+ Melissa Hedges Beth Schefelker Math Alliance April 26, 2011 Making Sense of Volume… the third dimension!

+ WALT and Success Criteria We 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 Misconceptions Counting 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…

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+ How many cubes? Visualizing Volume Examine 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?