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Trip Functions – Complete Tables and Write Function Rules

Teacher Notes

Students use facts to complete rate tables and write rules in words to describe the relationship between the input and the output. All functions are of the form of y = a \cdot x + b, that is, the sum of an initial value (number of miles showing on odometers/pedometers before the start of a trip) and the product of number of hours traveled and average speed in miles per hour.

Solutions:

Trip Functions 1

Rule: Number of miles is the sum of 23,500 and the product of number of hours and 40 mph.

Trip Functions 2

Rule: Number of miles is the sum of 72,160 and the product of number of hours and 30 mph.

Trip Functions – Complete Tables and Write Function Rules

Read the facts. Follow the steps.

Facts: Before the start of the cross-country trip, the odometer in Mrs. Wilson’s car showed 4,100 miles. On the trip, she averaged 50 miles per hour.

First: Complete the table to show changes in Ms. Wilson’s odometer for the first 6 hours.

Second: Write a rule that describes how the number of hours traveled is related to what the car odometer shows.

Rule: _______________________________________________________

& \mathbf{Describe:} && \text{Before the start of the trip, Ms. Wilson's car odameter showed} \ 4,100\\&&& \text{miles. On the trip, she drove an average of} \ 50 \ \text{miles each hour. The table}\\&&& \text{shows} \ 4,100 \ \text{miles at} \ 0 \ \text{hours.}\\\\& \mathbf{My \ Job:} && \text{Use the facts to complete the table. Write a rule that shows how the}\\&&& \text{number of miles on the odometer is related to the number of hours of}\\&&& \text{travel on the trip.}\\\\& \mathbf{Plan:} && \text{Start with the table. Add} \ 50 \ \text{to} \ 4,100 \ \text{for each new hour. Then write the}\\&&& \text{rule.}

& \mathbf{Solve:} && \text{Rule: Number of miles is the sum of} \ 4,100 \ \text{and the product of number of}\\&&& \text{hours and} \ 50 \ \text{mph.}\\\\& \mathbf{Check:} && \text{Use the rule and to verify the facts.}\\&&& 4,100 + 1 \times 50=4,150\\&&& 4,100 + 2 \times 50=4,200\\&&& 4,100 + 3 \times 50=4,250\\&&& 4,100 + 4 \times 50=4,300\\&&& 4,100 + 5 \times 50=4,350\\&&& 4,100 + 6 \times 50=4,400

Trip Functions 1

Facts: Before he left on his trip, Mr. Patterson’s truck odometer showed 23,500 miles. He averaged 40 miles per hour on his drive from Sacramento to San Diego.

First: Complete the table to show changes in Mr. Patterson’s truck odometer for the first 6 hours.

Second: Write a rule that describes how the number of hours traveled is related to what the truck odometer shows.

Rule: _______________________________________________________

Trip Functions 2

Facts: The Karene City School Bus averaged 30 miles per hour on its trip to the state basketball competition. At the start of the trip, the bus’s odometer showed 72,160 miles.

First: Complete the table to show changes in the bus’s odometer for the first 6 hours.

Second: Write a rule that describes how the number of hours traveled is related to what the bus odometer shows.

Rule: _______________________________________________________

Extra for Experts: Trip Functions – Complete Tables and Write Function Rules

Trip Functions Extra 1

Facts: Charlie’s pedometer is on his belt. It registers the number of miles walked. Before the hike, the pedometer showed 27 miles. Charlie hiked for several days and averaged 3 miles per hour.

First: Complete the table to show changes in Charlie’s pedometer for the first 6 hours.

Second: Write a rule that describes how the number of hours traveled is related to what the pedometer shows.

Rule: _______________________________________________________

Trip Functions Extra 2

Facts: Before Brent left on his bike hike, his bike’s odometer showed 62 miles. Brent averaged 8 miles per hour.

First: Complete the table to show changes in Brent’s bike odometer for the first 6 hours.

Second: Write a rule that describes how the number of hours traveled is related to what the bike odometer shows.

Rule: _______________________________________________________

Solutions:

Trip Functions Extra 1

Rule: Number of miles is the sum of 27 and the product of number of hours and 3 mph.

Trip Functions Extra 2

Rule: Number of miles is the sum of 62 and the product of number of hours and 8 mph.

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