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ORC Resource Number #115

Mystery Liquids

http://www.pbs.org/teachers/mathline/lessonplans/hsmp/mystery/mystery_procedure.shtm

PROFESSIONAL COMMENTARY

This lesson is a data analysis lab in which students gather mass and volume data for two mystery liquids--oil and water--and then use the data to explore linear functions. Connections to science are an important part of this algebra lesson, which deals with density. Active learning and communication are also essential aspects of the lesson. Students work in groups to collect, verify, and display the data. They then discuss the physical meaning of the slopes and y-intercepts of the various lines they have created from their scatterplots. In addition to the lesson plan, the site includes ideas for assessment, teacher discussion, extensions of the lesson, additional resources, and a discussion of the mathematical content. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Mystery Liquids lesson and then access the appropriate video clips. (author/pk)

OHIO STANDARDS

Mathematics Academic Content Standards

Measurement Standard

Patterns, Functions and Algebra Standard

Benchmarks (8 - 10)

Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.

Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.

Solve and graph linear equations and inequalities.

Model and solve problem situations involving direct and inverse variation.

Describe and interpret rates of change from graphical and numerical data.

Grade Level Indicators (Grade 8)

Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form.

Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems.

Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.

13.

Compute and interpret slope, midpoint and distance given a set of ordered pairs.

14.

Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation.

15.

Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts.

16.

Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern.

Grade Level Indicators (Grade 9)

Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.

Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.

Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.

14.

Describe the relationship between slope and the graph of a direct variation and inverse variation.

15.

Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs.

Grade Level Indicators (Grade 10)

10.

Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

Data Analysis and Probability Standard

Mathematical Processes Standard

NATIONAL STANDARDS

Principles and Standards for School Mathematics

Algebra Standard

Understand patterns, relations, and functions

Expectations (9 - 12)

analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;

Represent and analyze mathematical situations and structures using algebraic symbols

Expectations (6 - 8)

explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;

Expectations (9 - 12)

analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;

use symbolic algebra to represent and explain mathematical relationships;

Use mathematical models to represent and understand quantitative relationships

Expectations (6 - 8)

explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;

model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Expectations (9 - 12)

analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;

use symbolic algebra to represent and explain mathematical relationships;

identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;

draw reasonable conclusions about a situation being modeled.

Analyze change in various contexts

Expectations (6 - 8)

explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;

model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Expectations (9 - 12)

analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;

use symbolic algebra to represent and explain mathematical relationships;

identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;

draw reasonable conclusions about a situation being modeled.

approximate and interpret rates of change from graphical and numerical data.

Measurement Standard

Data Analysis and Probability Standard

Communication Standard

Connections Standard

RESOURCE TYPE

Instructional Resource

PRACTICE LEVEL

Best Practice

STANDARDS ALIGNMENT

Grades 8–10

TOPICS

Mathematics --
Algebra;
Graphing;
Linear functions;
Measurement;
Volume;
Weight, mass;
Communication;
Connections, applications;
Statistics;
Data analysis;

KEYWORDS

line of best fit;
scatterplot;
interdisciplinary;
TI-82;
density

Publisher: Public Broadcasting Service

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