Vocabulary
If a part of the original figure matches up with a part of the copy, we call them ____________ parts. The part could be an angle, point, or side.
What is Corresponding?
Figure B is a scaled copy of Figure A. Select all of the statements that must be true:
A. Figure B is larger than Figure A.
B. Figure B has the same number of edges as Figure A.
C. Figure B has the same perimeter as Figure A.
D. Figure B has angles with the same measures as Figure A.
What is B and D?
Find 3 different ratios that are equivalent to 7 : 3.
If James types 120 words in 3 minutes, what is his typing rate?
What is 40 words per minute?
The point (0,0) on a graph is called the ____________.
What is Origin?
Two ratios a : b and c : d are ____________ _______ if there is a number (x) that you can multiply both a and b by to get c and d (respectively).
In other words, a * x = c and b * x = d.
What are Equivalent Ratios?
A science textbook uses a scale of 3 cm = 2 mm for drawings of small insects. What is the actual length of a flea if the drawing is 7.5 cm long?
The variables x and y are proportional, with a constant of proportionality of 3.5 from x to y. Write an equation to represent this relationship.
What is y = 3.5x?
A truck driver drives from Chicago to Cincinnati in 14 hours. the distance traveled is 840 miles. Find the unit rate.
What is 60 miles per hour?
Decide whether or not the given ratios are proportional and explain why:
12/20 and 3/10
Not proportional, Explanations Vary
The _______ _________ is the factor by which every length in the original figure is increased or decreased when you make a scaled copy.
What is Scale Factor?
The scale on a road map is 1 centimeter = 500 miles. If the distance on the map between New York City and Memphis is 2.2 centimeters, find the actual distance between the two cities.
What is 1,100 miles?
The graph of a proportional relationship must be ___________ and go through ___________.
What is linear and (0,0) or the origin?
Define Unit Rate.
What is "How much of something PER 1 unit of something else?"
On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is t = 1/500d. How long will it take the airplane to travel 800 miles?
What is 1.6 hours? [Since 1/500 x 800 = 1.6]
If there is a positive constant k so that the quantities x and y are related by the equation y = kx, then we say that y and x are in a _____________ _______________.
What is Proportional Relationship?
Jill's room is 12.5 feet long and 11.5 feet wide. She made a scale drawing of the room with a scale of 0.5 inch = 2 feet. What is the perimeter of Jill's room in the drawing?
What is 12 inches?
Every package of a certain toy also includes 2 batteries. Are the number of toys and the number of batteries in a proportional relationship? If so, what are the two constants of proportionality? If not, explain your reasoning.
Yes. 2 and 1/2 are the constants of proportionality.
If 10 bags of Hot Cheetos cost $3.50, then how much does 1 bag cost?
What is $0.35?
The equation c = 2.95g shows how much it costs to buy gas at a gas station on a certain day. In the equation, c represents the cost in dollars, and g represents how many gallons of gas were purchased. What does 2.95 represent in this situation?
One gallon of gas costs $2.95, or gas costs $2.95 per gallon {constant of proportionality}
In a proportional relationship, the constant k is called the ____________________________________.
For a school project, Lee is making a model of the Empire State Building. He uses a scale of 1 centimeter = 8 feet. Find the height of the model given that the Empire State Building is 1,252 feet tall.
What is 156.5 centimeters?
Concrete building blocks weigh 28 pounds each. Using b for the number of concrete blocks and w for the weight, write two equations that relate the two variables.
What is w = 28b and b = 1/28w?
Which is the better deal?
$20 for 5 T-Shirts or $24 for 8 T-Shirts
Give the Unit Rate for the better deal.
What is $24 for 8 T-Shirts, $3 per shirt?
Quadrilateral A has side lengths 3, 4, 5 and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2. Select all of the following that are side lengths of Quadrilateral B.
A. 5
B. 6
C. 7
D. 8
E. 9
What are B and D? [The side lengths of Quadrilateral B would be 6, 8, 10, and 12.