1/6 1 1/6x3
TRANSCRIPT
Name: _______________________________________
Unit 5 and 6 Review Notes 1
Vocabulary
Vocabulary
Ratio is a comparison of two quantitieswith the same units.
Rate is a ratio comparing two numbers with different units.
Proportion is an equation showing two ratios are equal.
Ratios
What is a Ratio?A ratio is a comparison of two quantities with the same units.
The 3 ways to write a ratio.
Remember that a ratio must always be in simplest form but have two numbers.
Colon Fraction Bar Words
2:3 23
2 to 3
Types of Ratios
Types of Ratios.There are three different types of a ratio.1) Part to Part
2) Part to Whole
3) Whole to Part
White 4 2Black 6 3
= , 2:3, 2 to 3
White 4 2Black 6 3= , 3:2, 3 to 2
White 4 2Total 10 5
= , 2:5, 2 to 5
Black 6 3= , 3:5, 3 to 5Total 10 5
White 4 2Total 10 5= , 5:2, 5 to 2
Black 6 3= , 5:3, 5 to 3Total 10 5
Unit Rates
Unit Rate is how many units of the first quantity (numerator) corresponds to one unit of the second quantity (denominator).
Vocabulary
Examples:
mi/gal$/oz
ft/secmi/hr$/lb
Unit Rates
3 1 8 96 3
1 80 990
Hours is on bottom because it says per hour.
Jo takes 3 hours to deliver 189 newspaperson his paper route. What is the rate per hourat which he delivers the newspapers?
NewspapersHours
1893
= x1
Answer: 63 NewspapersHour
*Hint
3x = 189
Cross Multiply
3 3
x = 63
OneStep Equation
Proportion Example
Example Problem #1
If 1/2 gallon of paint covers 1/6 of a wall, then how much paint is needed for the entire wall?
Word Statement Proportion SolutionGallons 1/2 x 3 gallons wall =
=
(Cross Multiply)
(Then divide by what is with the variable) =
1/6 1
1/6x 1/21/6 1/6
X 3
Name: _______________________________________
Unit 5 and 6 Review Notes 2
Proportion Example
Example Problem #2
If Tommy runs three miles in 24 minutes, then how long will it take him to run 5 miles?
Word Statement Proportion Solution
=
=
=
milesminutes
324
5x
120 3x3 340 x
40 minutes(Cross Multiply)
(Then divide by what is with the variable)
Percent Proportions
Percent ProportionsPercents are parts of a whole. If a percent is lower than 100, it has a value <1. If the percent is equal to 100, its value =1. If the percent is higher than 100, its value is >1.
Part (is) Percent(%)Whole (of) 100
=
Setting Up Percent Proportions
Setting Up Percent Proportions
Steps:
Part (is) Percent(%)
45 is what percent of 66?
45 is the Part
66 is the whole
"What percent" is the variable
Whole (of) 100=
45 x66 100=
1) Multiply to find the cross products.
2) Solve the onestep equation.
66x = 450066 66x = 68.18%
Practice Problems
What number is 70% of 600?
28 is 35% of what number?
What percent of 90 is 36?
isof
= %100
x600 =
70100
42000 = 100x100100
420 = x
28x = 35
10035x = 2800
3535x = 80
3690 = x
10090x = 3600
9090x = 40
isof
= %100
isof
= %100
Practice Problems
Jaylen got an 87.5% on his last Science test. If there were 40 questions, how many did he get correct?
isof = %
100x40 =87.5100
3500 = 100x100100
35 = x
35 questions correct
Practice Problems
On his homework, Trevor only completed 16 of the 25 questions. What percent of the questions did he finish?
isof = %
1001625 = x
100
25x = 16002525
x = 64
64% of the questions were completed
Name: _______________________________________
Unit 5 and 6 Review Notes 3
Formulas Perimeter and Area
Perimeter Add up all the sides (P =s + s + s...)
Square A = side2 A = S2
Rectangle A = Length x Width A = lw
Parallelogram A = Base x Height A = bh
Triangle A = Base x Height A = bh2 2
h h
h
w
L
s
b
b
b b
*Height is found at the 90 angle.o
A = 1/2bh*Height is found at the 90 angle.o
Perimeter
Perimeter The distance around a polygon.
Examples:
14 cm
3 cm20 m
7 m
8 m8 m
P = ____________ P = ____________
P = _______ P = _______
14 + 3 + 14 + 3
34 cm
8 + 8 + 20
36 m
Perimeter
Perimeter The distance around a polygon.
