percent

% A number

A number

of

is

IS THE PERCENT GIVEN?

YES OR NO?

IF NO, THEN FIND IT!!!!!

What percent of 10 is 7?

P ( 10 ) = 7

P ( 10 ) = 7

10 10

P7

10=

P .7 70 %

==

IS THE “of”

GIVEN?

YES OR NO?

IF NO, THEN FIND IT!!!!!

70% of what is 7?

.70 ( n ) = 7

.7 ( n ) = 7

.7 .7

n 10 =

IF BOTH ARE

GIVEN!

JUST MULTIPLY

.70 (10) = n

7 = n

T HEN THE % IS G IVEN AND T HE "OF"IS G IVENM ULT IPLY T HE % AND T HE "OF"

70% OF 10 IS W HAT?

YES NO70% OF W HAT IS 7?

IS T HE "OF" G IVEN?

YES NOW HAT PERCENT OF 10 IS 7?

IS T HE % G IVEN?

ADDITION OF ADDITION OF INTEGERSINTEGERS

SAME SIGNSSAME SIGNS JUST ADD !!JUST ADD !!

4 + 7 = 114 + 7 = 11 -4 + (-7) = -11-4 + (-7) = -11

8 + 2 = 108 + 2 = 10 -8 + (-2) = -10-8 + (-2) = -10

• DIFFERENT SIGNSSUBTRACT THE ABSOLUTE VALUES!!!

4 + (-7) = |-7| - |4| = 7 - 4 = 3

USE THE SIGN OF THE NUMBER WITH THE GREATER ABSOLUTE VALUE!!IN THIS CASE: -7

SO….. 4 + (-7) = -3

18 + (-5) = 13- 8 + (-3) = -11 16 + (-9) = 5-12 + (-4) = -16 9 + (-13) = - 4

The distance acrossthe circle, throughthe center.

The distance acrossthe circle, throughthe center.

The distance from the center to the edge.

The distance from the center to the edge.

d = 2rd = 2r

2r2r

GRAPHING GRAPHING LINEAR LINEAR

RELATIONSRELATIONS

““GRAPHING GRAPHING LINESLINES””““GRAPHING GRAPHING LINESLINES””

2x + 3

X values go in…..

Y values come out!!

x y2-204

y = -1 x 2

-1 1 0-2

OUT OF OUT OF 100!!100!!

2525

10010025 %25 %

1 % = .01 = 1/100 = 2 % = .02 = 2/100 = 1/50

3 % = .03 = 3/100 = 4 % = .04 = 4/100 = 1/25 5 % = .05 = 5/100 = 1/20 6 % = .06 = 6/100 = 3/50 7 % = .07 = 7/100 = 8 % = .08 = 8/100 = 2/25 9 % = .09 = 9/100 = 10 % = .10 = 10/100 = 1/10

11 % = .11 = 11/100 =12 % = .12 = 12/100 = 3/2513 % = .13 = 13/100 =14 % = .14 = 14/100 = 7/5015 % = .15 = 15/100 = 3/2016 % = .16 = 16/100 = 4/2517 % = .17 = 17/100 =18 % = .18 = 18/100 = 9/5019 % = .19 = 19/100 =20 % = .20 = 20/100 = 1/5

21 % = .21 = 21/100 =22 % = .22 = 22/100 = 11/5023 % = .23 = 23/100 =24 % = .24 = 24/100 = 6/2525 % = .25 = 25/100 = 1/426 % = .26 = 26/100 = 13/5027 % = .27 = 27/100 =28 % = .28 = 28/100 = 7/2529 % = .29 = 29/100 =30 % = .30 = 30/100 = 3/10

31 % = .31 = 31/100 =32 % = .32 = 32/100 = 8/2533 % = .33 = 33/100 = 34 % = .34 = 34/100 = 17/5035 % = .35 = 35/100 = 7/2036 % = .36 = 36/100 = 9/2537 % = .37 = 37/100 =38 % = .38 = 38/100 = 19/5039 % = .39 = 39/100 =40 % = .40 = 40/100 = 2/5

