1/6 1 1/6X3

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: _______________________________________


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: _______________________________________


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


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


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: _______________________________________


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: _______________________________________


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: _______________________________________


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: _______________________________________


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: _______________________________________


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

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