In this activity, students connect the idea of “nearest multiple” to rounding. They are reminded that to round to the nearest thousand, ten-thousand, and hundred-thousand is to find the nearest multiples of these values. When they find all of the numbers that round to a given number, students need to think carefully about place value and may choose to use a number line to support their reasoning (MP5).

If students list some, but not all, of the numbers that can be rounded to 500,000 (or 490,000), consider asking:

• “¿Cómo sabes que esos números se redondean a 500,000?” // “How do you know that those numbers round to 500,000?”
• “¿Qué números no se pueden redondear a 500,000 por ser demasiado pequeños? ¿Qué números no se pueden redondear a 500,000 por ser demasiado grandes?” // “Which numbers cannot be rounded to 500,000 because they are too low? Which numbers cannot be rounded to 500,000 because they are too high?”

• Display the number line from the activity.
• Select students to share their responses and reasoning for the first three problems. Record their responses.
• If no students mentioned using number lines to help them identify all the possible numbers that round to 500,000 and 490,000, ask them to try showing the ranges on the number line.
• Display students’ annotated number lines or the following:

  

  

• “¿Cómo encontraron los números que se pueden redondear tanto a 500,000 como a 490,000?” // “How did you find numbers that can be rounded to both 500,000 and 490,000?” (I chose numbers that are between 485,000 and 494,999, since all of them can be rounded to 500,000. Numbers outside of that interval cannot be rounded to 490,000.)

In this activity, students round numbers to various place values. For the first time, students encounter a number that rounds to one million and some that round to 0. (For example, 4,896, rounded to the nearest hundred-thousand is 0.) Students may wonder why we round a number in the thousands to the nearest hundred-thousand. Make note of such ideas to discuss in the next lesson where students explore rounding in context and see that it often involves giving meaningful information.

• Display the blank table from the activity. Invite students to share their responses to complete the table. Discuss any disagreements.
• “El número 96,500 está a la misma distancia de 96,000 que de 97,000. ¿Cómo sabemos cuál escoger si queremos redondearlo al múltiplo de mil más cercano?” // “The number 96,500 is the same distance from 96,000 and 97,000. How do we know which way to go if rounding to the nearest thousand?” (By convention, we round up.)

In this optional activity, students round multi-digit whole numbers in the context of population. They describe the effect of rounding large numbers to different places and how the rounded values may illuminate or obscure a situation, and may help or hinder problem solving. Along the way, students engage in aspects of mathematical modeling (MP4).

• Select groups to share the matches they made and their reasoning.
• Display the completed table.
• Invite students to briefly share their responses to the last problem, using the table to aid their explanations.
• Point out that, in reality, it is unlikely to accurately count the exact number of people in a state. Highlight that rounding can be a useful way to get a sense of a quantity, but it requires making some decisions about what is most meaningful in a situation.