The purpose of this activity is for students to consider what it means for an answer to make sense. They see that rounding is a useful strategy to estimate the answer to a problem and to determine if an answer makes sense.

The quantities chosen are close to multiples of 100 (and multiples of 10) to encourage students to round as they decide if an answer makes sense. The first problem also says that “Priya makes an estimate” and “about 400 beads.” If students begin computing the exact numbers of beads, remind them of the situation and that they do not need to solve to determine if the answer makes sense.

As students work, prompt them to explain their strategies for making estimates and relate them to the idea of rounding (MP3). When students use language such as “about 600 beads” to convey that they are estimating, they practice communicating with precision (MP6).

• “In general, how can rounding help us estimate?” (Rounding makes the numbers easier to think about quickly. Rounding to the nearest hundred or the nearest ten means dealing with only hundreds, or with only hundreds and tens, rather than with hundreds, tens, and ones.)
• “When we are deciding whether an answer makes sense, we are not solving the problem to get an exact answer. We are estimating the answer. Rounding is a strategy that can be useful when we estimate an answer.”

The purpose of this activity is for students to solve two-step word problems involving addition and subtraction. After students solve the problems, they trade answers with a partner to decide if their answers make sense.

When students assess the reasonableness of each other’s answers and communicate their assessment, they construct logical arguments and critique the reasoning of others (MP3).

• “What is this problem about? What can be counted or measured in this situation?”
• “How could you represent the problem?”

• “What was helpful about having someone look at your work for each problem?” (They thought my answer made sense, which helped me know that I had answered correctly. They caught a mistake that I made that I didn’t notice.)
• “What was helpful about looking at someone else’s work for each problem?” (I was able to see a different strategy that they used for the problem. I was able to help them catch a mistake they made.)