Applying Representation
 Introduction | Building Rafts with Rods | Classroom Practice | Representation in Action | Classroom Checklist | Your Journal

Reflect on each of the following questions about the Building Rafts with Rods problem that you saw Ms. Mullin's class work on, and select "Show Answer" to reveal our commentary.

 Question: How does this task stimulate students to use various representations to model their mathematical thinking? Show Answer
 Our Answer: Students begin with models of the rafts to help them determine volume and surface area, and then record this information in tables. They translate the pattern in the tables into a mathematical expression, and then translate the information in the table into a visual representation in the form of a graph.
 Question: What tools are available for students to use in making their representations? Show Answer
 Our Answer: Rods, various types of graph paper, markers, and rulers are all available for student use.
 Question: How is the classroom discussion enhanced by students' representations? Show Answer
 Our Answer: The graphs help students explain their reasoning and encourage questions from other students and from the teacher. Within the groups, the representations help students clarify their thinking and explain their reasoning to one another.
 Question: Several of the students are using bar graphs as their representations. Do you think this would be a good time for them to extend their knowledge of graphing to using a linear graph? How would you help students make this transition? Show Answer
 Our Answer: Keep in mind that one of the goals for middle-grade teachers is to help students move to conventional forms of representation. So, yes, at some point we want to move students from using bar graphs to using linear graphs. During the class discussions, you could ask students to describe what patterns they see in the bar graphs and in the line graphs and to discuss the advantage of using one type of graph over the other.

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