Our next unit of study will be devoted to rates, ratios, and proportions. Fraction and decimal notation will be used to express rates and ratios and to solve problems.
Ratios compare quantities that have the same unit. These units cancel each other in the comparison, so the resulting ratio has no units. For example, the fraction 2/20 could mean that 2 out of 20 people in a class got an A on a test or that 20,000 out of 200,000 people voted for a certain candidate in an election.
Another frequent use of ratios is to indicate relative size. For example, a picture in a dictionary drawn to 1/10 scale means that every measurement in the picture is 1/10 the corresponding measurement in the actual object. Students will use ratios to characterize relative size as they examine map scales and compare geometric figures.
Rates, on the other hand, compare quantities that have different units. For example, rate of travel, or speed, may be expressed in miles per hour (55 mph); food costs may be expressed in cents per ounce (17 cents per ounce) or dollars per pound ($2.48 per pound).
Easy ratio and rate problems can be solved intuitively by making tables. Problems requiring more complicated calculations are best solved by writing and solving proportions. Students will learn to solve proportions by cross multiplication. This method is based on the idea that two fractions are equivalent if the product of the denominator of the first fraction and the numerator of the second fraction is equal to the product of the numerator of the first fraction and the denominator of the second fraction. For example, the fractions 4/6 and 6/9 are equivalent because 6 * 6 = 4 * 9. This method is especially useful because proportions can be used to solve any ratio and rate problem and will be used extensively in algebra and trigonometry.
Students will apply these rate and ratio skills as they explore nutrition guidelines. The class will collect nutrition labels and design balanced meals based on recommended daily allowances of fat, protein, and carbohydrate. You might want to participate by planning a balanced dinner together and by examining food labels while shopping with your child. Your child will also collect and tabulate various kinds of information about your family and your home and then compare the data by converting them to ratios. In a final application lesson, your child will learn about the "Golden Ratio" - a ratio found in many works of art and architecture.
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Do-Anytime Activities:
1. Look with your child through newspapers and magazines for photos and check to see if a size-change factor is mentioned in the caption. (Such as 2X for an enlarged photo or 1/2 X for a photo reduced by half). Have your child explain to you what that size-change factor means.
2. Encourage your child to read nutrition labels and use a proportion to calculate the percent of fat in the item.
3. Help your child distinguish between part-to-part and part-to-whole ratios. When comparing a favorite sports team's record, decide which ratio is being used. For example, wins to losses (such as 5 to 15 for 5 wins and 15 losses) are part-to-part ratios. Part-to-whole ratios are used to compare wins to all games played (such as 5 to 20 for 5 wins out of 20 games played).
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View the Unit 8 Outline:
http://apps.gcsc.k12.in.us/blogs/jellars/files/2010/08/Unit-8-Outline.pdf
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