7.RP.1
Anticipation and Goals for Unit Rate Learning Cycle
Goals:
1.
2.
3.
4.
Identify unit rate
Compute unit rate.
Compare and contrast unit rate
Apply implications of density as a unit rate
Development anticipation:





Calculation mistakes
Students will get the units confused
Missed labeling
Put as a ratio but denominator not a one
Attempt to describe a unit rate where there is no proportion.
Solidify anticipation:
 Measurement issuers
 Redirection/connection between one problem and the next.
 Making the jump in reasoning in order to solve Archimedes problem
Practice anticipation:
 Candy bars- 2 for 50 cents or 3 for dollar ounces or bar as unit
discussion.
 Movie ticket discount when 12th ticket purchased
 Pesos exchanged reversed variables.

Remembering unit rate is one.
Which is better?
1. There are three stages of a 100 meter race: a start, middle, and
finish. When reviewing the video it was revealed that at 10
meters 1 second had elapsed. At 50 meters 5 seconds had
elapsed, and at 100 meters 10 seconds had elapsed. What would
you anticipate the elapsed time would be at 150 meters? Use a
chart to justify your answer.
2. Sally is a runner trying to qualify for the summer Olympics in
London. She completes her 100 meter dash in 10 seconds.
a. What is her speed?
b. Lorraine is attempting the 100 meter dash as well. She
covers each meter in .3 seconds. Who is faster, Sally or
Lorraine?
3. Peter is at the store and decides that he wants something sweet.
When he goes to the candy aisle, he decides he either wants an
almond joy or a Milkyway candy bar. The Almond joys are on sale
for 50 cents each. The Milkways are on sale 3 for a dollar Which
is the better buy? Justify your answer using a visual model.
Would your decision change if Milkyways cost 65 cents each
unless three were purchased together?
4. When we purchase gas to fill our cars, we typically are concerned
with how many miles we can travel per gallon. However, airlines
are concerned with how many gallons are used per mile. What
would explain this difference in thinking?
5. A 767 jumbo jet was filled with 2000 gallons of fuel in
anticipation of its 800 mile flight. Johnny claims the jet would
have a unit rate of 2.5 miles per gallon. Is he right or wrong?
Explain.
Unit Rates in Density
Part 1: For each substance, identify the unit rate of mass per volume.
TYPE of CUBE
CUBE MASS
(g)
CUBE VOLUME
(cm3)
1.Acrylic
19.2
16.25
2. Aluminum
43.8
16.25
3. Brass
136.5
16.25
4.Pine (lighter
wood-dark rings)
5.68
16.25
5.Poplar (lighter
wood-light rings)
8.1
16.25
CUBE DENSITY
(g/cm3)
Part 2: Which object do you think is the most dense? Make a prediction,
then describe a method you could use to find out.
Object
MASS (g)
VOLUME (cm3)
Substance 1
Substance 2
Substance 3
Substance 4
Substance 5
1. What do you notice about Substance 3 and 5?
DENSITY (g/cm3)
2. What do you think this means?
Archimedes was a famous early scientist in Greece who was approached by a King
that suspected he had been cheated. He had given a gold smith a block of gold and
asked him to make a crown from the gold. When the crown was delivered, the king
suspected the goldsmith had kept some of the gold and used a junk metal to make
up the missing mass. How could you tell if the crown was pure gold or not? Design a
method and justify your answer.
Unit Rate Practice
1. Granola comes in a 14 ounce box for $2.00 or a 72 ounce box for $9.00?
Justify the better buy using a visual model.
2. Determine the missing number of grams of trail mix and explain how you know your answer
is correct.
Grams of Trail Mix
Calories
50
150
150
450
300
900
500
1500
1350
3.
Find the unit rate (per bead) if it costs 12 cents for 20 beads.
Find the unit rate (per cent) if it costs 30 cents for 50 beads. (Be careful!)
Are these rates the same? Convince me with a written explanation.
4. Gerardo is traveling to Mexico. The exchange rate is 3 Pesos per dollar. When he was
returning home he exchanged his Pesos back into dollars. He exchanged 42.75 Pesos and got
$125. Should he complain to a manager? What would be his justification, if he does?
5. Use the following table to determine the cost of 18 gallons of gas. Are you sure that your
answer is correct? What
makes you sure?
Gallons of Gas
3
5
8
13
Cost
8.55
14.25
22.80
37.05
6. Use the table below to find the cost of one movie ticket. How did you obtain that cost?
Movie Tickets
Total Cost
2
4
5
10
8
16
12
20
If you were responsible for purchasing tickets for a group of 24, how much would you charge
each member of the group, including yourself?
7. The current 100-meter dash world record is 9.58 seconds. A local sprinter ran 55 meters in
5.1 seconds at a recent competition. Will he threaten to break the 100-meter dash world
record? Explain your reasoning.
Learning Cycle on Unit Rates:
Goal: Students will be able to compute unit rates
Goal: Students will be able to apply implications of density as a
unit rate
Develop: Which is better?
Solidify: Unit Rates in Density
Practice: Unit Rate problems