This lesson begins with a wide-open problem solving challenge. Students are given a shape, represented in a drawing, and asked to determine the volume.
Students can use a variety of methods to figure this problem out.
My purpose in giving this to students as a warm up is to evaluate their previous knowledge on the topic of volume.
I love using food in my classroom for experiments, and hands-on activities. In this lesson, I've used mini marshmallows. Using the marshmallows, the students need to create cubes and rectangular prisms of set sizes. If I have them create a 36 marshmallow cube, they can see that the entire thing gets filled it. It is 36 cubic units. We then count the marshmallows on the length, the width, and the height. We multiply the dimensions together, and you get 36 cubic units!
I guide students in determining how many unit cubes will fit inside of 3 x 2 x 1 units. First, students draw a unit (cubed) cube. I emphasize that we are counting cubes and not faces of cubes. I highlight and color in each cube as we count how many fit into the box. I think this is an important visual step that helps students make meaning, as well as holding their attention.
Next, I guide students in diagramming a centimeter cube that will hold water. Students are presented with a real world situation of removing cubes from a plastic box and wanting to fill that box with water.
What's Step 1? Find the volume of the plastic box in cubic centimeters. In Step 1, it is very important to show students that we are looking at each layer of cubes separately. Then, Step 2: Find the liquid of the plastic box in milliliters. On to Step 3: Determine whether the water will fit in the plastic box. As we work through each step, the process is modeled as a think-aloud.
To differentiate, I noticed that some students needed a bit more remediation in building the shapes and drawing, so we use a different kind of paper.
Using MP3, students worked in Think-Pair-Shares to accomplish this task. Students had to draw diagrams to determine the answer.
Paulina and Jackson are measuring the volume of the same box using unit cubes. Paulina can fit 9 unit cubes inside the box without any gaps or overlaps. Jackson can fit 16 unit cubes inside the box without any gaps or overlaps. Is it possible that they are using unit cubes of the same size? Explain your thinking.
To close out the lesson, students worked with a partner to determine which box held each missing present. Students determined the volume of each present, and match it to the key.