Come gather 'round people
Wherever you roam
And admit that the waters
Around you have grown
And accept it that soon
You'll be drenched to the bone
If your time to you
Is worth savin'
Then you better start swimmin'
Or you'll sink like a stone
For the times they are a-changin'.
- Bob Dylan
Well Bob, 50 years later, your words still ring true.
I intentionally asked to proctor the PSAT Wednesday October 14. I wanted to see our students in action.
Derek Green, sophomore, was sitting in the front of the room. I was pleased to see Derek working backwards in one of the multiple choice questions. He worked from the answer back to the question.
$$x^2y+x+2xy+2$$
is a problem that is solved by factoring out the GCF by grouping terms together. In Algebra 1 we call it factoring by grouping. This is a particularly difficult one because you must use the factoring by grouping technique twice. The answer (of course) is \((x+2)(xy+1)\). Derek multiplied the binomials in the answer together to prove that it was equivalent to the original problem.
Of course as a math teacher, I was focused on the last two sections of the PSAT, but it was interesting to see how many graphs and charts were in the first two sections (technical reading). I observed a real shift in emphasis by the College Board. There were very few problems in sections 3 and 4 where a student was asked to graph a line in the form \(y=mx+b\), solve a system of two equations and two unknowns by elimination, or solve a linear inequality.
In over half of the problems, they were asked use their mathematical skills in context (these are not the actual problems):
- T= .08(A-M) represents the equation that is used in a state to tax its citizens based on income. T represents the tax, A represents the income of the individual, and M represents the minimum income threshold. A>M. If the tax generated on an income of $40,000 is $1,200, find the minimum threshold income.
- A customer has two types of gas he is mixing together. X represents the number of gallons of 78 octane gas and Y represents the number of gallons of 96 octane gas. The customer wants to have at most 10 gallons of gas that is at least 84 octane. Set up a system of inequalities that will allow you to solve this problem.
- In a baseball stadium 50% of the seating is in the upper level. 35% is in the lower level, 10% is premium field level seating, and 5% are luxury boxes. If the number of seats in the upper level is 6,300 more than the lower level, find the total seating capacity of the stadium.
- In a college level lecture class there are 150 students. 62% are women. If 58% of the men pass the class and 64% of the women pass the class, what percent of the entire class failed?
Tim’s Catering presented the following bill to a customer:
20 sandwiches 5 salads 25 bottles of water 25 cookies ________________________________ Delivery charge $22.50 Grand Total $168.50 What percent did Tim add-on to the bill for delivering the food?
As Ignatian educators we must adapt to our ever changing world. The new PSAT, ACT, and SAT call us to refocus our teaching techniques to emphasize a problem solving approach. Sure, we must still teach the fundamental processes of solving linear equations, graphing linear equations in two variables, factoring polynomials, the quadratic formula, and the laws of exponents. Creating meaningful, challenging, and interdisciplinary problems for our students must be the goal of our STEAM initiatives.
FOR THE TIMES… THEY ARE A CHANGIN’
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