**Misconception / Error**The student holds any of several misconceptions about what it means to round to the nearest 100 (see Examples of Student Work). | **Examples of Student Work at this Level**The student truncates the ones and tens digits of the three- and four-digit numbers (i.e., writes the numbers as 400, 600, and 1400). The student explains that rounding to the nearest 100 means writing the ones and tens digits as zeros. The student does not know what to do with the two-digit number or writes it as 00.
The student always rounds up (i.e., writes the numbers as 100, 500, 700, and 1500). | **Questions Eliciting Thinking**Can you round these numbers to the nearest 10? How would you round 86 to the nearest 10? Which digit do you have to look at when rounding to tens? Why?
What digit do you think you need to look at when rounding to the nearest 100? Why?
Do you know the rules for rounding? When do you round up? When do you round down?
Can you tell me which of these numbers look like they have been rounded to the hundreds place: 2300, 810, 400, 28, 100, 3980? Why do you think that? | **Instructional Implications**Provide the student with direct instruction on how to round. Begin by rounding two-digit numbers to the nearest 10. Then introduce rounding three- and four-digit numbers to the nearest 10. Next, introduce rounding three-digit numbers to the nearest 100. Finally, have the student round two-and four-digit numbers to the nearest 100. Teach the rules for rounding but also guide the student to round by finding the nearest multiple of 100. For example, if the student is rounding 432 to the nearest 100, ask the student to find the next smallest multiple of 100 (i.e., 400) and the next largest multiple of 100 (i.e., 500). Then, guide the student to consider which of these multiples 432 is closest to (on the number line). Model for the student how to round a variety of numbers to the nearest hundred. The teacher should do a "think-aloud", i.e., verbalize his or her thinking as he or she rounds numbers so that the student can observe the kind of mathematical thinking that one engages in when rounding.
Consider using MFAS task *Rounding to the Nearest Ten* (MACC.3.NBT.1.1). |

**Misconception / Error**The student can only round three-digit numbers to the nearest 100. | **Examples of Student Work at this Level**The student correctly rounds 432 to 400. When rounding 1420 to the nearest 100, the student rounds to 1000. The student does not know how to round 86 to the nearest 100. | **Questions Eliciting Thinking**Let’s look at the numbers 86 and 1420 again. What digits were you looking at when you rounded to the nearest hundred?What if you ignore the one in the thousands place in 1420 and think of this number as 420. Can you round 420 to the nearest 100? So, what should 1420, rounded to the nearest 100 be?
Can you skip count by hundreds? Which two multiples of 100 is 86 between? Is it closer to 0 or to 100? | **Instructional Implications**Work with the student on rounding two-and four-digit numbers to the nearest 100. Guide the student to consider the tens digit when rounding to the nearest 100, regardless of how many digits the number contains. Also guide the student to round by finding the nearest multiple of 100. For example, if the student is rounding 1420 to the nearest 100, ask the student to find the next smallest multiple of 100 (i.e., 1400) and the next largest multiple of 100 (i.e., 1500). Then, guide the student to consider which of these multiples 1420 is closest to (on the number line). |

**Misconception / Error**The student does not know whether to round up or not when the critical digit is five. | **Examples of Student Work at this Level**The student correctly rounds 86, 432, and 1420 but does not know whether to round 650 to 600 or 700. | **Questions Eliciting Thinking**Can you round 65 to the nearest 10?
How would you round 649 to the nearest 100? What about 651? | **Instructional Implications**Provide direct instruction on rounding numbers when the critical digit is five. Acknowledge that numbers like this can be rounded either up or down but the convention is to round them up unless the context requires that one do otherwise. For example, in estimating the cost of a purchase, prices are rounded up so that the buyer can be sure he or she has enough money. |

**Misconception / Error**The student provides complete and correct responses to all components of the task. | **Examples of Student Work at this Level**The student correctly rounds each number to the nearest 100. In addition, the student can correctly explain how he or she rounded each number. | **Questions Eliciting Thinking**Can you round 5675 to the nearest 10? 100? 1000?
Can you round 9821 to the nearest 1000? | **Instructional Implications**Have the student round numbers in which more than one digit is affected. For example, ask the student to round 397 to the nearest 10 or 4971 to the nearest 100.
Extend the concept of rounding to fractions. Ask the student to locate fractions such as 1/4, 3/8, 2/3, and 3/4 on a number line and round them to the nearest whole. |

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