Unit Content
While teaching my Geometry, Pre-Calculus and AP Calculus students, I have realized that my students have a lot of gaps in their knowledge of fractions. My AP Calculus students can solve a definite integral, plug in the limits represented by fractions, but fail to subtract fractions at the final step. Let’s say students should solve the following problem:2
All of my students will find an antiderivative and apply the First Fundamental Theorem of Calculus by plugging in the limits, but later many of them will fail to compute the sum involving fractions. In fact, the situation is so desperate that AP Calculus students are not required to complete this step in the free -response section. As long as they plug in the limits correctly, the problem is considered to be done, and they receive full points for it on the AP test. However, to get their points for a multiple-choice problem student should be able to complete calculations with fractions. Most of them will fail due to the lack of skills with basic Math.
My Geometry students do not do any better. At the end of the year they take a pretty hard standardized test. The test is being constantly modified to become more rigorous. The newer version includes a lot of problems on ratios and proportions be it similarity or relationships between the volumes and/or surface areas of space figures when their dimensions change. Solving such problems requires a lot of skills on operations with fractions. As a result, students feel insecure and unconfident. My unit is designed to fill in the gaps in adding, subtracting, multiplying and dividing fractions to help students succeed at all Math levels.
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