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Volume 

What is volume and how do we use it? Volume is how much 3D space a shape takes up. We first calculate the area of one of the sides, and then extend this calculation to include the length of the object through multiplication. Volume is absolutely everywhere - every time you fill a bowl, save leftovers from dinner into containers, put toys in a box or drink a glass of water, volume is involved! Let's get really good at calculating volume together.

Students will finish workbook #4 in addition to completing the in-depth packet that explores volume in more detail, enjoy several games and activities that help discover more about these ideas with volume, and complete our last Geometry Lab Challenge project!

Beginner Level Math Class

Download your Geometry Workbook #4

We're going to begin working through workbook #4. All levels of students will work through Geometry Workbook #4: Surface Area & Volume. Plan to complete 2-3 pages per day. After you complete the pages, you may check the answer key. Step-by-step instructional videos coming soon!

Geometry Workbook:  2D & 3D Geometry

This is the fourth 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 #8: 

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.

Intermediate Level Math Class

Part 10: Volume (Parts #1-3)

Volume is the amount of 3D shape a shape takes up, and we have different ways of talking about this space. You'll hear volume referred to as "capacity", "size", or even  incorrectly as "mass", although mass isn't the same as volume. (Mass is the amount of stuff that makes up an object, independent of how much space it takes up.)

For most shapes, the base of a 3D object names the figure, like when we studied prisms and pyramids. Exceptions are shapes with more common names, like cylinders and spheres.

We'll first start with cross-sections, which is the 2D shape you get when you slice a 3D object, like when you cut disks of cookies from a cylindrical log shape. You can get different cross-sectional areas depending on how you cut the cookie roll. Let's get started with cross-sections, and then move into our main volume content. 

Geometry Review: Quiz

Let's review what we've covered so far with a short quiz. (HINT: The quiz is included in Packet: Surface Area on pages 13-14). Take the quiz first, before watching the video below!

Part 10: Volume (Parts #4-5)

Let's finish the packet by looking at applications of volume and composite 3D figures.

Math Activity: Scavenger Hunt

Do you enjoy scavenger hunts? This is a fun version that will help you review and practice your volume calculating skills by solving a set of math puzzles that lead you to the next one (like a treasure hunt).

Math Activity: Card Sort

This is a fun way to practice your cross-sectional area skills with a matching game!

Math Activity: Two Mazes

Let's get lost in a maze while calculating the volume of rectangular prisms!  You can do one or both mazes - it's up to you!

Math Activity: Triangular Prisms Cut & Paste

This is a neat way to continue to work on your skills at being able to calculate volume and missing side lengths of triangular prisms.

Math Activity: Error Analysis

It can be confusing to know who's right! Let's see if we can figure out the right answer using our new math skills. Take your time with this activity, and spend most of your time setting up the problem to figure out exactly what the problem is asking, so you don't get swayed by the wrong answer!

Geometry Review Activity: 28 Stations

We're about to wrap everything up in our study of volume by taking a test, but before we do, this activity is a fun way to review all we've worked on. You don't have to do all 28 stations - pick at least two per page to complete. If you get stuck, the video below will walk you through one problem on each of the seven pages to help get you rolling again.

Volume Review Study Guide & Unit Test

Now that you've finished the packet on volume and completed several hands-on activities that helped you practice your new math skills, let's do a quick review using this study guide (link below). This will get you ready for the test that follows. Be sure to complete the Unit Test FIRST, before watching the Unit Test video below!

Math Challenge Project #7: Lab

You are going to be a field geologist for the day! You'll first attend a two-part Geology class where you'll learn all about minerals, rockets and crystals, and then you'll go outside and explore the rocks where you live (or use your own personal rock collection). Then you'll come back for a class in Volcanoes and Earthquakes, and calculate the epicenter of several different earthquakes from real scientific data using math!

Materials:

• Magnet
• Distilled vinegar
• Nail (the kind made of steel)
• Rocks (6-10 different ones 1-3” long)
• Kitchen scale (measures in grams)
• Clear glass that is okay to scratch (NOT your favorite one)
• Coffee mug (NOT your favorite one) or unglazed size of a white tile
• Glass measuring cup with mL measurements on the side
• White granulated sugar (at least 8 cups)

If you’d like to make the crystals, you can do the Rock Candy crystals or the Borax crystals:

• White granulated sugar (about 10 cups) OR Borax Laundry Whitener
• Wood skewer or pipe cleaners
• Clean, empty glass jar
• Stove with adult help and a pot (don’t mix up borax in your good cookware, get one from a thrift store just for doing kitchen science along with a dedicated spoon)

Optional: (pick one if you’d like to add to your current rock collection!)

• Geology Field Trip in a Bag
• Washing Student Rock Kit

Bonus Rock Hound Labs from Kits

This next part is for students who would like to purchase a rock kit, and would also like step-by-step instruction on how to use the ideas discussed in this lab with the student rock kits we recommend. Start with the first video, and you can progress as your interest in rocks, minerals and crystals grow!

Advanced Level Math Class

During the live class, I did two example problems on how we use area and volume to do real calculations to help us estimate how much ice is on a planet or an asteroid using just a photograph of the object.

Once you've worked through the live class examples, try the labs outlined below. Each of the labs below are in-depth application-based problems like you'd find in 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.

Math Challenge