Transcript Document

Math Warm Up
10 minutes
Place from least to greatest
• ½, .025, 1/4 , 0.2
•
0.002, 0.03, ¾, 0.78
3. 1.2, 1.023, 1.23, 0.246
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Quote of the Day
Accept challenges, so that you may
feel the exhilaration of victory.
-George S. Patton
Math Chapter 8-1
Ratios and Equivalent Rations
Standard:
Number Sense 1.2: Interpret and use ratios in different contexts; to show
the relative sizes of 2 quantities.
Content Objective: We will read and write ratios and equivalent ratios.
Language Objective: We will interpret the notes, do a think-pair-share,
and write ratios on white boards.
A Ratio is the
comparison of two or
more numbers.
Fractions that name
the same number.
Three Ways to Write a
Ratio
The ratio of 3 boys to 5 girls
can be written as:
a) 3 to 5
b) 3: 5
c)
3
5
Which ratio shows the ratio of 2 fish to 3 bear?
A
B
C
D
E
Which ratio shows the ratio of 1
soccer ball to 3 basketball?
A
B
C
D
E
Which ratio shows the ratio of 3
butterflies to 1 apple?
A
B
C
D
E
Equivalent Fractions
3
5

6
3
10
4

75
100
Practice-
Math Warm Up
10 minutes
Find each missing number.
• 2 = x
2. 15 = 5
7 21
18
t
3. 6 = 3
g 14
4. r = 3
12
4
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Quote of the Day
Difficulties are meant to rouse, not
discourage. The human spirit is to
grow strong by conflict.
-William Ellery Channing
Math Chapter 8-2 and 8-3
Proportions and Solving Proportions Using Cross Products
Standard:
Number Sense 1.3: Use proportions to solve problems. Use cross
multiplication as a method for solving problems, understanding it as the
multiplication of both sides of an equation by the inverse.
Content Objective: We will solve proportions by using cross products.
Language Objective: We will explain the steps for solving proportions to a
partner and in our notebooks.
Two equal ratios form a
proportion.
In a proportion the
product of the means is
equal to product of the
extremes.
3 : 5 = 6 : 10
Means
Extremes
3
5
Means

6
10
Extremes
6 x 5 = 3 x 10
30 = 30
Determine if the following
are proportions.
1)
5
3

60
36
2)
8
15

4
8
5
3

60
8
36
15

4
8
3 x 60 = 5 x 36 4 x 15 = 8 x 8
180 = 180
60  64
Yes, it is a proportion.
No, it is not a proportion.
Math Warm Up
10 minutes
Find each missing number.
• n = 24
2. 20 = n
20 32
30 45
3. 144 = 720
g
125
4. 10 = 14
n
35
Quote of the Day
You really can change the world if
you care enough.
- Marion Wright Edelman
Math Chapter 8-5
Rates
Standard:
Algebra and Function 2.2: Demonstrate an understanding that rate is a
measure of one quantity per unit of value of another quantity.
Number Sense 1.3: Use proportions to solve problems.
Content Objective: We will use rates to solve problems.
Language Objective: We will write a word problem involving rates and
solve a partners word problem.
A rate is a ratio that
compares two
quantities that have
different units of
measure.
Example: 80 miles / 2 hours
A unit rate is a rate in
which the second
quantity is one unit of
measure.
Example: 40 miles / 1 hour
Step 1:
Write a proportion.
Step 2:
Solve. You can use cross
products.
Example:
A car uses 4 gallons of gas for every 1 ½ miles it is driven. What
is the average rate of gas used per mile?
Step 1:
112 miles = r
4 gallons
1 gallon
Step 2:
4r = 112
4
4
r= 28
*The unit rate is 28 miles per gallon.
Unit Rate
Written as a Ratio
Miles per hour (MPH)
Number of miles/ 1 hour
Miles per gallon (MPG) Number of miles/ 1 gallon
$45.00 per hour
$45.00/ 1 hour
$1.50 per pound
$1.50 / 1 pound
In 2004 Summer Olympics,
Justin Gatlin won the 100-meter
race in 9.85 seconds. Shawn
Crawford won the 200-meter
race in 19.79 seconds. Which
runner ran at a faster average
rate?
Practice
Write a word problem that involves
rates.
Math Warm Up
10 minutes
Find each unit rate.
• 120 miles in 4 hours
•
240 calories in 6 servings
•
114 miles on 12 gallons
•
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Quote of the Day
Kind words conquer.
- Tamil Proverb
Math Chapter 8-6
Unit Price
Standard:
Algebra and Function 2.3: Solve problems involving rates.
Number Sense 1.3: Use proportions to solve problems.
Content Objective: We will find unit prices to determine the better buy.
Language Objective: We will pictorially and verbally solve problems
involving unit price.
Unit Price:
A unit price is a ratio that
shows how much an item
costs for each unit of
measure.
Unit prices help you select
the better buy.

