Grade 08 Mathematics - EC: M08.B-F.2.1.1

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.2.1.1 M08.B-F.2.1.1

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.

Activities

Calculate the rate of change from the point (7, 2) to (10, -4).

Identify the rate of change and initial value from the table below.

Andrea started a babysitting service for her neighbors. She babysat for the Andersons for three hours and made $34. A couple nights later she babysat for the Chens and made $58 for six hours. Construct a function to represent what Andrea charges for her babysitting service.
The following graph represents the cost of using a storage facility to keep your belongings. Construct a function to represent the cost. Show your work.

Miguel is preparing his family pool for some cleaning and repairs by draining all the water. After two hours of draining the pool he still has 1,150 gallons left in the pool. When he comes back after 12 hours of draining there is still 900 gallons to go. What is the rate of change and initial value and what do they represent in this problem? Write a function Miguel can use to figure out how long it will take to drain the pool.

Answer Key/Rubric

Rate of change =
Initial value = (0, 7)

y = 8x + 10

y = 125x + 25
Student work may include, but is not limited to:

Find the slope/rate of change using the two given points: (1, 150) and (3, 400)

Set up an equation to find the initial value

Explanations should be similar, but are not limited to:
- Rate of change is which means the pool is losing water at a rate of 25 gallons an hour.
- The initial value is (0, 1200) which means the pool started with 1200 gallons of water.
- Function: y = -25x + 1200