Prepping for PSAT

This week is a little weird from a scheduling standpoint. Today is Monday and is a normal class schedule. Tomorrow is the state-mandated PSAT for all 10th grade students. Since we just completed the car project on Friday, it didn't seem to make sense to start our next unit today. I have a number of colleagues who have focused on prepping students since last week.  I chose to wrap up the surface area volume unit and catch up with the other teachers. (Inquiry and letting students make sense of the mathematics always seems to take longer than I plan. You just can't anticipate how long it will take for students to absorb the material.

After reviewing what students should do on test day (time to show up, what to bring, where to find class assignments, and such), I pulled up some sample practice problems for the class to tackle. The first set of PSAT Math Practice was 10 questions, mostly focused on algebra. Students worked through these and then we checked answers. Overall the questions went well, although some students struggled with using expression relationships that involved a variable.

The other question that was an issue dealt with finding the average of 1/3 and 1/6. Students always seem to freak out when they see fractions. They also seem to lack any sense of magnitude and of operational proficiency with fractions. As a result, many students chose 1/9 as their answer, since they simply added the numerators and the denominators together to form 2/9. Well, the average of this value is 1/9.

I drew out a pie graph and colored in 1/3 of the graph. I then drew 1/6 of the circle, non-adjacent to the 1/3 slice, and colored it in. I then asked the class if it made sense that adding these two segments together would result in a smaller slice of the pie? The agreed that it didn't. I reviewed the idea of common denominators and students quickly realized the answer should be 1/4.

The last piece we discussed had to do with the meaning of the term, "product." It was surprising to see that students did not know the mathematical meaning of this term. As a result, they added values together rather than multiplying them. In addition, they ignored the trailing decimal values, and rounded heavily to get to one of the given answers. It's a bit disheartening to see the lack of thinking and reasoning that takes place to arbitrarily truncate or round values just to get to an answer that doesn't match any of the given answers. And then to take this a step further and to select the answer with the closest value to the calculated result.

We wrapped up with look at some of the College Board's PSAT 10 practice problems and resources. These problems were a bit tougher than the first ten problems, although all were accessible to the class' ability level. Students did get stuck on solving a quadratic equation. This was a no calculator test and the problem involved a linear term coefficient of 14 and a constant of -51, not something most of my class would want to tackle by using the quadratic formula, especially without a calculator. It turned out (what a surprise) that the equation could be factored.

With that, we were done for the day. I encouraged students to look through the practice exam they had previously received. I think it's helpful for students to become familiar with the structure of the test and questions, even if they don't answer the practice questions. The more comfortable they are with what they are going to face, the less chance they have to panic when confronted with the test.

I won't be posting again until Wednesday, unless something really interesting and/or unusual happens at the PSAT.

We'll dive into the world of circles after the PSAT.