total price =
total units
price
1 unit
Make a picture and label your picture to
describe how to solve unit price.
Find the unit price and then
decide which is the better buy.
$2.52 or $3.64
42oz
52oz
Find the unit price and then
decide which is the better buy.
$28.40 or $55.50
8 yd
15 yd
Math Warm Up
10 minutes
Find each unit price.
• $2.10 for 6 bagels
•
2 pizzas for $10.50
•
7 gallons for $12.53
•
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Quote of the Day
Discipline is the bridge between goals
and accomplishment.
- Jim Rohn
Math Chapter 8-8
Similar Figures
Standard:
Number Sense 1.3: Use proportions to solve problems.
Content Objective: We will use proportions to solve problems involving
similar figures.
Language Objective: We will explain using the key vocabulary what are
similar figures.
Congruent Figures
In order to be congruent, two figures must be the
same size and same shape.

Similar Figures:
Figures that have the same
shape but not necessarily the
same size.
Similar Figures

This is the symbol that means “similar.”
These figures are the same shape but different sizes.

SIZES
Although the size of the two shapes can
be different, the sizes of the two shapes
must differ by a factor.
4
2
6
3
1
3

6
2
SIZES
In this case, the factor is x 2.
4
2
3

6
6
3
1
2
SIZES
Or you can think of the factor as
4
2
3

6
6
3
1
2
Enlargements
When you have a photograph enlarged, you make a
similar photograph.

X3
Reductions
A photograph can also be shrunk to produce a slide.
4

Determine the length of the unknown side.
15

12
?
4
3
9
These triangles differ by a factor of 3.
15
15
12

3= 5
?
4
3
9
Determine the length of the unknown side.
?
2
4

24
These dodecagons differ by a factor of 6.
?
2
4

24
Sometimes the factor between 2 figures is not obvious
and some calculations are necessary.

15
12
18
?=
8
10
12
To find this missing factor, divide 18 by 12.
15
12
18

?=
8
10
12
18 divided by 12
= 1.5
The value of the missing factor is 1.5.
15
12
18

1.5 =
8
10
12
When changing the size of a figure, will the angles of
the figure also change?
?
40
70
70
?
?
Remember, the sum of all 3 angles in a triangle MUST add to 180 degrees.
If the size of the angles were increased, the sum would exceed 180
degrees.
40
40
70
70
70
70
We can verify this fact by placing the smaller triangle
inside the larger triangle.
40
40
70
70
70
70
The 40 degree angles
are congruent.
40
70
70
70
70
1) Determine the missing side
of the triangle.
?
3
5
4
9
12
1) Determine the missing side
of the triangle.
15
3
5
4
9
12
2) Determine the missing side
of the triangle.
6
6
36
36
4
?
2) Determine the missing side
of the triangle.
6
6
36
36
4
24
3) Determine the missing
sides of the triangle.
39
33
?
?
8
24
3) Determine the missing
sides of the triangle.
39
33
13
11
8
24
4) Determine the height of the
lighthouse.
?
8
2.5
10
4) Determine the height of the
lighthouse.
32
8
2.5
10
5) Determine the height of the
car.
?
3
5
12
5) Determine the height of the
car.
7.2
3
5
12
Math Warm Up
10 minutes
Determine the missing sides of the triangle.
39
33
?
?
24
•
8
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Practice
Write directions, using the key
vocabulary, for how to solve problems
with similar figures.
Quote of the Day
A coward gets scared and quits. A
hero gets scared, but still goes on.
- Anonymous
Math Chapter 8-9
Scale Drawings
Standard:
Number Sense 1.3: Use proportions to solve problems.
Mathematical Reasoning 2.4: Use a variety of methods, such as words,
numbers, symbols, diagrams, to explain mathematical reasoning.
Content Objective: We will interpret scale drawings.
Language Objective: We will explain in 2-3 sentences how to use and
solve problems with scale drawings.
Scale:
Scale Drawings:
The ratio of the
measurement in a drawing to
the measurements of the
actual objects.
A drawing made so that
actual measurements can be
determined from the drawing
by using the scale.
Step 1:
Write a proportion using the scale as
one of the ratios.

Step 2:
Example: Let N represent the actual
length.
Solve the proportion.. Use cross
products (multiplication)






Drawing
Actual
1=6
1 N
N=6
Scale
Length
1cm = 6cm
1m
Nm