Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
For a week before this lesson, students worked with nonstandard and standard forms of measurement. In the video, students are engaged in problem solving and measuring with both standard and nonstandard units. Students work in groups to measure three different distances: ant farm tunnels, dinosaurs, and the length from the classroom window to the playground below. Students within each group first think about and then use a nonstandard measurement tool of their choice to measure with. Throughout the lesson, students are encouraged to communicate by discussing possible measuring strategies and reporting their findings and procedures. Students make connections to other subjects when they measure the lengths of dinosaurs they have been studying; to real life when they work with ant farms; and among different mathematical topics when they experience measurement as an approximation, work with fractional units, and perform computations. Once the class shares strategies and results, the lesson concludes as the first graders use themselves to measure the length of a Tyrannosaurus rex. Topics for Discussion
The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.
Using a Problem-Solving Approach
- How did problem solving provide the context in which concepts and skills could be learned? How did problem solving permeate the entire lesson?
- How did Mr. Reilly use these tasks to engage students and elicit their mathematical reasoning and communication?
- What are the advantages and disadvantages of having groups of students work on different activities during the same lesson? What did you think of each activity?
- Mr. Reilly let students decide what tools to use for measuring. Identify the advantages and disadvantages of this approach. What was the purpose of having different students use different materials?
- How did Mr. Reilly demonstrate flexibility in this lesson?
- Students used different strategies to find the lengths of the tunnels. Did any of their strategies surprise you? In what way? What would you have expected of these students?
- Some students used calculators in this lesson. How appropriate was it to allow students to use calculators? Defend your answer. How did calculators help students in their problem solving?
Developing Measurement Concepts
- The process of measuring involves choosing a unit, comparing that unit multiple times with the attribute of the object being measured, and reporting the number of units. Identify ways in which this lesson helped students develop an understanding of the measurement process.
- Describe ways in which the idea of measurement as an approximation was addressed in this lesson. How else might it have been emphasized?
- Formulate ways in which Mr. Reilly could have incorporated estimation into this lesson.
- Each pair of students first measured and marked the length of their dinosaur using standard units (not shown in the video) and then measured it in two other ways using objects of their choice. Why do you think Mr. Reilly wanted students to measure the length using nonstandard units after they had just used standard units? How could the children have been helped to explore why they got different answers when they measured with nonstandard units?
- List questions about their measurements that would have helped students develop some understandings about the need for standard units to communicate.
- The three groups who measured the distance to the playground reported measurements of twenty-eight feet, thirty feet, and sixteen feet six inches. These differences were noted, but they were not discussed during this lesson. How would you have handled this situation? How could the differences in measurements be addressed in the next lesson?
Other Measurable Moments: How Far? How Long?
Reflect on the past several months of your teaching. Determine through conversations with, or from observations of, students, what measurable objects or areas have captured students' attention. Create a list of interesting and somewhat unusual objects or areas for students to measure. What other measurable moments that would interest students might arise? For example, how wide or high is the classroom? How long is a real car? How wide is a city block?
Ant Farm Connections
Devise other investigations, mathematical or nonmathematical, that you can conduct with the ant farms. For example, how are the lengths of the tunnels related to the overall size of the farm or to the number of ants in the farm? What are the functions of the tunnels? How are the ant farms similar to, and different from, ant life in the real world?