- Course 1, Unit 5
|The words in bold represent vocabulary and concepts that students should have mastered in this unit.|
|a.||Compare and contrast prisms,
pyramids, cylinders, and cones.
|b.||Compare and contrast the
six special quadrilaterals.
|c.||For each shape in Parts a
and b, describe a real life application of that shape. What properties
of the shape contribute to its usefulness?
Examples of applications can be found in fields from art to engineering. Useful properties may include:
Triangles and, therefore, tetrahedrons, are rigid. Because of this, they are used in construction. Points on the curved surface of cylinders are the same distance from a line connecting the centers of the circular bases. Thus, cylinders are useful for rolling on a flat surface. Squares enclose a greater area for a fixed perimeter, than any other quadrilateral. Likewise, cubes enclose a greater volume, for a fixed surface area, than any other rectangular prism.
|d.||Describe a variety of ways
you can represent (draw or construct) space-shapes.
Space-shapes (the term used for three-dimensional shapes) can be represented using face-views, isometric drawings, or geometric sketches according to which representation is more helpful. They could also be drawn as two-dimensional nets. (A net shows all the lateral faces and how they connect to each other.) Space shapes can be constructed out of solid material such as clay.
|e.||Pose a problem situation
which requires use of cubic, square, and linear units of measure.
Describe how you would solve it.
One situation in which all three types of measures would be required is related to a swimming pool. The amount of water needed to fill the pool (volume) would require cubic units of measure. The amount of material needed for a pool cover (area) would be reported in square units. The distance around the pool (length) would use linear units of measure.
|f.||Describe how to make a strip
pattern and how to make a tiling of the plane.
A strip pattern or tiling of a plane typically has a specific unit of design that is repeated. The repeat may be accomplished by translating the design unit repeatedly, or by reflecting and translating, or by rotating and translating. (Students used these ideas to create tessellations.)
If you would like to see specific problems from Course 1, Unit 5, a link is provided to Examples of Tasks from Course 1, Unit 5. If you are interested in following up on the Geometry strand in general, then the Scope and Sequence will help you see where different concepts are introduced. On the Geometry page, you can read an explanation of the main geometry concepts as they are developed in all four courses.