I am starting this introductory lesson about volume with a probing question. I have found that my students are able to persevere when solving problems if they are familiar with the content. When something is (or seems) entirely knew, they have trouble getting started.
Today, I am asking them to work with 3D shapes and solve problems about volume. This is new. I have students work for 4 minutes completely independently. Then, I pause the students and give them a chance to ask questions. Here, I allow them to ask questions to one another, I take a back seat at this time to let them ask and answer questions to help with something that is new.
Before moving on to the launch, I hear 3 different answers from students, ask them to include their reasoning, and write these on the board. Then, I let the students know the correct answer, but explain that we will find out why throughout the lesson.
To launch this lesson, students will participate in a few activities to activate prior knowledge about three-dimensional shapes.
First, I post a rectangular prism on the board and students are called up to trace various components of the shape and label it using a vocabulary term (face, edge,vertex). When working with shapes, precise language is essential. In order to emphasize this, and encourage students to use the proper terms throughout the lesson, I activate their thinking with this common experience.
Next, I provide groups of students with cubes, each group selects a number card (8, 16, 18, 20, and 30) and the following prompt is posted on the board.
Work together to create a rectangular prism using the number of cubes on your card.
• Record the dimensions of your prism.
• Make 3 or more statements about your prism (record these in your math journal).
• Can you make more than one rectangular prism using the same number of cubes?
After about 10 minutes of exploration, students are asked to leave their prism intact and walk around the room for a quick math museum. Here, students see examples of prisms with various volumes.
Following the math museum walk, students are asked to share the dimensions of one or more of their prisms, these are recorded on the board using a table. As I record these dimensions, I ask students to make observations (I am hoping they will begin to recognize that the dimensions can be multiplied together to find the total number of cubes).
You have been working with volume of rectangular prisms. What is volume? How is it measured? (Call on students to share their thoughts. Remember to give adequate think time.)
Students work with various representations of rectangular prisms to find the volume of each. These representations follow a logical progression:
When finding the volume of rectangular prisms with cubic units drawn, it might be challenging for some students to understand that the image shows only the cubes of 3 surface areas. Rather than finding out down the road which students struggle with this, I encourage all students to check their thinking by building the prism with cubes as well. Having the students build the shape will help them to interpret the visual representation.
Next, students move to finding the volume of a rectangular prism when the dimensions are given, but the cubic units are not shown. Here, students are still encouraged to use the cubes to check their thinking.
Next, students are asked to find the volume of rectangular prisms that are just too large to build. Here, students rely on the experience of building each prism in the previous examples to solve this problem using just the dimensions and the formula for volume.
Finally, students solve problems involving area of a variety of rectangular prisms.
The problems for this handout are taken from the text book. I have chosen to combine lessons in order to increase the rigor by moving students through this progression to the formula in fewer lessons. Following this lesson, students will work on find the volume of irregular shapes (combined rectangular prisms). I will spend additional time working with this, more challenging concept. While working with the more complex concepts this initial understanding is continuously reinforced.
Students revise their thinking about the volume of the cubic watermelons shown at the beginning of class. Revision is a powerful learning tool, so don't skip this step. After our museum walk, and think and share time, it is a powerful opportunity for your students to make meaning of their hard work today.