After our right triangles unit, we move on to our volume unit. This unit usually goes pretty quickly for us. The process is simple – just apply the formula. Read on to see how I use a Geometry Interactive Notebook to teach Volume.
Geometry Interactive Notebook Formula Reference Sheets
Before we even begin the unit, we add two reference sheets to our notebook. The first one is for area and perimeter formulas for two-dimensional shapes. I include everything students need to know for rectangles, squares, triangles, and circles. My students do not have to find the area for trapezoids or regular polygons. The second reference sheet is a copy of the same one students will get when we take our state exam. On this page, we highlight all of the formulas we use.
Area & Perimeter Interactive Notebook Page
To start our unit, we review area and perimeter. We find perimeter and/or area of the different shapes. When working with circles, we make sure to note the difference between rounding and expressing answers in terms of pi. We also make sure that we know to find the right angle in a triangle to identify the base and the height of a triangle.
Then, we move on to some word problems. The word problems I include in our class notes are from past state exams. Also, I make sure to include the formula for population density. Our state exam loves to ask questions about population density. We only spend one day on two-dimensional shapes. The real focus of our unit is three-dimensional shapes.
Solids Notes & Activity
Our introduction to three-dimensional solids is brief. We discuss the difference between polyhedra and non-polyhedra, and then we dive right in to rotating two-dimensional shapes to produce three-dimensional shapes. This is very difficult for students to visualize, so I always show them this video. After the video, students are able to answer the practice questions.
Next, we shift our focus to finding two-dimensional shapes within three-dimensional shapes. We define cross-sections, and discuss the different cross-sections of a cube. Again, students may struggle to visualize this. One of my favorite activities we do every year in Geometry is finding cross-sections of solids with Play-Doh. I give every group a container of Play-Doh and fishing line. Students create shapes with the Play-Doh, and then use the fishing line to cut the shape. Then, they look at the surface they cut to determine the shape of the cross-section.
Geometry Interactive Notebook: Prisms & Pyramids
To help simplify the content, I like to teach prisms and pyramids on the same day. Since their volume formulas are almost the same, I want my students to lump prisms and pyramids together mentally.
We start with prisms. Students find the formula for prisms (and pyramids) tricky because it is dynamic. They have a hard time remembering that the B in the formula for base AREA rather than just a base number. For a straight forward problem, we find the area of the base first, then substitute that number for B. Unfortunately, we cannot do this all the time. If we are solving for a variable, then we need to substitute a formula. We practice this concept with a few problems.
Then, we move on to pyramids. We compare pyramids to prisms, and note that the pyramids come to a point to explain the one-third. The rest of the lesson we practice applying the formula.
Cylinders and Cones Interactive Notebook Pages
Much like the prisms and pyramids, we learn about cylinders and cones on the same day. Students are much more comfortable with cylinders and cones because their volume formulas do not change from problem to problem. After discussing each formula, comparing cylinders to cones, and understanding the need to use one-third for cones, we complete practice examples.
Spheres Geometry Interactive Notebook
By the time we reach spheres, students are confident. Typically, on this day we have our unit quiz, and when students finish early, they complete the notes on their own. Once all students finish the quiz, we go over the notes together, and most students only need to check their work. After completing notes for the five three-dimensional solids, we have a practice day to get comfortable with applying the volume formulas in different situations. This year we tried an escape room.
Cavalieri’s Principle
For this lesson, I keep it brief. Actually, I include this as a mini-lesson when we are working on prisms. Using a past state exam question, we consider if two prisms have the same volume. Using Cavalieri’s Principle, we note that prisms in the example have the same height, and check to see if the bases have the same area. We simplify the principle to “same base area + same height = same volume.”
Similar Solids Lesson
For our last lesson of the unit, students start the left side of the notes as their warm up. They are asked to consider the ratio of similar figures, find their perimeter and area, and compare the resulting perimeters and areas to determine their ratios. Students repeat the process with similar solids to determine a ratio of their volumes. Then, we summarize what they figured out about the ratios, and complete some practice examples.
Geometry Interactive Notebook: Volume Resources
Are you looking for materials to teach this unit? Look no further! All of the pages you see in my Geometry Interactive Notebook: Volume are now available. Prior to uploading these pages for your use, I taught each lesson as described above. Some of the pages may not look exactly as they do in this post because they have all been edited and updated. Additionally, I separated all five three-dimensional shapes for teachers that like to teach different shapes together. (Previously, I used to teach prisms and cylinders together (with Cavalieri’s Principle) and pyramids and cones together.). Also, a full answer key for each page is included.
New for this unit, I created lesson videos for finding the volume of prisms, pyramids, cylinders, cones, and spheres. You can share them with your students as an additional resource, especially if you are implementing distance learning.
- Volume of Prisms Video
- Volume of Pyramids Video
- Volume of Cylinders Video
- Volume of Cones Video
- Volume of Spheres Video
If you would like to stay up to date with which videos are available, subscribe to my new YouTube channel.
Looking for more resources? Check out my interactive notebook resources page!
