Description of the Mathematical Task:
1. students can work with any circular objects such as such as: canned goods (soup, beans, fruit, etc.), oatmeal container top, Frisbee, cake pan, coffee mug bottom, any lid to a glass jar (baby food, pasta sauce, etc.), a half-dollar or quarter.
2. Students will measure the diameter and the circumference of different circular objects and write down all the values of the diameter, circumference and their corresponding rations on the activity sheet.
3. Then I will ask my students about their findings and the mystery ratio.
4. Then I will introduce the idea of Pi.
Grade: 6-8
Topics that the task develop: Ratio, Fractions, Pi, and properties of circle.
Material List: Rulers, strings, circular objects, and the actitivity worksheet.
Solution: The ration of diameter and circumference of a circular object is always will be approximately 3.14 which represents the value of Pi.
CCSS Standards: "Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations." CCSS.MATH.CONTENT.8.NS.A.2
1. students can work with any circular objects such as such as: canned goods (soup, beans, fruit, etc.), oatmeal container top, Frisbee, cake pan, coffee mug bottom, any lid to a glass jar (baby food, pasta sauce, etc.), a half-dollar or quarter.
2. Students will measure the diameter and the circumference of different circular objects and write down all the values of the diameter, circumference and their corresponding rations on the activity sheet.
3. Then I will ask my students about their findings and the mystery ratio.
4. Then I will introduce the idea of Pi.
Grade: 6-8
Topics that the task develop: Ratio, Fractions, Pi, and properties of circle.
Material List: Rulers, strings, circular objects, and the actitivity worksheet.
Solution: The ration of diameter and circumference of a circular object is always will be approximately 3.14 which represents the value of Pi.
CCSS Standards: "Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations." CCSS.MATH.CONTENT.8.NS.A.2