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8th grade Math vocabulary / Calendar2015-2016

Concept 1

  1. 1. integer: one of the set of whole numbers and their operations.
  2. 2. rational number: any number that can be expressed as a ratio in the fraction form a/b where a and b are integers and b is not equal to 0.
  3. 3. scientific notation expresses a number as the product of a number between 1 and 10 , and a power of 10.
  4. 4. perfect square: a number that has integers as its square roots.
  5. 5. irrational number: can be written as a non-terminating or a non-repeating decimal.
  6. 6. real numbers: formed by combining the set of rational numbers and the set of irrational numbers.
  7. 7. Density Property: between every 2 real numbers, rational or irrational, there is always another real number.

Concept 2

  1. 1. odds: a ratio that compares the number of favorable outcomes and the number of unfavorable outcomes.
  2. 2. proportion: an equation which states that 2 ratios are equivalent.
  3. 3. rate: ratios that compare quantities of different units.
  4. 4. unit rate: when the 2nd term of the ratio is 1, the rate is a unit rate.
  5. 5. unit price: a unit rate for prices is often called a unit price.

Concept 3

  1. 1. numerical expression: includes numbers and at least one of the operations of addition, subtraction, multiplication, and division.
  2. 2. algebraic expression: an expression that is written using at least one variable.
  3. 3. variable: a letter that represents one or more numbers.
  4. 4. equation: a mathematical sentence that uses an equals sign to show that 2 expressions are equal.
  5. 5. inequality: a mathematical sentence that compares expressions that are not equal, using the symbol <, >, or <, > or not equal.
  6. 6. evaluate: find the value of.
  7. 7. equivalent: when numerical expressions have the same value.
  8. 8. coefficient: the number that is multiplied by the variable; can be positive or negative.
  9. 9. term: a real number, a variable, or the product of real numbers and variables.
  10. 10. like term: when 2 or more terms have the same variables and the same powers of these variables
  11. 11. combine like terms: to add or subtract like terms.
  12. 12. simplify: when you combine like terms in an algebraic expression.
  13. 13. simplest form: the expression that results from simplifying.

Concept 4

  1. 1. solution: if a value of a variable makes an equation true, the variable is the solution.
  2. 2. substitute: put the value in place of the variable.
  3. 3. 2-step equation: represents 2 different operations.

Concept 5

  1. 1. algebraic inequality: an inequality that contains a variable.

Concept 6

  1. 1. solution of an equation with 2 variables: an ordered pair if the equation is a true statement when the values of x and y are substituted in the equation.
  2. 2. graph of an equation: the graph of all its solutions.
  3. 3. linear equation: equation whose graph is a straight line.
  4. 4. parabola: the U-shaped curve on each graph.

Concept 7

  1. 1. tessellation: a repeating pattern of plane figures that completely covers a plane with no gaps or overlapping.
  2. 2. basic unit: the shape that is repeated in a tessellation.
  3. 3. Platonic solid: 5 regular polyhedron: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
  4. 4. semi regular polyhedron: solid formed from patterns of more than one kind of regular polygon; meet in same arrangement at each vertex.
  5. 5. spiral: a curve traced by a point rotating around and around from a fixed point.
  6. 6. Archimedean spiral: spiral in which the loops are evenly spaced.
  7. 7. equiangular spiral: spiral in which a ray drawn from the center intersects the loops at a constant angle.
  8. 8. helix: spiral-shaped curve in space that goes around an axis.
  9. 9. spirolateral: geometric design that is generated from a sequence of numbers.
  10. 10. consecutive integers: integers that are next to each other in counting order, such as 3, 4 and 8, 9, 10.
  11. 11. fractal: structure with repeating patterns containing shapes that are like the whole but of different sizes throughout.
  12. 12. diverge: get large without bound.
  13. 13. converge: become small.
  14. 14. scale factor: ratio for pairs of corresponding sides of similar figures.
  15. 15. Sierpinski triangle: geometric images that imitate nature.

