Definitions for Math 7:
(MA.07.01) Commutative and associative properties:
Commutative property: Numbers may be added or multiplied together in any order.
The commutative property of addition states that a + b = b + a.
The commutative property of multiplication states that ab = ba.
Example: 5 + 2 = 2 + 5, because both sides of the equation equal 7.
5 x 2 = 2 x 5, because both sides of the equation equal 10.
Associative property: Properties that denote an operation is independent of grouping.
The associative property of addition states: (a + b) + c = b + a.
The associative property of multiplication states: (a * b) * c = a * (b * c).
Example: 12 + (5 + 9) = (12 + 5) + 9, because both sides of the equation
equal 26 (12 + 14) = (17 + 9).
(9 x 8) x 3 = 9 x (8 x 3), because both sides of the equation equal 216 (72 x
3) = (9 x 24).
(MA.07.02) Systems of equations with two unknowns:
Definition: An equation is a mathematical sentence that contains an equals sign. An unknown is usually denoted by a letter of the alphabet (for example x or y). A system of equations is two equations. You can use one to solve the other.
Example: 2x + 3y = 33 and x - 12y = 30. From the second you can solve for x (x = 12y + 30), then substitute this for x in the first equation: 2 (12y + 30) + 3y = 25. This becomes 24y + 60 + 3y = 33, then 27y = -27, or y = -1. Now that you know what y is, you can plug that into the second equation to solve for x: [x = 12(-1) + 30], or (x = -12 + 30), simplified to x = 18. the solution is y = -1 and x = 18. You can check this by replacing x and y with these values in both equations.
(MA.07.03) Equations with one unknown:
Definition: An equation is a mathematical sentence that contains an equals sign. An unknown is usually denoted by a letter of the alphabet ( for example x or y )
Example: x + 2=6
(MA.07.04) Interpret rate as measure on line graphs:
Definition: Rate can be shown on a line graph as rise (vertical movement up or down) over run (horizontal movement up or down).
Example: The rate of savings from the 10th to the 20th was (90-40) / (20-10) = $50 / 10 days = $5 / day.
(MA.07.04) Interpret data points located between access labels:
Definition: Can the student interpret a number that is not on a labeled line?
Example: How much money was saved in the bank on the 15th? ($65)
(MA.07.05) Bar graphs:
Definition: A graph that uses horizontal or vertical bars to display countable data.
Example:
(MA.07.05) Make inferences:
Definition: Deriving logical conclusions from premises known or assumed to be true.
Example: Can you infer that the temperature at noon on April 2nd is likely to be between 45 and 55 degrees?
(MA.07.05) Extrapolate trends:
Definition: To infer or estimate by extending or projecting known information.
Example: Is the temperature at 4:00 am likely to be between below 35 degrees?
(MA.07.09) Mixed numbers:
Definition: A mixed number is a number written as a whole number and a fraction.
Example: 1 ½
(MA.07.10) Right angle:
Definition: An angle whose measure is 90 degrees.
Example:
(MA.07.10) Rotation of objects:
Definition: To move an object in a specific direction around a given axis.
Example: This circle has been rotated 45 degrees each time. Once you do that 8 times, it has been rotated 360 degrees and is back to its original position.
(MA.07.11) Coordinates:
Definition: Coordinates are pairs of numbers that are used to determine points in a plane, relative to a special point called the origin. The origin has coordinates (0,0). We can think of the origin as the center of the plane or the starting point for finding all other points. Any other point in the plane has a pair of coordinates (x,y). The x value or x-coordinate tells how far left or right the point is from the point (0,0), just like on the number line (negative is left of the origin, positive is right of the origin). The y value or y-coordinate tells how far up or down the point is from the point (0,0), (negative is down from the origin, positive is up from the origin). Using coordinates, we may give the location of any point we like by simply using a pair of numbers.
Example: (1,2) represents 1 unit to the right of zero and 2 units up.
(MA.07.11) Object flipped, slid, or rotated on the coordinate plane:
Definition: An object that is flipped displays the "mirror image" of the original figure. A slid object looks identical, but appears in a different spot in the coordinate plane. A rotated object is turned.
Example:
(MA.07.11) Symmetrical objects:
Definition: An object has symmetry if one half of it is the mirror image of the other half.
Example: A butterfly and the letters A, T, and O. In the square below, four different axes (or lines of symmetry) are shown: horizontal, vertical, and two diagonal. You can prove this by printing this page and cutting out the squares and folding along the dotted lines.
The square also has rotational symmetry. If you cut out the square below and place it on a flat surface. Place a pen or pencil on the point in the center of the square. If you rotate that square 90, 180, or 270 degrees clockwise or counterclockwise, the square will look exactly the same as it did before you rotated it.
