Mini Lesson: Volume & Capacity
Created by Hailey Yan & Brie MacDonald
Grade 6
Intended length: 50 minutes
Introduction
The concepts of capacity and volume are addressed throughout all the grades in geometry, building
on understanding of the properties and attributes of shapes and space. This mini lesson
demonstrates two potential ways students can explore capacity and volume using both physical and
digital manipulatives.
Guiding Questions
● How do different shaped objects vary in their capacity?
● What attributes of 3D objects affect their capacity and volume?
● What are potential strategies for finding the volume of 3D objects?
● What is the rule for finding the volume of 3D objects, and how can this rule be expressed in
equation form?
Learning Objectives
At the end of this lesson, students will be able to:
– Compare and describe the different capacities between different 3D objects (cube, cylinder,
etc)
– Compare and describe the different capacities between different sizes of the same 3D object.
– Explain and demonstrate the rule for determining the volume of a 3D object.
Curricular Connections
Big Ideas:
● Properties of objects and shapes can be described, measured, and compared using volume,
area, perimeter, and angles.
Curricular Competencies:
● Estimate reasonably
● Use tools or technology to explore and create patterns and relationships, and test conjectures
● Develop, demonstrate, and apply mathematical understanding through play, inquiry, and
problem solving
● Explain and justify mathematical ideas and decisions
Curricular Content:
● Volume and capacity
○ referents and relationships between units (e.g., cm3, m3, mL, L)
○ using cubes to build 3D objects and determine their volume
First People’s Principles of Learning
● Learning involves time and patience
○ The activities in this lesson are about exploring and discovering volume and capacity
which will take time and patience.
● Learning is holistic, reflexive, reflective, experiential and relational (focused on
connectedness, on reciprocal relationships, and a sense of place)
○ Both activities are intended to be experiential where students are exploring and
discovering aspects of volume and capacity. The first activity requires students to
reflect on their prior estimations and question their assumptions. Both activities
require students to use their prior knowledge and understanding of geometry and
measurement and bring them together to complete the activities.
Important terms
● Volume
● Capacity
● Area
● Width, Depth, and Height
● Names of various 3D shapes (prism, pyramids, spheres, cubes, etc)
Assessments
This lesson is part of introducing volume and capacity so we will only be using formative assessment
strategies. There are many discussion points and activities for students to engage with and show their
learning. To judge student achievement of learning objectives, you can look for the following:
– Students will be participating in class discussions about their predictions in the first activity
– Students will be sharing and explaining their rules for finding the volume of objects with each
other in the second activity
– Students will be engaging in discussions with each other about their findings and discoveries
in both activities
At the end of the lesson, students can write in their math journals to reflect on their new discoveries,
explain their thinking, and ask further questions. Students can also reflect on their own learning by
providing a silent finger rating from 1 to 4 on how comfortable they are with finding capacity and
volume, where
– 1 is “I am still just starting to learn and need more guidance”
– 2 is “I am starting to get it but have a few questions”
– 3 is “I got this and can do it on my own”
– 4 is “I got this and I can help a friend”
This would allow the teacher to quickly glance around the classroom to see if the class needs to
revisit the ideas of finding volume and capacity the next day.
Required Materials
● Plastic fillable geometric solids
● Water, measuring equipment (such as graduated cylinder or scale), and containers to hold and
pour water
● Paper, pencils, pens
● Boxes and unit cubes
● Access to this website for use (laptops):
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/
Lesson Activities
Introduction to students
Introduce volume and capacity and have students write down what they think are the similarities and
differences. You can the provide them with the following definitions and discuss;
a. Capacity: The maximum amount that something can contain.
b. Volume: Quantity of three-dimensional space enclosed by a closed surface.
Do a brief review of the prior knowledge, especially terms, that students should be familiar with for
these activities.
GeoMetric Solid Sorts (Capacity)
Lay out all the solids on a table where all the students can see them. As a group discussion, arrange
all the solids into an order, from smallest to largest. Prompt students to give evidence for their ideas
(why do they think that one is bigger/smaller). Each student will record the predicted order onto a
sheet of paper. You can do this in two ways;
a. Have each student record the order they individually think is correct.
b. Have the students come to a consensus about the order and only record that order; this way
creates more mathematical thinking, since students must explain and justify their ideas to
each other in order to come to an agreement.
Once you have the order recorded, gather your data. Fill each solid with water – get as accurate as
you can, filling right to the edges. Pour the water from the solid into the graduated cylinder as
carefully as possible to not spill any water. Have students record the amount of mls in the cylinder for
the solid on their recording sheet. Repeat this process for each of the solids.
Once you have gathered all the data, rearrange the solids into their correct order, discussing as you
do this. Here are some questions/ideas that might come up during this discussion (from students or
teacher);
● Why did we predict this one solid was smaller than this other one, when it is actually the other
way around?
● This solid is WAY (bigger/smaller) than we all thought it would be – how did that happen? Why
did we (under/over) estimate so much?
