September 14, 2011

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Classroom activities ready for use

- Mathematics > General

- Professional Education & Development
- Higher Education
- Graduate
- Undergraduate-Upper Division
- Undergraduate-Lower Division

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Table of Contents

- Linear Modeling - Barbie Bungee Jump
- Factoring Research - Projectile Motion
- Cooking Lab - Fractions for Culinary Arts
- Paying the Price - Rational Equations
- Trapping Lab - Linking Equations and Graphs
- Introduction to Functions - Basics and Applications
- Mixing - Simulating Mixture Problems with Beads
- Down to Business - Rewriting Formulas
- Modeling Gas Prices - linear functions, systems
- Scientific Notation - How Big? How Far? How many?
- Proportions, Systems of Equations - Batting Averages in Baseball
- Linear Modeling - Forearm Length vs. Height
- Linear Modeling - Modeling CO
_{2}Levels - Rate and Slope - Car Depreciation Activity
- Graphing - Scaling a Graph
- Linear Functions Matching Activity
- Linear Equations - Multi Step Equations Group Practice
- Discovering the Pythagorean Theorem
- The Coffee Shop - Linear Inequalities
- Equations versus Identities (Understanding Solutions to Linear Equations)
- Quadratic Equations: From Factored to Standard Form

Classroom activities ready for use

The project has students create their own data and graph it and then choose a reasonable line, which represents their data. The data comes from measurement of how far a Barbie doll bungee jumps, using rubber bands and a tape measure. From there, they find the equation of their line (this will be unique for each group since each will be working with a different Barbie doll) and answer questions related to their doll’s bungee jumping habits using their equation.

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Students use the internet to research values relevant to projectile motion such as acceleration due to gravity and the height of objects. Using the given information students will have to make unit conversions to ensure that all units are the same. They will then solve problems on projectile motion by factoring.

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Students will make the necessary conversions using basic equivalency tables for standard measurements used in cooking. The problems in this activity are from the San Diego Mesa College Culinary Arts department and are examples of real world situations.

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The purpose of this activity is for students to explore the use of rational equations to solve practical problems.

This activity uses the standard bookstore formula for calculating the price of textbooks and materials. This is not the standard simple percent increase that most textbooks use. Formulas have been submitted by the Mesa College bookstore. In addition, the student is given the formula for calculating the monthly payments on a loan.

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This activity reinforces the relationship between the solution to a system of equations and the intersection of their corresponding graph. Generally, students begin to solve systems by using graphing and then algebra. Once a student learns to solve the system by algebra, they often forget the connection to the graph. Hence in this lab, they will use algebra first and then graph their answers.

The student is asked to determine where an animal trail intersects with an access road. Given linear equations which represent the placement of the access roads, assign each person/group one or more equations representing an 'animal trail'. They will then determine where their trail intersects each of the two roads. This represents the spot where they will lay their have-a-heart trap. (A have-a-heart trap is one which is baited with food and catches the animal alive without hurting it.)

After solving the systems, a graph is drawn to determine if the placement of the traps is accurate.

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The purpose of this activity is to reinforce the concept of function and the use of functional notation rather than to teach the concepts.

This lab looks at input/output pictures to emphasize that a function has only one output for every input even through the output need not be unique. Using functional notation, students determine both range and domain values from a graph and then do the same for a variety of given functional equations. The real world applications include a piecewise function (cell phone costs) and require the student to find a variety of values as well as determining realistic domains.

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This activity, created by Arthur N. DiVito, Ph.D, simulates mixture problems by using red and white colored beads.
Mixture A is 70% red, and mixture B is 40% red (as determined by weight).
The students are asked to created a "solution" with a given weight whose concentration of red is between 40% and 70% using the above solutions. Students empirically verify the final "solution" has the proper percent of red beads by separating colors and weighing them separately.
As the author mentions, many students have difficult with mixture problems because they don't understand percents well. This hands on activity gives a tangible representation of percents in addition to the overarching concepts needed to solve mixture problems.

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Students often do not see the point in solving formulas for a particular variable when there are no values given. This lab is not designed to teach how to solve literal equations, but rather to give students an understanding of why one might need to do so.

This lab has students substitute values into the basic interest formula and then solve for the missing value. After solving several problems in this form, they solve the formula for that variable and then evaluate it by substituting in the given information. Students discover for themselves that it is sometimes better to solve for the variable first and then input the values when solving several problems for the same variable.

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Students will be presented with two different gas stations, and will have to come up with equations to determine the price of gas at each. They will do this by first calculating a few values, then using that process to come up with a general equation for each. The equations will be graphed in order to see the "break-even point", and this will be followed by a discussion of methods for finding solutions to systems of equations.

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Students will calculate relationships in the solar system using scientific notation. This requires that students understand how to multiply and divide exponential expressions

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Using systems of equations, students determine the missing components in the ratios used to determine batting average.

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The main purpose of this lab is to explore the proportionality of forearm length and height. Students record their heights and forearm lengths, first plotting on a table. Each group plots their 12 points on the given graph paper, and then draws a “best-fit-line”. Each group is asked to give the linear equation—in both slope-intercept form as well as standard form.

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In this activity students explore levels of Carbon Dioxide (CO_{2}) in the atmosphere over time. There is concern that levels of CO_{2} are rising, and finding a good mathematical model for CO_{2} levels is an important part of determining if this is attributable to human technology. Students draw a scatter plot, choose two points to create a linear model for the data, then use the model to make predictions.

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The purpose of this activity is for students to use the concept of the rate of depreciation in a real world situation to investigate the relationship between rate and slope.

Students create ordered pairs, graph depreciating car values, and calculate rates of depreciation, then identify that the rate of depreciation = slope of the line. Using the equation they then solve for future values and times.

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In science, students often start their graphs at an origin other than (0, 0). Also the scales are often very large or very small and variables, other than x and y, are used. The students will need to use breaks in the graph to accommodate the values. For example with the first problem they will want to start the vertical axis at 350, and the horizontal at 0.1000.

In the answer key a graph created in Excel gives a general view of the data, however it is not possible to insert the necessary break to indicate that the intersection of the axis in not (0, 0).

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This activity is designed to help students connect various representations (verbal, tabular, graphical) of linear functions. The activity is designed to be completed in groups of 2. This would be an appropriate review activity towards the end of the unit on graphing linear functions.

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A set of 4 practice sheets on solving multi-step equations. Students will complete these worksheets in groups of 4. Teacher instructions are enclosed.

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Students will use a variety of different size squares to form right triangles. After recording the lengths of the sides, students will square the values and look for the relationship.

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Students are asked to write inequalities based on given information and graph the two inequalities. Using the given information about profit, the students write an equation and determine the number of each type of donut needed to produce the maximum profit.

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This worksheets leads students to discover the differences between linear equations and identities. The well formulated questions force students to employ critical thinking. The activity involves both algebraic and graphing approaches, and definitely emphasizes a conceptual understanding of the material.

website: http://www.mathedpage.org/ copyright information: http://www.mathedpage.org/rights.html

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This activity leads students to understand the utility in the factored form of a quadratic equation. Students then express quadratic equations in standard form in the corresponding factored form. The activity is concluded with four critical-thinking questions.

website: http://www.mathedpage.org/ copyright information: http://www.mathedpage.org/rights.html

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