41 % = .41 = 41/100 =42 % = .42 = 42/100 = 21/5043 % = .43 = 43/100 =44 % = .44 = 44/100 = 11/2545 % = .45 = 45/100 = 9/2046 % = .46 = 46/100 = 13/5047 % = .47 = 47/100 =48 % = .48 = 48/100 = 12/2549 % = .49 = 49/100 =50 % = .50 = 50/100 = 1/2

51 % = .51 = 51/100 =52 % = .52 = 52/100 = 13/2553 % = .53 = 53/100 = 54 % = .54 = 54/100 = 27/5055 % = .55 = 55/100 = 11/2056 % = .56 = 56/100 = 14/2557 % = .57 = 57/100 =58 % = .58 = 58/100 = 29/5059 % = .59 = 59/100 =60 % = .60 = 60/100 = 3/5

61 % = .61 = 61/100 =62 % = .62 = 62/100 = 31/5063 % = .63 = 63/100 =64 % = .64 = 64/100 = 16/2565 % = .65 = 65/100 = 13/2066 % = .66 = 66/100 = 33/5067 % = .67 = 67/100 =68 % = .68 = 68/100 = 17/2569 % = .69 = 69/100 =70 % = .70 = 70/100 = 7/10

71 % = .71 = 71/100 =72 % = .72 = 72/100 = 18/2573 % = .73 = 73/100 =74 % = .74 = 74/100 = 37/5075 % = .75 = 75/100 = 3/476 % = .76 = 76/100 = 19/2577 % = .77 = 77/100 = 78 % = .78 = 78/100 = 39/5079 % = .79 = 79/100 =80 % = .80 = 80/100 = 4/5

81 % = .81 = 81/100 =82 % = .82 = 82/100 = 41/5083 % = .83 = 83/100 =84 % = .84 = 84/100 = 21/2585 % = .85 = 85/100 = 17/2086 % = .86 = 86/100 = 43/5087 % = .87 = 87/100 =88 % = .88 = 88/100 = 22/2589 % = .89 = 89/100 =90 % = .90 = 90/100 = 9/10

91 % = .91 = 91/100 = 92 % = .92 = 92/100 = 23/25 93 % = .93 = 93/100 = 94 % = .94 = 94/100 = 47/50 95 % = .95 = 95/100 = 19/20 96 % = .96 = 96/100 = 24/25 97 % = .97 = 97/100 = 98 % = .98 = 98/100 = 49/50 99 % = .99 = 99/100 = 100 % = 1.00 = 100/100 = 1

1 % = .01 = 1/100 = 2 % = .02 = 2/100 = 1/50 3 % = .03 = 3/100 =

4 % = .04 = 4/100 = 1/25 5 % = .05 = 5/100 = 1/20 6 % = .06 = 6/100 = 3/50 7 % = .07 = 7/100 = 8 % = .08 = 8/100 = 2/25 9 % = .09 = 9/100 =

10 % = .10 = 10/100 = 1/10

11 % = .11 = 11/100 = 12 % = .12 = 12/100 = 3/25 13 % = .13 = 13/100 = 14 % = .14 = 14/100 = 7/50 15 % = .15 = 15/100 = 3/20 16 % = .16 = 16/100 = 4/25 17 % = .17 = 17/100 = 18 % = .18 = 18/100 = 9/50 19 % = .19 = 19/100 = 20 % = .20 = 20/100 = 1/5

21 % = .21 = 21/100 = 22 % = .22 = 22/100 = 11/50 23 % = .23 = 23/100 = 24 % = .24 = 24/100 = 6/25 25 % = .25 = 25/100 = 1/4 26 % = .26 = 26/100 = 13/50 27 % = .27 = 27/100 = 28 % = .28 = 28/100 = 7/25 29 % = .29 = 29/100 = 30 % = .30 = 30/100 = 3/10

31 % = .31 = 31/100 = 32 % = .32 = 32/100 = 8/25 33 % = .33 = 33/100 = 34 % = .34 = 34/100 = 17/50 35 % = .35 = 35/100 = 7/20 36 % = .36 = 36/100 = 9/25 37 % = .37 = 37/100 = 38 % = .38 = 38/100 = 19/50 39 % = .39 = 39/100 = 40 % = .40 = 40/100 = 2/5

