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 GoalsContent: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 Anticipated Student Responses and Teacher

Prompts / QuestionsAction! 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 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 AFLLook around the room. What are some things shaped like rectangular prisms?What makes them rectangular prisms?

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 ComponentAfter / Consolidation / Reflecting and Connecting

Consolidation Highlights and Summary(Uncover Learning Goal, Success Criteria)

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.

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

Student Next Steps (Large Group/Small Group/Individual)

Homework

Exit Card:

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 3-D 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