Concept 8

  1. 1. term of a sequence: a number in the sequence.
  2. 2. common difference: a fixed number added to form a new term of sequence.
  3. 3. arithmetic sequence: what the sequence is called after new terms are added.
  4. 4. common ratio: the constant factor that is used to multiply to form new terms.
  5. 5. geometric sequence: what the sequence is called after new terms are multiplied.
  6. 6. Fibonacci sequence: branching pattern in growth of a plant.
  7. 7. Golden Ratio: any ratio that has a decimal value of about 1.6.
  8. 8. Golden Rectangle: a rectangle that has a length-to-width ratio of about 1.6 to 1.

Concept 9

  1. 1. similar figure: have same shape but not necessarily the same size.
  2. 2. proportional: equal.
  3. 3. similarity ratio: the scale factor of 2 similar figures is the common ratio of the lengths of pairs of corresponding sides.
  4. 4. scale drawing: represents a real object or place
  5. 5. self-similarity: when a scale has a special similarity property; small parts of the figure are scale drawings of the whole figure at different scales.

Concept 10

  1. 1. scale model: a proportional model of a solid, or 3 dimensional object.

Concept 11

  1. 1. percent of increase: the amount something increases in ratio of 100; per hundred.
  2. 2. percent of decrease: the amount something decreases in ratio of 100; per hundred.
  3. 3. commission: a fee paid to a person for making a sale.
  4. 4. commission rate: the percent the person is paid.
  5. 5. sales tax: the tax on the sale of an item or a service.
  6. 6. withholding tax: a deduction from a person's earnings as an advance payment on income tax.
  7. 7. interest: a fee paid for the use of money.
  8. 8. principal: amount of money borrowed or invested.
  9. 9. rate of interest: the percent charged or earned.
  10. 10. time: (in years) that the money is borrowed or invested.
  11. 11. compound interest: computed on both the principal and the interest previously earned.
  12. 12. annually: computed once a year.
  13. 13. semiannually: computed twice a year.
  14. 14. quarterly: computed 4 times a year.

Concept 12

  1. 1. sample:part of a group.
  2. 2. population: the whole group.
  3. 3. side-by-side histogram: one way to organize, display, and compare 2 sets of similar data.
  4. 4. back-to-back stem-and-leaf plot: another way to organize, display, and compare 2 sets of similar data.
  5. 5. interpolation: an estimate or prediction of an unknown value between 2 known values.
  6. 6. extrapolation: an estimate or prediction of an unknown value beyond known values.

Concept 13

  1. 1. central tendency: type of average.
  2. 2. variability: spread of values.
  3. 3. box-and-whisker graphs: organization of data that shows how far aprat and how evenly the data are distributed.
  4. 4. second quartile: the median of a set of data, that is the middle number, or the sum of the 2 middle numbers divided by 2, when the numbers are arranged in order.
  5. 5. first quartile: the median of the lower half of a set of data.
  6. 6. third quartile: the median of the upper half of a set of data.
  7. 7. scatterplot: a graph made by plotting points on a coordinate plane.
  8. 8. line of best fir: a straight line drawn through as much data as possible on a scatterplot.
  9. 9. positive correlation: a relation in which 2 sets of data increase or decrease at the same time.
  10. 10. negative correlation: a relation in which one set of data increases as the other decreases.
  11. 11. no correlation: when data points are scattered, there is no relationship between the 2 variables.

Concept 14

  1. 1. sample space: all possible outcomes in a given situation.
  2. 2. tree diagram: a branching diagram which shows all possible outcomes.
  3. 3. Fundamental Counting Principle: the principle which states that all possible outcomes in a sample space can be found by multiplying the number of ways each event can occur.
  4. 4. factorial: the product of all whole numbers, except zero, less than or equal to a number.
  5. 5. permutation: an arrangement of things in a definite order.
  6. 6. combination: an arrangement of items or events in which order does not matter.
  7. 7. mathematical probability: the number used to describe the chance that an event will happen.
  8. 8. independent events: outcome of first event does not affect the outcome of the second event.
  9. 9. dependent events: events for which the outcome of one event is affected by the outcome of the other event.

Concept 15

  1. 1. transversal: a line that intersects 2 or more lines.
  2. 2. interior angle: angles on the inner side of 2 line cut by a transversal.
  3. 3. exterior angle: angles on the outer sides of 2 line cut by a transversal.
  4. 4. bisect: to divide into 2 congruent parts.

