Download - Learning Target:
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Learning Target:
I can…Set up and solve proportions
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Proportion:
An equation that shows two ratios are equivalent
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To check to see if it is a proportion:
= Cross multiply and see if you get the
same number or find the unit rate
=
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Is the following a proportion? (a = yes, b = no)
1. 3 = 2_ 25 15
2. 6 = 4_24 16
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Solving Proportions
To solve proportions, cross multiply – then divide!
Example:
y_ = 10_15 25y ∙ 25 = 15 ∙ 10y ∙ 25 = 150y = 6
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Use a proportion to fill in a table or find missing points.1) Cindy took two trips. There is a proportional relationship between the number of miles she travels and the gallons of gas her car uses. Fill in the blank.
Trip 1 Trip 2Miles Traveled
200 160
Gallons Used 4600
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2) Amaya types as the same speed for all of her essays so there is a proportional relationship between the number words she types and the minutes it takes her. Fill in the blank.
Essay 1 Essay 2
Words 3120
Minutes 30 12
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3) James is making muffins. As he makes more servings, there is a proportional relationship between the cups of sugar he uses and the cups of flour. Fill in the blanks.
Serving 1
Serving 2
Serving 3
Serving 4
Serving 5
Sugar 1
Flour 2 3
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Knowing Missing Points
4) Line k show a proportional relationship between x and y. If (2,5) is a point on this line, then fill in the missing coordinates below:
a. (4, ______) d. (_______, 15)
b. (1, ______) e. (_______, 7.5)
c. (7, ______) f. (_______, 0)
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Knowing Missing Points
5) Line k show a proportional relationship between x and y. If (4,6) is a point on this line, then fill in the missing coordinates below:
a. (8, ______) d. (_______, 15)
b. (1, ______) e. (_______, 7.5)
c. (7, ______) f. (_______, 0)
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Proportions and Percent:Write a proportion to solve the following, always putting the percent over _____________.
1) Lila wants to score at an 86% on her test. If her test has 50 points, how many points must she earn on the test to reach her goal?
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2) Reynaldo wants to score at an 90% on his test. If his test has 70 points, how many points must she earn on the test to reach his goal?
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Ratio and Proportions
1) A local Humane Society houses 200 animals. The ratio of dogs to all animals is 13:20. a. Write a proportion that gives the number of dogs d.
b. How many dogs are in the Human Society?
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Ratio and Proportions
2) The ratio of boys to all students in a school is 1:3. There are 600 students in a school.a. Write a proportion that gives the number of boys b..
b. How many boys are in the school?
c. How many girls are in the school?
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Ratio and Proportions
3) Mona counted a total of 56 ducks on the pond in Town Park. The ratio of female ducks to male ducks that Mona counted was 5:3. What was the total number of female ducks Mona counted on the pond?
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The female to male ratio at General Sherman is 1:2. If there are 720 students at General Sherman, how many are girls?
A. 360B. 1440C. 240D. 300
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Review
The ratio of male to female horses is 2:5. How many male horses are there if there are a total of 21 horses?
A. 15B. 6C. 10D. 4
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Exit
The ratio of male to female students is 2:3. How many male students are there if there are a total of 300 students?
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Learning Target:
I can…Solve word problems using a proportion
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To solve proportions, ____________________________ – then ______________!
Word Problems – MAKE SURE YOU SHOW THE PROPORTION WITH _________!!!
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Cross Multiply 3 ∙ 10 = 4 ∙ x
30 = 4x
Divide by 4 x =$7.50
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Quick Check!
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Quick Check!
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Proportions Review
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Erica gets 24 miles per gallon of gas when driving on the open highway. How many gallons of gas will her car use traveling a distance of 384 miles?
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The scale on Myra’s atlas reads 1 inch equals 40 miles. How many inches on the map represent 125 miles?
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CPS Quick Check!
1. How much would 4 pounds of oranges cost if 2 pounds cost $3?
2 pounds = 4 pounds $3 $6
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Shadow Proportion Problems
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2) A 5-ft tall student casts a 12-ft shadow. A tree casts a 27-ft shadow. How tall is the tree?
a. 11.25 ftb. 64.8 ftc. 297 ftd. 34 ft
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SCALES
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Chan is designing a new swimming pool that will have a length of 34 feet. He plans to make a scale drawing of the pool. In his drawing inches represents 1 foot. What should be the length, in inches, of Chan’s scale drawing of the pool?
