7th Grade Math by

real numbers

mistiegorajewski — 2025-08-01 21:09:18 UTC

the combination of rational and irrational numbers. In general, all operations can be performed on these numbers and they can be represented on a number line, too.

real number system

mistiegorajewski — 2025-08-01 21:12:07 UTC

a graphic organizer used to organize the many types of real numbers: rational, irrational, integers, whole, and natural

natural number

mistiegorajewski — 2025-08-01 21:13:17 UTC

the set of real numbers that includes all counting numbers starting from 1

whole number

mistiegorajewski — 2025-08-01 21:19:36 UTC

the set of real numbers that includes all natural numbers and zero

integers

mistiegorajewski — 2025-08-02 20:05:24 UTC

the set of real numbers that includes all whole numbers and natural numbers, and their opposites

rational number

mistiegorajewski — 2025-08-02 20:08:25 UTC

the set of real numbers that includes all integers, whole numbers, natural numbers and any number that can be written as a fraction and/or a decimal

place value

mistiegorajewski — 2025-08-02 20:11:39 UTC

the value of each digit in a number, based on its position

decimal

mistiegorajewski — 2025-08-02 20:12:52 UTC

a number that consists of a whole and/or a fractional part

terminating decimal

mistiegorajewski — 2025-08-02 20:14:32 UTC

a decimal which has a finite number of digits, that is, it comes to an end and does not go on forever

repeating decimal

mistiegorajewski — 2025-08-02 20:16:30 UTC

a decimal in which after a certain point a particular digit or sequence of digits repeats itself indefinitely

negative number

mistiegorajewski — 2025-08-02 20:17:46 UTC

a number less than zero

positive number

mistiegorajewski — 2025-08-02 20:18:45 UTC

any number greater than zero

factor

mistiegorajewski — 2025-08-02 20:23:30 UTC

a number that is multiplied by another number

product

mistiegorajewski — 2025-08-02 20:24:23 UTC

the total amount from multiplying two or more factors

dividend

mistiegorajewski — 2025-08-03 15:56:50 UTC

the number that is to be divided or distributed into a certain number of equal parts

divisor

mistiegorajewski — 2025-08-03 15:57:31 UTC

any number that divides another number

quotient

mistiegorajewski — 2025-08-03 15:58:15 UTC

the number we obtain when we divide one number by another, also known as the answer

remainder

mistiegorajewski — 2025-08-03 16:02:38 UTC

amount left over after dividing a number

fraction

mistiegorajewski — 2025-08-03 16:04:42 UTC

used to represent smaller pieces (or parts) of a whole

denominator

mistiegorajewski — 2025-08-03 16:06:46 UTC

the number below the line in a common fraction; a divisor. This number cannot be zero

numerator

mistiegorajewski — 2025-08-03 16:08:28 UTC

the part of a fraction that is above the line and signifies the number to be divided by the denominator

improper fraction

mistiegorajewski — 2025-08-03 16:10:36 UTC

a fraction in which the numerator is greater than the denominator

mixed number

mistiegorajewski — 2025-08-03 16:12:53 UTC

a number consisting of an integer and a proper fraction

simplified form

mistiegorajewski — 2025-08-03 16:18:15 UTC

the most reduced or simplified representation of a fraction and occurs when the numerator and denominator have no common factors other than 1

reciprocal

mistiegorajewski — 2025-08-03 16:20:06 UTC

the inverse of a value or a number

equation

mistiegorajewski — 2025-08-03 16:21:31 UTC

a statement that the values of two mathematical expressios are equal.

This is indicated by the = sign.

variable

mistiegorajewski — 2025-08-04 17:35:39 UTC

a symbol, typically a letter, that represents a number

coefficient

mistiegorajewski — 2025-08-04 17:37:59 UTC

a number placed before and multiplying by the variable in an algebraic expression

constant

mistiegorajewski — 2025-08-04 17:38:45 UTC

a constant is a number on its own (without a variable)

inverse operations

mistiegorajewski — 2025-09-04 12:06:33 UTC

the opposite or buddy operation used for solving.

