Teacher Commentary Integrating Problem-solving Math/Science Investigations University City High School, Philadelphia SLC: Math/Science Magnet Teachers: Deborah Andrew, Lakshmi Pillalamarri, Dina Portnoy School Phone: 215-387-5100

Unit of Study Summary This unit of study was an integrated math and science course for ninth grade students before they began the Interactive Mathematics Program. Using a variety of technological tools, including graphing calculators and Calculator Based Labs (CBL), students developed their skills in data collection and analysis. They explored scientific phenomena by making connections between science and math. They were also encouraged to explore the physical world using this technology and their data collection. Students conducted a variety of activities to measure length, area, volume, density, and mass. Students also developed communication skills by writing and demonstrating their understanding of the task through oral, visual, and graphic presentations. Thus students were engaged in developing multiple skills in a range of curricular areas. What should students know and be able to do? School District of Philadelphia Standards: Math #4,Patterns, Algebra, and Function-Use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data and graphs in problem solving situations and communicate the reasoning used in solving these problems. What were students asked to do? The student work is a lab report on the study of using a beam balance for measuring the mass of an object. Students were expected to recognize relationships between parts and the whole. Using a banana, students used math skills to find percent and fractions and developed various graphs to show the relationships between the edible and non-edible parts of a banana. Students were asked to measure the mass of an empty cup, and then, measure the mass of the same cup with an unpeeled, whole banana. Next the students measured the mass with a peeled banana in the cup. Students placed the peel in the cup and measured its mass. They were then asked to repeat this process for eight different bananas (two bananas for each student, and four students in each group). They tabulated their data, found the ratio of peeled to unpeeled and unpeeled to whole, and found the percent of edible and inedible parts of the banana. They drew bar, pie, and line graphs to find the relationship between the variables. They also used the TI-83 graphing calculator and entered their data in the lists to draw the graphs and find the regression equations. What story does the work tell? This sample of student work shows the process and product of the student's work for this activity. Along with graphs showing the findings of her data and the relationship between the edible and inedible parts (C&D), this student also wrote out the purposes of this activity (A). Looking at this sample, we can see that this student learned how to use the scale to find the mass of the object (B). As a result of this activity, she knows the unit of measurement required for this activity and she learned how to develop a graph by differentiating between the independent and dependent variables (?). She learned how to choose a proper scale for the available data (C). She was able to explain the procedure and her findings in writing and recognize the relation of the part to the whole as a percent (?). Using her work, we can also learn that she was unable to transfer information from the bar graph to a pie graph (D). Rather than making separate pie graphs for each banana, she combined the edible parts of all the bananas into one pie graph. This could reflect her misunderstanding of the function of the pie graph and that the total has to be 100%. An excellent piece needed to include: The purpose; the theory; the materials used; the procedure; the charts of observational data; the calculations; bar graph; pie graphs; two line graphs; a conclusion which explained what was learned in this experiment. This was a total of 25 points. Students, as a group, also did an oral presentation of their findings to the class. The oral presentation was ten points, which included the completeness of their findings, the visual graphs, and the clarity and style of their communication to the class. This sample represented 22 out of 25 points because the pie graphs were incorrect and she failed to demonstrate an understanding of ratios and the line of best fit in her line graph (F). Her description of the purposes and procedures, and her observation charts demonstrated her understanding of the concepts of the activity. How can your analysis guide further instruction? We can see that understanding the concept of a pie graph is more complex than interpreting the basic data in the bar graph. Her chart indicates that she did not get a clear understanding of the concept of a ratio. This might be due to a problem with following directions or, at the same time, it may be that this concept can be better understood with multiple activities using different materials. Also, in her line graph, she was unable to find the line of best fit. This was the first activity leading to a linear graph, which possibly explains why she had difficulty finding the line of best fit.

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