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Problem SolvingSession 03 Overviewtab atab btab cTab dtab eReference
Part D

Applying Problem Solving
  Introduction | Measuring Ant Tunnels | Problem Reflection | Classroom Practice | Problem Solving in Action | Classroom Checklist | Your Journal


Reflect on each of the following questions about the problem you've watched in Mr. Reilly's class, and then select "Show Answer" to reveal our commentary.

Question: The process of measuring involves choosing an appropriate unit, which can be standard (an inch, a centimeter) or non-standard (the width of your hand, the length of your pace); comparing that unit multiple times with the characteristic (length, width) of the object being measured; and then reporting the number of units. Can you identify ways in which this problem helped students develop an understanding of the measurement process?

Show Answer
Our Answer:
Measurement processes are imbedded throughout the problem. Students choose a unit and then compare that unit many times with the length of the ant tunnel; both actions are part of the measurement process. Those using the links measure the tunnels in small pieces and then count all of the pieces. Those using string measure the entire length of the tunnel and then compare their string with the units on the ruler. Both methods are models of the process of measuring.

Question: In this lesson, Mr. Reilly asks his students to select the tools and units they will use to measure the tunnels. Some students choose standard units and others choose non-standard units. How does this use of different tools and units encourage students' understanding of the measurement process?

Show Answer
Our Answer:
Students who use the links are comparing the length of the link with the length of the tunnel multiple times. Students who use the string measure the tunnel and then use the markings on the ruler to determine the number of units –– in this case, the number of inches there are on the string. By measuring with different units, students gain experience with the process of measuring, which is the same no matter what unit of measure is being used.

Question: How did problem solving provide a context in which mathematical ideas and skills could be learned?

Show Answer
Our Answer:
Students used successful problem-solving processes to measure the ant tunnels. After discussing the problem and the question, they had to determine an appropriate tool and strategy to use to solve the problem. After solving the problem, they explained their solution process to the class.

Question: How did Mr. Reilly use this problem to engage students and elicit their mathematical reasoning and communication?

Show Answer
Our Answer:
The students were interested in the ant farms. The task built on their natural curiosity about the length of the tunnels. The fact that the tunnels were not straight lines encouraged students to reason about how they would approach the task. Students were also encouraged to communicate throughout the lesson. First, they discussed their strategies and then shared their solutions at the end of the lesson.

Question: Mr. Reilly let students decide what tools to use for measuring. What are the advantages of this approach?

Show Answer
Our Answer:
Recall that the goal of developing mathematical concepts through problem solving is to help students make sense of the mathematics they are learning. Students have to make sense of the problem in order to choose appropriate strategies and tools. In this case, they need to understand that the tunnel is "squiggly" and that it will be difficult to measure with a straight ruler. In making their decision about what tool to use, they bring understanding to the elements of the problem. They may begin with tools that do not lead to a solution, which means that they will need to modify or change their approach.

Question: How did Mr. Reilly's questions help students with the problem-solving process?

Show Answer
Our Answer:
Mr. Reilly's questions helped students think the problem all the way through before coming up with a plan. He helped students refine their process as they worked, but he did this without telling them what to do. His questions encouraged children to explain their thinking.

Next  Use the Classroom Checklist

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