Build a Digital World

You have inherited a big plot of land! It is up to you and your peers to bring it back to life!

Introduction

This math cycle will guide students through the process of designing and programming a virtual world using geometry and computer science principles. Each part will introduce new geometry concepts and computational thinking skills, culminating in a final interactive digital environment.

Across three parts of this cycle, you’ll use geometry skills to plot out a town with your team, apply transformations to create building layouts, and calculate 3D volume to design specific areas of your choice. By the end, you’ll have created a full-color blueprint and 3D model of a section of the town that you will then integrate with your class. Along with a complete plan with calculations and written explanations that show your mathematical thinking, you will build your own digital world!

Essential Questions

• What are the key relationships between a circle's radius, diameter, circumference, and area?
• How do angle relationships help solve problems in geometric figures?
• How is the Pythagorean Theorem used to calculate distances in two-dimensional space?
• How can triangles be classified and constructed using their side lengths or angles?
• How is the Distance Formula derived, and how is it applied to solve problems in the coordinate plane?
• How is volume calculated?
• How are dilations performed and described?
• What is the scale factor, and how is it calculated?
• What are similar figures, and how are they identified?
• What are congruent figures?
• How are figures transformed in the coordinate plane?
• How can 2D and 3D Geometry be applied to real-life problems and situations?

Learning Objectives

• Calculate missing measurements of circles, including radius, diameter, circumference, and area.
• Use algebraic equations to represent and solve for values in geometric figures.
• Identify and draw unique triangles based on side lengths or angles.
• Solve problems using the Pythagorean Theorem, including those involving the distance between two points.
• Apply geometric formulas to solve real-world problems involving circles, triangles, and distances in the coordinate plane.
• Calculate scale factor and describe dilations of figures.
• Perform dilations on figures.
• Identify similar figures.
• Graph points and polygons on a coordinate plane.
• Apply transformations to figures on the coordinate plane.
• Identify congruent figures.
• Calculate missing measurements in congruent figures.
• Calculate volumes of 3D shapes.
• Calculate missing dimensions on 2D and 3D shapes.