A “brain dump” is a summary of important information you write down at the beginning of a test. You could think of it as a fair “cheat sheet”. You create it as you study and learn it carefully. Practice writing it from memory until you can do it fast.
Write your brain dump as soon as you are allowed to begin your test. (Write it on the test sheet, so no one needs to wonder if you slipped it out of a pocket or had it hidden in your scratch paper!) Writing before you do anything else gives confidence and avoids any brain freeze that might come from seeing a problem you feel unsure about. Doing an initial brain dump puts your mind at ease — you know you have put down the important information already, so now you can think about the individual questions and not fear you’re going to forget something.
Refer to the brain dump during the test to give yourself guidance or reassurance whenever you need it.
A good brain dump...
- is short enough to learn by heart.
- contains the most important information you're likely to forget.
- uses symbols and abbreviations that make it quick to write.
- doesn’t need to include things that you consistently get correct.
- has meaning to you.
Examples of good types of content for a brain dump:
- definitions of terms
- formulas
- key examples, especially of “tricky” concepts
- summaries of important procedures
Writing a brain dump at the beginning of a test is a great strategy, even when you don’t get credit for it directly, since it is almost guaranteed to boost your grade. When you’re writing just for yourself, write only what you need.
When you’re writing for credit on a test or to share with a friend, it’s good to use “complete sentences”. In math terms, a complete sentence is an equation or an inequality. The verb may be a math verb written as a symbol, such as $=, <, \text{or} >$. Without one of those signs, you’ve probably written just an expression, and that is not a complete sentence. For definitions, you might use a format that isn't a complete sentence, as I did with ‘perimeter’ below.
Sample Items for a Brain Dump Covering Whole Numbers, Integers, and Related Word Problems
- Perimeter — the distance around an object; add the lengths of the sides. For a rectangle, $P = 2l + 2w$
Use linear units: $in, m$.
- Area of a rectangle — the number of squares it takes to cover it:
$A = l \cdot w$
Use square units: ${in}^2, m^2$
- Volume of a 3D shape — the number of cubes it takes to fill it: for a box measuring $l$ by $w$ by $h$ units, $V = l \cdot w \cdot h$
Use cubic units: ${in}^3, {cm}^3$.
- P E MD AS — the order of operations.
[Note how I left spaces to show that multiplication and division are done together and addition and subtraction are done together.]
- $\displaystyle \frac{0}{3} = 0, \text{but } \frac{3}{0}$ is undefined.
- Average: $ A = \frac{\text{sum of the numbers}}{\text{the number of numbers}}$
- Absolute value of a number (written $|a|$) is never negative;
$|3| = 3$ $|-3| = 3$ but $-|-3| = -3$
- quotient / product $ \times $ sum $+$ difference $- $
Divide to get quotient, multiply to get product;
add to get sum, subtract to get difference.
- “Less than” means “left of”; “greater than” means “right of” on the number line.
$-5 < -3$ $-3 > -5$ $0 > -2$ $1 > -5$
[Write some simple examples to show how comparing integers works, some written in both directions if it helps you.]
- To remember how adding and subtracting integers works, you might write a little table like the following:
[Note: (+) and (-) mean a positive number and a negative number, respectively. The large, bold signs mean numbers of the given sign with a larger absolute value than the others. The interpretation is:(+) + (+) = (+)
(-) + (-) = (-)
(+) + (-) = (+)
(+) + (-) = (-)
- The sum of two positives is a larger positive.
- The sum of two negatives is a “larger” negative.
- The sum of a mixed pair has the sign of the “larger” one, but is “smaller” than it is.]
- Subtract a number by adding the opposite of the number:
$5 - (-2) = 5 + (+2)$
[You might want to write just the math example and not the explanatory words.]
- When multiplying or dividing two numbers, same signs make positive, opposite signs make negative. OR show this in a little chart:
(+)$\cdot$(+) = + (-)$\cdot$(-) = + (+)$\cdot$(-) = - (-)$\cdot$(+) = -
(+)/(+) = + (-)/(-) = + (+)/(-) = - (-)/(+) = -
Therefore: the product or quotient of an even number of negatives is positive, of an odd number of negatives is negative.
The important thing when writing for yourself is to capture what you need to remember in a form that helps you.