Our team focused on the following standards:_7.G3

The mathematics for our learning cycle is about cross sections (although that terminology is never used in the seventh grade core)

Our goal statement is students will be able to describe the two-dimensional figures resulting from slicing prisms, pyramids, cylinders, and cones vertically or horizontally

Our develop task is cutting square watermelons open (using playdoh models) into as many shapes as possible using a single cut. In our develop understanding task, we wish to surface ideas such as prior knowledge regarding 2 dimensional shapes, how to slice shapes, and the different directions shapes may be sliced and to highlight the different 2-d shapes one can obtain by slicing from a cube.

The solidify task we chose is identifying cross sections of prisms and pyramids. The solidify task goals are for students to recognize the relationships between shapes of slices and the three dimensional figures they were sliced from, and understand the idea of a cross sections. (i.e. in right prisms the shape of the slice in the same direction as the base is congruent to the base, and in right pyramids the shape of the slice in the same direction as the base is similar to the base.)

The practice task we chose is identifying central slice shapes from three dimensional figures, and three dimensional figures from central cross sections. The practice task goals are for students to recognize slice shapes without building the shapes out of playdoh. Task: In Japan, growers have developed ways of growing “square” watermelon that fit into small refrigerators.

For more information, visit http://articles.cnn.com/2001-06-15/world/square.watermelon_1_seedless-melons- watermelon-lovers-round-watermelon?_s=PM:asiapcf

If you were given one of these unique square watermelons, into what shapes could you cut it open using only one cut? Be able to explain your process and your result. Anticipations

Students will find that a cut parallel to a face and a cut perpendicular to a base make squares.

Students will find that they can create a rectangle by either cutting off one edge or cutting diagonally vertically or horizontally.

Students may find the following shapes:

Students may find only one or two shapes and feel they are “done”. We will need to question with, “Is that all the shapes you can make?”

Students may struggle with using playdoh to cut shapes.

Students may get more involved in playing with the manipulative than in using it.

Students may struggle with the concept of “different” shapes. They may find multiple rectangles or multiply triangles and either classify them as different shapes or classify them as the same shape.

Students may get confused between two dimensional and three dimensional shapes (i.e. saying they cut off a triangular pyramid instead of showing the resulting triangle shaped cut) Students may get confused regarding WHICH shape they are looking at. (i.e. they may see a triangle in the top right figure instead of the rectangle)

Task:

1. How is the shape created by cutting a prism in the same direction as its base related to the prism? Draw multiple visual representations as part of your explanation.

2. How is the shape created by cutting a prism in the opposite direction as its base related to the prism? Draw multiple visual representations as part of your explanation. 3. How is the shape created by cutting a cylinder in the same direction as its base related to the cylinder? Draw multiple visual representations as part of your explanation.

4. How is the shape created by cutting a cylinder in the opposite direction as its base related to the cylinder? Draw multiple visual representations as part of your explanation.

5. How is the shape created by cutting a pyramid in the opposite direction as its base through the top vertex related to the pyramid? Draw multiple visual representations as part of your explanation. 6. What happens when you make a cut in a pyramid going the opposite direction as its base NOT through the top vertex? Draw multiple visual representations as part of your explanation.

7. How is the shape created by cutting a cone in the same direction as its base related to the cone? Draw multiple visual representations as part of your explanation.

8. How is the shape created by cutting a cone in the opposite direction as its base related to the cone? Draw multiple visual representations as part of your explanation. 9. What happens when you make a cut in a cone going the opposite direction as its base NOT through the top vertex? Draw multiple visual representations as part of your explanation.

Practice Task:

For each of the solids below, sketch two cross sections. One cross section should be through the center of the shape parallel to the base, and the other perpendicular to a base through the center of the shape. Identify each of the cross sections with the correct name of the planar figure. Show a solid which could have the given cross sections. Explain your reasoning.