Teacher resources and professional development across the curriculum

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RepresentationSession 05 OverviewTab atab btab ctab dtab eReference
Part A

Observing Student Representation
  Introduction | Representing Data | Problem Reflection #1 | Is This Circle Graph Correct? | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal

 
 

Think about Martina's work and reflect on the following questions. After you've formulated an answer to each question, select "Show Answer" to see our response.


Question: How does this problem provide an opportunity for students to build their understanding of numbers, including percents, which are often used when representing information in a graph?

Show Answer
Sample Answer:
The writing assignment encourages students to think about what the fractions, decimals, percents, and grid mean. Martina has some understanding that the whole 100-grid represents the total, or the 60 students who were surveyed. She understands that 0.999999 in her table is a numerical representation of the number 1 (it is approximately equal to 1). She is beginning to understand that the fraction of the group that prefers basketball can also be represented as a decimal part, and as a percent, of the whole group. Her plan for her circle graph shows that she understands some link between the percents shown on the 100-grid representation and the circle graph that she plans to draw.
 

Question: How is representation a critical part of analyzing data? Why is it helpful to use percents?

Show Answer
Sample Answer:
Using percents makes it easier to compare several groups to one another because they are all fractions of 100. In this situation, percents are easier to work with than lengthy decimal representations. A 100-grid provides a visual tool for comparing and analyzing data. It might be particularly helpful for those students who were having trouble initially seeing the relationships between data categories.
 

Question: What does the empty square on the grid represent?

Show Answer
Sample Answer:
Several of the ratios yielded repeating decimals, and Martina wrote them as they appeared on her calculator. She filled in the grid after rounding down several of the decimals and expressing each amount to the nearest percent. The empty square on the grid is the result of rounding down in several cases. Notice that the total of the actual decimals in the chart is approximately equal to 1.
 

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