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A Fraction of the Possibilities

Overview | Activities

Introductory Activities | Learning Activities | Culminating Activity
Cross-curricular Extensions | Community Connections

Introductory Activities - "shopping"-defining the terms

Compare labels from a variety of household products. Using the PRODUCT LABEL EQUIVALENTS handout, record the units used to convey how much of each product is in its container. You will notice that on most household products, there are at least two different values given for the quantity or amount of the item in the container. Since the product is in the same bottle, the two values must be equivalent! This is the beginning of our working understanding of fractions in real life. All equivalent values can be expressed as a ratio (a proportion) to be compared.
1. Identity units: The first label used is for a bottle of orange juice. The amount listed on the label indicates that the bottle contains 96 FL OZ (3 QTS) or 2.84 L of juice; what do these measures mean?

• 96 FL OZ = 96 fluid ounces
• 3 QTS = 3 quarts
• 2.84 L = 2.84 liters

NOTE: This orange juice label shows both English units and metric system units so as to accommodate consumers who are more familiar with other measuring systems. The numbers represent quantity amounts while the units tell you the system you are using. Fluid ounces and quarts are units of volume in the English system. Liters are units of volume in the metric system.

2. Develop mathematical definitions: A different label has a Net Weight of 5-1/8 OZ (145 g); this label suggests that 5-1/8 ounces = 145 grams. Write five mathematical definitions using five different product labels to practice this skill with your students.

3. Convert definitions to ratios: Once a definition can be determined, you can use it to compare different quantities based on the same units. 96 fluid ounces = 2.84 liters can be expressed as two different but related fractions:

 96 fluid ounces2.84 liters OR 2.84 liters96 fluid ounces

These expressions can be read as 96 fluid ounces in 2.84 liters or 2.84 liters in 96 fluid ounces. Other mathematical equivalents can be established with the data from the orange juice label. For example, you can compare fluid ounces to quarts or compare quarts to liters. What are the equivalent relationships that you can write using those two comparisons? What are the fractions that you came up with to compare fluid ounces and quarts? [96 fluid ounces/3 quarts or 3 quarts/96 fluid ounces. Expressed in words, these mathematical relationships are saying, there are 96 fluid ounces in 3 quarts or there are 3 quarts in 96 fluid ounces.] Using the given example, write out at least one pair of equivalent ratios for each of your five labels.

Learning Activities - Art imitating math life

Now that we have seen that equivalent fractions can be expressed in words as well as numbers, the next logical step in this progression is to show that equivalent fractions can be expressed using objects as well.
1. Simple fractional representations-Complete the FRACTIONAL REPRESENTATIONS WORKSHEET. Check your answers against the key provided separately.

2. Complex fractional representations
Log on to the "Melvin Makes a Match" (http://pbskids.org/ cyberchase/games/ equivalentfractions/equivalentfractions.html) Web site. Choose equivalent fractions for the graphical charts shown. Once you have selected an image, choose the equivalent fraction. Drag and drop each onto the pan near the bottom of the screen. In each subsequent round, the fractions become more complex. Take scrap paper (or a calculator) to the computer with you just in case you need to check your answers.

3. Play the Saloon Snap game
(http://www.bbc.co.uk/education/mathsfile/shockwave/key/snapkey.html) to make sure that you can quickly respond to the challenge of comparing equivalent values. Use a calculator if you need to but keep in mind, Fast Fingers Malcolm could beat you to the buzzer if you move too slowly.

Printable versions of each level are available online:

If you need to review the process for doing these types of conversions, go to the Saloon Snap Key Ideas page (http://www.bbc.co.uk/ education/mathsfile/shockwave/key/snapkey.html) to brush up your skills.

Culminating Activity - Putting yourself to the test!

1. Fraction Word Problems Practice sheet
Print out the FRACTION WORD PROBLEM SKILL SET handout and the FRACTION WORD PROBLEM SET, which is available online at http://home.att.net/~clnetwork/math/fracword.pdf. Use page 1 of the FRACTION WORD PROBLEM SKILL SET handout as a guide as you complete the FRACTION WORD PROBLEM SET on a separate sheet of paper. After you have checked your answers against those supplied on page 2 of the FRACTION WORD PROBLEM SKILL SET handout, get ready to take the GED Connection Practice Test #1.

2. GED Connection Math Practice Test #1
The table shown below details all of the items from Practice Test #1 and the skills being tested according to problem type and skill tested.

GED Connection Practice Test #1
 Number, Number Sense and Operations Measurement and Geometry Data, Statistics and Probability Algebra, Functions and Patterns Procedural Knowledge 12, (3), (7), (15), (17) (2), (9), (21) (18) (4), (10), (11), (13), (24) Conceptual Knowledge 14 (16) (19), (20), (22) Application Modeling and Problem Solving 6 (23) (1) (5), (8), (25)

The item numbers shown in parentheses pertain to math skills not addressed in this lesson. This chart gives you some idea of the kind of tasks you will be asked to complete on the GED math test and the distribution of skills in each category on a standard GED math test.
Cross-curricular Extensions
• Math communication/Media literacy
CYBERCHASE, Episode #203 "Harry Hippo & Mean Green" reviews strategies for comparing equivalent fractions. You can also visit the Cyberchase Web site (http://pbskids.org/cyberchase/ parentsteachers/episodes/203.html) and watch the Real video to see how this skill can be applied to real-life problem solving.

• Science
Scientists in the United States often use the metric system but sometimes the products they need are only sold in English unit quantities. Get in the habit of looking at the units and performing the conversions mentally. Knowing that a gallon is approximately 4 liters (3.78 L to be exact), you will find it easier to mentally picture quantities in your head for fast recall on a multiple choice test, because in most cases, rough estimates will help you choose the correct response. Check out one of the many dimensional analysis tutorials available online, such as this Science Education Web site (http://www.wfu.edu/~ylwong/chem/ dimensionanalysis/example1.html) that carries out a step-by-step procedure for converting units. (Uses Shockwave plug-in)

• Foreign language
Thinking in this way is not very different from learning a new language. On index cards, record five new words that you want to learn in a different language. Set up parallel statements to show the language equivalents of the terms.

Community Connections

• Organize a study group with other members of your class. Review the rules for working with fractions with them. You can serve as the tutor or help facilitate discussion by working with them to solve the fraction problems on the original worksheet, and to help with problem-solving hints when needed. Plant a garden, paint a wall space in an "unconventional" shape, or divide the normal space into segments rarely considered before. Once you have created the space, invite visitors to your masterpiece and ask them if they can figure out the dimensions or the numerical equivalents to specific segments or the whole thing.

• The GED Connection Workbook can also be used to practice math problem solving using decimals, fractions and percentages. The series of books can be purchased through the Thirteen/WNET's Adult Education Department by contacting Mr. Andrč Gleaton at gleatona@thirteen.org. Chapter 30 addresses the use of decimals and Chapter 31 addresses the use of fractions.

• Organize team play of the Reducing Fractions game online. Visit the "Reducing fractions game" Web site at http://www.quia.com/cb/84915.html along with a partner and play the two-player version. Keep tabs on your scores and compare them with other players in your class.