Explore how dilation and congruence can help you understand the vastness of space by mapping constellations. Through hands-on activities, you'll visualize how stars appear differently based on their positions and distances, connecting mathematical concepts to real-world astronomy. This project encourages critical thinking and problem-solving as you create models and reflect on the learning process, fostering a deeper understanding of both math and the universe.
Learning goals
Explore how dilation can alter the appearance of constellations by creating a scale model that demonstrates their positions from various perspectives. Understand and describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Develop self-directed learning skills through reflection and peer feedback, enhancing your ability to monitor and guide your own learning process. Engage in critical thinking and problem-solving by applying mathematical concepts to real-world contexts, such as mapping stars.
Standards
[Common Core] CCSS.Math.Content.8.G.A.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
[Common Core] CCSS.Math.Content.8.G.A.4 - Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
[California] 8.G.A.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
[California] 8.G.A.4 - Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Competencies
Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.
Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.
Products
Create a scale model of a constellation using glow-in-the-dark stickers on a black poster board. Demonstrate how dilation affects the appearance of stars from different vantage points. Facilitate a gallery walk where you can view and provide feedback on each other's constellation models, discussing the impact of dilation and congruence on the representations.
Launch
Begin by dimming the classroom lights and projecting an image of a starry night sky onto the ceiling. Use a laser pointer to trace constellations, discussing how their shapes change with perspective. Encourage you to imagine you're an astronomer mapping the stars, setting the stage for creating a scale model of a constellation. This immersive experience will spark curiosity and set the tone for exploring dilations and congruence in the context of outer space.
Exhibition
Facilitate a gallery walk where you display your constellation scale models on the classroom walls. Use glow-in-the-dark stickers to highlight each constellation's unique pattern and discuss how dilation affects their appearance from different perspectives. Invite peers to provide feedback on your model and share reflections on the challenges and successes of the project. Consider incorporating a brief presentation where you explain your process and the scientific concepts behind the constellations' relative positions in space.