Division and Multiplication

Addition and Subtraction

adding and subtracting fractions

mistiegorajewski — 2025-09-04 12:10:37 UTC

finding the sum or difference of fractions by finding the least common denominator so the whole is the same size.

Multiplying fractions

mistiegorajewski — 2025-09-04 12:15:22 UTC

Dividing Fractions steps

mistiegorajewski — 2025-09-04 12:21:18 UTC

Mixed number to improper fraction

mistiegorajewski — 2025-09-04 12:23:12 UTC

Which operation

mistiegorajewski — 2025-09-04 14:36:33 UTC

integer rules

mistiegorajewski — 2025-09-18 12:32:58 UTC

all negative and positive rules

This also applies to inequalities

one-step variable equations

mistiegorajewski — 2025-09-18 12:35:23 UTC

multiplication chart

mistiegorajewski — 2025-09-19 16:53:39 UTC

open and closed dot

mistiegorajewski — 2025-09-21 21:24:35 UTC

When showing an inequality solution on a number line, the open dot shows that a point is NOT included in the solution.

A closed dot means it IS included.

inequality

mistiegorajewski — 2025-09-21 21:33:52 UTC

the relation between two expressions that are not equal

*indicated by a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”

solution

mistiegorajewski — 2025-09-21 21:35:02 UTC

is a value or set of values that satisfy an inequality

Multiplying or Dividing an inequality by a negative

mistiegorajewski — 2025-09-21 21:43:25 UTC

When dividing an inequality by a negative number, you must flip the symbol

Two step inequalities

mistiegorajewski — 2025-09-21 21:46:23 UTC

Multiplying or Dividing an inequality

mistiegorajewski — 2025-09-21 21:47:10 UTC

Inequality Symbols

mistiegorajewski — 2025-09-30 15:12:15 UTC

Less than and greater than have OPEN dot because the value is NOT an answer option.

Less than OR equal to AND greater than OR equal to have a closed dot because the value IS an answer option. (Stamp of approval)

Unit Rate

mistiegorajewski — 2025-10-05 19:06:44 UTC

a comparison of two different measurements in which the numerator or denominator has a value of one unit.

Proportion

mistiegorajewski — 2025-10-05 20:22:18 UTC

an equation that states two rations are equal

scale

mistiegorajewski — 2025-11-04 13:42:15 UTC

a ratio that compares two measures

scale drawing

mistiegorajewski — 2025-11-04 13:44:18 UTC

is a representation of a real object or place that is in proportion to the real object or place it represents

Scale drawing anchor chart

mistiegorajewski — 2025-11-04 13:45:04 UTC

percent

mistiegorajewski — 2025-11-04 13:48:07 UTC

another way of showing a fraction whose denominator is 100. Percent means part per hundred

percent decrease

mistiegorajewski — 2025-11-04 13:49:10 UTC

occurs when the new amount is less than the original amounts. Is is a ratio of the amount of decrease to the original amount.

percent increase

mistiegorajewski — 2025-11-04 13:50:01 UTC

occurs when the new amount is greater than the original amount. It is a ratio of the amount of increase to the original amount.

Percent of change anchor chart

mistiegorajewski — 2025-11-04 13:50:42 UTC

congruent figures

mistiegorajewski — 2025-11-04 14:26:27 UTC

figures that have the same size and shape

corresponding sides

mistiegorajewski — 2025-11-04 14:27:44 UTC

sides in the same position in figures

corresponding angles

mistiegorajewski — 2025-11-04 14:28:22 UTC

angles in the same position in figures

scale factor

mistiegorajewski — 2025-11-04 14:28:51 UTC

When you multiply a measure by a scale to produce a reduced or enlarged measure, the scale is called the scale factor.

similar figures

mistiegorajewski — 2025-11-04 14:29:17 UTC

Figures that are proportional in size, or have the same proportional dimensions, are called similar figures.

