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at the per capita data in Task 3. I was occasionally approached with a procedural question or detail that needed explaining. Overall, the students un derstood the expectations and proceeded with un easiness and blind faith that inquiry brings forth.

apartments for as little as $390 and were pleased that it was so affordable. As the discussion turned to their own expenses in the theoretical minimum wage life, students began to realize the necessity of paring down their current living expenses due to the reality of their minimum - wage jobs. One stu dent even announced to the class (with great dis tress) that she was “ Already in debt $430 and it wasn ’ t even the end of the month yet! ” This same student then asked me if it was allowed for her to live in a homeless shelter instead. I laughed and told her it wouldn ’ t be in the spirit of the project, but rather asked her to reflect on what she was learning. She said, “ It ’ s so expensive to live, I don ’ t see how someone making minimum wage could do it! ” My follow - up comment was, “ And yet we love getting fast food and expect to have low prices when we go to Target to shop. ” Other students turned to Excel to create graphs of the da ta points they were generating in their calculations. I informed the class they could hand - draw or use Excel for any graphs they were making and assist ed some groups with programming in Excel if they chose to use it. I closed the class session by explaining homework expectations for the night: everyone was to work more on their income and bills calculations de pending on what they still needed to accomplish. I explained that the next day they would need to be ready to create their presentations, so they needed to come to class ready to do this. I also suggested that they think about what they wanted to include in their presentation: PowerPoint, a hand - drawn poster on a giant sticky note, Excel graphs, hand drawn graphs, a short skit or demonstration. Stu dents were to think about these options overnight and discuss with their partner so that class on the third day could begin with an action plan in place. The third day was reserved for tying up loose ends and creating presentations. The presentations would be held on the fourth day, when students would also be self - assessing using the Assessment Rubric (see Lesson Plan file). Students came to class ready to get started, since they had worked hard to gain momentum on Day 2. Most of the stu- Day 3

Day 2

Students on the second day were already in the groove of the project. Their homework on the first day was to discuss their family ’ s bills and expenses with parents; they came into class on the second day talking about this information. Things started much quicker and we went directly to the Comput er Lab to begin working. Students were asking how their family ’ s expense data translated to a sin gle person and I helped explain the differences in cost for a standard single person in our city. The students started recognizing the relationship of their income and expense data to graphs, and some asked questions about how they would graph the information. The most common misconception was the use of bar graphs. I explained to these students that a bar graph wasn ’ t appropriate because it showed that each day you made the amount of money of that bar, so every day would be the same size bar. This didn ’ t, however, show them the in creasing money in their bank account as the work ing days of the month went by. I explained that it would be much more useful to visualize the entire amount of money in their bank account by looking at the cumulative increase over time; they started to understand the relationship to a line graph and plotting points that corresponded to money versus time. Most students then made the inverse realiza tion that if their income had a positive slope, then their expenses would have a negative slope. Look ing back, I had not anticipated their need for this handholding to make the leap between the money calculations to the line graph. All the students in the class had seen financial graphs before, because I taught them last year and did a stock market pro ject. However, an inquiry - based teacher must al ways be flexible and adapt to unexpected behavior from the students. I was most impressed with one group that logged onto ApartmentFinder.com to look up actual rent costs for different areas of the city. They found

Virginia Mathematics Teacher vol. 47, no. 2

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