Examples:
6 ft
P = ____________ P = ____________
P = _______ P = _______
I
I
I
I
10 in
16 in
3 in
9 in
6 + 6 + 6 + 6
24 ft
16+9+10+6+6+3
50 in
Perimeter
Perimeter The distance around a polygon.
Examples:
P = ____________ P = ____________
P = _______ P = _______
3x + 2
II
I
I I
4cm 17cm
9cm
24cm
11cm
5
5(3x + 2)
15x + 10
9 + 17 + 24
50 cm
Area
Area The number of square units it takes to cover the figure. (The size of the figure.)
Examples:
14 cm
3 cm20 m
7 m
8 m8 m
A = ____________ A = ____________
A = ____________ A = ____________
A = ____________ A = ____________
Length x Width Base x Height 2
14 x 3
42 cm2
20 x 7 2
70 m2
Area
Area The number of square units it takes to cover the figure. (The size of the figure.)
Examples:
A = ____________ A = ____________
A = ____________ A = ____________
A = ____________ A = ____________
Base x Height Base x Height 2
2 m 11 m
8 m
18 m
6 m
4yd
1yd
9yd
5yd
9 x 4
36 yd211 x 6 2
33 m2
Name: _______________________________________
Unit 5 and 6 Review Notes 4
Working Area Backwards
How to solve area problems backwards?
Steps:
(1) Write the Formula.
(2) Plug in all information you know.
(3) Solve for unknown information.
(4) Make sure you answered what the question is asking.
(5) Write units on your answer.
Working Area Backwards
Examples:A = 42 yd2
7 yd
Find the length. Find the height.
A = 70 m2
14 m
A = L x W
42 = L x 777
6 = L
6 yd
A = b x h 2
70 =14 x h 270 = 7h
7710 = h10 m
Finding Volume
Volume The number of cubic units needed to fill a given space.
Volume of a Rectangular Prism
8 cm
3 cm
20 cm
V = L W H
V = 20 8 3
V = 480 cm3
*Units are always cubed*
Finding Volume with Fractions
Volume The number of cubic units needed to fill a given space.
Volume of a Rectangular Prism
2 3/4 m
1 1/2 m
14 1/2 m
V = L W H
V = 14 1/2 2 3/4 1 1/2V = 59 13/16 m3
*Units are always cubed*
Finding out How Many Cubes Fit into a Prism
A right rectangular prims has edges of 1 1/4 ft, 1 ft, and 1 1/2 ft. How many cubes with a side length of 1/4 ft would be needed to fill the prism?
1 ft
1 1/2 ft
1 1/4 ftSteps:
Find the Volume of the prism.
Find the Volume of the cube going into the prism.
Divide the Prism Volume by the Volume of the cube going into it. This will tell you how many cubes it takes to fill the prism.
*See work to the right*
Finding out How Many Cubes Fit into a Prism
A right rectangular prims has edges of 1 1/4 ft, 1 ft, and 1 1/2 ft. How many cubes with a side length of 1/4 ft would be needed to fill the prism?
1 ft
1 1/2 ft
1 1/4 ft
Volume of Prism
V = L x W x H
V = 1 1/2 x 1 x 1 1/4V = 1 7/8 ft3
Volume of the CubeV = L x W x HV = 1/4 x 1/4 x 1/4V = 1/64 ft3
Step #1
Step #2Step #31 7/8 1/64 =158
1 64
K C F158 1
64
=
=120120 cubes
Name: _______________________________________
Unit 5 and 6 Review Notes 5
Nets and Surface Area
6.G.4 Nets and Surface Area
I can...identify the different types of ________ that go with different 3dimensional figures.
I can ...find the _____________ of different 3 dimensional figures.
_________is a twodimensional representation of a threedimensional figure.
Surface Area (S.A.) is the _____________ that covers a 3 dimensional figure.
A Polyhedron is a 3D solid with __________
nets
surface area
A net
total area
flat faces
Formulas Review
Review:
• To find the area of a rectangle: Area = ________________
• To find the area of a triangle:
Area = ____________ or _______________
Length x Width
Base x Height2
1/2 (Base x Height)
Prisms
A Prism: • is a ____________________• it is a 3dimensional shape with 2 ________,
parallel bases. • all other faces are ______________ • a prism takes its name from the shape of its
_______
Triangle Rectangle Pentagon Octagon
polyhedronidentical
rectangles
bases
Parts of a #D Figure
Vertex: Vertices is the plural form of vertex. It is where the edges of a 3D figure meet.
