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Melissa HedgesBeth Schefelker

Math AllianceApril 26, 2011

Making Sense of Volume…

the third dimension!

+WALT and Success CriteriaWe are learning to…

Understand how children make sense of volume.

Identify skills needed to transition from 2-D to 3-D space.

Success Criteria…We will be successful when we develop

meaningful methods for measuring the space in a box.

Use 3-D rectangular arrays to determine the area of a box.

+How many cubes?How did you see it?

How many cubes are needed to make up this solid?

Work independently.

Share with your table.

+How many cubes? How did you see it?

+Thinking about the cube

What must we understand about this solid to reason through how to derive the volume?

What misconceptions do you anticipate students might encounter when approaching this task?Turn and talk

+Student Misconceptions

Unstructured Sets

Unstructured Sets

+Student MisconceptionsCounting Sides and Faces

Counting Faces

+Seeing Arrays in Terms of Layers

+Visualizing Volume

What do you notice about the boxes?How are they similar? How are they different?

Which box fits the flat pattern?How do you know?

What’s the relationship between a net flat pattern and volume?

+Build the image you see…

+Build the image you see…

+Build the image you see…

+How many cubes?

Visualizing VolumeExamine the “net” and estimate the

number

of cubes needed to fill the box.

Cut out the net and tape the box together.

Fill the box with cubes.

Compare your estimate to the results.

+Visualizing 3-D Space

Build a 4 by 3 by 2 solid.

Prove that your solid fits these dimensions.

Using grid paper, draw a 4 by 3 by 2 net flat pattern. Mark the dimensions on each face.

Is there only one net flat pattern that fits this solid? Explore this idea with your table.

+Concrete representational abstract

Complete Box 1, 2, and 3.Keep track of your thinking.How is the worksheet scaffolded to move children from…

Concrete representational abstract

Try the back…Box 4, 5 and 6.

+Reaching All Learners

Reflecting on the session you just experienced:What barriers did you grapple with?What supports were needed to persevere?

Picture a student in your classroom…What would they struggle with and what supports would they need to begin to make sense of volume?

+Textbook Analysis

As you study your materials on rigid motion, you may want to consider how the series supports the instructional strategy:

Concrete representational abstract

For example:Lesson development?Practice pages?Homework?