Vocab
What do you call a figure that is an enlarged or reduced version of another figure, where all lengths are multiplied by the same number?
Scale Copy
If a rectangle has a length of 4 cm and its scaled copy has a length of 8 cm, what is the scale factor?
2
If there are 2 red marbles and 5 blue marbles in a bag, what is the ratio of red marbles to blue marbles?
2 to 5
If 3 apples cost $6, how much do 6 apples cost, assuming the cost is proportional?
$12
If y=4x, what is the constant of proportionality?
4
What term describes the number that you multiply all dimensions of an original shape by to create a scaled copy?
Scale Factor
A triangle has a base of 5 inches. Its scaled copy has a base of 15 inches. What is the scale factor from the original triangle to the scaled copy?
3
A recipe calls for 3 cups of flour and 2 cups of sugar. What is the ratio of flour to sugar?
3:2
A car travels 60 miles in 1.5 hours at a constant speed. How far will it travel in 3 hours at the same speed?
A recipe uses 3 cups of water for every 2 cups of rice. What is the constant of proportionality when comparing the cups of water to the cups of rice?
3/2 or 1.5
What term describes a relationship where two quantities increase or decrease at the same rate, such as miles per hour or price per item?
Proportional Relationship
The side length of a square is scaled by a factor of 3 to create a new square. If the original square’s side length was 6 meters, what is the side length of the new square?
18 meters
In a classroom, the ratio of boys to girls is 4:3. If there are 12 boys, how many girls are there?
9
If 5 notebooks cost $10, what is the constant of proportionality that relates the cost to the number of notebooks?
$2 per notebook
In a table of values, if x=5 corresponds to y=15, what is the constant of proportionality?
3
What is the specific term for the ratio that describes how one quantity changes in relation to another in a proportional relationship?
Constant Proportionality
A photograph is reduced in size by a scale factor of 0.5. If the original photograph was 12 inches wide, how wide is the reduced photograph?
The reduced photograph is 6 inches wide.
A car travels 150 miles using 5 gallons of gas. What is the ratio of miles traveled to gallons of gas used?
30 to 1
A map uses a scale of 1 inch for every 10 miles. If two cities are 5 inches apart on the map, what is the actual distance between the two cities?
50 miles
A worker earns $120 for 8 hours of work. What is the constant of proportionality between the earnings and hours worked?
$15 per hour
What is the term for the ratio that represents the change in one variable relative to the change in another, often used in the context of linear functions?
Rate of Change
An artist makes a scale model of a sculpture where every dimension is scaled down by a factor of 1/4. If the height of the original sculpture is 20 feet, what is the height of the scale model?
The height of the scale model is 5 feet.
The ratio of cats to dogs in a pet shop is 7:5. If there are 35 cats, how many dogs are there?
25
The amount of paint needed to cover a wall is directly proportional to the area of the wall. If 2 gallons of paint are needed for 300 square feet, how many gallons are needed for 450 square feet?
30 gallons
A car travels 180 miles in 3 hours at a constant speed. What is the constant of proportionality between the distance traveled and the time?
60 miles per hour