 8.G.2

• CA CCSS Mathematics 8.G.3

• CA CS 6-8.DA.8