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G-C-1-1

Page history last edited by Brenda Butz 6 years, 3 months ago

G.C.1.1 Apply the properties of circles to solve problems involving circumference and area, approximate values and in terms of π, using algebraic and logical reasoning.

In a Nutshell

Students will solve real-world and mathematical problems that involve circumference and area of circles where answers can be written in terms of π or an approximate value.

Student Actions	Teacher Actions
Develop deep and flexible conceptual understanding: Students will use the equations for the circumference and area of a circle correctly. Identifying which equation is a appropriate for a particular problem. Develop Mathematical Reasoning: Students will correctly apply the formulas for area and circumference to solve real-world problems. Sometimes students will have to use both equations at different parts of a problem solution. Develop strategies for problem solving: Students will determine which method to use when solving problems involving various representations of circles and parts of circles. Develop Accurate and Appropriate Procedural Fluency: Students will be able to give answers in terms of 𝝅 and in a decimal approximation.	Teachers will implement tasks that promote reasoning and problem solving by presenting problems that require students to start with circumference and solve for radius before finding the area or vice versa. Teachers will pose questions that require students to compare and contrast the circumferences and areas of different circles. Teachers will support productive struggle in learning mathematics by having the students decide which equation will give them the desired solution to particular problems. Teachers will use student responses to guide them as they decide how to approach problems about circles.
Key Understandings	Misconceptions
Students understand which equation will give the circumference of a circle and which equation will give the area of a circle. Students understand the difference between an exact answer involving π and a rounded answer. Students understand that pi is a constant and represents the ratio of the circumference to the diameter of the circle.	Students don’t understand the difference between leaving an answer in terms of 𝝅 and giving a decimal approximation as an answer. Students confuse the equation for area with the equation for circumference, sometimes combining them. Students forget to take the square root when finding the radius of the circle from the equation for the area. Students use diameter instead of radius in the formula for area or circumference.