Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Observing Student Problem Solving
 Introduction | How Many Vehicles? -- Using Counters | Problem Reflection #1 | How Many Vehicles? -- Using Numbers and Cubes | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal

This is the problem the teacher posed to the students:

 We have been collecting information about the different ways that teachers and students traveled to school the in last several days. Today I counted the number of wheels in the parking lot. There were 24 wheels. How many vehicles could be in the parking lot?

As part of the problem-solving process, students need to decide what materials to use to help solve the problem, determine how to record their answer, and explain what they did to solve the problem.

Angela and Mariko have decided to use plastic-circle counters to help them solve the problem. Even though all the students have read the problem and talked about it in their own words, the two girls are having a difficult time getting started. The teacher begins by checking that they understand the problem:

Teacher: What do you know?
Angela: There are 24.

Teacher: Twenty-four what?
Angela: Twenty-four wheels.

Teacher: Where?
Angela: In the parking lot.

Teacher: What question are you trying to answer?
Angela: How many cars? Veee . . . vehicles?

Teacher: That's right! What other vehicles have we seen in the parking lot?
Mariko: Buses, bikes, and I think there was a motorcycle one day.

Teacher: Yes, those are all vehicles! Now, what question are you trying to answer?
Mariko: How many vehicles there could be in the parking lot.

Teacher: I see you have some counters here. Why have you chosen to use the counters?
Angela: Because they're round like wheels.

Teacher: So, what can you do with the counters to get started?
Mariko: We can show the wheels of a car like this?

Teacher: Show me the wheels of some different vehicles using the counters.
Angela: These are for a bike:

Mariko: These are for a bus because a bus has six wheels:

Teacher: You got the idea! Keep working on the 24 wheels now, and I'll be back in a bit.

Mariko and Angela continue to work while the teacher moves on to another group. When the teacher returns, she sees the following:

Teacher: Tell me what you have here.
Mariko: There are 24 wheels.

Teacher: I see 24 wheels. Now, what is the question we are trying to answer?
Angela: How many wheels?

Teacher: Look at the board and look at the problem again.
Mariko: Oh, yeah -- we need to find how many vehicles there could be.

Teacher: How can you show me a vehicle?

Angela moves some counters and draws the following:

Teacher: Explain what you did.
Angela: I put four wheels together. That means it is a car. I drew a circle around the car.

Teacher: Are there enough wheels to make another vehicle?
Mariko: Oh, I get it . . .

The girls move their counters and draw circles to make this arrangement:

Teacher: So, what do you have now?
Angela: Six cars.

Teacher: How do you know there are six cars?
Angela: Each circle is a car, and there are six circles.

Teacher: Write that down on your paper. Now, is there another answer to the question?
Angela: I don't know. Maybe . . .

Teacher: Well, try it. See if you can find another answer.

The teacher moves on to another group while the girls rearrange the counters to find another answer:

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