Face: a flat surface of a 3D figure.
Edges: The side of a polygon where two faces of a solid figure meet.
Square Prism
Square Prisms (cubes) have
• 6 square faces all of ______ size.
• 8 _________
• 12 ______ edges
equal
vertices
equal
Square Prism Net
Nets of a _________________Square Prism (Cube)
Name: _______________________________________
Unit 5 and 6 Review Notes 6
Rectangular Prism
Rectangular Prisms have
• 6 faces that are ___________
• Opposite faces are parallel and ________
• 8 vertices
• 12 edges
rectangles
congruent
Rectangular Prism Net
Net of a ___________________Rectangular Prism
Triangular Prism
Triangular Prisms have
• 2 identical triangular bases, they are congruent and _____________
• 2 bases (triangles) and 3 faces (rectangles)
• 9 ___________
• 6 ___________
parallel
edges
vertices
Triangular Prism Net
Nets of a __________________Triangular Prism
Pyramid
Pyramid: • is a polyhedron.• a solid shape (3D shape ) with a _________
as its base. • has __________faces that taper into one
point (vertex).• A pyramid takes the name of the shape of its
________.
Triangle Rectangle Pentagon Octagon
polygon
triangular
base
Slant Heights on Pyramids
h h
Slant height is the height of each __________.lateral face
Triangular
Pyramid
Rectangular
Pyramid
Name: _______________________________________
Unit 5 and 6 Review Notes 7
Square Pyramid Net
Net of a ___________________Square Pyramid
I
I
II
Rectangular Pyramid Net
Net of a ___________________Rectangular Pyramid
Triangular Pyramid Net
Net of a ___________________Triangular Pyramid
Compare and Contract of Prisms and Pyramids
Prism Both Pyramid
Congruent Faces
Parallel Bases
Takes the name of its base
3Dimensional
Tapers to a point
Has lateral faces
Has triangular faces
Surface Area of a Cube
Find the surface area of the cube.
What is the AREA of one face?_______
How many faces does the cube have?______
Multiply the area of one face by the total number of faces. __________
Total Surface area:_________
5 cm
5 cm25cm2
6
25 x 6
150cm2
Surface Area of a Rectangular Prism
8"
5"
3"
Find the surface area of the rectangular prism.3"5"
8"5"
3"
Top and Bottom 2 x l x w Two side areas2 x h x wFront & Back2 x l x h
Total Surface Area:____________
Add these Numbers
2 x 8 x 3
2 x 5 x 3
2 x 8 x 5
48
30
80158 square inches
Name: _______________________________________
Unit 5 and 6 Review Notes 8
Surface Area of a Triangular Prism
Find the area of the triangular prism.
10m
8m
15m
Triangles ½bh x2Rectangle #1 l x wRectangle #2 l x wRectangle #3 l x wTotal Surface Area:___________________
Add these Numbers
10m
1/2 x 10 x 8 x 2
10m
10 x 15
10 x 15
10 x 15
150
150
150
80
530 meters squared
Surface Area of a Square Pyramid
Find the area of the square pyramid. 3 cm.
6 cm.
Square (l x w)Triangle #1 (1/2 x b x h)Triangle #2 (1/2 x b x h)Triangle #3 (1/2 x b x h)Triangle #4 (1/2 x b x h)
Surface Area:_______
Add these numbers
6 x 6 36
1/2 x 6 x 3 9
1/2 x 6 x 3 9
1/2 x 6 x 3 9
1/2 x 6 x 3 972 cm2
Surface Area of a Rectangular Pyramid
Find the area of the rectangular pyramid.
Rectangle(l x w)Triangle #1 (1/2 x b x h)Triangle #2 (1/2 x b x h)Triangle #3 (1/2 x b x h)Triangle #4 (1/2 x b x h)
Surface Area:_______
12 m
8 m 6m
14 m8 x 6 48
1/2 x 8 x 12 48
1/2 x 8 x 12 48
1/2 x 6 x 14 42
1/2 x 6 x 14 42228 m2
Surface Area of a Triangular Pyramid
Find the surface area of a triangular pyramid (base is an equilateral triangle)
10 cm
6 cm
Triangle #1 (1/2 x b x h)Triangle #2 (1/2 x b x h)
Triangle #3 (1/2 x b x h)
Triangle #4 (1/2 x b x h)
Surface Area:________
1/2 x 6 x 10 30
1/2 x 6 x 10 30
1/2 x 6 x 10 30
1/2 x 6 x 10 30
120 cm2