Here is a rectangular prism and a pyramid with the same base and same height.

1. Think about slicing each solid parallel to its base, halfway up. What shape would each cross-section be? What is the same about the two cross-sections? What is different?

2. Think about slicing each solid parallel to its base, near the top. What shape would each cross-section be? What is the same about the two cross-sections? What is different?

Your teacher will give you a set of cards. Take turns with your partner to group the cards.

1. For each group that you find, explain to your partner how you know it’s a match.
2. For each group that your partner finds, listen carefully to the explanation. If you disagree, discuss your thinking and work to reach an agreement.

Draw and describe each cross-section.

1. Here is a picture of a rectangular prism, 4 units by 2 units by 3 units.

   

   1. A plane cuts the prism parallel to the bottom and top faces.

      

   2. The plane moves up and cuts the prism at a different height.

      

   3. A vertical plane cuts the prism diagonally.

      

2. A square pyramid has a base that is 4 units by 4 units. Its height is also 4 units.

   1. A plane cuts the pyramid parallel to the base.

      

   2. A vertical plane cuts the pyramid.

      

3. A cube has an edge of length 4.

   1. A plane cuts off the corner of the cube.

      

   2. The plane moves farther from the corner and makes a cut through the middle of the cube.

      

Your teacher will show you two different containers filling with water. You will investigate the height of water in each container as functions of the water volume.

1. Container A:

   1. What shape is the container?
   2. Make a prediction about the shape of the graph.

   3. Record the measurements given in the video in the table.

      volume (ml)	0	10	20	30	40	50
      height (cm)

   4. Create a graph that shows the height of the water in the container as a function of the water volume.

      

2. Container B:

   1. What shape is the container?
   2. Make a prediction about the shape of the graph.

   3. Record the measurements given in the video in the table.

      volume (ml)	0	5	10	15	20	25
      height (cm)

   4. Create a graph that shows the height of the water in the container as a function of the water volume.