Grade 08 Mathematics - EC: M08.B-F.1.1.2

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

Instructional activities designed to be integrated into planned lessons
Questions/activities that grow in complexity
Opportunities for differentiation for each student’s level of performance

Grade Levels

8th Grade

Course, Subject

Mathematics

Related Academic Standards / Eligible Content

M08.B-F.1.1.2 M08.B-F.1.1.2

Compare properties of two functions, each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions). Example: Given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Activities

Identify the rate of change for the fees charged by a library as shown in the table below.

A medium size car has a gas mileage of 22 miles per gallon. The gas mileage of a sport utility vehicle is represented by the function shown below. Compare their gas mileage.

The function k = 320h, where k is the kilometers traveled in h hours, represents the speed of Japan’s Bullet train. The speed of a high-speed bullet train in China is shown in the table below. Compare the speeds of the trains.

Amir is a pizza deliveryman in town. All the local pizza places have offered him jobs in various ways as shown below. Compare the rate of change for each place and explain what it represents in this situation.

Answer Key/Rubric

$0.35 per day

Acceptable answers may include, but are not limited to:

Rate for medium car is 22 miles per gallon
Rate for sport utility is 19 miles per gallon
- Find the slope of the line using and the points (2, 38) and (4, 76)
The medium car has a better rate of change getting 22 miles per gallon, than the SUV that only gets 19 miles per gallon.

Acceptable answers may include, but are not limited to:

Rate for Japan’s bullet train is 320 km/hr.
Rate for Chinese bullet train is 275 km/hr.
- Find the slope of the line using and any two points from the table
- Using (2, 550) and (4, 1100):
- The Japanese bullet train is faster with a speed of 320 km/hr compared to the Chinese train that only goes 275 km/hr

Acceptable answers may include, but are not limited to:

Find the slope (rate of change) of the function for each pizza place using and any two points from the table or graph
Rate of change for this problem is the cost per pizza that Amir would be paid
Rate of change for Pizza House is $3/pizza
- Find the slope of the line using and any two points from the table
- Using (0, 48) and (2, 54):

Rate of change for Pie Face Pizza is $2.75/pizza
- Function is in the form y = mx + b where m is the slope
Rate of change for Champ’s Pizza is $2/pizza
- Find the slope of the line using and any two points from the graph
- Using (0, 60) and (10, 80):

Pizza House has the best rate of change paying $3 per pizza that Amir delivers.