SWBAT understand the relationships between the volumes of cylinders, cones, and spheres.

Through hands-on exploration, students develop and test hypotheses about the volume relationships among these related solids.

8 minutes

For today's Warm Up assignment, I wanted to review key vocabulary. Although students have likely encountered these words previously in their coursework, I wanted to ensure that students had a common understanding. By drawing each of the shapes, students can connect the word to its physical shape. I also included the vocabulary 'radius' and 'diameter' as these words will come into play later in the unit when we make sense of the volume formulas.

- Quantum of Solids Day 1 Notebook.pdf (Notebook PDF file)
- Quantum of Solids.notebook (Smart Notebook file)

1 minutes

After verifying students' responses to the Warm Up assignment, I introduce today's Learning Objective: Students will understand the relationships between the volumes of cylinders, spheres, and cones.

I entertain a brief conversation about volume to activate students' prior knowledge. I then move quickly to introduce today's Work Time activity.

12 minutes

During Work Time Part 1, students will work with their partners to complete the Solids Exploration Lab using a tub of colored rice*, hollow geometric solids (which I purchased from EAI for about $14 a set), and a ruler.

For the first part of the lab, students must predict and order the volumes of the cylinder, cone, and sphere. Then, they must test their prediction using a method of their choice. I intentionally do not give student measuring cups so that they are forced to consider the volumes in relation to the other solids. Once students begin to discover these relationships (for example, the volume of a cone is half that of a sphere and one-third that of a cylinder), I ask them to record those relationships on their lab sheet. Once the Work Time timer sounds, I bring the class attention to the SmartBoard to build consensus.

*Colored rice is a wonderful manipulative for exploring volume. It can be easily created and it lasts for years. It is also easy for students to sweep up if they create a mess while working!

8 minutes

To build consensus from Work Time, Part I, I ask students to tell me the order of volumes from greatest to least. I then ask for students to contribute to a list of relationships that they discovered between the volumes of shapes. If no one volunteers a relationship involving a fraction, I ask for one. In this way, I am leading to conceptual understanding of the volume formula in the subsequent lesson. I want students to be able to think and work flexibly with fractions during this unit.

9 minutes

For Work Time Part 2, I want students to analyze the attributes of the solids. This, too, will help students make sense of the volume formulas we will learn in the subsequent lesson.

Because some students may not have much experience with Venn diagrams, I ask for a volunteer to give me an attribute of a cylinder. I then ask where I would write that attribute in the Venn diagram. This is typically enough to get students started. I encourage students to find at least one attribute for each section of the diagram.

When the timer sounds after 9 minutes, I call the class together to build consensus.

5 minutes

With the assistance of the class, I fill in the Venn diagram, asking for specific evidence when it is volunteered. Sometimes, I must ask guiding questions to help students along like, "What shape do you get if you sliced through the center of a cylinder and a sphere?" so that each section of the Venn diagram has an attribute.

2 minutes

To consolidate student thinking, I explain that I want them to spend the last two minutes explaining at least one thing they learned from the day's lab, one minute for each partner.

Previous Lesson