41 % = .41 = 41/100 = 42 % = .42 = 42/100 = 21/50 43 % = .43 = 43/100 = 44 % = .44 = 44/100 = 11/25 45 % = .45 = 45/100 = 9/20 46 % = .46 = 46/100 = 13/50 47 % = .47 = 47/100 = 48 % = .48 = 48/100 = 12/25 49 % = .49 = 49/100 = 50 % = .50 = 50/100 = 1/2

51 % = .51 = 51/100 = 52 % = .52 = 52/100 = 13/25 53 % = .53 = 53/100 = 54 % = .54 = 54/100 = 27/50 55 % = .55 = 55/100 = 11/20 56 % = .56 = 56/100 = 14/25 57 % = .57 = 57/100 = 58 % = .58 = 58/100 = 29/50 59 % = .59 = 59/100 = 60 % = .60 = 60/100 = 3/5

61 % = .61 = 61/100 = 62 % = .62 = 62/100 = 31/50 63 % = .63 = 63/100 = 64 % = .64 = 64/100 = 16/25 65 % = .65 = 65/100 = 13/20 66 % = .66 = 66/100 = 33/50 67 % = .67 = 67/100 = 68 % = .68 = 68/100 = 17/25 69 % = .69 = 69/100 = 70 % = .70 = 70/100 = 7/10

71 % = .71 = 71/100 = 72 % = .72 = 72/100 = 18/25 73 % = .73 = 73/100 = 74 % = .74 = 74/100 = 37/50 75 % = .75 = 75/100 = 3/4 76 % = .76 = 76/100 = 19/25 77 % = .77 = 77/100 = 78 % = .78 = 78/100 = 39/50 79 % = .79 = 79/100 = 80 % = .80 = 80/100 = 4/5

81 % = .81 = 81/100 = 82 % = .82 = 82/100 = 41/50 83 % = .83 = 83/100 = 84 % = .84 = 84/100 = 21/25 85 % = .85 = 85/100 = 17/20 86 % = .86 = 86/100 = 43/50 87 % = .87 = 87/100 = 88 % = .88 = 88/100 = 22/25 89 % = .89 = 89/100 = 90 % = .90 = 90/100 = 9/10

91 % = .91 = 91/100 = 92 % = .92 = 92/100 = 23/25 93 % = .93 = 93/100 = 94 % = .94 = 94/100 = 47/50 95 % = .95 = 95/100 = 19/20 96 % = .96 = 96/100 = 24/25 97 % = .97 = 97/100 = 98 % = .98 = 98/100 = 49/50 99 % = .99 = 99/100 = 100 % = 1.00 = 100/100 = 1

1 % = .01 = 1/100 = 2 % = .02 = 2/100 = 1/50 3 % = .03 = 3/100 = 4 % = .04 = 4/100 = 1/25 5 % = .05 = 5/100 = 1/20 6 % = .06 = 6/100 = 3/50

7 % = .07 = 7/100 = 8 % = .08 = 8/100 = 2/25 9 % = .09 = 9/100 = 10 % = .10 = 10/100 = 1/10

11 % = .11 = 11/100 = 12 % = .12 = 12/100 = 3/25 13 % = .13 = 13/100 = 14 % = .14 = 14/100 = 7/50 15 % = .15 = 15/100 = 3/20 16 % = .16 = 16/100 = 4/25 17 % = .17 = 17/100 = 18 % = .18 = 18/100 = 9/50 19 % = .19 = 19/100 = 20 % = .20 = 20/100 = 1/5

21 % = .21 = 21/100 = 22 % = .22 = 22/100 = 11/50 23 % = .23 = 23/100 = 24 % = .24 = 24/100 = 6/25 25 % = .25 = 25/100 = 1/4 26 % = .26 = 26/100 = 13/50 27 % = .27 = 27/100 = 28 % = .28 = 28/100 = 7/25 29 % = .29 = 29/100 = 30 % = .30 = 30/100 = 3/10

