Vocab
The quantity k in a relationship
C.O.P
The table shows the total costs of different numbers of tickets. Decide whether it makes sense to use a constant rate to describe the relationship. Explain.
Number of tickets: 6 8 10 14 25
Total Cost ($): 34.50 44.00 52.50 73.50 131.25
No
34.50/ 6 = 5.75
44.00/8 = 5.50
What is my favorite type of math to teach? (grade level or subject)
Algebra I 9th grade
A runner completes 4 1/2 miles in 3/4 of an hour. What is the runners average speed in miles per hour?
6 mph
Martine’s town is building a volleyball court based on a scale drawing that is 40 centimeters by 80 centimeters and uses the scale 1 cm:22.5 cm. A.
Write an equation for the proportional relationship between the scale drawing’s lengths x in centimeters and the actual court’s lengths y in centimeters.
y = 22.5x
A comparison of two quantities by division
Ratio
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger. Complete the table. Then decide whether it makes sense to use a constant rate to describe the relationship. Explain.
Weight (lb): 2 3 4 5
Cost ($) : 7.00 ? 14.00 17.50
10.50
yes, $3.50 per pound
What is Ms. Lewis' favorite character?
Hello Kitty
1 1/5 m per minute
Martine’s town is building a volleyball court based on a scale drawing that is 40 centimeters by 80 centimeters and uses the scale 1 cm:22.5 cm.
What are the length and width in meters of the actual court? Show your work.
(22.5) (80) = 1800 cm = 18m
(22.5)(40) = 900 = 9m
A rate that is simplified so that its denominator is equal to 1 unit.
Unit Rate
Ken rode his bike on Monday. The table shows the distance that he was from home at various times. Can the relationship be described as a constant rate?
Time (min): 20 40 60 80 100
Distance (km): 5 10 12 14 16
No
5/20 = 0.25
10/ 40 = 0.25
12/60 = 0.20
14/80 = 0.175
How many steps do I am for each day?
10k
2 1/2 cups per batch
The students in Roberto’s school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet.
Write an equation for the proportional relationship between the drawing’s lengths x in feet and the actual mural’s lengths y in feet.
y=2.5x
The starting point (0, 0) on a coordinate plane where the x-axis and y-axis
intersect.
origin
Flo measures the amount of water her high pressure sprayer uses and finds that it uses 20 gallons of water in 4 minutes and 30 gallons in 6 minutes. Complete the table. Then decide whether it makes sense to use a constant rate to describe the relationship. Explain.
Time (min): 2 4 ? 10 18
Water (gal): 10 ? 30 50 90
6, 20
Yes, k = 5 gal / min
If I could only eat at one fast food restaurant ever again, what would I pick?
Chickfila
A lawnmower uses 2/3 gallon of fuel to mow 5/6 of an acre. How many gallons of fuel are needed per race?
4/5 gallon per acre
The students in Roberto’s school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet.
What are the length and width of the scale drawing in feet? Show your work
Length: 15 = 2.5x, x = 15/2.5 = 6 ft
Width: 8 = 2.5x, x = 8/2.5 = 3.2 ft
An equation stating that two ratios or rates are equal (e.g., 1/2 = 4/8).
Proportion
The amount of money Chaz earned for walking dogs is given in the table. Can the relationship be described by a constant rate? Explain.
Dogs walked: 6 8 11
Money earned: 112.50 150.00 206.25
Yes, $18.75 a dog
What tv show does Ms. Lewis watch everyday?
Bobs Burgers
A painter covers 3/4 of a wall in 1/2 of an hour. What is the painter's speed in walls per hour?
1 1/2 walls per hour
A map has a scale of 1 in.:10 mi. Find the distance on the map between two cities that lie 147 miles apart. Show your work.
14.7 in
147 x 1/10 = 14.7 in