Mathematics Alignment Lesson

Mathematics Alignment Lesson
Grade 5 Quarter 3 Day 129
Common Core State Standard(s)
5.MD.3 Recognize volume as an attribute
of solid figures and understand concepts
of volume measurement.
Standards for Mathematical Practice
Standard 3: Construct Viable Arguments and
Critique the Reasoning of Others.
Standard 4: Model with Mathematics.
Standard 5: Use Appropriate Tools Strategically.
Standard 6: Attend to Precision.
Materials Needed:
Chart paper
Pop Cubes
Transparency/Blackline Masters“Perspectives of Volume”,“Building
Rectangular Prisms”
Blackline Masters-“Questioning
Volume”, “Volume-A Journal Prompt”
 During group work, listen and record
discussions students are having as they
build prisms.
 Transparency/Blackline “Perspectives
of Volume”
Alignment Lesson
Exploring the Concept of Volume (Day 1 of 3)
Content Note: This unit represents the first time that students begin
exploring the concept of volume. In third grade, students begin working
with area and covering spaces. The concept of volume should be
extended from area with the idea that students are covering an area (the
bottom of cube) with a layer of unit cubes and then adding layers of unit
cubes on top of bottom layer. Students should have ample experiences
with concrete manipulatives before moving to pictorial representations.
This is a 3-day lesson. Please make sure you read all lessons prior to
1. Pose the question, “What is volume?” Ask students to write some
their own ideas in the first column “I THINK volume is…” on
Transparency/Blackline “Perspectives of Volume”. (on their
2. Elicit student responses and write different responses on chart
paper, “I THINK volume is….” (Chart paper is best for this
activity so you can keep displayed and make changes to the list as
you spend time with the concept of volume). At this time, accept
all responses. Let students know that this is not our final
definition, but instead our ideas that we are allowed to make
changes to as we work in the volume unit the next few weeks.
Note: Students’ prior experiences with volume were restricted to
liquid volume.
3. How can we determine the volume of a figure? With today’s
activity, students will investigate what volume is. It is important
that the traditional algorithm is not taught or given first.
Students will spend the next few days exploring volume using
models. In today’s lesson, students will build different prisms
out of cubes and discuss that volume is measured by cubic units.
Bring in a rectangular prism box for use
beginning in Alignment Lesson Day 132
and throughout the volume unit
Blackline Master “Volume-A Journal
Rectangular Prism: a prism with six
rectangular faces
Dimension: length, width or height of a
Volume: the amount of space, measured in
cubic units that a 3-D object occupies
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4. In small groups, students will use pop cubes to create as many
rectangular prisms as they can with a given amount of cubes: 12,
20, 36, and 40. (You may need to review “rectangular prism”
with students. Ask them to identify “rectangular prisms” around
the room. Define “rectangular prism” as a class). Make sure
that each group has plenty of pop cubes to experiment and build.
You may want to assign each group 1 or 2 of the given amount of
cubes (12, 20, 36, or 40) to focus their time on-this will ensure
that each given amount of cubes has the time to be built and may
also help with your pop cube supply. As students are building
their prisms, monitor each group by circulating the room and
posing questions as groups need assistance. Encourage all
students to be a part of the building process. “Is there a different
way you can build a rectangular prism with 36 cubes?” “Have
you built all the possible prisms?” “How are you sure?”
“How does orientation play a role in your construction or
Alignment Lesson
Exploring the Concept of Volume (Day 1 of 3) continued
5. After students have built their prisms, have students record the class findings on
Transparency/Blackline “Building Rectangular Prisms”. Discuss the meaning of dimensions (length,
width, and height). Use one rectangular prism as an example. Ask each student group to share their
prisms. As students share, have a student leader record on a class chart and while each student records
on their own copy.
Teacher Content Note/Background: We often get caught up on which is the length, width, and
height – interchanging the three. When discussing with students, focus on the base of the prism to
identify the length and width and the height is the remaining dimension (see picture below). This will
eliminate misconceptions later when students are asked to find volume of other figures. In later grades,
students will learn the mathematical formula for any prism is V=Bh, where B is the number of cubic
units needed to cover the base and h is the number of layers. For a rectangular prism, the B represents
the base of the prism which is a rectangle; therefore it is length x width. For a triangular prism, the B
represents the base of the prism which is a triangle; therefore, the area of the base is ½bh. (see picture
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Alignment Lesson
Exploring the Concept of Volume (Day 1 of 3) continued
6. After the class chart is complete and the class has discussed all the possible prisms for 12, 20, 36, and
40 cubes, have partner groups discuss and answer the questions on Blackline Master “Questioning
Volume”. (Answers; 1) 8, 2) No, see student response, 3) See student response)
7. Once students have worked with a partner and have had a partner discussion about their prisms, have
the class come back together to have a Math Talk discussion about what they noticed about volume today.
