Sixth Grade Math Vocabulary

Algebraic Expression An expression that is written using one or more variables Examples 3x x – 4y 2a + 5 x 2 + x – 6 2x + x 3x

Bias A sample that is not representative of the entire population Or A survey that is not fair because of the population questioned Example For a survey about favorite types of movies of 6 th graders: Asking students attending a horror movie “what is your favorite type of movie?”

Composite A whole number, greater than one, with more than two whole-number factors Examples 6 is composite because 6 = 1 X 6 and 6 = 2 X 3 The factors of 6 are 1, 2, 3, 6 3 is NOT composite (it is prime) because 3 = 1 X 3 and the only factors of 3 are 1 and 3. = 3X91, 21X13 7X39, 1X273 Composite 1 is not prime or composite

Conjecture (with data) To guess or make a prediction about future outcomes based on patterns, logic or survey results Example: Add consecutive odd numbers starting with 1: 1+3 =4, 1+3+5=9, =16, A good conjecture would be that the sums of consecutive odd numbers starting with 1 are always perfect squares.

Coordinate Plane ( Ordered Pairs ) A plane formed by a horizontal number line (x-axis) and a vertical number line (y-axis) The ordered pairs (x,y) shown on the coordinate plane are: A: (4,4) B: (-3,-3) C: (3,-6) D: (-5,2) The origin is the point (0,0)

Degrees (Angle) The most common unit of measure for angles Examples The angle ABC that is shown below has a measure of about 40°. The right angle below has a measure of 90°.

Equation (Solving) An equation is a mathematical sentence that shows that two quantities are equal To solve an equation, find a value for the variable that makes the sentence true Examples x + 3 = 4 2c = 6 h – 5 = 12 Solution: x = 1 c = 3 h = 17 X X=2

Evaluate To find the value of a numerical expression Or In an algebraic expression, to replace the variable with a number and perform the operations Examples Evaluate: Evaluate if x = 2: 16 – 2(3+4) = 3x + 12 – x – 2(7) = 3(2) + 12 – = 16 – 14 = – = 18 – = = 18 2l+2w L=5, w=6 2(5)+2(6) =22

Formula A rule showing the relationship between certain quantities Examples A = lw (Area of a rectangle) P = 2l + 2w (Perimeter of a rectangle) V = lwh ( Volume of a rectangular prism) l w l w h

Function A relation or rule that assigns one and only one output for each input (Given an input, you get exactly one output) Examples Rule: y = x+4, each output is 4 more than the input if input=2 then output=6, (2,6) if input=4 then output=8, (4,8) From table: input=1 then output=5 input=2 then output=6 input=3 then output=7 input=4 then output= n Input/Output: Function machine

Inverse Operations that undo each other Examples Addition and subtraction are inverse operations (undo adding 3 by subtracting 3) multiplication and division are inverse operations (undo multiplying by 2 by dividing by 2) To solve an equation: x + 3 = 5 x + 3 – 3 = 5 – 3 x = 2

Measures of Central Tendency A measure used to describe or represent data The mean, median, and mode are measures of central tendency Examples Given six test scores: 85,87,78,88,88 and 96 Three measures of central tendency are : Mean = 87, ( )/6 Median = 87.5, The average of the two middle scores after putting them in order (78,85,87,88,88,96), (87+88)/2 Mode = 88, The score that appears most often

Odds Odds in favor: A ratio that compares favorable outcomes to unfavorable outcomes Odds against: A ratio that compares unfavorable outcomes to favorable outcomes Example If you roll a six-sided number cube (1-6): The odds in favor of getting a 3 are 1 to 5 (There is one 3, there are five numbers that are not 3) This is different than the probability of getting a 3, which is one out of six or 1/6

Order of Operations In order to make sure that everyone gets the same answer when simplifying, there is a set of rules to follow: 1.Do all operations within parentheses (P) 2.Simplify exponents (E) 3.From left to right: do all multiplication and division (MD) 4.From left to right: do all addition and subtraction (AS) The acronym for this is PEMDAS Example: 2 + 3(7 – 4) – = 2 + 3(3) – = – = 11 – = = 7 He needed to do the multiplication FIRST

Percent Per 100 or out of 100 A percent is a ratio that compares a number to 100 Examples 10/10 %

Prime A number greater than one with exactly two factors, one and itself Examples 2 is the smallest prime number (1x2 = 2) 17 is a prime number, the only factors of 17 are 1 and is NOT prime (it is composite) because the factors of 15 are 1, 3, 5 and 15 Sieve of Eratosthenes

