Comparing irrational numbers

The  exercise appears under the 8th grade (U.S.) Math Mission. This exercise approximates irrational numbers geometrically and numerically.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine which point is which number: This problem provides a number line with several points labeled with letters and some numbers. The student is asked to match each irrational number with it's place on the number line.Ainwac1.png
 * 2) Order from least to greatest: This problem provides a list of irrational numbers. The student is asked to use the manipulative to slide the provided numbers into increasing order.Ainwac2.png

Strategies
Knowledge of radicals and powers of numbers are encouraged to ensure success on this exercise.
 * 1) The number $$\pi$$ is estimated by 3.14 or $$\frac{22}{7}$$.
 * 2) A root of a number can be estimate without a calculator by recognizing a perfect power that is close to the given number.
 * 3) A trick to remember two square root estimates is Valentine's Day $$\sqrt{2}=1.4$$ and St. Patrick's Day $$\sqrt{3}=1.7$$.

Real-life Applications

 * 1) An understanding of approximate values of irrational numbers can help with estimation and checking answers in mathematics.