● How corners and points can affect volume (“Do you all think we overestimate or
underestimate the volume of objects with points or corners? Can you link this to evidence
from our results today?”)
● Ways of seeing and thinking about the world – ask kids for examples of this type of estimation
mistake in their lives (under or over estimating the capacity or volume of something, or
incorrectly comparing the capacity/volume of two objects)
● Measurement error – where could it come from in this activity? How can we improve our
measurements? How can measurement error affect our data?
● How could you determine volume only using numbers, and not measuring the water (or air)
inside!?!
Discovering rules for determining volume of a box (rectangular prism) (Volume)
Ask students to come up with ways to find volume without measuring the amount it can hold using
water (volume and capacity are closely related). Introduce them to unit cubes and explain how
volume is measured in cubic units so one cube is equal to one cubic unit of volume. Show students
that if you fill a rectangular prism (a small box) with neatly stacked unit cubes and count them, you
will find the volume in cubic units. Ask students if it is possible to have two different sized boxes with
the same volume. Show them by rearranging an equal number of unit cubes various different ways to
get different sized boxes with the same volume. Point out how each box has a different base area.
Now show students how to use this website and get them to explore finding volume:
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/
Remind them what width, depth, and height mean and how you can represent the dimensions of a
rectangular prism (for example, 5 x 7 x 3). Ask them these questions to help them discover the rule
for finding the volume of a rectangular prism:
● Can you find a rule for measuring the volume of a rectangular prism without always filling it
with cubes? If so, what is it? Can you write it in an equation? Explain why it works.
Also provide them with these extension questions for students who would like more of a challenge and
extend their thinking:
● What is the volume of a rectangular prism that measures 4 x 3 x 5? How about 3 x 5 x 4? Why
are they the same or different?
● Can you find two rectangular prisms with different measurements but the same volume? How
did you find them?
● If you are feeling super comfortable, extend your thinking and find a general rule for finding the
volume of any prism (like a triangular prism) or a cylinder.
Afterwards, come together as a class and have students share their discoveries, namely their rules for
finding volume and why they work, or any challenges they came across.
Wrap up class discussion and student reflection
To conclude the lesson, have students share with the class what they learned and are curious about
volume and capacity. Also provide students the time to write in their math journals to reflect on their
new discoveries, explain their thinking, and ask any questions. This is also a great opportunity for all
students to justify the equation for volume that they possibly discovered or explain any challenges
they faced. Lastly, ask all students to provide a 1-4 finger rating, as explained above.
Differentiated Learning
The first activity regarding capacity is intended to be a whole class activity and discussion. Some
students may feel uncomfortable participating in large group activities, especially those who are
unlikely to verbalize their thoughts. Therefore, to ensure that they also benefit from this activity and
reach the intended learning outcomes, these students can do the activity on their own or with a peer
and write down their answers to the discussion questions. The class could also take short partner
breaks where they discuss questions and their thinking with each other, which would provide space
for everyone to contribute.
The second activity consists of a lot of student choice in that students can choose the dimensions of
the rectangular prisms that they will work with. Thus, students who need less complex numbers can
use smaller numbers and students who need a challenge can use larger numbers; all students can
work at their own level. Since students are to explore on the provided website, you can provide
physical manipulatives (i.e. various box sizes and many unit cubes) for students who are more
kinesthetic and prefer to do this activity with physical objects.
Follow up Activities
● Students could do another version of the first activity with the GeoMetric Solids but with
irregular-shaped, everyday household objects like jars, vases, or plant pots. By picking items
that are relatively the same size, students can rearrange them based on their capacity and
check their estimations/predictIons with water.
● Another fun activity would be to measure the capacity of different types of sponges. You
could fill them with water (submerge in water for 10 minutes), squeeze the water out, and
measure the amount of water. This could lead to a discussion about the differences between
sponges like their density, shape, and size.
● Using 8.5×11 paper, students could try to make an open-top box with the largest volume or
smallest. You could talk about the differences and why they are different. To extend this,
students can create two cylinders with the same size piece of paper where one is tall and
skinny and the other is short and fat. Using dry ingredients like rice or popcorn kernels
students can measure their respective volumes to see which is larger.
Cross-Curricular Connections
Science 6: Curricular Competencies
● Questioning & Predicting: Make predictions about the findings of their inquiry
● Planning and conduction: Observe, measure, and record data, using appropriate tools,
including digital technologies
● Processing & analyzing data and information: Compare data with predictions and develop
explanations for results; Identify patterns and connections in data
● Applying & innovating: Generate and introduce new or refined ideas when problem solving
● Communicating: Communicate ideas, explanations, and processes in a variety of ways
English Language Arts: Curricular Competencies
● Comprehend & Connect: Access information and ideas for diverse purposes and from a variety
of sources and evaluate their relevance, accuracy, and reliability; Synthesize ideas from a
variety of sources to build understanding
● Create & Communicate: Exchange ideas and viewpoints to build shared understanding and
extend thinking