standard_description: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
problem_activity: Narrative
The purpose of this activity is for students to round given numbers to the nearest ten and hundred and see that the result can be the same for some numbers. Students think about what it means to round a number that is exactly halfway between two tens or two hundreds and are introduced in the synthesis to the convention that these numbers are rounded up (MP3).
MLR1 Stronger and Clearer Each Time:
Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to “What does 97 round to when we are rounding to the nearest 10? To the nearest hundred? Why does that happen?” Invite listeners to ask questions, to press for details and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive.
Advances: Writing, Speaking, Listening
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were most useful to solve the problems. Display the sentence frame, “The next time I round numbers to the nearest ten and nearest hundred, I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing
Launch
Groups of 2
“Let’s round some numbers to the nearest ten and the nearest hundred. Remember ‘round to the nearest ten (or hundred)’ is another way of saying find the nearest multiple of 10 (or 100).”
Activity
“Work with your partner to complete the table.”
3–5 minutes: partner work time
Monitor for students who notice 97 and 601 round to the same number whether rounding to the nearest ten or the nearest hundred.
Select previously identified students to share their responses.
“Why did 97 and 601 round to the same number when we rounded to the nearest ten and the nearest hundred?” (The closest multiple of 10 was also a multiple of 100. 100 and 600 are multiples of 100, but they are also multiples of 10.)
“Complete the second problem with your partner. Explain your reasoning.”
3–5 minutes: partner work time
Monitor for the following in student explanations to share in the synthesis:
415 is halfway between 410 and 420.
415 is the same distance from 410 and 420.
415 has two closest multiples of 10: 410 and 420.
750 is halfway between 700 and 800.
750 is the same distance from 700 and 800.
750 has two closest multiples of 100: 700 and 800.
Student Facing
Round each number to the nearest ten and the nearest hundred. Use number lines if you find them helpful.
| number | nearest ten | nearest hundred |
|--------|-------------|-----------------|
|   18   |             |                 |
|   97   |             |                 |
|  312   |             |                 |
|  439   |             |                 |
|  601   |             |                 |
Kiran and Priya are rounding some numbers and are stuck when trying to round 415 and 750.
Kiran said, “415 doesn’t have a nearest multiple of 10, so it can’t be rounded to the nearest ten.”
Priya said, “750 doesn’t have a nearest multiple of 100, so it can’t be rounded to the nearest hundred.”
Do you agree with Kiran and Priya? Explain your reasoning.
Student Response
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Activity Synthesis
Select previously identified students to share their responses.
“Kiran and Priya are correct. There isn’t one closest multiple of 10 to 415 because it’s right in the middle of two multiples of 10. There isn’t a closest multiple of 100 to 750 because it’s right in the middle of two multiples of 100.”
“In cases like this, we round up. For example, since 415 is halfway between 410 and 420, we would round up to 420 to round 415 to the nearest ten.”
“Since 750 is halfway between 700 and 800, we would round up to 800.”
”In both of these situations we could go the other way, but it is helpful if we all do the same thing in these situations.”


aligns: no