Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
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|
Let's look at how three upper elementary students approached the following problem:
First, think about the problem and imagine approaches that students with minimal prior experience with division and ratios might take. Then, read the teacher's questions and the students' statements. As you reflect on these conversations, consider the general usefulness of the students' methods in other problem-solving situations.
Teacher: What did you find out about this problem?
Teacher: Can you explain what you mean by "paid a lot"?
Teacher: So what does that tell us about each can that Group 3 bought?
Teacher: Why is that?
Teacher: OK. Evan, what about Group 1's cans? What did you find out?
Teacher: How can we find out how much each can costs for Group 1?
Teacher: Tell us more about what you are thinking. If we had a picture of each of the six cans, what would you do?
Teacher: Shall we try 10 cents each at first? Will that make $1.80?
Teacher: Can we use division to check to make sure that 30 cents for each can is correct?
Teacher: Who agrees? (The others in the group nod in agreement.) I think you might also divide in your head, use a calculator, or even use manipulatives to divide. Teresa, what could we divide to find out how much each can costs, to find out the unit cost, for Group 2's cans?
Teacher: OK. Kelly, can you help us decide whether Group 3 or Group 1 paid more for each can?
Teacher: What's that on the calculator?
Teacher: Yes, sometimes when you share out -- that is, distribute or partition evenly -- the answer doesn't come out exactly even. With money problems, we usually care about rounding to the nearest cent. Who can underline the part of this decimal that shows the dimes and cents? (Teresa underlines the 4 and 1.)
The numbers behind the cents' place show that there is part of a cent more for each can. I see that this decimal is closer to 42 cents than to 41 cents. We'll learn more about decimals like these sometime soon.
Take a minute to make a final decision about which group paid more for each can of soda. Write a statement about how to find the cost of one can in your journal.
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