Monday, January 18, 2016

How To Pass The Algebra Regents (Or At Least Score Several Points Higher)

Welcome. If you found this page while looking for answers to Common Core Algebra Regents answers, please read what this column has to say.
Or just review my Regents tab for more answers and reviews.

I am a New York City high school teacher and I have been grading Regents exams for about 15 years. I have put in overtime grading the exams and have gone to training about what is acceptable and what isn't (and what might be worth, say, 1 point instead of 0). The scorers have very little leeway in how they grade things, but one thing is certain: you cannot get full credit for any problem without a completely correct response with the work shown or graphs labeled.

Most of what is written below may seem to be common sense. My students tell me that it is, and yet they make these little mistakes time and again.

Scoring Higher on the Common Core Algebra Regents

It's simple really. There are two things that you have to do:

  1. Don't make silly mistakes
  2. Don't give away points by skipping questions

One piece of advice you need to forget: Just write something. No, do not just write something. Write something thoughtful. If you take two numbers and multiply them, most times, it will be incorrect. If you use the Quadratic Formula but it isn't a quadratic equation, it is "totally incorrect".

Now the positive things you should do:

Round Your Decimals Correctly

Rounding errors will cost you one point. For a two-point question, that's half the credit, regardless of how much work you did.

If the problem says to round to the nearest tenth, then you include one decimal place. If it says nearest hundredth, two decimal places, etc.

If the problem is money, then you have either two place or zero places (nearest cent or nearest dollar). Never write $2.5 as your answer. (I've seen it.)

If the next digit is 5-9, round up. If the next digit is 0-4, round down.

And DO NOT confuse TENTH with TEN and HUNDREDTH with HUNDRED. (Again, I've seen it.)

Final warning: DO NOT round in the middle of the problem. Wait until the end to round your numbers or errors will creep in.

If you round 1/3 to .3 in the middle of the problem and then multiply (.3)(60), you will get 18 instead of the correct answer 20. You just lost a point.

Use the Correct Formulas -- and Write Them Out

Some of the formulas are given to you, but not all of them. Don't expect the one you need to be there. Don't use one just because it is there. (Seriously, if you're in high school you should know that the Area of a rectangle is length times width and the Volume of a rectangular prism is length times width times height. I shouldn't see pi mentioned.)

Write the formula out. It isn't required, but it can't hurt. And it will help when you substitute for the variables that you have.

Calculator Issues: Use Parentheses

Calculators have a bunch of issues. Make sure you know how to use them and how to find the functions that you think you might need.

In particular, don't forget to use parentheses. Some of the biggest mistake involve parentheses.

Exponents: -32 is NOT the same as (-3)2.

Fractions: 4 + 5/6 - 7 is NOT the same as (4 + 5)/(6 - 7) or 4 + 5/(6 - 7)

Square Roots: SQRT(4 + 9 is NOT the same as SQRT(4) + 9.
I can't draw the root symbol, but the calculator will give you an open parenthesis. It doesn't require a close parenthesis. However, the syntax of your equation may DEMAND one.

Absolute Value: abs(-8 + 3 - 4 is NOT the same as abs(-8 + 3) - 4.
Same reasoning as with Square Roots. The close of the Absolute Value in the expression means close the parentheses in the calculator.

Don't Forget to Answer the Question

If you do all that work to figure out what x equals, make sure you go back and answer the question. Was x in the question or did you make it up (use it for the unknown in the problem)? Did the question ask you to find x, or did it ask to find some other expression that uses x?

If you found x, do you also need to find y, and state the answer as coordinates?

Whatever they ask, answer it. Don't stop and say, well, I did enough. "It's obvious." "It means the same thing." Why take a chance?

Answer in a Sentence

Write out your answer. Put it in a box. If you clearly defined your variables, you have half of a sentence already. Just put an = sign and the answer.

Make sure that your final solution can be found, especially if you have a lot of work on the paper. (Also, "a lot of work on the paper" is A Good Thing.)

Label Your Graphs

Along with labeling your answers to algebraic solutions, you need to label your graphs. If there are two equations or inequalities, you must label at least one of them. (Both would be better.) Again, it is NOT "obvious" which one is which. The scorer needs to know that you know. So tell them.

Furthermore, if it is a system of equations, label the point of intersection. If the lines do not meet at an integer point, you probably made a mistake. HOWEVER, if you cannot find a mistake that you made, estimate the answer as best as you can. You can get a point for a "consistent mistake" if you correctly label the intersection of two lines, even if one is incorrectly graphed.)

If you label a bunch of points when you graph -- e.g., (1, 3), (2, 5), (3, 7) ... -- then make sure you circle the solution to the system and label it as such. You won't get credit for having (3, 7) written if there are a bunch of other points labelled as well.

Speaking of Graphs -- DON'T SKIP THEM

Some students are intimidated by the graphs? Why? You have been doing them for a good part of the year. And you should have a graphing calculator at your disposal.

Using a calculator means that you may have to rewrite an equation to isolate y, so you can use the y= key.

Once you GRAPH it, look at the TABLE. You have all the points you need to plot the graph.

And, speaking of which, DRAW THE GRAPH FROM EDGE TO EDGE. Don't plot four points, connect the dots and stop.

The One Exception to this rule is if you are given a domain to use, such as, -4 < x < 4, in which case, DO NOT GO PAST THOSE NUMBERS and do NOT use ARROWS.

And, obviously, you won't be able to go to an edge in the numbers are outside of the domain of the function, such as with the square root function.

For inequalities, shade one inequality with lines going in one direction. Shade the other with lines going in a different direction. The criss-cross pattern is your solution. Put a big "S" in that section of the graph. Don't just scribble in three sections of the graph.

Look Below the Graph for Extra Questions

If there is a question below the graph, ANSWER IT. Don't ignore it. Don't say you didn't see it.

If they are for a point that is in the solution to a system of inequalities, remember that any point on a broken line, including the intersection point, is NOT in the solution.

EXPLAIN

If you are asked to "explain", then that's what you need to do. And you need to reference what is on the page and what mathematical concepts or principles are being addressed.

Take it from me, whatever B.S. you might put on your English essays will not work here. By the way, it doesn't work in English class, either.

Don't write, "I don't agree with Angelica's solution because she is wrong." That isn't an explanation to why Angelica isn't correct.

Trust Yourself and Succeed

Be careful. Look over your work with an eye for these "silly" mistakes. I say "silly" because students don't like when I say "STUPID" in class. They think I'm calling them "stupid" instead of the mistake.

A second read-through can find mistakes you missed the first time.

Follow these tips and you'll score a few extra points that you would've lost otherwise. Every point matters. You won't know what mistake will drop you below 65 or 75 or 90, or whatever your target grade is.

Just do your best, but remember that cutting corners and skipping questions is NOT doing your best.

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