The Decimal Expansion of π
Related Topics:
Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 8
Common Core For Grade 8
Examples, solutions, and videos to help Grade 8 students learn how to calculate the decimal expansion of π using basic properties of area and estimate the value of expressions such as π2.
• Students estimate the value of expressions such as π2.
Lesson 14 Classwork
Opening Exercises
1. Write an equation for the area, A, of the circle shown.
2. Write an equation for the circumference, C, of the circle shown.
3. Each of the squares in the grid below has an area of 1 unit2.
a. Estimate the area of the circle shown by counting squares.
b. Calculate the area of the circle using a radius of 5 units and 3.14 for π.
Exercises
4. Gerald and Sarah are building a wheel with a radius of 6.5 cm and are trying to determine the circumference. Gerald says, “Because 6.5 × 2 × 3.14 = 40.82, the circumference is 40.82 cm.” Sarah says, “Because 6.5 × 2 × 3.10 = 40.3 and 6.5 × 2 × 3.21 = 41.73, the circumference is somewhere between 40.3 and 41.73.” Explain the thinking of each student.
5. Estimate the value of the irrational number (6.12486...)2.
6. Estimate the value of the irrational number (9.204107...)2.
6. Estimate the value of the irrational number (4.014325...)2.
Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 8
Common Core For Grade 8
Examples, solutions, and videos to help Grade 8 students learn how to calculate the decimal expansion of π using basic properties of area and estimate the value of expressions such as π2.
New York State Common Core Math Grade 8, Module 7, Lesson 14
Download Worksheets for Grade 8, Module 7, Lesson 14
Lesson 14 Student Outcomes
• Students calculate the decimal expansion of π using basic properties of area.• Students estimate the value of expressions such as π2.
Lesson 14 Summary
Irrational numbers, such as π, are frequently approximated in order to compute with them. Common approximations for π are 22/7 and 3.14. It should be understood that using an approximate value of an irrational number for computations produces an answer that is accurate to only the first few decimal digits.Lesson 14 Classwork
Opening Exercises
1. Write an equation for the area, A, of the circle shown.
2. Write an equation for the circumference, C, of the circle shown.
3. Each of the squares in the grid below has an area of 1 unit2.
a. Estimate the area of the circle shown by counting squares.
b. Calculate the area of the circle using a radius of 5 units and 3.14 for π.
Exercises
4. Gerald and Sarah are building a wheel with a radius of 6.5 cm and are trying to determine the circumference. Gerald says, “Because 6.5 × 2 × 3.14 = 40.82, the circumference is 40.82 cm.” Sarah says, “Because 6.5 × 2 × 3.10 = 40.3 and 6.5 × 2 × 3.21 = 41.73, the circumference is somewhere between 40.3 and 41.73.” Explain the thinking of each student.
5. Estimate the value of the irrational number (6.12486...)2.
6. Estimate the value of the irrational number (9.204107...)2.
6. Estimate the value of the irrational number (4.014325...)2.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.