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- From: CRS Collaboration
- Contributed By: Joe Schlessinger
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).
- Created by: by Alan Bass and Terrie Teegarden, San Diego Mesa College
Topic: Linear functions and modeling
Resource type: In-Class Activity Time Required: 30 minutes Content: Critical thinking/ concept development Materials: graph paper DESCRIPTION: 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.Created by: Paul Young, San Diego City College
Type of activity: hands on activity Course level: Pre-Algebra Topic: Geometry (perimeter and surface area) Materials:- Scotch tape -- 1 roll per group
- Ruler -- 1 per group
- Scissors -- 1 pair per group
- A LOT of tape will be required for this lab, so make sure that the students are not too wasteful.
- Most of the learning will be through the students filling out their lab write-ups. Make sure they spend time answering all questions.
- This lab is suggested to follow the introduction of perimeter and area of polygons. Additionally, it would be beneficial to introduce surface area before doing this lab.
- This lab is supposed to be fun! However, make sure to keep the students on task (e.g., don't let them spend too much time coloring.)
Group Work, In-Class Activity (also can be used as Homework)
Time Required: 30 minutes Materials: regular graph paper Objectives:- Solve systems of equations
- Accurately plot points and graph lines
- Interpret the relationship between the solution to a system of equations and the corresponding graph
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.
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.
Created by: Paul Young, San Diego City College
Type of activity: hands-on activity, small group Course level: Pre-Algebra Topic: ratios and proportions Materials: 1 water bottle per group, 100 pinto beans per group, 15 black beans per group Time required: 20+ minutes Description: Students will demonstrate the importance of proportions, namely the cross product, via the following lab:- The students are to do an experiment that enables them to predict the number of pinto beans in the bottle, without spending time counting every single bean.
- Each group will make an initial guess to the number of pinto beans, recording it into their lab worksheets.
- The students will add the black beans into the bottle and shake up the bottle to establish an even distribution of pinto and black beans.
- After mixing up the beans, the students will pour out a small number of beans, approximately 15 to 20, and count and record the number of pinto beans vs. black beans. This is used to create the proportion.
- The students can use the cross product to solve for the total number of pinto beans.
In-Class Group Activity
Time required: 60+ minutes Topics:- Slope-Intercept Fom
- Point-Slope Form
- Linear Modeling (Collect data, Create a linear model to represent data, Use a linear model to make predictions)
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.
Learning Goals:
o Prealgebra solving equations by dividing both sides by the same amount. o Work with subscript notation o Substituting values into equations o Percents and rational fractions Prerequisite knowledge: o Substituting values into a formula o Multiplication property of equality Time Required: o 20 to 30 minutes Students use a formula to solve equations for problems with a medical slant provided by the Mesa College 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.Open or Download This File:
Medical Math Solving Equations Activity student worksheets and instructor notes.zip (193kb)
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.
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.
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.
Created by: Alexander Juden, Southwestern College
Type of activity: hands-on activity Course level: Intermediate Algebra Topic: Motion Materials:- Tape measure
- Stopwatch
- Two battery powered toy trains (cars, or other) that can travel on the tray of the whiteboard at a constant velocity (ideally, the two trains will have different velocities).
Created by: Susan Working, Grossmont College
Type of activity: small group Course level: Pre-Algebra (maybe Beginning) Topic: Graphing points Materials: Grid paper Time required: 10 minutes Description: This is a great warm-up for students who have just learned about the Cartesian coordinate system and how to plot ordered pairs. Implementation notes: 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". I normally have them plot a ship which contains 3 ordered pairs in a row--either vertically, horizontally, or diagonally. Have them draw around their ordered pairs to make it look like a "battleship". Next they take turns calling out ordered pairs looking for their partners ship. If the ordered pair that has been called out is part of the ship, then the student says "hit", if not, then they say "miss". They continue back and forth calling out ordered pairs until one student has "sunk" the other ones battleship by finding all 3 ordered pairs. Each student must keep track of what ordered pairs they have already called out. They can do this by making a mark with a colored pencil at each point they have already called. When they get a hit, they can mark it with an "X". They can use the same grid with their ship or the second grid on the paper.Created by: Alexander Juden, Southwestern College
Type of activity: hands on activity Course level: Pre Algebra Topic: Volume Materials:- One small container, in the shape of a rectangular solid or right circular cylinder.
- One large container in the shape of a rectangular solid, or right circular cylinder, or a cone. This container should be about 2/3 to þ filled with water.
- 1 large bowl, or other container that you can easily pour water into. This bowl should easily hold the amount of water in the large container.
- 1 ruler per group
- Each group will measure the dimensions of the small container, and calculate the volume of the water in the container (when full).
- Each group will measure the large container, and the height of the water as required to calculate the volume of water in the large container.
- For the competition, each group will estimate how many times the small container can be filled completely with the water in the large container (after filling the small container, it will be emptied into the large bowl, and refilled again from the large container). On the last filling of the small container, it will not fill completely. Students will estimate the height of the water in the small container on this last filling. The closest group wins.
- The instructor should make a chart on the board with a row for each group, and a column for the group estimates on 1) How many times the small container will be completely filled, and 2) Height of water in the small container after last (incomplete) filling (to the nearest 1/8 of an inch). Write all group estimates on the chart before performing the experiment.
- Discuss what factors might affect their estimates (thickness of container, rounding, etc.)
- This lab is suggested to follow volume of geometric solids.
- Make sure students understand that the last filling (which will not be complete) does not count as one of the "complete" fillings of the small container.
Created by: Nick Slinglend, San Diego City College
Type of activity: hands on activity, small group Course level: Pre-Algebra Topic: speed and unit conversion Materials: On tennis ball per group, stop watch feature on cell phone, tape, and yard sticks Time required: 20+ minutes Description: Students determine average speeds from data collected and convert units for speed problems. Students try to roll the ball with a prescribed average speed based on intuition. Then, based on unit conversion we will see how accurate the rolls really were. Implementation notes: See the lab outline (attached). The archive file SpeedLab.zip contains three documents, an outline of the lab and two versions of the student worksheet.This is the exponential functions section which explores some special exponential functions and show how to fit exponential functions to data.
Description: 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.
Download from CK-12: http://www.ck12.org/flexbook/pdf/6bcca1dfcf1b5b0780d18264a5627ff9.pdf