Concept 16

  1. 1. image: the figure in a new position, location, or size that is the result of a transformation.
  2. 2. dilation: a transformation that enlarges or reduces a figure.

Concept 17

  1. 1. perspective: a technique used to make 3 dimensional objects appear to have depth and distance on a flat surface.
  2. 2. vanishing point: in a perspective drawing, parallel lines running directly away from the viewer which are drawn so that they come together at a point.
  3. 3. horizon line: a horizontal line that represents the viewer's eye level.
  4. 4. cross section: the figure formed by the intersection of a plane and a solid figure.

Concept 18

  1. 1. direct variation: a relationship between 2 sets of data such that the data increase or decrease together at a constant rate.

Concept 19

  1. 1. slope: the measure of the steepness of a line; ratio of vertical change to horizontal change.
  2. 2. x-intercept: x-coordinate of the point where the graph crosses the x axis.
  3. 3. y-intercept: y-coordinate of the point where the graph crosses the y axis.
  4. 4. slope-intercept form: y=mx+b; the m is the slpe and the b is the y-intercept
  5. 5. system of equations: 2 or more linear equations graphed in the same coordinate plane.
  6. 6. solution of the system: sometimes the graphs of the equations intersect at a point, the coordinates of the point are the solution of the system.
  7. 7. relation: a set of ordered pairs.
  8. 8. domain: the set of the 1st elements of a relation.
  9. 9. range: the difference between the greatest number and the least number on a set of data.
  10. 10. function:a relation in which no 2 ordered pairs have the same x-value.
  11. 11. vertical line test: if any vertical lines intersect a graph at more than one point, the graph does not represent a function; otherwise it does
  12. 12. linear function: a function whose graph is a straight line.
  13. 13. nonlinear function: a function whose graph is not a straight line.

Concept 20

  1. 1. monomial: an expression that is a number, a variable, or the product of a number and one or more variables.
  2. 2. simplify a polynomial: to combine (add or subtract) like terms.
  3. 3. standard form: polynomial whose terms are arranged so that the exponents or a variable decrease from left to right.

Concept 21

  1. 1. network: a figure made up of vertices and edges that show how objects are connected.
  2. 2. vertex: a point where 2 or more rays meet, where sides of a polygon meet, or where edges of a polyhedron meet.
  3. 3. edge: the line segment along which 2 faces of a polyhedron intersect.
  4. 4. odd vertex: odd number of lines coming from it.
  5. 5. even vertex: even number of lines coming from it.accuracy: shown by the number of significant digits.
  6. 6. significant digits: tell the number of digits used to express the accuracy of a measure.surface area: the sum of the areas of the faces, or surfaces, of a solid figure.
  7. 7. lateral surface: the curved surface of a cylinder or a cone.
  8. 8. slant height: the distance from the base of a cone to its vertex, measured along the lateral surface.

Concept 22

  1. 1. leg: in a right triangle, either of the 2 sides that intersect to form the right angle; in an isosceles triangle, one of the 2 congruent sides.
  2. 2. hypotenuse: in a right triangle, the side opposite the right angle.
  3. 3. Pythagorean Property: in any right triangle, if a and b are the lengths of the lges and c is the length of the hypotenuse, the a2+b2=c2.
  4. 4. trigonometric ratio: ratio which compares the lengths of the sides of a right triangle; common ratio are tangent, sine, and cosine.
  5. 5. trig ratio: another name for trigonometric ratios.


Lesson Plans

1-Thinking with Mathematical Models (Linear and Inverse Variation)
2- Looking for Pythagoras (The Pythagorean Theorem)
3- Growing, Growing, Growing (Exponential Relationship)
4- Frogs, Fleas, and Pained Cubes (Quadratic Relationship)
5- Kaleidoscopes, Hubcaps, and Mirrors (Symmetry and Transformation)
6- Say it With Symbols (Algebraic Reasoning)
7- The Shapes of Algebra (Linear Systems and Inequalities)
8- Samples and Populations (Data Analysis and Probabilities – Data and Statistics)