The beauty of this challenge is that students can immediately test their own answers by comparing them to the computer print-out. By overlaying the computer key and their answer and holding both up to the light, students can clearly see how close their construction is. We'll follow this up by a discussion of which strategy achieved the most accurate results and why that is.
"Draw a shape that is exactly twice as large as this one." How would you use only physical tools (ruler, protractor) to complete this task I set to my Geometry class? Most of my students solved this challenge by doubling the sidelengths and replicating the angles. While this is a valid approach, as you work your way around the shape, small errors compound, and your final point may be very far off from where you intended. Only one student attempted, though did not complete, another construction suggested by the diagram below. In this approach each new point drawn is drawn twice as far away from a focus point. Because each new point drawn references the same focus point, slight errors to not compound. The construction I was able to make with only a ruler (no protractor needed) was extremely close to my computer print-out.
The beauty of this challenge is that students can immediately test their own answers by comparing them to the computer print-out. By overlaying the computer key and their answer and holding both up to the light, students can clearly see how close their construction is. We'll follow this up by a discussion of which strategy achieved the most accurate results and why that is.
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According to Pennsylvania's Act 35 of 2016, all new money allocated for primary and secondary education will be allocated to the school districts according to a complex formula. Each district will receive an amount of money proportional to the product of its Student-Weighted Average Daily Membership (SWADM), its Median Household Income Index (MEII), and its Local Effort Capacity Index (LECI). Each factor is meant to distribute funding to the districts where it is most needed. SWADM is approximately equal to a school district's enrollment, with extra weight given to districts with higher rates of poverty and more students learning English. MEII is designed to give more money to districts with a lower median household income and less money to districts with a higher median household income. LECI is a combination of a number of terms. The most significant of these terms is the Local Effort Factor which increases when a district has a higher local tax rate. Both the SWADM and the MEII are designed to funnel more money to the districts with less. The final factor is different. The LECI gives state money to districts that are working to help themselves. These are all reasonable ways to allocate money and even to incentivize districts. Even so, after the money is doled out, it's up to the district to spend it well. Public school funding is a much thornier issue than the personal finances of a college loan. Even once you are able to make your way through the details of each of the three component factors, there are still the questions of fairness as well as how districts raise the rest of the funds they need (often property taxes). If I were to pursue this issue further, I would find a spreadsheet of district-by-district spending and compare this to the state funds each district receives.
For those interested, you can read the text of the law here. You can also download the state's spreadsheet with explanations of the calculations here. There are public schools in Pennsylvania that have swimming pools, projectors in every classroom, and bassoons in the band. There are also public schools in Pennsylvania that do not have libraries. What accounts for this disparity? The state's education budget is a good place to start one's investigation. Pennsylvania passed a law in June of 2016 establishing a formula that determines how state funds are allocated to school districts. With the formula in place, when student populations shift from year-to-year, school funding will automaticallly adjust to compensate. After a brief review of the law, a few numbers stand out.
The formula is designed to provide additional funding to school districts with
As I further pick apart the details of the law, there are a few questions I want answered.
If you have answers for any of these three questions, I encourage you to contact me. You can read more about the new law here, and see the exact text here. |
About Me
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Hanoi, Vietnam. Your comments are always welcome. Archives
May 2021
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