(MA.07.14) Obtuse angles:
Definition: An angle whose measure is greater than 90° and less than 180°
Example:
(MA.07.14) Acute angles:
Definition: An angle whose measure is less than 90°
Examples:
(MA.07.14) Parallelism:
Definition: Lines in a plane that never intersect.
Example:
(MA.07.14) Equal angles:
Definition: Equal angles are angles that have the same measure.
(MA.07.14) Apply properties of angles to triangles:
Definition: The angles in a triangle add up to 180 degrees. Because this is an equilateral triangle, the angles in this triangle are all equal.
Example:
(MA.07.14) Apply the properties of angles to polygons:
Definition: The sum of the angles of a polygon is (n-2)180, where n stands for the number of sides.
Example: This polygon has 6 sides, so the sum of its angles is (6-2)180, or 720 degrees. In a regular polygon like this, given the measure of one angle the student should be able to tell that another angle has the same measure. In an irregular polygon, the student
(MA.07.14) Apply the properties of angles to vertices:
Definition: An angle is formed by two rays with a common endpoint called a vertex.
Example: For any two lines that meet, the opposite angles are called vertical angles and are equal. In the image below, the student should be able to tell that angle 4, 5, and 8 are also 75 degrees.
(MA.07.18) Expanded notation:
Definition: A way of writing a numbers in which the numbers are written to show the place value of each digit.
Example: 547 = 500 + 40 + 7 = 5x102 + 4x101 + 7x100
(MA.07.20) Prime numbers:
Definition: A positive number that is divisible only by itself and the number one.
Examples: The numbers 2, 13, and 29 are examples of prime numbers.
(MA.07.22) Negative numbers:
Definition: A number less than 0.
Examples: -5, -168, -0.79, and -3/4 are negative numbers.
(MA.07.25) Functions:
Definition: A relationship between two quantities in which one quantity depends on the other.
Example: The function table represents the function: y = 5x + 4
| x |
0 |
5 |
10 |
15 |
20 |
|
y |
4 |
29 |
54 |
79 |
104 |
(MA.07.25) Apply function to a sequence:
Definition: Given a sequence we can find the related function.
Example: (1, 3, 5, 7, 9, 11...) is represented by the function x + 2 = y
(MA.07.26) Calculate the mean (average) of four numbers:
Definition: The mean is the sum of the set of numbers is a set of data divided by the number of pieces of data.
Example: The mean of the set (4, 7, 2, 11) is 6, calculated by adding all the numbers, arriving at the sum of 24 and dividing by the total data elements (4).
(MA.07.27) Assess probability of events in ratios:
Definition: The chance that an event will occur expressed as the ratio of the number of favorable outcomes to the number of possible outcomes or A measure of the likelihood of an event. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of 0. If there is a chance that an event will happen, then its probability is between 0 and 1.
Example: If you have 3 dimes and 2 nickels in your pocket, and you reach in your pocket and pull out one coin, then the probability of that coin being a nickel is 2/5. The probability of that coin being a penny is 0, because there are no pennies in your pocket!! If you have 5 nickels in your pocket, and you reach in your pocket and pull out one coin, then the probability of that coin being a nickel is 1, because you have only nickels in your pocket.
(MA.07.25) Ratio:
Definition: A comparison of two quantities that have the same unit of measure.
Example: Suppose that you have a bag of 52 marbles. You pour 15 marbles into your hand. The ratio of marbles in your hand to the total number of marbles is 15 to 52, or 15:52, or 15/52.
(MA.07.28) Proportional reasoning using basic ratios:
Definition: A proportion is a sentence that states that two ratios are equivalent.
Example: 2/3 = 6/9 or using an unknown: 4/5 = 16/x in this case you take (5)(16)¸4 = 20
(MA.07.28) Deductive:
Definition: Deductive reasoning uses a rule to make a conclusion or a decision. It is reasoning from the general to the specific. Deductive reasoning is when you move from things you know or assume to be true - called 'premises' - to conclusions that must follow from them.
Example: All circles are round. Figure A is round. Therefore, figure A must be a circle.
(MA.07.29) Order of operations:
Definition: When given a problem with several operations to be performed, perform the operations in the following order: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. (Please Excuse My Dear Aunt Sally) is a mnemonic to help you remember the order. Order makes a difference in results. The results are poor if you put your sock on after you’ve put your shoe on. It is necessary to put your sock on first. The order in which the two actions are performed makes a difference in the result of the activity. The order in which operations or actions are completed makes a difference in the result in mathematics also.
Example: Simplifying 420 ÷ 2(3 + 4) - 6 · (5)2 First do what's in the parentheses (3+4)
420 ÷ 2(7) - 6 · (5)2 Then the exponents (5)2
420 ÷ 2(7) - 6 · 25 Then both multiplications (2 · 7) and (6 · 25)
420 ÷ 14 - 150 Then division (420 ÷ 14)
30 - 150 Then subtraction (30-150)
-120
©2003 Galena City School District
