September 14, 2011

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- Mathematics > General

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

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Table of Contents

- Order Of Operations (multiple individual and group activities)
- Whole Numbers - When in Rome
- Medical Math applications (Solving Equations)
- The Pie Business (Arithmetic operations with decimals)
- Ratios - Baseball Lab
- Integers in the Real World
- Cooking Lab - Fractions for Culinary Arts
- Percents and Fractions - Distribution of Wealth Ten Chairs
- Proportions - Scaling Up and Down
- Percents - It Costs What?
- Measurement - Discovering Conversions
- Battleship
- Comparing Volumes
- Average Speed and Unit Conversion
- Perimeter and Surface Area -- Building a Sierpinski Pyramid
- Building an Icosahedron
- Integer Arithmetic (+,-) Flash Cards
- Integer Arithmetic (*, /) Flash Cards
- Measuring Household items- Discovering Conversions
- Waste
- Bicycle Gears
- Consumption vs. Production
- Signed Number Arithmetic
- Bingo -- Order of Operations
- Mixing Beans
- Population Growth
- Scaling Up and Down
- Percent Matching Activity
- People Proportions

Classroom activities ready for use

Contains several activities, sequenced into a cohesive module to develop capability with Order of Operations:

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The students perform the Sieve of Eratosthenes in class to find the prime number between 1 and 100. They also look for patterns such as where the multiples of 2 or 5 appear in the sieve. At home or in a computer lab they then research the Fibonacci Sequence and other number systems.

The zipped file contains a word and pdf version of the student worksheet and the instructor's note with an answer key.

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Students use a formula to solve equations, for problems with a medical slant provided by Mesa College’s Veterinary Program. This requires the use of subscript notation and the multiplication property of equality to solve. The equations are the simplest of linear equations however the application makes them more interesting.

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This lab allows students to practice their skills with the multiplication and division of decimals in a real world situation. Using a menu from a pizza house, students will determine the cost per unit area of the pizzas to determine the best buy. In addition they will decide whether it is better to buy the combo pizza or add toppings to a cheese pizza, and if it is a better deal to buy two medium pizzas or one extra large.

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Using batting averages, students will create ratios and convert them to rounded decimals (3 places). In addition, they will take decimals and determine several possible equivalent ratios. Then using the relationship that batting average = hits/at bats, the students can use proportions or equations to find either the number of hits or the number of at bats for a given situations.

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Given real world situations, students will represent the given numbers using the appropriate signs, then write the arithmetic expression which illustrates the situation and finally perform the required arithmetic operation to answer the question.

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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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This activity covers the mathematical concepts of percents and fractions. A group of ten students and ten chairs serve as a model for the distribution of wealth in the United States. I’ve used this twice in classes, and adult learners appreciated the relevance of the material. I found it worked best after group work on fractions and percents, because the students were less shy about participating when their whole group volunteered. I spent about 5 to 10 minutes on background material including basic definitions of wealth. As I implemented it, the activity took approximately 20 minutes.

Key words: Percents, fractions, economics, social justice

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Students will investigate the use of linear scaling to enlarge or shrink a variety of objects. Students are lead through a series of hands on activities and then are asked to apply the concepts to some real world situations.
Ensure that the students realize that if they scale an object in one direction by a given amount; they must scale the same amount in the other direction. By having the students do the activity in class they can 'see' that scaling in one direction may cause the other to over flow the allowable dimension or under fill it..

The last question asks the students to enlarge a cartoon. Although this is a take home activity, you may need to explain how to create a cm. grid over a picture.

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Using the standard percent increase and decrease formulas students will look at the pricing of college materials. Many college bookstores use the relationship: price = cost/(1 - mark up %) and this formula will also be used to determine pricing. This gives students a different way to look at pricing which requires using division instead of just multiplication and addition.
Many college bookstores use this second method to determine the price to students for the materials bought in the bookstore. You might want to check with your college bookstore to determine the method used. These prices were calculated by the San Diego Mesa College Bookstore for materials which they sell.

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Students measure a variety of objects in both metric and English systems. It is recommended that everyone in the group take each measurement and they then average them to obtain the most accurate measurement for the item. The next step is to create the ratios, convert them to decimals to two places and then average all the like decimals. Example all the measurements for the 5 small objects would be averaged to find the best estimate for the conversion factor for centimeters and inches. Using their conversion factors, they then convert a variety of measures. Finally, they are asked to look up the actual conversion factor and determine how accurately they were able to determine it.

• General Notes: o Student may need to have directions on how to accurately measure. o A review of factions may be needed so that they can accurately measure 1 yard 15 inches and 1 15/36 yards or 1 5/12 yards. o This activity can be used in a beginning algebra course by having the students graph the measure of the objects in metric and English units. Let x = the English unit and y = the metric. The conversion factor is then the slope of the line.

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You play this game just like battleship. The students need to pair up and hide their grid from each other. They need to plot at least one “ship”.

This is a great warm-up for students who have just learned about the Cartesian coordinate system and how to plot ordered pairs.

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The purpose of this lab is to investigate volume (capacity). Using multiplicative comparisons, students will try to predict what times the amount of water of one container will fit in another container.

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Students determine average speeds from collected data and convert units for speed problems. Students try to roll the ball with a prescribed average speed based on intuition. Then, based on unit conversions they see how accurate the rolls really were.

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The purpose of this lab is to enable students to compute the perimeter and area of equilateral triangles, and to make the connection between area of triangles (2-D) and the surface area of pyramids (3-D). Furthermore, a secondary purpose to this lab is to allow students to construct -- with contributions from everyone -- a piece of art full of mathematical meaning and implications (from geometry, algebra, and even calculus!)

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This project allows students to be hands-on in building a platonic solid. It is a good project to do after solids are covered in your class.

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Use these flashcards to help your students practice on their own addition and subtraction with integers.

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Use these flashcards to help your students practice on their own multiplication and division with integers.

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By accurately measuring the length of five different objects in both metric and English units, students will develop their own conversion factors. Students choose five small items to measure in centimeters and inches (calculators, books, pens, etc.) and five large items to measure in yards and meters (a table both width and length, the room dimensions, the chalkboard, etc.), and then create their own conversion factors.

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Students look at the amount of waste generated each year by people and make various calculations about percent increases.

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Students experiment with and learn about the gear ratios on a bicycle—thus enhancing their understanding of circumference of a circle, proportions, etc. Actual gear ratio would be the ratio between the front and rear sprocket, NOT between pedal and rear wheel.

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Students explore ratios by calculating and comparing/contrasting the ratios of consumption of resources between the United States, Europe, Asia, Africa and the Middle East.

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Using the rules of arithmetic, students complete the attached worksheet or any problems the instructor wishes for them to complete. With much practice, the rules will become second hand to them and they will recognize the patterns for integer arithmetic.

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This is a fun game for students who have just learned their order of operations. It is great practice and a good review before an exam.

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Students will demonstrate the importance of proportions, namely the cross product, via a lab that involves estimating the proportions of two types of beans in a bottle.

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These activities explore population growth rates and its consequences with
regard to the distribution of natural resources. Population growth is perhaps the most important environmental issue of our time.

As population increases and as people seek to raise their standard of living, more stress is put on our earth’s finite resources.One aspect of the population issue is the sheer magnitude of the numbers involved. World population did not reach 1 billion until the year 1800. Since then it has grown exponentially to reach our current 6.7 billion.

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Students investigate the use of linear scaling to enlarge or shrink a variety of objects.

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This group activity connects verbal descriptions of percent problems to algebraic representations. Students will match the verbal description to an equation, then solve the equation. This activity is designed for groups of 2 students.

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Metric measuring tapes meter sticks and rulers are needed for this activity. After measuring a variety of body parts, students look at the proportions as both rational and decimal fraction to determine which form is easier to compare. The values for each ratio are then averaged to determine an approximation to the actual relationship. Using these values students are then asked to determine the size of a person given the length of a bone.

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