By Jen McAleer, posted May 22, 2017 —

1. Establish a routine: It is important to establish a routine, so that students can rely on regularity and learn to expect this type of mathematics every day. Pick a time daily or weekly to devote to estimation. Carry over the work to a next class period, depending on the depth of the math involved.

2. Provide students with a way to show their thinking and keep track of their estimations over time: I use a graphic organizer, which allows students a chance to make high and low estimates. We call this “low-entry access” to tasks because it’s safe. We share these estimates as a class but do not discuss reasoning at this point. After discussion, I want the students to settle on their choice to see where their numbers fall between the high and low estimates. It is important to note that I never let a student make an estimate without also asking that he or she justify the choice; I want to make sure that the student is using the given information and mathematics to devise an answer. This is not a quick process. Some students will take more time than others. I do not lead this discussion because I want to see students’ thinking. If students finish quickly, I ask, “How did you get that answer? Is there a different way you could think about it? How did you know to do that?”

3. Give students ample time to reason on their own: Never rush the process. Depending on the richness of the task, I want my students to think on their own for at least 5 minutes. This time gives them the opportunity to (1) make sense of the information they have, (2) develop an approach or strategy to find a solutions, and (3) develop a justification for their number. If particular students reveal their strategy, students will never have the chance to adjust their thinking in the future.

4. Display the estimations in a meaningful manner, so that all students can see all estimates: I provide an area in the classroom for students to display their number choice. Students write their estimates anonymously on a sticky note and place it on a number line, which can either contain or not contain a scale. I want students to reason where to place their estimates relative to those already on the wall, thus offering a chance to develop their number sense and to understand the magnitude of numbers. Once all have placed their estimates, I ask the students to come to the number line in groups to look over the placements. If they would like to move any sticky note, we discuss the findings as a class and make the adjustment. See the example below.

5. Throw out or disregard any estimates that are unreasonable and explain why: I ask students if they see any unreasonable estimates. Whenever a student proposes an estimate that is believed reasonable, they must also state why: “I think _________ is unreasonable because _________.” We then debate and weed out estimates.

6. Discuss students’ strategies and how they evolved: Step 6 takes practice. I ask students to share their estimation strategies and then allow the class to ask clarifying questions and agree or disagree with any of the reasoning. Since there is not enough time for every student to share, I am very intentional in my choice of sharing the strategic thinking of students by identify those students while asking questions earlier in the process. Steps 5 and 6 are the most important and subsume the most time. Sometimes we are unable to finish the discussion.

7. Allow time for students to adjust their estimations as the discussion progresses: After the class discussion, I allow and encourage students to update their choices. I want them to look at their estimates and rework their thinking along the way. It is common when viewing their the graphic organizer to see the “actual estimate” crossed out multiple times and changed before the answer is revealed. Although the original sticky-note estimates stay on the wall, it is important to encourage students to rethink their process along the way.

8. Reveal answers, discuss why the answer was or was not surprising, and how students could adjust or be more effective with their estimations: The answer is not as important as the process. Where did our process lead us? What did we learn from our approach? What could we change in the future to be more accurate?

In the next post, I will share two examples of estimation lessons and the discussion that followed.

Jen McAleer is the head of middle school mathematics (grades 6–­8) at the Carroll School in Lincoln, Massachusetts. The Carroll School serves students with language- based learning difficulties who also tend to struggle with mathematics. McAleer has been teaching middle school for ten years and has a passion to give all students a voice in mathematics and provide them with opportunities to be and feel successful working with higher-level content, despite their struggles with procedures and computation.