Listening

What Are We Listening To?

Introduction:
Students will gather data from a web site on number of music albums sold by genre for the last two years. They will convert these figures to fractions, decimals, and percents. They will then display the results in bar graphs (using the raw data) and pie charts (using percents and degrees). Finally, they will answer questions about their graphs.

Objective:
Upon successful completion of the lesson, students will have converted fractions to decimals to percents, and then used these numbers in various forms of graphic displays.

Evaluation:
Student graphs will be collected.

Prior Knowledge:
Some knowledge of fractions, decimals, and percents, as well as bar graphs and pie charts.

Learning Advice:
2 - 5 class periods.
Remind students that their task is to gather data, and they are to stay on the one page with data. (If a window appears with the web page, have them close it)

Resources:

Web site - http://members.tripod.com/~chartts/SALE98US.HTM
Student worksheets - #1(html) / (pdf), #2(html) / (pdf), #3(html) / (pdf), and #4(html) / (pdf)
Rulers, calculator, protractor, pencil, colored pencils
computer spreadsheet (optional)

Process:

Review basics of fractions, decimals, and percents.
Review Internet procedures.
Pass out Student Worksheet #1 (html) / (pdf) and discuss that genre is another name for style.
Students go to http://members.tripod.com/~chartts/SALE98US.HTM, close the banner window, and scroll to bottom where they will find “1998 GENRE SALES REPORT”.
Students copy information from the web page to the Student Worksheet #1 (html) / (pdf).
From this data, they construct a double bar graph on Student Worksheet #2 (html) / (pdf), using a different color for each year.
Students then write fractions by writing units sold for each genre OVER total units sold for each year on Student Worksheet #3 (html) / (pdf).
Using their calculator, they convert each fraction to a decimal. (Computation can be done by hand if preferred.)
Students convert decimals to percents.
Students sketch a pie graph for each year using the percents.
Finally, students multiply each decimal by 360 to find the degrees of each genre on Student Worksheet #3 (html) / (pdf).
They then, using their protractors, draw the pie charts for each year by measuring degrees on Student Worksheet #4 (html) / (pdf). They compare these pie charts with the ones in Step 10.
Lastly, they answer the questions on Student Worksheet #4 (html) / (pdf) about all the graphs they have made.

Extensions:
As soon as figures for the new year are posted, compare them with this lesson.

Conclusion:
Students calculate and graph data about current music.

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California Academic Content Standards:

Grade 7:
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.3 Convert fractions to decimals and percents and use these representations in estimation, computation, and applications.

Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:

1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.

2.4 Make and test conjectures by using both inductive and deductive reasoning.

2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.6 Express the solution clearly and logically by using appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.8 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

NCTM Standards:

Grades 5-8:
Standard 1: Mathematics as Problem Solving
Standard 2: Mathematics as Communication
Standard 3: Mathematics as Reasoning
Standard 4: Mathematical Connections
Standard 5: Number and Number Relationships
Standard 7: Computation and Estimation
Standard 10: Statistics
Standard 13: Measurement
Grades 9-12:
Standard 1: Mathematics as Problem Solving
Standard 2: Mathematics as Communication
Standard 3: Mathematics as Reasoning
Standard 4: Mathematical Connections
Standard 7: Geometry from a Synthetic Perspective
Standard 10: Statistics