Properties of Similar Figures Anchor Chart

mistiegorajewski — 2025-11-04 14:30:06 UTC

Multidigit Multiplication

mistiegorajewski — 2025-11-08 15:32:37 UTC

STAAR reference sheet page 1

mistiegorajewski — 2025-11-08 15:36:04 UTC

STAAR Reference sheet page 2

mistiegorajewski — 2025-11-08 15:37:23 UTC

Division steps

mistiegorajewski — 2025-11-08 15:42:23 UTC

Dividing Decimals in the Dividend

mistiegorajewski — 2025-11-08 15:49:27 UTC

Dividing decimals in divisor

mistiegorajewski — 2025-11-08 15:51:37 UTC

y-intercept

mistiegorajewski — 2025-11-17 16:20:11 UTC

the point on a graph where a line crosses or touches the y-axis.

This is the b value in y=mx+b

slope intercept form

mistiegorajewski — 2025-11-17 16:21:37 UTC

an equation of a straight line

slope

mistiegorajewski — 2025-11-17 16:26:26 UTC

a number representing the steepness and direction of a straight line, defined as the "rise over run" or the ration of the vertical change

Slope Intercept Anchor Chart

mistiegorajewski — 2025-11-18 15:51:35 UTC

Linear Equation

mistiegorajewski — 2025-11-30 22:14:06 UTC

An equation that represents a straight line on a graph. Variables don’t have exponents and are not multiplied with another variable

constant rate of change

mistiegorajewski — 2025-12-01 13:49:56 UTC

rate is constant when the ratio of the output to the input stays the same at any given point on the function.

sales tax

mistiegorajewski — 2025-12-15 14:10:27 UTC

Money added to the cost of some goods, services, and transactions.

simple interest

mistiegorajewski — 2025-12-15 14:14:26 UTC

is calculated by finding a percent of the principal (original) amount and multiplying by the time period of the investment. The final value of an investment can then be found by adding/subtracting the simple interest to the principal amount.

principal

mistiegorajewski — 2025-12-15 14:15:15 UTC

Denoting an original sum invested or lent

rate

mistiegorajewski — 2025-12-15 14:16:50 UTC

Refers to an interest rate that is calculated only on the original principal amount borrowed

time

mistiegorajewski — 2025-12-15 14:18:15 UTC

the Time the money is Invested,

or Borrowed, in Years.

radius of a circle

mistiegorajewski — 2026-01-05 17:39:53 UTC

a straight line form the center to the boundary line.

diameter of a circle

mistiegorajewski — 2026-01-05 17:40:41 UTC

a straight line passing from side to side through the center of a circle.

circumference of a circle

mistiegorajewski — 2026-01-05 17:41:26 UTC

the distance around a circle calculated by multiplying the diameter by pi.

pi

mistiegorajewski — 2026-01-05 17:43:23 UTC

the ratio of the circumference of a circle to its diameter, approximately 3.14159

circumference

mistiegorajewski — 2026-01-05 17:44:52 UTC

Area of a circle

mistiegorajewski — 2026-01-07 12:55:31 UTC

Number of square units that cover the inside of a circle.

Area of Composite Figures

mistiegorajewski — 2026-02-04 16:48:00 UTC

the area of combined shapes of one or more simply polygons and circles.

composite figures

mistiegorajewski — 2026-02-04 16:49:52 UTC

a shape made up of two or more basic shapes, such as triangles, rectangles, or circles

decompose

mistiegorajewski — 2026-02-04 16:53:17 UTC

the process of breaking a composite figure into simpler, more basic shapes so you can calculate its area

Semi-circle

mistiegorajewski — 2026-02-04 16:56:30 UTC

1/2 circle:

Area can be calculated 2 ways:

Area = (3.14 x r x r) DIVIDED by 2

Area = 1/2 x pi x r x r

Circumference:

C= pi x r

area with formulas

mistiegorajewski — 2026-02-04 17:00:15 UTC

how many square units of space are INSIDE the shape

perimeter

mistiegorajewski — 2026-02-04 17:02:37 UTC

the DISTANCE AROUND an object or shape

Lateral Surface Area

mistiegorajewski — 2026-02-06 12:58:23 UTC

Lateral surface area (LSA) is the area of only the side faces, EXCLUDING the top and bottom bases.

lateral faces

mistiegorajewski — 2026-02-06 13:00:20 UTC

the faces of a three-dimensional figure that are NOT bases (ex: the sides of a prism or pyramid).