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Using a Map Scale
If the distance from the swimming pool to the horse corral is 4cm, how many meters away is it?
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Using a Map Scale
If the from the lodge to the horse corral is 3cm in the picture, how many meters away is it in real life?
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Using a Map Scale
If the distance from the mess hall to the swimming pool is 350m in real life, how many centimeters away is it in the drawing?
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Similar Figures
1. Shape but different size2. They are proportional• Symbol ~
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Similar Figures
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Determine the length of the unknown side.
12
9
15
4
3
?
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Determine the length of the unknown side.
4
2
24
?
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Find the value of x
K
L
H G
J
4
6
x
15
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What is the perimeter of ABC?
12
9
15
4
3
?A
B
C
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Two Step Proportions
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Lisa’s father is an architect. He builds a cardboard model of each building he designs. The scale of his model to the actual building is 1 inch = 8 feet.
How tall will the actual building be when the model is 3 feet tall?
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On a scale drawing of a house a rectangular bedroom has a length of 4 inches and a perimeter of 20 inches. The scale is 1 inches = 2 foot. What is the actual width of the bedroom?
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On a scale drawing of a house a rectangular bedroom has a length of 5 inches and a perimeter of 26 inches. The scale is 1 inches = 2 foot. What is the actual width of the bedroom?
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2 step proportions
What is the perimeter of triangle DEF?15
2025
60
80
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Learning Target:
I can…Solve ALL types of proportion problems
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Below is a scale drawing of a house. If the kitchen actually has a length of 12 feet, what is the scale of the drawing to the actual house?
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Learning Target:
I can…Find the missing side of similar figures
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Similar Figures
• Have the same _______________ and _______________ sides.
• To find a missing side of similar figures, set up a ________________________ and solve.
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1.
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2. Solve for x
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• Shapes within shapes are also ________________________.
• To find the missing side, ____________ the shapes and set up a proportion.
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Find the value of x
K
L
H G
J
4
6
x
15
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How tall is the tree?
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Find the value of x
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To find the perimeter of shapes, ___________________________.
The two rectangles are similar. What is the PERIMETER of rectangle EFGH?
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To find two missing sides:
1. )
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2)
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X
Y Z
J
K
A.(1, 1)B.(4, 5)C.(6, -3)D.(4, -3)
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Exit – Solve for x
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Learning Target:
I can…Master ratio and proportions
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Shadow problems 1,
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2.
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3. A landscape architect uses scale drawings to design layouts for his clients. The plan he is working on now is for a yard that is 150 feet long and 120 feet wide. When making a scale drawing he uses a ratio of 12:1, actual number of feet in the yard that he is working on to number of inches on the drawing. What are the dimensions of the scale drawing?
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4.
Find the actual dimensions (length and width) of the kitchen. *Hint: you will need to use two proportions!
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5. On a scale drawing of a house a rectangular bedroom has a length of 5 inches and a perimeter of 26inches. The scale is 1 inch = 2 foot. What is the actual width of the bedroom?
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6. An architect builds a cardboard model of each building he designs. The scale of his model to the building is 1 in = 3 ft. How tall will the actual building be when the model is 3ft tall?
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• Find the perimeter of each triangle.
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Learning Target:
I can…Show what I know on my ratio and proportions
quiz
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Ratio Review
Write the ratio of roses to flowers if Big Bob’s flowers has 13 tulips and 5 roses.
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Ratio - Exit
In the local coed softball league, the female to male ratio is 4:6. If there are 160 players in the league, how many are female?
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EXIT
An architect builds a cardboard model of each building he designs. The scale of his model to the building is 1 in = 4 ft. How tall will the actual building be when the model is 2 ft tall?
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Challenge1.
2. On a scale drawing of a house a rectangular bedroom has a length of 5 inches and a perimeter of 26inches. The scale is 1 inch = 2 foot. What is the actual width of the bedroom?
3. An architect builds a cardboard model of each building he designs. The scale of his model to the building is 1 in = 3 ft. How tall will the actual building be when the model is 3ft tall?
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Proportion Review!
3.125 inches
$3.25
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