Finding Volume of Combined Prisms

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SWBAT find interpret diagrams of combined prisms to solve problems about volume.

Big Idea

This lesson provides students with additional support and practice on the challenging task of interpreting diagrams to solve problems.

Warm-Up & Guided Practice

15 minutes

As a warm-up, students are presented with the lesson image.  Students are called up to take turns highlighting edges, faces, and vertices.  Then, students are encouraged to estimate the volume of this shape (assuming each cube represents one cubic unit).

Next, I focus the students attention on one of the cubes.  

How can we determine the volume of this cube?  (L xWxH).

Lets say one edge of the cube measures 3 cm.  What would the volume of this cube be? (27 cubic cm)

How could we then determine the volume of the entire solid? (Find the volume of each prism and then combine them to make the volume of the solid)

I encourage students to label each prism (A, B, C, etc.) to help with their organization.  This strategy will help students as the solve more problems on their own.

Following this warm-up, I present students with today's assignment by projecting this  Screen Shot of Guided Practice on the smart board, because it comes from a problem they struggled with before. I explain to the students that I have designed this lesson because I noticed many students were struggling with making sense of the diagrams when we last worked with volume.  

Note: You many notice the same struggles in your students.  Spending additional time with this critical area is important. Critical Area #3. Developing understanding of volume. Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.

Using interactive modeling, I have the students work through the problem together.  Strategies for organization are shared. Videos of this process are included.

Next, I show the students two examples of the problems they will work on today.  These diagrams are shown from above, a different angle than the other prisms they have worked with. This Screen Shot of Diagram Interpretation demonstrates how I helped the students make sense of the models before asking them to solve the problems on their own.

I also use this time to emphasize the importance of labeling! 

Independent Practice

20 minutes

When presented with diagrams of combined rectangular prisms, students struggle with determining the length, width, and height of the separate prisms.  I create a handout using Common Core Sheets.

I choose this resource because the layers of each prism are shown on each of the diagrams. It also provides a modification option that shows the students the dimensions of each prism more clearly.

To create the handout for this lesson, I combined the modified diagram (example 1) and the lesson modified diagrams (example 2).  Based on evidence collected from previous lessons, I assign students to work with different types of problems.  The end goal is go have all students solving unmodified diagrams of rectangular prisms. 


5 minutes

Students are presented with a diagram of three connected prisms, and a graphic organizer to assist them in finding the volume of each prism in order to determine the total volume.