Getting Started 
Misconception/Error The student is unable to identify a range of numbers that fits the given conditions. 
Examples of Student Work at this Level The student identifies a range of numbers that includes values that do not round to 80 (when rounded to the nearest 10) and do not round to 400 (when rounded to the nearest 100). The student:
 Calculates 80 ± 10 and 400 ± 100 and gives each range as 70 to 90 and 300 to 500 or 70 to 80 and 300 to 400.
 Includes numbers that do not fit the given rounding conditions.

Questions Eliciting Thinking If I rounded 72 to the nearest 10, would I get 80? What about 89? Why don’t I get 80 for any of those numbers?
If I rounded 301 to the nearest 100 would I get 400? What about 499? Why or why not? 
Instructional Implications Review the rules for rounding to the nearest 10 with the student. Give the student a multiple of 10, such as 60, and have the student make a list of all numbers that round to 60 when rounding to the nearest 10. Guide the student to use a number line to locate 60 and highlight the portion of the number line that contains numbers that will round to 60 (when rounding to the nearest 10). Then review the rules for rounding to the nearest 100 with the student. Give the student a multiple of 100, such as 200, and have the student use a number line to explore numbers that round to 200 when rounding to the nearest 100. Ask the student to highlight the portion of the number line that contains numbers that will round to 200 (when rounding to the nearest 100).
Have the student use a number line to highlight all numbers that when rounded to the nearest 10 result in 80. Practice with other multiples of 10. Do the same for numbers that result in 400 when rounded to the nearest 100. Practice with other multiples of 100. Provide assistance, as needed. 
Moving Forward 
Misconception/Error The student identifies a subset of numbers from the full range of possible solutions but is unable to identify the smallest and the largest possible numbers. 
Examples of Student Work at this Level The student identifies the lower and upper limits as:
 79 to 81 and 399 to 401.
 80 to 80 and 400 to 400.

Questions Eliciting Thinking If I rounded 81 to the nearest 10 what would I get? Is there a number larger than 81 that I could round to the nearest 10 and get 80?
If I rounded 375 to the nearest 100, would I get 400? What about 425? Can you think of numbers smaller than 375 and larger than 425 that when rounded to the nearest 100 would give you 400? 
Instructional Implications Have the student use a number line to highlight all numbers that when rounded to the nearest 10 result in 80. Practice with other multiples of 10. Do the same for numbers that result in 400 when rounded to the nearest 100. Practice with other multiples of 100. Provide assistance, as needed.
Pose a multiple of 10 or a multiple of 100 rounding question to the class, and ask for examples of numbers that round to these values. Record student responses on the board and ask students to verify whether or not the numbers would round as specified. Continue until the smallest and largest numbers are identified and tested. 
Almost There 
Misconception/Error The student identifies a subset of numbers from the full range of possible solutions that includes some lower and upper limits but not all. 
Examples of Student Work at this Level The student correctly identifies:
 The upper limits but not the lower limits.
 The lower limits but not the upper limits.
 Both the lower and upper limit for one number but only a subset of the range of values for the other.

Questions Eliciting Thinking Can you locate 80 on a number line? If you are rounding to the nearest 10, which numbers smaller than 80 will round up to 80? Which numbers larger than 80 will round down to 80? What are the smallest and largest values that round to 80?
Can you locate 400 on a number line? If you are rounding to the nearest 100, which numbers smaller than 400 will round up to 400? Which numbers larger than 400 will round down to 400? What are the smallest and largest values that round to 400? 
Instructional Implications Have the student use a number line to highlight all numbers that when rounded to the nearest 10 result in 80. Practice with other multiples of 10. Do the same for numbers that result in 400 when rounded to the nearest 100. Practice with other multiples of 100.
Pose a multiple of 10 or a multiple of 100 rounding question to the class, and ask for examples of numbers that round to these values. Record student responses on the board, and ask students to verify whether or not the numbers would round as specified. Continue until the smallest and largest numbers are identified and tested. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student identifies 75 as the lower limit and 84 as the upper limit in the first problem. The student identifies 350 as the lower limit and 449 as the upper limit in the second problem. The student is able to justify his or her answers. 
Questions Eliciting Thinking Suppose I asked you for the smallest possible number that would round to 3000 when rounded to the nearest 1000. What answer would you give? Why? 
Instructional Implications Have the student work with a partner to pose and solve similar problems.
Consider implementing the MFAS task Mystery Number Rounding Problem (3.NBT.1.1). 