Ms Jennifer O (Adams) Busch

Divisibility: 

Important Math Terms

Misc Math terms:

1. Product: Answer to a multiplication problem--EX: 4 x 5 = 20 ==> 20 is the product.

2. Quotient: Answer to a division problem--EX: 20÷4 = 5 ==> 5 is the quotient.

3. Difference: Answer to a subtraction problem--EX: 20 - 4 = 16 ==> 16 is the difference.

4. Sum: Answer to an addittion problem--EX: 4 + 5 = 9 ==> 9 is the sum.

5. Factor: Smaller n umber that divides evenly into a larger number; one of two or more numbers that multiply together--EX: the factors of 24 are: 1, 24, 2, 12, 3, 8, 4, & 6

6. Multiple: The product of any counting number (1, 2, 3, ...) and that number--EX: the 1st five multiples of 9 are: 9, 18, 27, 36, & 45

7. Greatest Common Factor (GCF): The largest factor that is common (shared) between 2 or more numbers--The common factors of 18 & 24 are: 1, 2, 3, & 6. 6 is the largest (greatest) so it is the GCF.

8. Least common Multiple(LCM): The smallest multiple that is common (shared) betweeb 2 or more numbers-- The first 5 multiples of 9 are: 9, 18, 27, 36, & 45. The first 5 multiples of 12 are: 12, 24, 36, 48, & 60. The smallest (least) of these is 36, the LC M .

9. Prime number: counting number greater than 1 that has only 2 factors, 1 & itself. (2, 3, 5, 7, 11, 13, 17, 23, etc)

10. Composite number: counting number that has MORE than 2 factors. (4=1, 2, 4; 12=1, 2, 3, 4, 6, 12)

11. Numerator: The TOP (Northern) number (or variable) in a fraction--EX: In the fraction ¾, 3 is the numerator.

12. Denominator: The BOTTOM (Down) number (or variable) in a fraction.--EX: In the fraction ¾ , 4 is the denominator.

13. Reciprocal: when you flip a fraction upside down EX 2/5 becomes 5/2

14. Improper Fraction: When the numerator is larger than the denominator ex: 15/8

15. Mixed Number: When there is an integer or whole number and a fraction. Ex: 1 & 1/2.
16. Equivalent Fractions: When two fractions simplify to the same exact fraction. Ex: 4/8 reduces to 1/2 and so does 50/100. So 4/8, 1/2, &   50/100 are all equivalent fraction
17. Diameter: A line segment that starts on the edge of a circle, goes through the center, & ends on the other edge.
18. Radius: A line segment that starts in the center of a circle & ends on the circle's edge

FORMULAS:

1. Area: is used to calculate how much tile, carpet, grass, sod, etc is needed. It is in a unit squared.

2. Perimeter: A The distance around a polygon (non rounded shape) that is used to calculate how m uch wallpaper border, floor trim, fence, etc is needed. It is measured in linear units.

3. Circumference: the distance around (perimeter) a circle or circular object.

4. Volume: The amount that is needed to completely fill a 3D object such as a cube or pool. It calculates how much pesticide spray, pool water, chlorine, etc is needed. It is measured in cubic units

5. Area of a triangle : 1/2 x b x h

6. Circle formulas : Area = pi x radius squared & circumference = 2 x pi x radius

7. Distance Formula: D=Distance, R=Rate or speed, T=Time: D=R*T

8. Surface Area: The area of all sides of a 3D shape added together.

Translating English to Math & Math to English

1. Is: = (Equal sign) [the sum of 1 & 2 is 3 ~~> 1+2=3]

2. Of: * (multiplication sign) [1/2 of 50 is 25 ~~> 0.5 * 50 = 25]

3. Less: - (subtract) [a number less 12 is 7 ~~> n - 12 = 7]

4. Less than: - (subtract) [15 less than 35 is a number ~~> 35 - 15 = n]

5. More/more than: + (Add) [a dozen more than Sarah is 15 ~~> S + 12 = 15]

6. Increased by: + (Add) [a dozen increasaed by Tiffany is 15 ~~> 12 + T = 15]

7. Decreased by: - (subrtract) [a gross decreased by 2 dozen (24) is what? ~~> 144 - 24 = n]

8. Squared: n^2 (the power of 2) [7 squared is what? ~~> 7^2 = 49]

9. Cubed: n^3 (the power of 3) [2 cubed is what? ~~> 2^3 = 8] ]

10. Distributed Evenly: ÷ (divide) [24 dollars distributed evenly between 4 people~~> 24 ÷4=6]

Algebraic Terms:

