As an extension, the question “Would the remaining area change if I increased the size of the square and the circle?” Students could, on their own or in small groups, create their own Pie Area Square problem, using different measurements, and see if the remaining area of the square changes. A discussion of any connections or discoveries/realizations should be had following the completion of these experimentations. Other adjustments can be made to this problem as well, such as changing the size of the circle but maintaining the size of the square, etc. This can be adapted for students as fits their needs. Assessment Can students illustrate and explain that the diameter is twice the radius in a given circle? Can students illustrate and explain that the circumference is approximately three times the diameter in a given circle Can students explain that, for all circles, pi is the ratio of the circumference to the diameter (C/d) and its value is approximately 3.14? Can students solve a given contextual problem involving circles? Can students generalize a rule to create a formula for determining the area of parallelograms? Can students solve a given problem involving the area of triangles, parallelograms and/or circles? Can students apply a formula for determining the area of a given circle? Units This activity can be used in the following unit: Unit 4: Circles and Area
As an extension, the question “Would the remaining area change if I increased the size of the square and the circle?” Students could, on their own or in small groups, create their own Pie Area Square problem, using different measurements, and see if the remaining area of the square changes. A discussion of any connections or discoveries/realizations should be had following the completion of these experimentations. Other adjustments can be made to this problem as well, such as changing the size of the circle but maintaining the size of the square, etc. This can be adapted for students as fits their needs. Assessment Can students illustrate and explain that the diameter is twice the radius in a given circle? Can students illustrate and explain that the circumference is approximately three times the diameter in a given circle Can students explain that, for all circles, pi is the ratio of the circumference to the diameter (C/d) and its value is approximately 3.14? Can students solve a given contextual problem involving circles? Can students generalize a rule to create a formula for determining the area of parallelograms? Can students solve a given problem involving the area of triangles, parallelograms and/or circles? Can students apply a formula for determining the area of a given circle? Units This activity can be used in the following unit: Unit 4: Circles and Area
7-BirchBarkBitingInquiry.docx