Examine the jar containing marbles. On your own, write down how many marbles you think are present and how you arrived at your estimate.
What information and materials would you need to solve the problem?
Share your estimate of the number of marbles in the jar with other members of your group. Discuss each other’s predictions and approaches.
Ask a member of your group to write down everybody’s ideas and share the estimates and approaches with the rest of the class.
In your group, come up with an agreement about how to test the ideas about estimating the number of marbles. As much as possible, avoid counting every marble. Prepare to share your ideas with the rest of the class.
Share your findings. As a class, discuss the merits of each approach.
Based on what you have observed and heard, write down the strengths and weaknesses of the approaches. Which approach makes most sense?
In your own words, explain an approach for estimating large numbers that makes sense to you and explain why you support that approach.
Here we dealt with estimating large numbers of marbles. What are some other examples of estimating large quantities you can think of?
Who are some of the people who use estimation?
What are some other questions or problems on estimating large numbers that you would like to explore? How would you proceed?
Teaching for K-12 mathematical understanding using the Conceptual Change
Model