1. Expression: "Math Sentence" that uses numbers, operation symbols, & sometimes variables

2. Equation: "math sentence" that uses numbers, operation symbols, the equal sign, & sometimes variables

3. Solution: Answer

4. Evaluate: solve

5. Variable: a letter or symbol that represents a value (in the expression a+5, a is the variable)

6. Constant: a value that never changes (in the expression a+5, 5 is the constant)

7. Inverse: the opposite of

8. Inverse Operation: the opposite operation (inverse of adding is subtracting)

9. Distributive property: asd

GENERAL GEOMETRY :

1. Point: a location usually identified with a dot and a letter
2. Plane: a flat surface that has no end
3. l ine segment: straight line that has 2 endpoints; it is named by the endpoints and a miniature picture above the two endpoints
4. Endpoints: The ends of a line segment
5. Line: goes on in both directions; it is named by ANY two points on it with a miniature picture above them
6. Ray: has one endpoint and goes on indefinitely in the other direction; it is named with its endpoint first, any other point 2nd, and miniature picture above them
7. Angle: Two rays that share an endpoint; it is named by using 3 letters: the vertex is the middle letter, any point (one from each ray) are around the vertex. A B C ABC
8. Vertex: The vertex is where two lines, line segments, or rays meet to form an angle; “A” is the vertex of the angle above.
9. Degree: is the unit of measure for angles
10. Protractors: are used to measure an angle
11. Angle rulers: are used to measure an angle Congruent: ≈ : The same measurements/size geometric figure (line segment, polygon, circle, shape, etc). Symmetry: When two sides are mirror images of themselves/each other

ANGLES
12. Acute angles: measure >90^o
13. Obtuse Angles: measure 90^o
14 . Right angles: measure exactly 90^o
15. Straight angles: measure exactly 180^o

CIRCLES
16a. Angle ruler: works like a compass to measure the size of angles AND like a protractor to draw angles of certain sizes.

16b. Compass: is used to construct a circle
17. Radius: a line segment with 1 endpoint on the edge of the circle & the other in the center of the circle.
18. Chord: a line segment whose endpoints are on the outer edge of a circle
19. Diameter: a chord that passes through the center of the circle.
20. Arcs: are the distance between two points on a circle
21. Central Angles: are angles whose vertexes are at the center of the circle. They are made of radii

Circumference: is the distance around (perimeter) of a circle

"Special" ANGLE PAIRS / RELATIONSHIPS
22. Congruent: the same or equal
23. Vertical angles: are formed when two lines or line segments intersect; they are the angles that are opposite of each other (corner to corner); they have the same angle measurement
24. Adjacent Angles: have a common vertex and a common ray; they are next door neighbors
25. Complementary angles: are angles whose sum of their measurements is exactly 90o
26. Supplementary angles: are angles whose sum of their measurements is exactly 180o
27. Parallel lines: never intersect; they have the same slope
28. Perpendicular lines: intersect to form 90o angles
29. Transversal lines: are lines that intersect parallel lines.
30. corresponding angles: are in the same position on different parallel lines; they have the same angle measurement

SHAPES/POLYGONS

31a. Polygon: a shape consisting of ONLY line segments--no arcs, circles, etc.
31b. regular polygons: have all sides’ and angles’ measurements congruent, where irregular polygons' sides & angles are NOT congruent.
32. triangle: 3 sided polygon
33. quadrilateral: 4 sided polygon
34. Pentagon: 5 sided polygon
35. Hexagon: 6 sided polygon
36. Heptagon: 7 sided polygon
37. Octagon: 8 sided polygon
38. Nonagon: 9 sided polygon
39. Decagon: 10 sided polygon

"Special" QUADRALATERALS
40. Trapezoid: only two sides are parallel (looks like a triangle that’s head got caught in a trap)
41. Parallelogram: opposite sides are parallel and congruent; opposite angles are congruent
42. rhombus: opposite sides are parallel and all sides congruent (a squashed square)
43. Rectangle: opposite sides are parallel and congruent; all angles are 90^o
44. Square: opposite sides are parallel; all sides congruent; all angles are 90^o

