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Plane Geometry: Circles
Circles are figures with no line segments and no vertices, which makes them pretty unique. We're explore radius, diameter, circumference and area and the relationship between each of these so it's easy for you to calculate the things you need accurately.
We use circles when we calculate surface area, volume, or take cross sections of objects, so before we dive into those areas, we have to really explore circles to get a good understanding of this unique figure.
Every time you drill a hole, bounce a ball, ride a roller coaster or drive down the freeway, circles are involved. Astronomers use circles and ellipses to describe the motion of planets, stars, and comets. Engineers use circles in their technical drawings for gears, tires, wheels and showing how holes line up when bolting plates together; circles are used to ensure they have large enough diameter pipe for the water flow; and so much more! Mechanical engineers use circles to calculate the different speed each car tire makes when taking a left turn.
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!
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 just 4 pages for this session, as we are only working with circles. 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 just four pages this week. 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 #4: Stepping through Paper
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.
Plane Geometry: Sessions #4: Circles
Imagine a flat piece of paper that stretches out as far as you can see in all directions. That's a plane! We're going to spend time learning all about the figures and flat shapes that we can draw on this infinitely wide and infinitely long piece of paper.
In this session, we'll start learning about the properties of circles including circumference, diameter and area! Next session we'll move into area of rectangles and parallelograms, triangles, trapezoids and composite figures Packet #4 Parts 3-6). In our final session, we'll look at similar figures (Packet #4 Parts 7-8).
Part 1: Circles & Circumference
Circles are shapes with no line segments and no vertices. They have special properties that relate their perimeter, called the circumference, with their width, called the diameter. Let's explore circles together with this fun set of class work, homework and activities!
Part 2: Area of a Circle
The area of a circle is used all over science and engineering! Let's get really good at being able to calculate area and knowing when to use which equation for each situation.
Math Build: Möbius Puzzle
This seems almost too simple to be a puzzle, but the result will leave your audience scratching their heads while trying to figure out what happened! Do this yourself first and see if you can figure it out on your own, and then test it out on your audience after dinner. Guaranteed to be a conversation-starter!
Bonus: Escape Room in Circles!
Practice your skills with calculating the area and circumference of circles with this fun escape room activity! Students will receive a completion code after the last level to show to the teacher that they have broken out.
Answer key is published in following Session near the bottom of the page.
Math Challenge Project #4: Forest Ranger Lab
This is our fourth 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:
- Wood broom stick handle or long dowel (1” diameter, 3-4 feet long)
- Measuring tape
- Straw (paper or plastic)
- String
- Pushpins (tacks), 2
- Pennies or small coins (at least 10)
Below are two options for printing. The "NO PICTURES" is printer-friendly and does not include the color photograph instructions of the lab.
Advanced Level Math Class
We are going to do an in-depth study of how astronomy uses geometry to determine the size changes of stars, how fast planets move, and how we hunt for Earth-like planets outside our solar system! 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 #3 Math Challenge
The answer is shown in the video below for the Impossible Flap.
