1. 8.NS.2
The Number System
Part 2

2. 8.NS.2
Using rational approximations of irrational numbers to compare the size of irrational numbers, locate them on approximately on a number line diagram, and estimate the value of the number.
Ex. The square root of 2 is between the square root of 1 and the square root of 2
Further Ex. The square root of 2 is between 1.4 and 1.5

3. 8.NS.2
Students locate rational and irrational numbers on a number line
Ex. 1 The square root of 49 is at 7 on a number line
Ex. 2 The square root of 80
It’s between the square root of 81 which is 9, and the square root of 64 which is 8
With this being the case the square root of 80 will be between 8 and 9 and closer to the number 9 on a number line.

4. 8.NS.2 Students find the approximate value of irrational numbers
Example The square root of 22
Step 1 – “Find which two square roots it’s in between” 16 and 25
Step 2 – “Find which square root it is greater than to determine the whole number.” The square root it is greater than is 16 so the whole number is going to be 4 because 4 is the square root of 16.
Step 3 – “Find the denominator” figure out the distance between the two square roots the number is in between which is 16 and 25 the distance is 25-16=9 so the denominator is 9
Step 4 – “Find the numerator” figure out the distance between your number and the whole number that has been determined. The distance between the two is 22-16=6 so the numerator is 6
Step 5 – “Put it all together” The whole number is 4 the numerator is 6 and the denominator is 9 so the approximate value is 4 and 6/9 or 4.3 “Repeating”