# Unit 1 - Variables, Expressions, Order of Operations, Absolute Value, Operations with Negative Integers, and Patterns

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### grouping symbols

symbols such as parenthesis and brackets that are used to group expressions

### equation

a mathematical sentence with an equal sign

### expression

a mathematical phrase (unfinished/no equal sign or inequality)

### numerical expression

a mathematical phrase that uses numbers and operation symbols

### variable

a letter that stands for a number

### variable expression

a mathematical phrase that uses variables, numbers, and operation symbols

### evaluate

replace each variable with a number, then simplify

### order of operations

the order in which a mathematical expression is evaluated: first grouping symbols, then exponents, then multiplication or division in order from left to right, then addition and subtraction in order from left to right

### absolute value

a number's distance from zero on the number line

### integers

the set of whole numbers and their opposites

### opposites

numbers that are the same distance from zero on a number line but in opposite directions

### different signs

To add two integers with different signs, find the difference of their absolute values. The sum has the sign of the integer with the greatest absolute value.

### same signs

The sum of two positive integers is positive. The sum of two negative integers is negative.

to change a subtraction problem into an addition problem, change the subtraction to addition and make the next integer its opposite

### zero pairs

a positive and a negative cancel out and make zero

### conjecture

a conclusion you reach by inductive reasoning

### counter example

an example that proves a statement false

### inductaive rasoning

making conclusions based on patterns

### guess and test

Make a series of guesses then use the results to get closer and closer until you get the actual answer.

### make a diagram/picture

Create a diagram or picture to better understand/visualize a problem.

### make a table/chart/graph/ organized list

Organize the data to find a pattern.

### work a simpler problem

Test a conjecture with easier to work with numbers.

### work backwards

Start with the end result and "undo" operations until you get back to the starting number. Then take the starting number and work through the problem to see if you get the same end result.

### dividing intgers

The quotient of two integers with the same sign is positive.
The quotient of two integers with the different signs is negative.
The quotient of zero and any integer is zero.

### mulitplying intgers

The product of two integers with the same sign is positive.
The product of two integers with the different signs is negative.The product of zero and any integer is zero.

### coffiecnt

number that is multiplied by a variable;
if a variable has no number multiplied by it, the coefficient is understood to be a 1.

### constant

a term that has no variable

### like terms

like terms have identical variables; that is, they have the same variable to the same power. Constants are classified as like terms as well.

### term

the parts of an expression that are added or subtracted

### equation

a mathematical sentence with an equal sign.

### open sentence

an expression that contains at least one unknown quantity and becomes true or false when a test value is substituted for the unknown.

### solution of an equation

a value for a variable that makes an equation true

### inverse operations

operations that undo each other

You can add the same number to each side of an equality

### subtraction of property of equality

You can add the same number to each side on an equality

### muplication property of equality

You can multiply each side of an equation by the same number.

### divison property of equality

If you divide both sides of an equation by the same non-zero number, the two sides remain equal.

### inequality

a mathematical sentence using less than, less than or equal to, greater than, greater than or equal to

### solution of an inequality

any number that makes an inequality true.

### addtion property of an inequality

you can add the same number from each side of an inequality.

### subtraction property of an inequality

you can subtract the same number from each side of an inequality

### multiplication property of an inequality

If you multiply each side of an inequality by a positive number, you leave the inequality symbol unchanged.
If you multiply each side of an inequality by a negative number, you reverse the inequality symbol

### divison property of an inequality

If you divide each side of an inequality by a positive number, you leave the inequality symbol unchanged.
If you divide each side of an inequality by a negative number, you reverse the inequality symbol.

### clustering

If all numbers being added are close to the same value, change them all to the same value and multiply by how many numbers there are.

### compatible numbers

Numbers that are close to the given numbers that make estimation or mental calculation easier.

### front-end estimation

First add the front-end digits then round to estimate the sum of the remaining digits. Combine these estimates.

### rounding

A way to shorten a number to a given place value by looking at the number after that place value—if the next number is five or higher add one to the given place value, but if the next number is less than five keep the given place value the same. Drop all digits after the rounded place value if they are after the decimal point. Fill in all digits after the rounded place value with zeros if it is before the decimal point.

### mean

the sum of the items in a set of data divided by the number of items in the set; also called average

### measures of central tendency

mean, median, and mode

### median

the middle number, or the mean of the two middle numbers in an ordered set of data

### mode

the data value that occurs the most

### outlier

a data value that is uncharacteristically high or low compared to the other data values; it can affect the mean of the data

### range

subtract the lowest data value from the highest

### formula

an equation created to solve a particular type of problem, where each variable always represents the same thing (example: d=rt, where d represents distance, r represents rate of speed, and t represents time)

### perimeter

the length around the outside of a figure

### perimeter formula for a rectangle

P = 2l + 2w, where l is the length and w is the width.

### substitution

to replace a variable with its numeric value

### variable

a letter that stands for a numeric value

### simplify a problem

change the problem to a simpler problem with easier/smaller numbers and look for a pattern

Example: