**Me**: Do you think there are more than 20 altogether?

**Estelle**: Yes, because 45 is more than 20.

**Me**: Are there going to be more than 50? They both think.

**Estelle**: Less.

**Denayah**: The same. They build the two numbers, then Denayah breaks off 5 cubes from the tower of 8 and adds them to the tower of 5.

**Me**: How did you know how much to add on?

**Denayah**: I knew it was 5 here and 5 and 5 make 10 so five more. Then they figure out the total number of cubes.

**Me**: Was it more than 50?

**Denayah and Estelle**: Yes. I know that the numbers in these problems are pretty large for 1st graders to add, and that they aren’t expected to add them without models and representations (CCSS.Math.Content.1.NBT.C.4.) But, asking them to estimate seemed to interrupt the more routinized approach they were taking and encourage them to think more about the numbers and the operation of addition. Most students recognized when one of the addends was larger than the estimated total; I wonder now how they would have responded to obvious overestimations, like 100. The thing I’m left thinking about is how powerful a practice estimation can be. As Jennifer Clerkin Muhammad says, in Becoming the Math Teacher You Wish You’d Had (Zager, 2017): “[Estimation is] supposed to be–not a chore–but something that really helps you! At certain times, it’s all you need, and other times, it’s all you have time for, and it always helps you think about reasonableness. In fourth grade, with division, sometimes all common sense goes out the window. As soon as paper and pencil get involved, it’s all about getting that answer, and they stop thinking about reasonableness. So I’ve been trying to push the kids to think about what makes sense or not.” Asking students to estimate is asking them to engage in math in ways that are essential to becoming powerful math thinkers. Expecting math to make sense and applying what they understand about mathematical structures and relationships should be a natural part of a student’s process of solving problems.

Latest posts by Arusha Hollister (see all)

- Are There Going to Be More Than 20? More Than 50? - November 18, 2019
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I am often looking for ways to move beyond “just getting the answer” and engaging the students in the process. Students are still caught in the idea that math is all about getting the right answer, even with a lot of constructivist thinking. I want to try bringing in estimation in various situations and see how it deepens the conversation. Thank you for your blog

Judith

Thank you for your comment, Judith. Once I started thinking more about the role of estimation I have noticed many different opportunities for estimation to be a helpful part of the problem solving process. I continue to think about and explore the power of estimation!

People might be interested in another post about estimation, from Dan Meyer: https://blog.mrmeyer.com/2019/estimation-isnt-just-calculating-badly-on-purpose/