# 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.