Use rational approximations of irrational numbers

Start lessonBegins with Trapping irrationals · Slides

Teacher tools for this standard

Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

8.NS.A.2

**8.NS.A.2**: 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., pi^2). For example, by truncating the decimal expansion of sqrt(2), show that sqrt(2) is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

8.NS.A.2: 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., pi^2). For example, by truncating the decimal expansion of sqrt(2), show that sqrt(2) is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

What you'll learn

Approximate an irrational number by successively narrowing the interval between two rational bounds (e.g., showing that sqrt(2) is between 1.41 and 1.42 by squaring both endpoints)
Locate irrational numbers on a number line diagram to a specified degree of precision using rational approximations
Compare the size of two irrational numbers by computing rational approximations of each to enough decimal places to determine which is larger
Estimate the value of expressions involving irrational numbers (e.g., pi^2, 3sqrt(5)) by substituting rational approximations and computing
Explain why rational approximations of irrational numbers can be made arbitrarily close but never exact, and describe how to obtain a better approximation

Review first: