Grades 4&5
Determining the Amount of Space Taken up by a Rectangular Prism
03/ 2014
Curriculum Expectations
Gr 4 estimate, measure using concrete materials, and record volume, and relate volume to the space taken up
by an object (e.g., use centimetre cubes to demonstrate how much space a rectangular prism takes up)
Gr 5 - determine, through investigation using stacked congruent rectangular layers of concrete materials, the
relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to
develop the formula (i.e., Volume = area of base x height)
What do students need to know and be able to do?
- Can determine area of rectangles and squares, using l x w; square units
- Grade 3 estimate, measure and record capacity using standard units
- Gr 3 – familiar with length, height, distance as distinct measures
Learning Goals
Content:
Well will
 Show ways to calculate the space taken
up by a rectangular prism made of cubes
that are the same size
 show that volume is the space taken up by
an object
 articulate that volume is 3-Dimensional
Process:
We will
 represent our thinking using numbers or
pictures or words
Lesson Components
Action!
Materials:
 linking cubes
 large paper
 markers
Students work in pairs or trios to solve the
following task:
Create 2 different rectangular prisms using connecting
cubes.
How many different ways can you show the number of
cubes that are in each prism?
Use pictures, numbers or words to show your thinking.
Anticipated Student Responses and
Teacher
Prompts / Questions
Anticipated Student Responses and Possible
Misconceptions


Counting the cubes (by 1’s)
Repeated Addition: added the number
of cubes in each layer
 number of cubes in the base (base
area) x number of layers (height)
 lxwxh ( multiplied 3 dimensions)
*************************************
 rotate the solid, changing the base, to
come up with a second
adding/multiplication statement
 deconstruct shape into 2 prisms and
determine the sum of the 2 prisms
Possible Misconceptions
 draw each face, then count the total
squares on the faces (surface area)
Sample Scaffolding Questions
How else can you represent this?
How are these ___the same or different?
If I add a layer/remove a layer, what will happen?
How do you know?
Have you found all the possibilities?
How could you arrive at the same answer in a different
way?
Minds-On
Look around the room.
What are some things shaped like rectangular prisms?
What makes them rectangular prisms?
AFL
What are we listening and looking for
from the student conversation and
responses?
Create a chart with student responses for
reference during Action task.




3-dimensional (length, width, height)
6 rectangular (or square faces)
8 vertices
12 edges
Examples: filing cabinet, storage bin,
cupboards
Lesson Component
After / Consolidation / Reflecting and Connecting
The following strategies to determine the number of cubes in
each rectangular prism were seen in student work:
1. Count the cubes
2.
Count the cubes
Count the cubes in each layer then add the
layers.
Consolidation Highlights and Summary
(Uncover Learning Goal, Success
Criteria)
3.
Count the cubes in each layer then add the layers.
Count the cubes in each layer, then multiply by the
number of layers.
Independent Practice:
 Exit Card
 Reflection
 Homework
Exit Card:
Student Next Steps
(Large Group/Small Group/Individual)



Finding Volume
Choose a strategy from Mr. Hocket's list.
What is the volume of the shape? Show your thinking.

Some students looking at square
faces of the cubes: work at
decomposing the cube, counting
them and then counting the cubes in
the prism again
For those struggling with drawing 3D shapes, work to draw each layer
instead, then show their work in
numbers
As a class, co-create
representations of each of the
strategies listed as anchors to guide
future student work (exemplars)
Develop formula for finding volume:
*area of base x height with grade 5
students rather than l x w x h
*(area of base x height) can be used when
finding the volume of any other 3-Day solids