Total Surface Area

mistiegorajewski — 2026-02-06 13:01:58 UTC

Total surface area (TSA) is the sum of the areas of all surfaces of a 3D object, including its bases.

bases

mistiegorajewski — 2026-02-06 13:04:01 UTC

the top and bottom faces of a 3D figure (ex: the squares of a square prism or the triangles of a triangular prism)

Nets of 3D Figures

mistiegorajewski — 2026-02-06 13:08:31 UTC

is the 2D shape you get by unfolding a 3D object, showing all of its faces laid out flat.

Surface Area

mistiegorajewski — 2026-02-06 13:09:31 UTC

Volume of prisms

mistiegorajewski — 2026-02-16 17:23:43 UTC

the amount of space inside a prism, found by multiplying the area of the base (B) by the height (h) of the prism.

Volume of pyramids

mistiegorajewski — 2026-02-16 17:25:01 UTC

the amount of space inside the pyramid, found by multiplying the area of the base (B) by the height (h) and then dividing by 3.

Volume and Surface Area

mistiegorajewski — 2026-02-16 17:25:55 UTC

Volume

mistiegorajewski — 2026-02-16 17:26:42 UTC

probability

mistiegorajewski — 2026-02-23 01:58:55 UTC

the extent to which something is probable; the likelihood of something happening or being the case

simple event

mistiegorajewski — 2026-02-23 02:00:04 UTC

the likelihood of a single, specific outcome occurring within a probability experiment

complement

mistiegorajewski — 2026-02-23 02:01:28 UTC

Complementary events are two exclusive outcomes of a single experiment where one event is the exact opposite of the other. They are the only two possible outcomes, meaning if one happens, the other cannot. The sum of their probabilities always equals 1, and this relationship is expressed mathematically as

P(Red)= 1/6

𝑃(Not Red)= 5/6

⅙ + ⅚ = 6/6 = 1

Probability

mistiegorajewski — 2026-02-23 02:02:26 UTC

Compound events

mistiegorajewski — 2026-02-23 02:03:43 UTC

Compound probability

mistiegorajewski — 2026-02-23 02:04:39 UTC

Data

mistiegorajewski — 2026-02-23 02:06:03 UTC

Facts or numbers collected to learn something.

Circle Graph

mistiegorajewski — 2026-02-23 02:06:33 UTC

A graph that shows parts of a whole as slices of a circle.

Circle Graphs

mistiegorajewski — 2026-02-23 02:07:23 UTC

bar graph

mistiegorajewski — 2026-02-23 02:07:54 UTC

A graph that uses bars to compare different amounts or categories.

Parts of a bar graph

mistiegorajewski — 2026-02-23 02:10:15 UTC

dot plot

mistiegorajewski — 2026-02-23 02:10:45 UTC

A graph that uses dots to show how many times each value occurs.

Dot plot

mistiegorajewski — 2026-02-23 02:11:45 UTC

Mean

mistiegorajewski — 2026-03-06 20:56:30 UTC

average of a data set

Mode

mistiegorajewski — 2026-03-06 20:57:49 UTC

Most frequently listed item in a data set

median

mistiegorajewski — 2026-03-16 15:01:28 UTC

the center point of a data set.

Data must be in order from least to greatest OR greatest to least in order to find the median.

IF it seems to have two medians then you find the mean of those two pieces of data.

range

mistiegorajewski — 2026-03-16 15:02:13 UTC

the difference in the data set from the largest to the smallest piece of data.

data shape

mistiegorajewski — 2026-03-16 15:18:45 UTC

Describes the distribution of data

Skewed Left

Symmetrical

Skewed Right

asymmetrical data distribution

mistiegorajewski — 2026-03-19 13:33:11 UTC

Not shaped symmetrical, but not skewed left or right

Box Plot

mistiegorajewski — 2026-03-27 13:35:50 UTC

Box Plot

mistiegorajewski — 2026-03-27 13:36:36 UTC

Interquartile range

mistiegorajewski — 2026-03-27 17:02:39 UTC

Difference between third and first quartile