"Special"   TRIANGLES
45. Acute Triangle: is a triangle in which all angles are >90o
46. Obtuse triangle: is a triangle in which one angle is 90o
47. Right triangle: is a triangle in which one angle is = 90o
48. Equilateral Triangle: all sides and angles are congruent (the same)
49. Isosceles triangle: two sides and angles are congruent (the same)
50. Scalene triangle: NO sides and angles are congruent (the same)
51. THE SUM OF ALL ANGLES IN A TRIANGLE IS EXACTLY 180^o

METRIC SYSTEM…
Gram: unit that measures weight/mass
Meter: unit that measures length
Liter: unit that measures liquid capacity
Be able to list pre-fixes: Kilo, Hecto, Deca, (unit), Deci, Centi, Milli
Give pneumonic device for recall:........King............ Henry...... died..... Monday...Drinking..Chocolate...Milk
Place value -- be able to relate it to this: Thousands..Hundreds..Tens ..... ONES .... Tenth...Hundredth...Thousandths
Metric system : ........................................ Kilo...........Hecto....... Deka.. (Meter, Liter, or Gram)..Deci.... Centi..........Milli
Prefix abrev ..............................................K..............h..............Da.....(m, L, g).......d..........c...............m

CUSTOMARY MEASUREMENT:
Dozen = ___12____ items
Gross= _12_ dozen = __144__   items
LENTH:
1 foot = ____12____ in
1 yard = ____3____ ft
1 yard = ____36____ in
1 mile = ____1760____ yd
1 mile = ____5280____ ft
LIQUID CAPACITY:
1 fluid ounce (fl oz) = __2__ tablespoon (tbsp)
1 cup (c) = ___8___ fl oz
1 pint (pt) = ___2___ c
1 quart (qt) = __2___ pt
1 gallon (gal) = ___4__ qt
WEIGHT:
1 pound (lb) = ___16___ ounces (oz)
1 ton (T) = ___2,000___ lbs
TIME:
1 minute (min) = ___60___ sec
1 hour (hr) = ___60___ min
1 day (d) = ___24___ hr
1 week (wk) = ___7___ d
1 month (mo) = ABOUT ___4 1/3 _____ wk
# days in each month:
31: Jan, Mar, May, July, Aug, Oct, Dec
30: Sept, April, June, Nov
28: Feb
1 year (yr)= _12_ mo = __365__ days
1 yr = __52__ wk

Roman Numerals:

I: 1 .................... V: 5 .................... X: 10 .................... L: 50

C: 100................ D: 500 ................ M: 1,000

When Roman Numerals of a smaller value are placed BEFORE ones of a larger value they are read to be that many BEFORE. EX: IV reads one before 5 (4); XL reads 10 before 50 (40); & XC reads 10 before 100 (90)

When Roman Numerals of a smaller value are placed AFTER ones of a larger value, they are read to be that many AFTER. EX--VI reads one after 5 (6); LX reads 10 after 50 (60); & CX reads 10 after 100 (110).

When they are strung together, you need to be careful in how you read them. EX--XIV reads 10 plus 1 before 5 (14); CLXX reads 10 and 10 and 50 after 100 (170)

Data:

Mean: the average of a set of numbers--to get this, add all numbers up, then divide by how many numbers you added

Median: the middle number when data is arranged from smallest to largest. When there are two middle numbers, it is the average of the two.

Mode the number that appears most often

Range: The smallest number in a set of data to the largest number in a set of data

Presenting Data:

Bar Graph*:asdf

Histograms*:asdf

Line Graph*:asdf

Stem & Leaf Plots*: asdf

Box & Whisker Plots*: asdf

Pie/Circle Graph: asdf

Scatter Plot: asdf

Math Course 2 text on page 135 describes the best use for each of these.

Classifying Numbers:

Counting numbers: 1, 2, 3, 4, 5, 6, 7, 8, .......

Whole numbers: counting numbers AND zero [0, 1, 2, 3, 4, 5, 6, .....]

Integers: Whole numbers AND their opposites [.....-4, -3, -2, -1, 0, 1, 2, 3, 4, .....]

Rational numbers: Integers AND any fraction that can be written as a decimal that either repeats or ends [....-4, -3 ½, -3, -2.3, -2, -1, 0, 0.33333, 1, 2, 2.5, etc......]

Irrational number(s): numbers that when changed from a fraction to a decimal do not repeat & do not end. [Pi ∏]

Real numbers: Rational AND Irrational numbers