31 % = .31 = 31/100 = 32 % = .32 = 32/100 = 8/25 33 % = .33 = 33/100 = 34 % = .34 = 34/100 = 17/50 35 % = .35 = 35/100 = 7/20 36 % = .36 = 36/100 = 9/25 37 % = .37 = 37/100 = 38 % = .38 = 38/100 = 19/50 39 % = .39 = 39/100 = 40 % = .40 = 40/100 = 2/5

41 % = .41 = 41/100 = 42 % = .42 = 42/100 = 21/50 43 % = .43 = 43/100 = 44 % = .44 = 44/100 = 11/25 45 % = .45 = 45/100 = 9/20 46 % = .46 = 46/100 = 13/50 47 % = .47 = 47/100 = 48 % = .48 = 48/100 = 12/25 49 % = .49 = 49/100 = 50 % = .50 = 50/100 = 1/2

51 % = .51 = 51/100 = 52 % = .52 = 52/100 = 13/25 53 % = .53 = 53/100 = 54 % = .54 = 54/100 = 27/50 55 % = .55 = 55/100 = 11/20 56 % = .56 = 56/100 = 14/25 57 % = .57 = 57/100 = 58 % = .58 = 58/100 = 29/50 59 % = .59 = 59/100 = 60 % = .60 = 60/100 = 3/5

61 % = .61 = 61/100 = 62 % = .62 = 62/100 = 31/50 63 % = .63 = 63/100 = 64 % = .64 = 64/100 = 16/25 65 % = .65 = 65/100 = 13/20 66 % = .66 = 66/100 = 33/50 67 % = .67 = 67/100 = 68 % = .68 = 68/100 = 17/25 69 % = .69 = 69/100 = 70 % = .70 = 70/100 = 7/10

71 % = .71 = 71/100 = 72 % = .72 = 72/100 = 18/25 73 % = .73 = 73/100 = 74 % = .74 = 74/100 = 37/50 75 % = .75 = 75/100 = 3/4 76 % = .76 = 76/100 = 19/25 77 % = .77 = 77/100 = 78 % = .78 = 78/100 = 39/50 79 % = .79 = 79/100 = 80 % = .80 = 80/100 = 4/5

81 % = .81 = 81/100 = 82 % = .82 = 82/100 = 41/50 83 % = .83 = 83/100 = 84 % = .84 = 84/100 = 21/25 85 % = .85 = 85/100 = 17/20 86 % = .86 = 86/100 = 43/50 87 % = .87 = 87/100 = 88 % = .88 = 88/100 = 22/25 89 % = .89 = 89/100 = 90 % = .90 = 90/100 = 9/10

91 % = .91 = 91/100 = 92 % = .92 = 92/100 = 23/25 93 % = .93 = 93/100 = 94 % = .94 = 94/100 = 47/50 95 % = .95 = 95/100 = 19/20 96 % = .96 = 96/100 = 24/25 97 % = .97 = 97/100 = 98 % = .98 = 98/100 = 49/50 99 % = .99 = 99/100 = 100 % = 1.00 = 100/100 = 1

Copyright, 1996 © Dale Carnegie & Associates, Inc.

Math PortfoliosMath Portfolios

IntroductionIntroduction

Each student will be required to Each student will be required to keep all daily assignments, all keep all daily assignments, all notes, quizzes, and tests in a folder notes, quizzes, and tests in a folder that will be held in class. This that will be held in class. This portfolio will be a major part ( 300 portfolio will be a major part ( 300 points) of the student’s grade. points) of the student’s grade. There will be five divisions or types There will be five divisions or types of work to be kept in the portfolio. of work to be kept in the portfolio.

DAILY CONDUCT GRADESDAILY CONDUCT GRADES

–These will be recorded on a These will be recorded on a sheet provided by the sheet provided by the teacher.teacher.

CLASS PREPERATION CLASS PREPERATION GRADESGRADES

– This grade will be based on This grade will be based on whether or not the student brings whether or not the student brings their book, paper, pencil, and their book, paper, pencil, and homework (if applicable) to class. homework (if applicable) to class. This grade will also be recorded This grade will also be recorded each day by the student on the each day by the student on the page provided by the teacher.page provided by the teacher.

