Transcript Complementary Angles

Measures of Central Tendency
and Range
Mean – average, add and divide by
number of numbers
Median – middle number, order
from least to greatest & find
middle number
Mode – most, number that occurs
most often
Range – Subtract the smallest from
the largest.
Complementary Angles
Two angles whose measures
add up to 90º.
Supplementary Angles
Two angles whose measures
add up to 180º.
PEMDAS
• PLEASE – Parenthesis () First
• EXCUSE – Exponents Second
• MY – Multiplication and
• DEAR – Division from left to right
• AUNT – Addition and
• SALLY – Subtraction from left to
right
TABLES AND PATTERNS
Look at the relationship of
the top number to the
bottom number
Place in
Sequence
Term
1
1
2
4
3
7
4
10
n
3n-2
This Pattern: Multiply by 3 then subtract 2
Coordinate Plane
Quadrant
III
y axis
Quadrant
II
Quadrant
I
x axis
Quadrant
IV
Plotting Points
run (x, y) jump
Start at (0,0), move left or
right, then up or down
(-x,-y)
y axis
(-x,+y)
(+x,+y)
x axis
(+x,-y)
Percent
When finding PART of something,
¾ of 24
OR
5% of $28
“Of” means “multiply”
¾ x 24 = 18
0.05 x $28 = $1.40
All the angles of every
triangle add up to 180º
Exponents
Good
2³ = 2 × 2 × 2 = 8
No!
2³ = 2 × 3 = 6
Bad
Percent Problems
Part
%
Whole
100
Sales Tax
$15.00 CD
Sales Tax Rate is 6%
Find 6% OF $15.00
0.06 x 15.00 = 0.9
Sales tax = $0.90
Add the sales tax to the original
price.
$15.00 + $0.90 = $15.90
Proportional Relationships
involve multiplication
or division by a specific
number,
never addition or
subtraction.
Real Life Examples
Proportional Relationships
•Photos (enlargement/reductions)
•Adjusting a recipe to feed more people
of fewer people.
•Similar shapes
•Shadows
•SOMETIMES prices are proportional,
sometimes not.
•Scale models, scale drawings, maps.
Naming Solid Figures
A solid figure is named after
the shape of its base(s).
Base
Base
Base
Triangular
Square
Prism Rectangular Pyramid
Prism
Triangular
Pyramid
Similar Shapes
Same shape, different size.
All angles congruent.
Side lengths are proportional
(multiplied or divided by the same number)
12
4
2
6
Similar figures have exactly the
same shape but may be different
sizes. Their corresponding sides
are proportional, and their
corresponding angles are
congruent.
10 in
5 in
3 in
6 in
Scale Factors
To find the scale factor of similar
figures or a real car and a model car,
compare lengths. Divide
new
old
10 in
5 in
6 in
3 in
Parts of a Circle
radius
5
Perimeter
•The distance around the outside.
•You can find the perimeter by ADDING all
the sides.
Real Life Example:
How many feet of fencing do you need to
surround your yard?
Find the perimeter of your yard.
30 + 30 + 10 + 10 = 80 ft
10 ft
30 ft
The perimeter is 80 ft. so you
need 80 ft of fencing.
Circumference
•The distance around the outside of a
circle.
•Use the formula on your chart to find
circumference.
Real Life Example:
How many feet of border do you need to
surround a circular flower garden?
Find the circumference of your flower
garden.
Area
•The number of square units needed to
cover something flat.
•Use the formula on your chart to find
area. BE SURE YOU USE THE FORMULA THAT
MATCHES THE SHAPE IN THE PROBLEM.
Real Life Example:
How much carpet do you need to cover
your floor ?
Find the area of your room.
DANGER! Different shapes need different
formulas. LOOK ON YOUR CHART!!!
Volume
•The number of cubic units needed to fill
something or to describe how much space
it takes up. Use the formula on your
chart to find volume.
•Real Life Example:
How many cubic feet of sand are needed
to fill up the sandbox?
Find the volume of the sandbox.
DANGER! Different shapes need different
formulas. LOOK ON YOUR CHART!!!
Multiplying Fractions
Not a problem
Top x top
&
Bottom x Bottom
Remember to Reduce!!!
Dividing Fractions
Keep, Change, Flip
Then multiply straight
across
Remember to
Simplify/Reduce!!!
Adding & Subtracting
Fractions
Must have a common
denominator,
then add or subtract the
numerators and
simplify/reduce.
Proportions
Label Them!!!!
3 people xpeople

1car
20cars
3 people 1car

xpeople 20cars
3 people 20cars

1car
xpeople
OK
OK
NO!!!
Fractions to Decimals
Top dog in the house!!
DIVIDE
3
 53
5
0 .6
5 3 .0
30
0
3
 0.6
5
Common Equivalents
1
4
1
3
= 0.25 = 25%
= 0. 3 3 =
1
33 %
3
1
= 0.5 = 50%
2
2
3
3
4
= 0. 6 6 =
2
66 %
3
= 0.75 = 75%
Decimals to Percents
•Use the DP rule. (Dr. Pepper)
•From D to P move the decimal two
places right and write a “%”.
•From P to D move the decimal two
places left and get rid of the “%”.
Example:
0.6 = 60%
Example:
5% = 0.05
Griddable Responses
73
73
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More on Griddables
Work these problems very
carefully. Without answer choices
as a way to check yourself, it is
important to take your time and
be accurate.
Write your answer using the
correct place values. Then fill in
the correct bubble in each
column.
A Plan for Each Problem
•Carefully read through at least twice
before you start working.
•Find and underline the question.
•Read through for details. Pay
attention to every word.
•If you are not sure what to do after
you read the problem twice, look at
the answer choices for clues.
•Circle or underline key info, cross out
useless info. and label every number.
A Plan for Each Problem
•If the questions talks about a figure
(square, circle, triangle, etc.) but doesn’t
have a picture, DRAW A PICTURE.
•If you are given coordinates (ordered
pairs), but you don’t know what to do, plot
the points. Maybe that will give you some
clues.
•Draw a diagram, picture, or table if
possible.
•If you are confused about a problem and
you see an equation, substitute numbers
for letters.
…Plan Continued
•Estimate an answer if possible.
•Work the problem step by step. Some
problems may require several steps.
Show all work to help you keep track.
•Keep your math chart on your desk and
use it!
•Check to make sure you’ve answered
the question being asked and that your
answer is reasonable.
•DO NOT LEAVE ANY BLANKS.
Keep Your Formula
Chart On Your Desk
•USE YOUR
CHART !!!
Read Carefully
Take Your Time
Relax
Think Positively
You Can Do This