Math Lesson Plan: Alternative Ways of Calculating Volume

This is a lesson plan on alternative ways of calculating volume. This lesson plan should be taught after students have learned the traditional method of calculating volume, at least for rectangular solids and cubes. This lesson plan will show students there is usually more than one way to find the answer to a question.

Students should also know the names of several geometric shapes. For a lesson plan on 3d geometric shapes, go here.

Lesson Topic: Alternative Ways of Calculating Volume
Grade Level: 3

Goals, Objectives, and Standards

Instructional Goals: The goal is to help children understand the concept of volume.

Specific objectives:

Cognitive Domain: Students will learn three different ways to calculate volume.

Affective Domain: Students will learn to share with each other and how to work in groups.

Psychomotor Domain: Students will develop their psychomotor domain through the use of tools for measurement. Students will learn that there is usually more than one way of finding a solution to a problem.

Rationale

Students learned briefly in yesterday’s lesson how to find the volume of a cube by using the length times width times height formula. In this lesson they will learn two more ways they can find the volume of an object.

Procedure

Brief Content Outline: Students will find the volume of various cubes and rectangular solids by the graduated cylinder method as well as the overflow cup method. They will then check their answers by measuring the length, width, and height of those shapes. They will also find the volume of other 3d shapes by the first two methods.

Introduction: Ask students, “Do you remember the 3d shapes we’ve been working with? Do you remember how we learned how to calculate volume? Well today we’re going to learn how to calculate the volume in different ways.”

Initiating Activity: Show students the graduated cylinder. Ask if anyone knows what it is. Now have someone come up to the front of the class, where you’ll have set up a small cup, a pitcher of water, a funnel, and a graduated cylinder. Ask the student how they think we can tell how much water fits in the cup. Say, “That is called the volume. Volume can also be thought of as how much space is inside an object. Since we can’t measure air…we fill the cup with water so we can measure the water.” Have the student fill the cup with water. Ensure that the cup is full, then have the student put the funnel in the cylinder and pour the water from the cup into the graduated cylinder. Ask if anyone knows why we had to use a funnel. (Because we’re pouring water from a big cup into a smaller space; the funnel ensures that no water spills.) Have another student come up to read the measurement. Have them give their answer, then show the class how, when reading a graduated cylinder, the water line isn’t straight, it’s curved. Tell students: “In this case, we read the number from the bottom of the curved water line, which is known as the ‘meniscus’.” Record the number shown and explain that this number represents the cup’s volume.

Lesson Development: Pass out the same materials to each group of students (about 3-4 students in a group). Instead of a cup, however, give each student a cube or rectangular solid that has one of its faces removed (so they can fill it with water).

Ask students to find the volume of their shape by the method you just showed them at the beginning of class.

After each group has found the volume and written it down, pass out rulers. Have them measure the length, width, and height of their shape. Finally, tell them to find out the volume of their shape by multiplying the length, width, and height. Now ask them to compare the two results they’ve gotten.

Now tell them we are going to learn one more way to find the volume. Pass out 3d shapes to each group, such as pyramids, spheres, and cylinders. Pass out “overflow cups”…cups that have a spout near the top so displaced water can drip out.

Have students fill the cup with water. Have them hold their graduated cylinder next to the spout to catch the displaced water. Then ask them to slowly lower their shape into the water, carefully letting go of the shape at the end so that their fingers don’t touch the water. Ask if anyone knows why letting their fingers go inside the water would skew the results. Have them record their answers.

Conclusion: Ask students which way they liked best for calculating the volume.

Assignments

Students’ assignment is to go home and use an overflow cup and graduated cylinder to measure the volume of 2 objects in their house. Have them choose one object, any shape, any size (as long as it fits inside the overflow cup) and measure its volume using the overflow method. Then have them choose a cup or any object that can be filled with water. Have them fill it with water and measure the volume by pouring the water into the graduated cylinder.

Materials and Equipment

A small plastic cup, and enough of each of the following items so each group has one: Funnels, graduated cylinders, pitchers of water, overflow cups, rulers, cubes and rectangular solids, and various 3d shapes.

Assessment

Assess students’ understanding by observing their interactions with their group as they do group work, as well as their participation in class, and finally by checking their take-home assignment.


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