Copyright © Swun Math Grade 8 Unit 1 Constructed Response Rubric TE

Unit 1 ∙ Constructed

ResponseSCORING RUBRIC

Unit 1 ∙ Constructed Response

Rational vs. Irrational Numbers

TASK 2: Estimate and Approximate Irrational Numbers

Answer/Exemplar Standard Points

4a. The square root of 125 is between 11 and 12. 8.NS.2 1

4b. I used what I know about perfect squares. is between

and. Since = 11 and is 12, then

must be between 11 and 12.

8.NS.2 1

4c. If the value was changed to , the process to solve would

change because the value inside the radical would be multiplied

by 5. Since the value of is between and , or

5 × 11 and 5 × 12. So the value of is between 55 and 60.

8.NS.2 1

5a. 9.43;

8.NS.2 1

5b. It was helpful to begin the estimation by comparing the square

roots of perfect squares. I noticed is slightly closer to 9 than

10, so it will be most likely between 9.4 and 9.5. After calculating

the squares of 9.4 and 9.5, I saw 9.4^2 is closer to 89 than 9.5^2 , which

helped me to make a reasonable estimate of the value in the

hundredths place.

8.NS.2 1

6a. False; is not larger than. The decimal equivalent of is

. I know. Since , then. Because
and , cannot be greater than.

8.NS.2 1

6b. 8.NS.2 1

0 1 2 3

2 6 = 2.666

9

2

6

9 2

6

9

(^2 69)