Facilitate class discussion by using Math Talk questions and probes such as:
 Can you repeat what _______just said in your own words?
 Would someone like to add on?
 Do you have another way to explain your thinking?
 Does anyone have the same answer but a different way to explain it?
 Do you agree or disagree with _______ and why?
 Does anyone else have comments or questions for __________?
**At this time, students should be defining volume by the number of cubic units. For example: the
prism built with 36 cubes has a volume of 36 cubic units or 36 u3. Students will work to derive the
formula for volume of any prism during the next two days of alignment lessons.
8. Ask students to complete Transparency/Blackline “Perspectives of Volume” with any information they
discussed today (during small group, partner, and/or whole group Math Talk).
9. As a class, revisit the chart paper from the beginning of class and make any changes needed. Have
students complete Blackline Master “Volume – A Journal Prompt” for homework. In addition, ask
students to bring in a rectangular prism box prior to the lesson on Day 132.
Source: Teacher Created
**Keep a few different rectangular prisms that students built for class models and for demonstration
purposes of future lessons or review.**
Note: This lesson is designed to facilitate the connections of volume and area as well as to determine the
vocabulary associated with volume. This activity allows for students to come to their own conclusions
about volume and allows them to explore dimensions.
Source: Teacher Created
Additional Resource: Classroom Discussions Seeing Math Discourse in Action, Faciliatior’s
Guide with Two DVDs (Each School received a copy of this resource Summer 2012).
Disc 2, Video Clips 8.3a, 8.3b, 8.3c, 8.3d.
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Transparency/Blackline Master
Grade 5
Day 129 Standard 5.MD.3
Perspectives of Volume
I THINK volume is…
Building rectangular prisms gave me the
following ideas about volume….
Drawings/ diagrams of one of my
rectangular prisms I made today with
included dimensions
I am taking away the following NEW
information about volume from today
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Transparency/Blackline Master
Grade 5
Day 129 Standard 5.MD.3
Building Rectangular Prisms
Directions: Use pop cubes to create rectangular prisms. How many
different prisms can you make with these cubes: 12, 20, 36, and 40?
Record the total number of cubes used and the dimension of each prism
you made.
Number of Cubes
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Blackline Master
Grade 5
Day 129 Standard 5.MD.3
Questioning Volume
How many different rectangular prisms can you make with
36 pop cubes? ______
Did each of the rectangular prisms you made with 36
cubes have the same dimensions? __________ Why do you
think this is?
Make some observations about the different prisms you
made. Think about the volume of these figures, the
dimensions and anything else you noticed while building
your rectangular prisms.
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Blackline Master
Grade 5
Day 129 Standard 5.MD.3
Volume- A Journal Prompt
Thinking about your exploration and discussion today in class, how
would you explain what volume is? Write your own thoughts using
pictures, numbers, and/or words. (DO NOT WRITE A BOOK
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Answer Keys & Teacher Guide Grade 5
Day 129 Standard 5.MD.3
Answer Key-Building Rectangular Prisms
Number of Cubes: 12
Number of Cubes: 20
1 x 1 x 12
1 x 1 x 20
1 x 2 x 10
Number of Cubes: 36
Number of Cubes: 40
1 x 1 x 36
1 x 1 x 40
1 x 2 x 18
1 x 2 x 20
1 x 3 x 12
1 x 4 x 10
2 x 2 x 10
Multiplication is commutative. The order of the numbers does not change the overall volume. See
example below - this is the same rectangular prism rotated to different positions. Remember from the
Teacher Note in the lesson that we identify the length and width of the prism by its base (or bottom
layer) and the height is “how many total layers”.
Since all 6 of these combinations are the
same prism (just different orientation), it
only counts as 1 prism, not 6. As
students are building their prisms, you
may need to have discussions about the
significance of the orientation of the
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