Build a Digital World

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 fo 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.