Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Problem SolvingSession 03 OverviewTab atab btab ctab dtab eReference
Part A

Observing Student Problem Solving
  Introduction | Which Group Paid More? | Problem Reflection #1 | Sharing-Division Word Problem | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Summary | Your Journal


Think about the student work and reflect on the following questions. After you've formulated your own answer, select "Show Answer" to see our response.

Question: What prior learning experiences are the students able to refer to as they tackle this challenging problem?

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Sample Answer:
First, it is evident that these students have learned that they can tackle complex problems on their own and that they can explain their thinking. Mathematically, they refer to informal understanding of ratios and comparisons of ratios; to repeated addition, skip counting, and a calculator as means of multiplying; and to sharing division as a means of finding out "how much for one."

Question: How does this problem provide an opportunity to learn about division through problem solving? What other mathematical concepts are introduced?

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Sample Answer:
The teacher helps the students explore Evan's idea of sharing the total cost among the number of cans. Students recall that the quotient will tell the same amount, or cost, for each can. They use "guess and check" to find the quotient. They also connect the problem to multiplication as a way of checking their division. In addition, the teacher introduces the term "unit cost" and the words "for each" to the students. They work with decimal quotients that extend several places on the calculator, which may be new to many students.

Question: How does this problem encourage the use of a variety of problem-solving strategies? What strategies do the students use?

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Sample Answer:
The problem is rich and complex; it does not ask for a single fact. It is connected to students' out-of-school experiences and prior lessons on basic division. It can be solved through a variety of methods, such as division, comparing ratios, making a diagram, and guessing a quotient and then checking it by adding or multiplying. Evan is able to recognize this as a sharing-, or share-out, division problem, where the question is, How much for one? First, the teacher helps Evan use his chosen method of "guess and check" to find one of the unit prices for the decimal amount of money. Next, they turn to long division. Teresa thought about the ratio of one price to a number of cans and then doubled the numbers in the ratio to check whether the total was more or less than the total in a different ratio. Kelly followed Teresa's lead and used the reasoning of her classmates to work on the problem.

Question: What are some questions and future instructional steps you might add if you continue to use this problem-solving situation to teach about division?

Show Answer
Sample Answer:
It would depend on what other mathematical goals the teacher has for these students and on their prior experiences. For example, if teaching about unit rates were the goal, the teacher could ask more questions to make sure that the students really understand the concept of how unit price and aggregate price relate. The teacher could also provide follow-up experiences where the students make up and solve both multiplication and division problems with unit costs and unit rates. Finally, it would be beneficial to help students represent their work and make diagrams that aid their thinking and communicating.

Next  Observe student work on another problem

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