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Plane Geometry: Rectangles, Parallelograms, Triangles, Trapezoids and Composite Figures

Plane Geometry is the study of two dimensional shapes and figures, and how they relate to each other. This is a large area of geometry, so we'll be spending extra time getting to know triangles and trapezoids, rectangles and parallelograms, circles and squares, and their infinite combinations! 

Engineers use composite figures to do their analysis, which means that they break down complex shapes into more manageable pieces, like triangles and quadrilaterals. Knowing how to handle each of these shapes is one of the most important skills we will learn in math, especially if you want to become an engineer.

Students will continue to work through their workbook in addition to their in-depth packet that explores geometry in more detail, several games and activities, and a Lab Challenge project!

Beginner Level Math Class

We're going to explore different geometry skills in our workbooks. We'll continue to practice with concept and word problems and have fun learning!

Download your Geometry Workbook #3

We're going to begin working through workbook #3 (this is the last workbook in the series).

All levels of students will work through Geometry Workbook #3: Plane Geometry. Plan to complete 2-3 pages per day. After you complete the pages, you may check the answer key. 

Geometry Workbook:  Plane Geometry

This is the third workbook in geometry. I've put together a set of videos that will walk you through selected problems in this workbook. Plan to complete 2-3 pages per day. After you complete the pages, you may check the answer key.

If you've already finished this workbook, start working on the Packet in the Intermediate section below.

Math Obstacle Course Challenge #5: Magic Dollar

During the live class, near the end of the beginner session, we had a special challenge.  Stay tuned during class for instructions for the challenge! This is announced at the end of the Math Lesson: Beginner: Day 1 video. Can you figure out how this works? What happens if you use more than one rubber band, or more than two paperclips?

Intermediate Level Math Class

Are you ready to really practice your new math skills? Let's get really good at geometry by doing several different activities and games as we are figuring out solutions!

Part 3: Area of Rectangles & Parallelograms

The first set of quadrilaterals we are going to study are rectangles (and squares) and parallelograms! These are fun and easy to work through so let's get started.

Part 4: Area of Triangles and Trapezoids

The next set of figures we are going to study are combinations of rectangles and triangles called trapezoids. These are fun and easy to work through so let's get started.

Part 5: Composite Figures

Most shapes in the real world are not perfect circles, squares, rectangles, triangles or even trapezoids. However, we can usually estimate shapes in the real world by breaking them into smaller, more recognizable shapes that are easier to work with. Composite shapes are figures made up of two or more simpler shapes. We're going to do a lot of examples and activities to pull all of these ideas together!

Part 6: Problem Solving with Composite Figures

Let's practice using composite figures in real life!

Math Game: Corridor Strategy Game

This is a fun game of strategy called Quoridor by Mirko Marchesi where players take turns advancing their pawn or setting up blocks (that look like mazes) for their opponent. If you enjoy this game, feel free to get a copy of the wood version to add to your game collection!

Math Build: Fold a Cube

Being able to visualize the flat form on a 3D shape is a skill we're going to learn and practice quite a bit! This is a fun introduction to the idea of "nets" which are the 2D flat form that can be folded into a 3D shape.

Math Challenge Project #5: Spacecraft Lab

This is our fifth challenge project! The purpose of these projects is to connect the math work we do in geometry with practical applications in science and engineering. You will need materials if you want to build these projects. These projects are designed to encourage kids to think about the challenge and come up with their on unique solutions!

Materials needed:

• Paper or foam cups (8+)
• Paper or foam plates (5+)
• Index cards (10+), any size
• String or yarn
• Aluminum foil or plastic wrap
• Small plastic figures (2cm), like plastic animals or LEGO minifigures or similar
• Scissors and tape
• Paper clips (10)
• Rubber bands
• Hair dryer
• Kitchen scale (measure mass in grams)
• Thermometer (you’ll be measuring the candy and the outside air temperature once per minute)
• Unwrapped chocolate candy (small or mini size) without nuts (nuts interfere with heat test)
• Bendable plastic straws or similar (watch video to see what you have that will work as a substitute, there’s a lot of wiggle room with this part)
• Choose up to three: construction paper, electrical tape, cotton balls, bubble wrap, spackling compound, foam material (packing peanuts, plates or trays), or cardboard scraps

Advanced Level Math Class

We are going to do an in-depth study of how astronomy uses geometry to determine how many solar panels we'll need on our satellites to power our instruments, how big the newly discovered ring around Saturn really is, how to plan a launch window to another planet (so we don't miss it!), designing mechanical arms on a mars lander and see what it's like on planets that are really different from our own.

Treat these labs like a real college-level class. First, take out your math journal to take notes as we go along. Write down the problems as I work them out so you have your own copy in your math journal. As you write, look for patterns: where are we using algebra? How are we using geometry to model the real world problem down on paper?

Math Challenge

Each session, I have a special Math Challenge for you to work on after you work through some of the content in this area of math. The goal for these special math challenges is for you to be able to communicate your great ideas with your family and friends, without them being in a math class or having any knowledge of a specific area of math. You should be able to convey your great ideas to most people that are interested in hearing what you have to share. Many families find this part of the math program exciting for them to participate in with their student!

Solution to Geometry Session #4 Math Challenge

Two. A quick experiment will show that the complete revolution of the moving penny adds an extra rotation.

Solution to Session #4 Circle Escape Room

Download the answer key below. If you are the teacher, confirm that the completion code matches the code the students show you for "breaking out" of their math escape room!