QUIZZESQUIZZES

–These will be kept in the These will be kept in the folder after they are graded folder after they are graded and recorded by the and recorded by the teacher.teacher.

TESTSTESTS

–All graded tests will be All graded tests will be included in the folder.included in the folder.

NOTES AND IN CLASS NOTES AND IN CLASS WORKWORK

– Any notes that are written on the Any notes that are written on the board and any handouts that are board and any handouts that are given in class should also be included given in class should also be included in the folder. This grade will be in the folder. This grade will be determined each Friday based on the determined each Friday based on the number of days the student took number of days the student took notes that week. These may be notes that week. These may be taken out of the folder at any time for taken out of the folder at any time for studying purposes, but should be studying purposes, but should be replaced by the time they are graded.replaced by the time they are graded.

1. Choose an appropriate scale.

Actual 1 ft.Drawing 1 in.

Actual 1 ft.Drawing 10 in.

2. Make at least two measurements.

3. Calculate drawing measurements.

Actual 1 30Drawing 5 x

=

x = 5(30)x = 150

3. Calculate drawing measurements.

Actual 5 30Drawing 1 x

=

5x = 1(30) x = 6

SOLVINGSOLVING

TWO STEPTWO STEP

EQUATIONSEQUATIONS

SOLVINGSOLVING

TWO STEPTWO STEP

EQUATIONSEQUATIONS

20 = 6x + 820 = 6x + 820 = 6x + 820 = 6x + 820 - 8 = 6x + 8 - 820 - 8 = 6x + 8 - 820 - 8 = 6x + 8 - 820 - 8 = 6x + 8 - 8

12 = 6x12 = 6x12 = 6x12 = 6x6666 66662 = x2 = x2 = x2 = x

6x + 8 < 206x + 8 < 206x + 8 < 206x + 8 < 206x + 8 - 8 < 20 - 86x + 8 - 8 < 20 - 86x + 8 - 8 < 20 - 86x + 8 - 8 < 20 - 8

6x < 126x < 126x < 126x < 126666 6666 x < 2x < 2 x < 2x < 2

221100

x < 2x < 2

5

710

912

64

8

25

30

15

10

GRAPHING LINES ON THE GRAPHING LINES ON THE COORDINATE PLANECOORDINATE PLANE

THE “MATH ENGINE”THE “MATH ENGINE”

x

y

0

Quadrant IQuadrant II

Quadrant III Quadrant IV

5-5

5

- 5

(3,3)

(x,y)

X’s go in...

Y’s come out...

y = 2x - 3

y = 2x - 3x y

Choose “x” values .

-3-113

x

y

0 5-5

5

- 5

0123

Find “y”.

x

y

0 5-5

5

- 5

y = x + (-2) x y

0123

-2-101

-1 -3

x

y

0 5-5

5

- 5

y = -x + 3

x y-1 4 0 3 1 2 2 1

y

0 5-5

5

- 5

y = 5

x y-1 5 0 5 1 5 2 5

y

0 5-5

5

- 5

x = 5

x y 5 4 5 3 5 2 5 1

CHAPTER 5CHAPTER 5

INTEGERSINTEGERS

LESSON GOALS:LESSON GOALS:

ABSOLUTE VALUEABSOLUTE VALUEOF INTEGERS OF INTEGERS

OPPOSITE OF INTEGERSOPPOSITE OF INTEGERS

COMPARING ANDCOMPARING ANDORDERING INTEGERSORDERING INTEGERS

THE ABSOLUTE VALUE OF A NUMBER IS THE DISTANCE THE NUMBER IS FROM ZERO ON A NUMBER LINE.

THE ABSOLUTE VALUE OF A NUMBER IS THE DISTANCE THE NUMBER IS FROM ZERO ON A NUMBER LINE.

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

4444

00 11 22 33 44 55 66-1-1-2-2-3-3-4-4-5-5

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

THE FURTHER LEFT THE SMALLER THE NUMBER

THE FURTHER RIGHT THE GREATER THE NUMBER