Summary:

There is a working cranberry bog near the Downey Elementary School in Westwood, Massachusetts, so cranberries are a natural tool for a second-grade lesson on estimation. The class begins with each student asked to predict and record the number of scoops of cranberries that will fit in a mason jar. A class graph is made of these predictions and the range of individual predictions discussed. After seeing a classmate partially fill a mason jar with three scoops of cranberries, groups are given their own partially filled jars containing three scoops and asked to reach consensus on how many total scoops it takes to fill their similarly sized jars. Group scoop estimates are reported and the range noted. Next, actual scoop counts are made so scoop estimates can be verified. Actual scoop counts are reported and variations again noted, which leads to a class discussion of measures of central tendency (i.e. mean, median, and mode). Using mean values, groups are able to come to consensus on the number of individual cranberries in each jar. During this lesson, besides honing estimation skills, students are able to use their spatial and repeated reasoning abilities.

Standard Connection:

(Practice Standard)—The Common Core Practice Standard that is most prevalent in this lesson is Practice #2—Reasoning abstractly and quantitatively—As students move from estimating number of scoops to estimating the number of individual cranberries in their mason jars, their estimation strategies became more and more apparent, albeit often unspoken. Students use "chunking" and/or "subdivision" techniques in conjunction with spatial reasoning to justify predictions [i.e. "I have three scoops that fill up about this much (indicating approximately one-third with fingers) when the whole jar must be nine scoops (using fingers to show each third)"]. This repeated reasoning requires abstracting the concept of a third of the volume of a jar and quantitatively thinking with skip counting. Looking back at answers allows students to determine the reasonableness of their answers and to share their thought processes.

(Content Standard)—The domain that captures the mathematics content most prevalent in this lesson is—Measurement and Data. Students demonstrate that they can solve problems involving estimates and measurements of quantities.

Questions to Consider:

What do you think the purpose was for placing three scoops in the jar before beginning the group estimates? What other estimation techniques have you used or seen used before? Which measure of central tendency (i.e. mode, median, or mean) would you have encouraged students to use in their estimations? Why?

2. Reason abstractly and quantitatively

3.MD Measurement and Data