Probability A ratio that compares the number of ways a certain event can occur to the total number of possible outcomes Examples If you roll a six-sided number cube (1-6): The probability of getting a 3 is 1/6 (there is one way to get a 3 out of six possible outcomes) The probability of getting an even number is 3/6 or 1/2 (there are three outcomes that are even: 2,4,6 out of six possible outcomes)

Properties of shapes and figures Characteristics or features that help to recognize and identify them Examples Properties of a square: Four sides of equal length Four right angles Properties of a trapezoid: Quadrilateral with exactly two parallel sides Properties of a parallelogram: Quadrilateral with opposite sides congruent, opposite sides parallel and opposite angles congruent

Proportion An equation stating that two ratios are equal or equivalent If the cross products of the two ratios are equal, then the pair forms a proportion Examples is a proportion because do not form a proportion because

Random Occurring without any pattern or order A chance pick from items which each have an equal likelihood of being chosen Examples There are six different colored marbles in a hat: If you choose one at random, there is an equal chance that you pick any one of them If a list of numbers is random, the numbers appear without regard to any order or pattern and each has an equal possibility of appearing

Rate of change A comparison of one quantity to the unit value of another quantity, A change in one measure with respect to another, The slope of a line Examples If a car drives 120 miles in 2 hours, Its rate of change is 60 miles per hour Students donated money to help hurricane victims. After 3 days they had collected $48 After 8 days they had collected $128 The rate of change was or $16 per day

Ratio A comparison of two numbers or quantities (usually by division) Examples If a class has 14 boys and 12 girls then The ratio of boys to girls is The ratio of girls to boys is The ratio of boys to total number of students is The ratio of girls to total number of students is can also be written as 7:6

Reciprocal The multiplicative inverse of a number Examples The reciprocal of is The reciprocal of -10 is

Sample A part of a group or population that is used to represent the entire population Examples Instead of surveying the entire sixth grade class about their favorite food, you only survey 2 sixth grade classrooms To find out the favorite type of movie of all students in your school, you only ask every tenth student walking down the hall.

Scale Drawing A drawing used to represent a figure that is too large or too small to be shown actual size It maintains the original proportions Examples Maps: if a distance of 75 miles is 1 inch long on a map the scale would be 1 inch = 75 miles Drawings: if the Eiffel Tower is 1000 feet tall and the drawing of it was 10 inches tall, the scale would be 10 inches=1000 feet or 1 inch= 100 feet. 1 inch = 75 miles

To write an fraction, expression or equation in its simplest form Examples Simplify: = Simplify: x + 50 = x + 50 = 67 x = 17 Simplify: 2x x – 2 = 5x + 3 Simplify x+4x=5 x 2x =8 x = 4

Simulation A model of an experiment The model is usually used because the actual experiment would be too difficult or time consuming to do Example Students participate in a stock market simulation game, buying stocks with play money and keeping track of mock portfolios to make predictions and follow trends in the real stock market

Statistics Collecting, organizing, and interpreting data, especially analyzing characteristics of populations by sampling Examples Statistics can be displayed using graphs, stem-and-leaf plots, box-and-whisker plots Statistics of a sample can include the range, mean, median, mode, upper and lower quartiles

Stem-and-leaf Plot A graph that uses the digits of each number in order to show the shape of the data Examples The scores on a test were: 83, 79, 84, 86, 84, 99, 98, 87, 98, 78, 96, 92, 90, 100, 84, 85. The stem-and-leaf plot would look like: (The stems represent tens, the leaves represent units)

Tessellation A repeating pattern of figures that completely covers a plane with no gaps and no overlaps Examples Hexagons will tessellate and completely cover a plane MC Escher is a famous artist who took basic geometric shapes and used them to make various figures that would tessellate in a plane

Transformation A change in the position, shape or size of a figure Transformations that change position are translations, reflections and rotations Examples Translation Reflection Rotation

Tree Diagram A branching diagram showing all possible outcomes or combinations of items or events Example Chris has three different colors of shirts and two different colors of pants How many different outfits are there? Blue Blue Tan GreenBrown Green White White There are 6 different outfits: Tan/Blue, Tan/Green, Tan/White Brown/Blue, Brown/Green, Brown/White

Volume The number of cubic units needed to fill a given 3-dimensional space The amount of space occupied by an object Examples Some volume formulas: Cube: Cylinder: Rectangular prism: