October 1, 2010

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A repository of student learning activities for Intermediate Algebra

- Mathematics > General
- Mathematics > Algebra

- Higher Education
- Graduate
- Undergraduate-Upper Division
- Undergraduate-Lower Division

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Table of Contents

- Hands on and real world application problems by Professor James Sandefur (Georgetown University) and Rosalie Dance (University of the Virgin Islands)
- Down to Business - Rewriting Formulas
- Factoring Research - Projectile Motion
- Trapping Lab - Linking Equations and Graphs
- Paying the Price - Rational Equations
- Introduction to Functions - Basics and Applications
- Working Together - Rational Equations
- Linear Modeling - Barbie Bungee Jump
- Packaging Lab - Volume and Surface Area
- Motion - Toy Train Collision
- Area - Calculating the Area of a Liver Lesion
- Real World Exponential Equation (Car Loan)
- The Coffee Shop - Linear Inequalities
- Logs and Exponents: Population, Earthquakes, and Sound
- Quadratic Equations: From Factored to Standard Form
- Repeating Decimals and Geometric Series
- Word Problems - WRAMPS - Writing and reading activities for math problem solving
- Angry Birds - Quadratic Graphing

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A repository of student learning activities for Intermediate Algebra

Each unit contains a complete package for students. In most cases, there is a reading assignment to be completed beforehand, in-class investigations, and homework to follow. You will find a Teacher's Guide for each unit discussing the mathematical content of the activities and pedagogical suggestions for optimal use of the lesson. Each teacher's guide provides a complete set of answers for the questions in the student materials.
Many of the units are mathematical investigations set in contexts that will usually provide new information of interest to students in the context itself, such as studying the problem of lead poisoning or the relationship between sickle cell anemia and malaria. This is intended to help students see that the mathematics they are learning now can be used to help solve significant real problems. It is expected that investigations in context will also help students whose learning style is holistic relate to the analytic methods of mathematics. Units in a context with real significance will be marked with (Real).
For more info: http://www9.georgetown.edu/faculty/sandefur/handsonmath/index.html

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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 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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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 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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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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The main purpose of this lab is to understand work rates and how working together affects the time it takes to complete a large task.
The groups will time a “fast” worker, a “slow” worker, and will calculate the time it will take these two workers to complete the job together. Groups will then compare their calculated estimate to the actual time.

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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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Using regular soda cans and their cardboard containers, students will calculate volume and surface area.

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The purpose of this lab is to investigate motion, and the use of the equation d=rt. The velocity of each train will be determined, and then the class will calculate the time/location of a collision between these two trains.

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Using imaging devices, medical professionals can calculate the size of an actual lesion by using the scale factor of the created image.

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This activity has been modified from Real World Learning Objects, Internet-based Activities for Higher Education. The need to access an online calculator has been removed. Students are asked to price a car, determine an acceptable monthly payment and then using the formula calculate the number of months needed to pay off the loan. This requires solving an exponential equation using logarithms.

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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 activity or homework assignment requires students to use a computer to access data on population, earthquakes, and sound.

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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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This activity begins by reviewing conversions between fractions and decimals with an emphasis on repeating decimals. The formula for the partial sum of a geometric series is bypassed and students are directed to use find partial sums by using the “multiply, subtract, and solve” technique which mimics the derivation of the formula for the partial sum of a geometric series. This sets the stage for students to quickly find the fraction representation of a repeating decimal number. This activity would be well-suited as a prelude to introducing infinite and partial sums of geometric sequences.
http://www.mathedpage.org/
copyright informaiton: http://www.mathedpage.org/rights.html

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Dr. Yu-Chung Chang has developed a nine step process to walk students through tthe process of synthesizing word problems. The process promotes student collaboration, critical thinking, and engagement. Dr. Yu-Chung Chang's data
suggests this to be a highly effective pedagogically. The WRAMPS website contains worksheets:
http://www.cfkeep.org/html/stitch.php?s=66561915414931&id=31477886560818

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Take-Home Quiz or In-Class Activity
Time required: 30 minutes
Materials: Attached graph paper
Objectives: Graph quadratic equations to determine if the graph goes through a designated point.
Prerequisites: Graphing quadratic functions by finding points or using the vertex formula.
Description: This worksheet challenges the student to answer the question: "Will the bird knock over the pig?" The worksheet begins by describing the premise of the game Angry Birds, and suggests that the answer can be found by graphing. Using the graphing templates on the second page, the students must graph 3 quadratic equations to determine if the bird will go through a designated point.
Teaching notes: This activity can be used to practice the vertex formula as well as general graphing techniques. Students could determine the answer by plugging the location of the pig into the given equation.
Follow Up/Discussion Questions: Are there other ways to answer the question or find the solution?

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