Investigating the Area of Circles INTERVIEW ASSESSMENT – Learning Goal: To investigate the relationship between circles and parallelograms to generalize and develop the formula for the area of a circle Question: Using concrete examples, can you explain how knowing the area of a parallelogram helped you develop the formula for the area of circle? LEVEL 4 3 LEVEL 2 LEVEL 1 Representing Creates an accurate and Creates a model of Creates a simple/slightly Did not create an appropriate precise model of mathematical mathematical ideas and inaccurate model of model of mathematical ideas ideas and applies it to solve a applies it to solve a problem mathematical ideas and problem applies it to solve a problem Connecting Makes connections between Makes connections between Makes connections between Has difficulty Making measurements of the circle and measurements of the circle and measurements of the circle and connections between - make connections between the the parallelogram with no the parallelogram with some the parallelogram when asked measurements of the circle and measurements of the circle and teacher prompting teacher prompting specific guiding questions by the parallelogram even with the parallelogram the teacher specific guided questions from - is aware of how to substitute Independently explains With some teacher prompting, the teacher developed relationships to develop substitutions and derives is able to explain how to use Requires direct teacher the formula for Area of a circle formula for the area of a the formula of a prompting to explain (or Has difficulty making circle parallelogram’s area to derive partially explain) how to use connection between the area of the formula for the area of a the formula of a the parallelogram and that of circle parallelogram’s area to derive a circle the formula for the area of a circle Communicating Effectively uses mathematical Uses mathematical vocabulary Uses mathematical vocabulary Uses mathematical vocabulary vocabulary to communicate to communicate orally and to communicate orally and to communicate orally and orally and visually visually with considerable visually with some visually with limited effectiveness effectiveness effectiveness
Investigating the Area of Circles – INTERVIEW ASSESSMENT Learning Goal: To investigate the relationship between circles and parallelograms to generalize and develop the formula for the area of a circle Question: Using concrete examples, can you explain how knowing the area of a parallelogram helped you develop the formula for the area of circle? LEVEL 4 3 LEVEL 2 LEVEL 1 Representing Creates an accurate and precise model of mathematical ideas and applies it to solve a problem Creates a model of mathematical ideas and applies it to solve a problem Creates a simple/slightly inaccurate model of mathematical ideas and applies it to solve a problem Did not create an appropriate model of mathematical ideas Connecting - make connections between the measurements of the circle and the parallelogram - is aware of how to substitute developed relationships to develop the formula for Area of a circle Makes connections between measurements of the circle and the parallelogram with no teacher prompting Independently explains substitutions and derives formula for the area of a circle Makes connections between measurements of the circle and the parallelogram with some teacher prompting With some teacher prompting, is able to explain how to use the formula of a parallelogram’s area to derive the formula for the area of a circle Makes connections between measurements of the circle and the parallelogram when asked specific guiding questions by the teacher Requires direct teacher prompting to explain (or partially explain) how to use the formula of a parallelogram’s area to derive the formula for the area of a circle Has difficulty Making connections between measurements of the circle and the parallelogram even with specific guided questions from the teacher Has difficulty making connection between the area of the parallelogram and that of a circle Communicating Effectively uses mathematical vocabulary to communicate orally and visually Uses mathematical vocabulary to communicate orally and visually with considerable effectiveness Uses mathematical vocabulary to communicate orally and visually with some effectiveness Uses mathematical vocabulary to communicate orally and visually with limited effectiveness
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