59 terms

# 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.
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