Summary:

After participating in a shared reading about a pumpkin, and singing about "five little pumpkins," Mrs. Richardson's six and seven-year-olds are ready to begin a lesson on estimating the number of seeds in an actual pumpkin. Students give their estimates of the number of seeds in a small, uncut, pumpkin while the teacher records their estimates on a large class chart. To give students a point of reference, Mrs. Richardson cuts open the pumpkin. After looking at the cut pumpkin, students revise their estimates. Working in small groups, students are challenged to come to a consensus estimate of the number of seeds, before performing a seed count.

Standard Connection:

(Practice Standard)—Common Core Practice Standard #3—Construct viable arguments for conclusions reached and critique the reasoning of others—is prominent in this clip. In one small group, we see two strong personalities try to construct viable arguments for their own estimates while critiquing group members. Initial attempts to reach group consensus fail. One boy holds fast to his estimate of 80 seeds, hoping that his reliance on observational cues (i.e. seeds dislodged during repeated stirring of the pumpkin pulp) will persuade the group to his side of the argument. A girl in the same group is just as adamant in her conviction that the estimate should be 100. She also engages in "majority rules" thinking by claiming consensus has been reached among group members. Her final argument reveals good mental mathematics skills but poor number sense when she proposes that the compromise number should be 180 because "Eighty plus one hundred equals a hundred eighty." It is not until the teacher intervenes that the two students abandon their unfounded and unsound arguments and reason that 90 is a good compromise.

(Content Standard)—These students demonstrate Content Domain Standard knowledge that straddles first and second grade domains. At the conclusion of the lesson they are able to reach consensus because they can "compare two two-digit numbers based on meanings of the tens ... digits" and conclude that, since 90 is less than 100 but greater than 80, a compromise has been reached. This compromise places their content knowledge in the Number and Operations in Base Ten—1.NBT domain. During their argument, it is clear that one student can compare two-digit and 3-digit numbers and "mentally calculate sums for numbers with tens and hundreds" even though she does not apply number sense reasoning to her 180 proposal. The skills she has mastered are outlined under the Number and Operations in Base Ten—2.NBT domain.

Questions to Consider:

Beyond reaching consensus, what questions could the teacher have asked the students in the group that would have encouraged them to construct mathematical arguments to support their thinking?

3. Construct viable arguments and critique the reasoning of others

1.NBT Number and Operations in Base Ten

2.NBT Number and Operations in Base Ten