Joe SchlessingerBerkeley, California, US,

March 15, 2011

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- Mathematics > General

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Table of Contents

- Mixing - Simulating Mixture Problems with Beads
- Graphing - Scaling a Graph
- Linear Modeling - Modeling CO<sub>2</sub> Levels
- Modeling Gas Prices - linear functions, systems
- Perimeter and Surface Area -- Building a Sierpinski Pyramid
- Trapping Lab - Linking Equations and Graphs
- Surface Area and Volume Project - Product Packaging
- Surface Areas of Right Rectangular Prisms - Measuring Boxes
- Mixing Beans
- Linear Modeling - Barbie Bungee Jump
- Whole Numbers - When in Rome
- Medical Math applications (Solving Equations)
- Proportions - Scaling Up and Down
- Measurement - Discovering Conversions
- Percents - It Costs What?
- A Fraction Finding Mission Lesson Plan
- Motion - Toy Train Collision
- Math 8 - Surface Area and Volume
- Investigating Characteristics of Quadratics
- Battleship
- Comparing Volumes
- Average Speed and Unit Conversion
- Algebra
- Reading and Making Scatter Plots
- Ch. 8.2 Exponential Functions and Their Uses
- Discovering the Pythagorean Theorem
- Sequences as Functions
- CK-12 Middle School Math (Grade 7)

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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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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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In this activity students explore levels of Carbon Dioxide (CO2) in the atmosphere over time. There is concern that levels of CO2 are rising, and finding a good mathematical model for CO2 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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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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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 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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In this project, designed to be completed over 1 to 2 weeks, students will take on the role of a Product Packaging Manager, reporting to the CEO of the company of their choice. Students will select a product of their choice (XBox, PS3, iPhone, Android phone, Blackberry, iPod or other) and design a package for it, keeping in mind that the product must be kept safe and the box must be appealing to look at. The surface area and volume of the packaging will be calculated, as well as the cost of materials.

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In this 80-minute lesson plan designed for Math 8 (textbook: Math Makes Sense), students will use rulers to measure the surface areas of various boxes (cereal, juice, crackers etc.). Students will use the collaborative activity, assigned questions, and quiz to understand the relationship between the net of a prism and its surface area.

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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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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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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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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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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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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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A Fraction Finding Mission project is an individual activity that stresses problem solving and critical thinking as applied to operations between rational numbers.

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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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This unit contains lesson plans, quizzes, and an assessment project. Students will investigate nets, which are 2D representations of 3D objects, surface areas and volumes of various prisms, and more. The project has students designing their own packaging, calculating the surface area, volume, and cost of materials, for a product of their choice.

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Lesson plan and activities for finding the vertex and y-intercept of a quadratic function.

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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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Introduction to Algebra

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Lesson revolves around collected data that is utilized in a scatter plot. Real life situations are used within the lesson to depict the basic 3 types of scatter plots. Best line of fit is also presented.

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This is the exponential functions section which explores some special exponential functions and show how to fit exponential functions to data.

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This is a packet where students will discover, using the areas of a square and triangle, the formula for Pythagorean Theorem.

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A guided discovery lesson show how to write a given sequence as a function.

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A work in progress, CK-12’s Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.

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