1. How do I show my work?

2. Why do I have to show my work?

3. I know a faster/better/different way of doing these problems, can I do it that way instead?

### 1. How do I show my work?

Examples:

-4 + 2

Since this is simple addition, there's no easy way to show your work.  However you can explain what you thought or did to solve it:

I wrote a number line, put my finger on negative 4, and moved to spaces to the right, so the answer is -2.

I knew that if I was short 4 bucks, and someone gave me two bucks, I'd still be short 2 bucks, so the answer is -2.

I saw that the bigger number was negative, so the answer had to be negative, and since there's one negative and one positive I had to take the difference.  The answer is -2.

All of these would be acceptable ways of showing your work.

Ex. 2. Multiplication/Division

4a * 2a^2

Again, it's not easy to show your work, so explain your thinking.

When multiplying variables you need to add the exponents.  Since having a variable at all is the same as 1, we have a^1 and a^2.  That's 3 in all, so it's a^3.  Since 4 * 2 is 8, that means the answer is 8a^3.

Ex. 3. Properties

Problem A: (4y + 2x) + 5x

changed to: 4y + (2x + 5x)

What property allows the change?

In a problem like this, again, the goal is to let your teacher know what you are thinking to get the answer, so start by identifying what changed, then finding the property that fits.

The parentheses were moved to go around different numbers.  The only property that allows this is the associative property.

Ex. 4. Fractions

When showing your work on fractions the most important things to show are the common denominator and the unsimplified as well as simplified fractions.

1/30 + 1/6

1/30 + 5/30 (your fractions shown with the common denominator)

In this case you don't have to explain your steps--since your teachers know what you're doing generally, they can usually see what's going on.  If your teacher can't tell what you're doing, s/he will ask.

Please space your work vertically, as I have shown above. Having your work strung together on one line is messy and difficult to read.

Ex. 5. Equations and Inequalities

When solving equations, it is absolutely critical that you show your teacher your work.  This goes for inequalities as well.

Pay attention to the instructions in the lesson.  Chances are good that the lesson itself gives you a step by step method to solve the equation--you can mimic this format when showing your work for your instructor.

4x + 2 = 10
4x + 2 - 2 = 10 - 2
4x = 8
4x/4 = 8/4
x = 2

7(x - 2) = (14x - 28)/2
7x - 14 = 7x - 14
sides are equal
"true for all x"

7(x - 2) = (14x + 28)/2
7x - 14 = 7x + 14
-14 = 14
x cancels, sides not equal
"no solution"

-4x + 5 >= 10
-4x + 5 -5 >= 10 - 5
-4x/-4 >= 5/-4  (dividing by a negative, flip the sign)
x <= -5/4

Do not turn in work where you do not include the variable, or where you leave out the inequality sign. This sort of work isn't helpful because you aren't showing the entire process. Also do not turn in a "check" of the work (where you fill in the value for the variable from the beginning). You must solve for the variable, as I have shown in all the examples above.

Please space your work vertically, as I have above. Having your work strung together on one line is messy and difficult to read.

Ex. 6.  Formulas

When working from a formula, start by showing the formula you are using, fill in the information you have, then solve.

If a plane is traveling 25 miles per hour for 30 minutes, how far has it traveled?

Distance Formula: d = r * t
d = 25mph * .5hr  (remember, the rate and the time must use the same measurement, hours, minutes, etc.)
d = 12.5

If a triangle has a hypoteneuse of 5 and a leg of 3, what is the length of the other leg?

Pythagorean Theorem: a^2 + b^2 = c^2
3^2 + b^2 = 5^2
9 + b^2 = 25
b^2 = 25 - 9
b^2 = 16
b = 4

Ex. 7. Factoring

Pay attention to what factoring method the lesson asks you to use.  If there is no method named, then you may use whatever you are most comfortable with.  Again, remember if you are using a formula, use the method outlined in the section above to show your work.

8r^2 - 5r^2s^2 + 8s^2 - 5s^4

factor by grouping
8(r^2 - s^2) - 5s^2(r^2 - s^2)

(8 - 5s^2)(r^2 - s^2)

x^2 + 4x - 5
(In this case, you may want to explain your thinking.)

I need two numbers that multiply to get -5, but add/subtract to get +4.

-1 and +5

(x - 1)(x + 5)

As you continue in mathematics, the problems get much more complex.  These examples, however, should give you a good basis for how to show your work.  Remember, the lesson itself probably gives you a step by step method of solving the problems--this is exactly what your teacher wants to see you using when you show your work.

### 2. Why do I have to show my work?

There are several reasons why you need to show your work.

1. Your teachers are not mind-readers.  If you're getting problems incorrect, chances are good that there's something you don't understand--but your teacher won't magically know what it is that's giving you trouble.  Showing your work lets your teacher see what you did to get your answer, so s/he can offer suggestions to help you.

2. You are less likely to make a mistake with your work in front of you.  When you write out your work, you often catch your own mistakes--like trying to say that -3 and +2 equal 5 (when really that should be -1).  When you do a problem in your head, these mistakes are harder to find and correct.

3. Practice!  Writing out the steps makes them harder to forget, and if you're having troubles there is no better way to practice than actually doing the steps.

4. To check that you're using the right method to solve the problem.  Often if a teacher can see your work, s/he can remind you that you are adding when you should be multiplying, or trying to factor through FOIL when you should be using the quadratic formula.

5. Because maybe you weren't wrong.  On occasion, there are mistakes in the tests used, and if the instructor can see from your work that you got the problem correct, then you'll still get credit for getting the right answer.

### 3. I know a faster/better/different way of doing these problems, can I do it that way instead?

This is something that must be evaluated on a case by case basis, so you'll need to ask your instructor.  Many times the answer will be no, because the lessons build on one another and are trying to reach an ultimate goal--one you won't reach if you don't understand the lesson.  (Put another way, there is a difference between knowing how to do something, and knowing why you do it that way--many of the lessons try to teach you both.)