![]() ![]() This task aims to formalize these observations by defining a cross section as the intersection of a plane and a three-dimensional object. Which of the following cross sections can be formed by the surface of the water? Which are impossible? a square a rhombus a rectangle a parallelogram a trapezoid a triangle a pentagon a hexagon an octagon a circle 3 SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY Any Way You Slice It Teacher Notes A Develop Understanding Task Purpose: The purpose of this task is to surface a variety of strategies for visualizing two-dimensional cross sections of three-dimensional objects, and to identify and/or draw such cross sections.ĥ Students encounter cross sections when they Slice a loaf of bread, a piece of cake, or a hard-boiled egg, or when they tilt a glass of water in different ways and examine the surface of the water. Try to imagine a cubical jar partially filled with colored water, and tilted in various ways. Draw the cross sections formed by the surface of the water in the jar. Partially fill a cylindrical jar with colored water, and tilt it in various ways. 2 SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY Experiment with various ways of examining the cross sections of different three-dimensional shapes.Ĥ 6. Another way is to partially fill a clear glass or plastic model of the three-dimensional object with colored water and tilt it in various ways to see what shapes the surface of the water can assume. One way is to do what Jumal and Jabari did cut a clay model of the solid with a piece of dental floss. Cross sections can be visualized in different ways. ![]() What type of quadrilateral is formed by the intersection of the plane that passes through diagonally opposite edges of a cube?ģ Explain how you know what quadrilateral is formed by this cross section. CC BY Sean Freese 1 SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 5. Draw some other possible cross-sections that can be formed when a cube is sliced by a plane. Draw and describe the cross section formed when Jabari sliced his cube. Draw and describe the cross section formed when Jumal sliced his cube. It can also be thought of as the intersection of a plane and a solid. Denton s instructions correctly? Why do you say so? When describing three-dimensional objects such as cubes, prisms or pyramids we use precise language such as vertex, edge or face to refer to the parts of the object in order to avoid the confusion that words like corner or side might create.Ģ A cross section is the face formed when a three-dimensional object is sliced by a plane. Which student, Jumal or Jabari, interpreted Mrs. Denton s class were given cubes made of clay and asked to Slice off a corner of the cube with a piece of dental floss. Denton’s instructions correctly?ġ SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY Any Way You Slice It A Develop Understanding Task Students in Mrs. Denton’s class were given cubes made of clay and asked to slice off a corner of the cube with a piece of dental floss. ![]() Denton s instructions correctly? Why do you say so? When describing three-dimensional objects such as cubes, prisms or pyramids we use precise language such as vertex, edge or face to refer to the parts of the object in order to avoid the confusion that words like corner or side might create.ĥ.1 Any Way You Slice It A Develop Understanding Task Students in Mrs. ![]() SECONDARY MATH III // MODULE 5 MODELING WITH GEOMETRY Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY Any Way You Slice It A Develop Understanding Task Students in Mrs. Example: confidence Search 5.1 Any Way You Slice It - uen.org ![]()
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