The purpose of this activity is for students to round to the nearest tenth and hundredth. Students have rounded in earlier grades but this is the first time they round to tenths or hundredths. This is a direct extension of rounding to the nearest ten, hundred, thousand, and other whole number values. Locating the numbers on the number line will recall this earlier work.

The Launch introduces the context of a doubloon, a major currency in Portugal and Spain in the seventeenth, eighteenth, and nineteenth centuries. Students round the weight of a doubloon to the nearest tenth and hundredth of a gram. In both cases, older doubloons are still heavier after rounding. However, when they are rounded to the nearest gram, they are the same. This is important from a practical perspective because it is easier to measure a weight to the nearest gram than it is to the nearest tenth of a gram or hundredth of a gram. It is also important because the numbers 6.9 and even 6.87 are not as complex as 6.867, and having fewer digits helps visualize the value more quickly.

• Invite students to share their answers for rounding the weights of the doubloons.
• “¿Cómo redondearon el peso del doblón más antiguo a la décima más cercana? ¿Y a la centésima más cercana?” // “How did you round the weight of the older doubloon to the nearest tenth? What about the nearest hundredth?” (It was closer to 6.9 than to 6.8, so I rounded to 6.9. It was closer to 6.87 than to 6.86. So, I rounded 6.87 to the nearest hundredth.)
• “¿Cómo les ayudaron las rectas numéricas a redondear los números?” // “How did the number lines help you round the numbers?” (I could see on the number line which tenth or which hundredth the number was closest to and then knew to round it there.)

The purpose of this activity is for students to examine numbers in different situations and decide if they are exact or approximate. In most cases, there is no definitive answer but it is likely that the numbers are approximate or rounded. Two important reasons for using rounded measurements are:

• It is easier to measure a length, for example, to the nearest kilometer or meter than to the nearest centimeter or millimeter.
• Rounded numbers can communicate the size of a quantity more clearly than exact numbers.

For example, we might say that the classroom is 15 meters long. That number is probably not exact but it gives a good idea of the length. It is possible that 14.63 meters is more accurate but it is also cumbersome. The goal of the Activity Synthesis is to discuss some of the ways you can tell if a measurement is exact or rounded and what that tells you about the measurement.

• Invite students to share their reasoning for the population of Los Angeles.
• “¿En qué es diferente el caso de la población de Los Ángeles al caso de los lápices?” // “How is the population of Los Angeles different from the pencils?” (There are so many people in Los Angeles that you can’t count them all. The pencils I can count one by one to check my answer.)
• Invite students to share their reasoning for the time of 19.87 seconds.
• “¿Por qué creen que la medida podría ser exacta?” // “Why do you think the measurement could be exact?” (It’s really precise. If it said 20 seconds then that sounds like an estimate but 19.87 seconds looks too precise to be an estimate.)
• “¿Por qué creen que la medida podría ser aproximada?” // “Why do you think the measurement could be approximate?” (It’s like the doubloons. There could be some thousandths of a second and 19.87 seconds is just an estimate.)