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# Critical Thinking through Estimation

By: Boucher, Alfred C. | Teaching Children Mathematics, April 1998 | Article details

# Critical Thinking through Estimation

Boucher, Alfred C., Teaching Children Mathematics

Young children are naturally intrigued with the world around them. They use everyday materials in their play not only to answer intrinsic questions but also to formulate new, more thought-provoking questions. The inquisitive nature of children is an excellent springboard to enhancing critical thinking through estimation.

Are children doing anything more than guessing when we introduce the concept of estimation? Is guessing an acceptable alternative to estimating? What are the differences, if any (Andrews 1995)? These questions will be addressed in this article, which explains how I incorporated critical thinking, communication, and estimation into an exciting problem-solving unit for first graders.

Our school is located in a working-class suburb of Atlanta, Georgia. In my own classroom I was fortunate to have a diversified student population composed of nine African-American children, eight white children, four Hispanic children, and one Asian child. This group worked well together in solving problems.

My planning for this project included purchasing unique as well as familiar materials for students to use. With a \$200 "minigrant" from our school district's foundation, I purchased nuts and bolts, trundle wheels, scales, timers, candy, and various "counting toys."

Estimating the Number of M&M's

One of the first activities we explored, at the beginning of the school year, was estimating the number of M&M's in a "fun-sized" bag. I recorded each child's name and his or her response to the number of M&M's in the bag. The estimates ranged from one to one million. I realized that these children lacked the base knowledge to really estimate the quantity of M&M's. Estimating was clearly not evident in this activity; guessing was the order of the day. How could I foster the necessary base knowledge on the part of my students?

I realized that my students were now equipped with the experiential base to expand the M&M's lesson (Leutzinger, Rathmell, and Urbatsch 1986). They discovered that the fun-sized bag contains twenty-five M&M's, which might be the base information they needed to make reasonable estimates of the number of M&M's in a regular-sized bag.

Groups of four students were given a fun-sized and a regular-sized bag of M&M's. The children were to estimate the number of M&M's in the regular-sized bag, without opening either package. I observed the groups and listened to the communication among the students as they began to make their estimates.

One group decided to place the smaller bag on top of the large one, thus using spatial sense to complete the task. They estimated visually that two or three smaller bags would hold as much as one large bag. After manipulating both packages of M&M's, they concluded that the large bag was about twice the size of the smaller one. This tactic was a step in the right direction so I waited to see how this group would use its new knowledge to solve the original problem. The children decided that they could add the number of M&M's from the small bag two times and wrote "25 + 25." They made two groups of twenty-five Unifix cubes each and counted them to get an estimate of fifty M&M's.

Their base knowledge of twenty-five M&M's in the small bag helped them estimate fifty M&M's in the large bag. The students were developing a sense of estimating an unknown quantity by comparing it with a known quantity (Leutzinger, Rathmell, and Urbatsch 1986). After opening the large bag and counting, they discovered that the actual number was fifty-six. I asked whether they thought that fifty was a "good" estimate when the actual count was fifty-six. Their responses included "Fifty is close to fifty-six," "Fifty-six is only six away from fifty," and "Some bags of M&M's might have just fifty M&M's."

Estimating the Volume of Slime

In late October I brought to class ā¦

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