Geometric & Spatial Reasoning
Georgia Standard: 7.GSR.5: Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.
Expectations
Measure angles in whole non standard units.
Measure angles in whole number degrees using a protractor.
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.
Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.
Solve realistic problems involving surface area of right prisms and cylinders.
Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in the plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.
Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems.
Examples
Fold a circle of patty paper or waxed paper in half four times to create an angle measuring tool with 16 wedges. This protractor can be used to determine the number of units (wedges) in an angle.
Students may be given angles to find precise measurements of angles. Here is an example of how students may use a protractor and measurement reasoning to determine precise angle measurements.
The seventh-grade class is building a mini golf game for the school carnival. The end of the putting green will be a circle. If the circle is 10 feet in diameter, how many square feet of grass carpet will they need to buy to cover the circle? How might you communicate this information to the salesperson to make sure you receive a piece of carpet that is the correct size: 𝐴=𝜋𝑟2 OR 𝐶= 2𝜋𝑟 ?
Cole is planning to cover a cylindrical drum in leather. The diameter of the drum is 10 inches, and its height is 16 inches. What is the minimum amount of leather Cole will need?
A farmer is storing ground corn in a silo during the winter months. What is the maximum capacity of the cylindrical part of each silo that has a 20-foot diameter and a 55-foot height for which the farmer can store the ground corn?