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Plane Geometry: Triangles
Triangles are the name of the game in this session! We get triangles when we have a shape with three sides and three angles. We notice triangles in the roof on homes, when we stack things in a pyramid, for cars on a truss bridge, the shape of sails on boats, and when satellites triangulate our position using maps and location information.
Engineers use triangles to figure out force vectors in buildings and how fast rockets are accelerating. Knowing how to handle triangles are 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 the second workbook in addition to having a new in-depth packet that explores triangles in more detail, several games and activities, and a Lab Challenge project!
This session is a continuation from the work we did in the previous session on Angles. We are now going to apply angles to geometric shapes (Triangles) so we can really get good at handling these!
Download your Geometry Workbook #2
We're going to finish working through workbook #2 (this is the same workbook from session #2).
All levels of students will work through Geometry Workbook #2 Constructions Part 2. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key.
Geometry Workbook: Constructions Part 2
This is the second workbook in geometry. I've put together a set of videos that will walk you through selected problems in this workbook, Constructions Part 2. Plan to complete 3-4 pages per day. After you complete the pages, you may check the answer key.
If you've already finished this workbook, start working on Packet #2 in the Intermediate section below.
Math Obstacle Course Challenge #3: Flipper
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.
Angles & Triangles
We are continuing the work we did in our last session on angles by expanding into the world of triangles! An triangle is a figure with three sides and three angles, and it's so important that there is an entire branch of math as well as engineering dedicated to studying them!
Math Activity: Angles & Triangles Reference Book
Let's make a quick-reference book for you to use as you work through the activities and unit study review!
Math Game: Error Analysis (He Said, She Said)
We have two contestants that answer a geometry question - and your job is to figure out who's right and why!
Math Activity: Task Cards
This is a fun way to practice everything we've covered in the past two sessions. Think of this like searching for clues scavenger-hunt style. I help you work through two out of each set of four problems, so you will still have plenty to do, even after watching the video!
Math Review and Unit Test in Angles & Triangles
Once you've completed the entire Packet #2 (Parts 1-2 were covered in the last session, Parts 3-5 covered in this session), it's time to study up for a test! Make sure you also work through several of the activities to help you work through different scenarios so you are comfortable with all of the math concepts we've covered so far.
Math Build: Hexaflexagons
This activity is a great demonstration of geometry in action! My family loves playing with "fiddle toys", and this one is made entirely out of paper. If you color in each side a different color, it will be easier to keep track of that elusive 6th side that baffles everyone until they finally find it!
Math Build: Kaleidocycles
This is a simple (and one of my favorite) math toy you can make out of paper. There are many templates you can find online that have different animals, shapes, characters and designs... just search for the word "kaleidocycle" and you'll find lots to choose from.
Math Challenge Project #3: Truss Bridge Challenge
This is our third 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:
- Popsicle sticks 4 ½ x ⅜” (get a box of about 300), not tongue-depressor size
- Hot glue (low temperature, kid-friendly) with glue sticks
- Bucket (1 or 5 gallon) for loading bridge with weight (we’ll use water)
- Kitchen scale (measuring in grams)
- Bathroom scale (for measuring in pounds or kg)
or use known weights (like a 10 lb bag of flour or 12 lb dumbbell weights…)
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
This session, we are going to join a college-level physics class in studying forces and motion. Each of the labs below are longer, about 45 minutes each, 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.
Bonus Labs in Civil Engineering
Once you've worked through all five videos above in the advanced section, you can attend my sophomore-level university class in civil engineering, where we use algebra and geometry to determine the forces in a loaded truss frame.
The point of sharing these advanced labs with you isn't to rush ahead and make you memorize a lot of advanced skills early, but instead I want you to look for patterns in what we are doing. Where do you notice algebra skills coming in? Where do you see me using geometry?
I want you to notice things like: how we use information about triangles to help us solve for unknown forces in a bridge; how we write equations so it makes the math as easy as possible. Look for the math skills that you know how to do, like dividing by fractions to solve a linear equation, and I'll handle the hard parts. It's like being in a cooking class with a master chef, and noticing just a few things that really make what you're learning about in our classes have meaning.
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 #2 Math Challenge
The answer is drawn in the image below. Both are valid solutions. How did you do this challenge?
