Lesson Title: Volume of Rectangular Prisms with Fractional Side Lengths_Course: CCM-6
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which Mathematical
Practices do you expect students to engage in during the lesson?
6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the
appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge
lengths of the prism. Apply the formulas V=lwh and A=bh to find volumes of right rectangular prisms with fractional
edge lengths in the context of solving real-world and mathematical problems.
MP4: Model with mathematics.
MP5: Use appropriate tools strategically.
MP6: Attend to precision.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
How many
1
units are there in 2 whole units?
3
What suggestions would you make to your relatives who
want to double their volume without compromising too
much space?
ANSWER: 6

What fractional unit could be used to represent 3
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
1
2
units? How many would you need?
POTENTIAL ANSWERS:
1
,7
2



1
, 14
4

1
1
, 21
, 26
6
8

Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? ? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Explain to students: Your relative is building a new storage closet for games and they want help in figuring out
a few things. First, they need to know how much carpet they need to put on the floor of the closet, and second,
they’d like to know how much space they are going to have inside for storage. (Look for evidence of MP4)
The closet is 2
1
1
ft  3 ft and is 6 ft high.
2
2
2. Have students determine the answers to these two questions in cooperative groups of 3-4. As they work
encourage them to create a model of the space to determine the amount of carpet needed and the space that they
will have inside the closet. Rotate between groups monitoring their work asking questions such as those below to

and to probe for understanding.
get them started
How much carpet will they need?
Answer: 35 ½
units2 or 8.75 units2
1
1
½
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Volume of Rectangular Prisms with Fractional Side Lengths_Course: CCM-6
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
(Look for evidence of MP5)
How do you know?
If students explain by using the formula,
ask them to justify by demonstrating the
answer with the other materials available to
them.
How many ½ units are in 1 square unit?
(from previous lesson)
4
2
1
1
2
What is the ratio of ½ units2 to units2?
35 to 8.75 = 4 to 1
How much volume will they have inside the closet?
 420 ½ units3 or 52.5 units3
Answer:
How do you know?
Construct a ½ unit3
What is the ratio of ½ unit3 to unit3?
8 to 1 = 420 to 52.5
Extension:
Will you gain more volume by adding ½ foot to the length of the base, width of the base, or height of
the closet? Does it make a difference? If so, how much volume is gained in each instance?
3. Help students relate the formula for the volume of a rectangular prism to their work: (Look for evidence of MP6)
Area of the Base x height or the number of cubes that fit on the bottom layer x the number of layers
(l  w)  h
NOTE: The formulas for circles and triangles are of less importance then the concept of the area of the base
times the height. What will change is the formula for finding the area of the base.

Ask: If we wanted to find the volume of
Area of the Base x height
how might we go about finding it?
Cylinder
(area of the circle x the height of the cylinder)
Area of the Base x height
Triangular prism
(area of the triangle x the height of the prism)
(  r 2 )  h
(

bh
)h
2
4. Have students complete the Area/Volume Venn diagram

Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Volume of Rectangular Prisms with Fractional Side Lengths_Course: CCM-6
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Students will demonstrate understanding of the relationship between area and volume of figures through a Venn
Diagram activity. Formatively assess their understanding of volume through their responses to questions posed in the
activity and through the modeling they choose to depict their conceptual understanding. Students will be able to
apply this understanding to accurately complete an assignment to determine the volumes of boxes having fractional
side lengths.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
This lesson is written for cooperative teams of 3-4. If your desks are not situated naturally in this way, you will need
to have students move accordingly.

Students have been exposed to the concept of volume 5.MD.3, the units appropriate for volume 5.MD.4, have found
the volume of rectangular prisms with whole number side lengths 5.MD.5, used formulas V  l  w  h and
V  b  h to find the volume of right rectangular prisms, and have found the volume of solid figures with nonoverlapping parts to solve real-world problems. They have multiplied and divided fractions and mixed numbers
5.NF.3-7. We are building off of these concepts as we work through this cluster. This lesson follows the lesson
progression for 6.G.1 in which students explore deeply the relationship betweenthe area of quadrilaterals and
triangles with fractional and whole number side lengths.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Examples of rectangular prisms, cubes of whole
number centimeter or inch side lengths, graph paper,
squares that are the same dimension as the cubes,
examples of cylinders, triangular and other prisms.
6.G.2 Student Homework
6.G.2 Vocabulary Checklist
6.G.2 Venn Diagram
6.G.2 Student Homework
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson objectives
and evidence of success, will you use to reflect on the effectiveness of this lesson?
Have students developed an understanding of volume of rectangular prisms with fractional edge lengths and are they
able to transfer the understanding to independently work through the student resource sheet?
Are there students who need additional support or acceleration of the concepts and if so, how will I adjust instruction
to meet their needs?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.