Module Design Format:

Modeling Linear Equations: The Water Drinking Experiment.

Topic(s)):

- use of quantitative variables.

- graphing of ordered pairs.

- linear equations in two variables.

- introduction to slope.

Course(if appropriate): Part of any algebra course

Designed by: Carmen Baila and Ernie Berman

Duration: One week.

Brief Description:

n The students will be doing an introduction, extension, or review of linear relationships between two variables.

n This will be done by experiment involving the change in the water level of a glass or bottle of water after each sip of water.

n One student, using a straw, will drink consistent sips of water.

n Before and after each sip, the height of the water will be measured.

n This process will be done until the bottle or glass is empty.

n The students will keep track of the number of sips and height of each sip.

n This information will be graphed on grid paper as well as on a graphing calculator, and interpreted.

Description of Learners (size of class/prerequisite skills, etc.):

Description of Learners

n Algebra students in college.

n Anywhere from 25 to 35 students.

n Ability to plot ordered pairs on a rectangular grid.

n Ability to measure width, length or height in millimeters, centimeters or inches.

n Obtain an understanding of independent and dependent variables.

n Learn how to represent quantitative and spatial relationships and how to use the language of mathematics to express relationships.

n Recognize that a linear equation in two variables is a function.

n Recognize that when the rate of change between two variables is constant, the graph is a straight line.

n Learn the appropriateness of technology usage.

n Ability to draw conclusions.

n Use of scientific methods.

n Represent situations using variables.

n Determine independent and dependent variables.

n Use of appropriate mathematical terminology.

n Select appropriate scaling and units.

n Realization that all measurements are approximate.

n Create an equation of the line of best fit from a set of ordered pairs, using technology.

n From a graph describe verbally and symbolically, the relationship represented.

Instructional Strategies:

n Problem Based Learning.
Is there any relationship between the number of sips and the height of the water?

n Use of technology.
Represent and find the line that best represents the data generated.

How well they answer a series of directed questions:

n That include open ended and closed ended questions.

n Linear graphs and interpretation of these graphs.

Pictorial representation of this experiment:

n Each student must draw a picture of the experiment.

n Each student includes a graph of the data.

Written description of the experiment and self-evaluation:

n Students will need to provide a written description of the experiment and summarize their findings and their unanswered questions.

Resources/Materials Required:

n Cylindrical containers of same and different sizes.

n Ruler (both inches and millimeters).

n Graphing Calculator.

n Written description of project.

n Written set of questions and exercises.

Two Experiments

Water Lab

Water and Ice

Example of a student product

Suggested next steps:

n Creation of appropriate worksheets and handouts.

n Easy to follow instructions for using the graphing calculator.

n A Grading Rubric for assessing student performance.

n How could this be adapted to different levels of algebra?

n Why is a cylinder the necessary shape as the container?

n What happens if you use similar shapes for the water container?

n What happens if you use non-similar shapes for the water container?

n What adjustments are needed to compare volume to the number of sips?