Reason with shapes and their attributes. (3.G.A.1)
Standards for Mathematical Practice
MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason quantitatively.
MP3.
Construct viable arguments and critique the reasoning of others.
MP5.
Use appropriate tools strategically.
MP6.
Attend to precision.
MP7.
Look for and make sense of structure.
Students continue to analyze three-dimensional shapes. They trace and describe the faces and then use these properties to compare, sort, and categorize shapes.
Content in this Lesson
Tracing faces of three-dimensional shapes.
Relating two-dimensional shapes to three-dimensional shapes.
Analyzing three-dimensional shapes using their properties [E2].
Identifying three-dimensional shapes using their properties [E3].
Identifying congruent faces [E5].
Justifying conclusions using geometric properties [E7].
2 different shapes from the Power Solids® set. See Materials Preparation.
drawing paper
crayons or colored pencils
Supplies for Student Groups
Sets of Faces of 3-D Shapes Cards Masters (Teacher Guide). See Materials Preparation.
rectangular prism from the 3-D Shape collection gathered in Lesson 6
Display and Expand Table. In Lesson 7 you made a large display version of some of the content of the Edges, Vertices, and Faces Table in the Student Activity Book. Add chart paper to the right of this chart and add three more columns. See Figure 1 below.
Divide Power Solids®. Remove the sphere and hemisphere from the two sets of Power Solids®. Divide the remaining shapes so that student pairs can work with at least two different shapes. Plan to distribute each shape to at least two student pairs for comparison.
Gather and Display Rectangular Prisms. In Lesson 6 students collected everyday objects representing 3-D shapes. Organize the rectangular prisms (e.g., tissue box and cereal box) to use as models in this lesson. Be sure the collection includes some cubes. Display this collection of rectangular prisms for all students to see. Each group will need one rectangular prism in Part 2.
Prepare Sorting Cards for a Learning Center. Copy the Faces of 3-D Shapes Cards Masters on heavier paper or cardstock to make sets of cards for each student group. Cut apart the cards and store each set in an envelope or with a rubber band. Place these cards and a set of Power Solids® in a learning center for students to play Guess My Shape. This can provide targeted practice with analyzing and describing 3-D shapes.
Prepare the Mystery Sort Game for a Learning Center. Prepare a few copies of the Mystery Sort: Faces Master for targeted practice. Cut apart the properties and the “Yes” and “No” cards and place them in an envelope along with a copy of the directions, a set of the prepared Faces of 3-D Shapes Cards Masters, or other representation of 3-D shapes.
Shapes with a base and all points on the base connect to a top vertex or apex. The base may be any shape. Using this definition, all pyramids are special cones. A circular cone has a base in the shape of a circle.
congruentx
Shapes with the same shape and size. Shapes are congruent if you can place one shape so it fits on top of the other and they match exactly.
cubex
A three-dimensional shape with six congruent square faces.
cylinderx
A three-dimensional shape with two congruent and parallel faces. Lines joining the corresponding points on the two bases are always parallel. All prisms are special kinds of cylinders. A circular cylinder has two congruent and parallel circles as bases.
edgex
A line segment where two faces of a three-dimensional figure meet.
facex
The polygons that make up the surface of a three-dimensional shape are called faces. For example, all the faces of a cube are squares.
hexagonal prismx
A prism with bases shaped like a hexagon. (See also prism.)
hexagonal pyramidx
XXXXX
netx
A way of representing the surface of a three-dimensional solid in two-dimensions. A net can be made by cutting the surface of a 3-D shape along edges until it can be laid fl at showig all faces at once.
parallelx
XXXXX
polygonx
A two-dimensional closed shape with straight sides.
polyhedrax
A connected three-dimensional shape whose surface is made of polygons.
polyhedronx
A connected three-dimensional shape whose surface is made of polygons.
Power Solids®x
A set of 12 plastic geometric three-dimensional shapes. (See also three-dimensional.)
prismx
A three-dimensional shape that has two congruent faces, called bases, that are parallel to each other, and all other faces are parallelograms.
rectangular prismx
A prism whose bases are rectangles.
rectangular pyramidx
A pyramid whose base is a rectangle.
spherex
A three-dimensional object shaped like a ball. Every point on the shape is the same distance from the center. Because a sphere is not a polyhedron, it does not make sense to talk about its faces, vertices, and edges. An ordinary sphere does not have edges or vertices.
square pyramidx
A pyramid with a square base.
triangular prismx
A prism with triangular bases.
triangular pyramidx
A pyramid with a triangular base.
vertex (vertices)x
A point where the sides of a polygon meet.
A point where the edges of a three-dimensional object meet.