Gold Seal Lesson:
Temperature Curve

Copernicus Education Gateway

Subject:

Mathematics

Grade:

9-12

ICLE Standards:

Functions: Represent and analyze relationships using equations and graphs.

Mathematics as Communication: Express mathematical ideas orally and in writing.

Performance Task:

Your task for this activity is to investigate the relationship between the cooling of water and time. You will need water, four beakers, and four thermometers.

Note to teacher: You may want to have the students do this investigation as a group activity. Heat some water so that you have, in three beakers, water at three different temperatures. One of the samples should be boiling water (212  F). In the fourth beaker, place some water at room temperature.

Record the temperature of each sample of water when you begin the investigation, and then record the temperature of the water in each sample every minute for 15-20 minutes. Organize your data in a usable table. For each sample, draw a graph which shows the temperature as a function of time. For each of your graphs, determine an algebraic model (equation) which best fits the graph. You may use a computer or calculator utility for this if you wish. In your math journal, write a brief summary of your investigation, including how you arrived at the equations for each of your graphs. State any conclusions and/or hypotheses that you can make from analyzing your data and graphs. List any other phenomena that you are familiar with that have a similar relationship. You may use your text or any other source to find other applications the pattern models.

Knowledge / Skills:

Understand the best procedures for statistical data collection, organization, and display.  (m5)

Find the solution of linear equations and inequalities where the variable appears on both sides and in which one or both sides must be simplified before solving the equation (e.g., solve x+2(x-3) = -4x+5 for x).  (m35)

Understand the concepts and uses of matrices in modeling (i.e., finite graphs (structures) can be represented geometrically and interpreted algebraically in the form of a matrix).  (m51)

Know how to find the graphic solution of systems of linear equations (e.g., find the point(s) common to a quadratic-linear pair).  (m71)

Use writing as a tool for learning in formats such as learning logs, laboratory reports, note-taking, and journals.  (ela40)

Rubric:

4 Points  =  The student independently carries out the investigation. He/she shows a sophisticated understanding of the procedures and concepts underlying the task. The student accurately and neatly draws the geometric model of the data and identifies each of these with an algebraic model. The mathematics is presented clearly and accurately. The journal entry addresses all requirements and is well communicated. The student understands and clearly describes the relationship between real-world phenomena and a mathematical model.

3 Points  =  The students needs some assistance in carrying out the investigation. He/she accurately completes the task and has a good understanding of the procedures and concepts underlying the task. The data are complete and well organized in the table, but the student has difficulty making the geometric models. These are not as accurate as they could be. The student has difficulty describing the graphs with an algebraic model, but does achieve it with help. The journal entry is complete, but not well communicated by the student. The student appears to have only a partial understanding of the relationship between real-world phenomena and a mathematical model.

2 Points  =  Even with assistance, the student is unable to complete the task. He/she does not have a good understanding of the procedures and concepts underlying the task. The data are incomplete and poorly organized in the table. Graphs are not drawn accurately, and the student is unable to write an equation for the graphs. The journal entry is vague and poorly written. The student appears to have little understanding of the relationship between real-world phenomena and a mathematical model.

1 Point  =  The student does not complete the task. He/she has little understanding of how to conduct an investigation. The data collected are sketchy and poorly organized. As a result the student is unable to use either a geometric or algebraic model to describe the data. The journal entry is meaningless and the student appears to have no understanding of the relationship between real-world phenomena and a mathematical model.

Keywords:

ALGEBRA
EQUATIONS
LINEAR PATTERNS 
DATA COLLECTION
HYPOTHESIS TESTING
TABLES
TECHNOLOGY INTEGRATION 
CALCULATORS
GRAPHING TECHNIQUES
LAB EXPERIMENTS

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [X] - 10 [X] - 11 [X] - 12 [X]

ICLE Application:

D

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