Activity 3: Percents
(Teacher Copy)

• Activity 3 Reference Sheet page 1 [optional]

Students will examine various concepts of percent while extending their understanding of percent daily intake of protein, carbohydrates, and fat and examining nutrition information for various food products. Use with Activity 3 Student Copy and Reference Sheet.

• To know the meaning of percent and be able to represent a percent in percent, fraction, and decimal forms.
• To informally find any of three missing values in a percent problem, such as a% of b =c.
• To become familiar with percents greater than 100%.
• To find the percent calories from fat, carbohydrates, and protein in a food product.
• To determine percent daily values for fat and carbohydrates.

Introduction

• 30% means how many parts out of every 100 equal parts? (30; literally "30 by the hundred" or "30 per hundred") What fraction is this equal to (ask for both original and simplified forms if students don't offer them)? (30/100; 3/10) Is 30% of something greater or less than 1/4 of it? (greater) How do you know? (1/4 of something is 25% of it because the equivalent fraction on a scale of 100 is 25/100, or 25 out of every 100 equal parts, which is less than 30 out of 100) Is it greater or less than 1/3? Explain. (less, because 1/3 of something is of it because the equivalent fraction on a scale of 100 is , or out of every 100 equal parts, which is more than 30 out of 100 [you might want to use 33 1/3 or 33.3 (rounded) in place of .])
  
  
• 30% means how many parts out of every 10 equal parts? (3, because 30 units out of 100 units on a 10 x 10 hundred chart is the same as 3 rows out of 10, and the fraction 30/100 is equivalent to 3/10) Thinking proportionally or in terms of equivalent fractions, you can determine that 30% means how many parts out of 200? (60-Since 30% is 30 parts out of each 100 parts, then there are 30 parts for each of the two hundreds; 30/100 = 60/200.) What is 30% of 50? (15-Since 30% of 100 is 30, then 30% of half that number is half of 30; three out of every ten units means 15 because 50 has five groups of ten; 30/100 = 15/50.) What is 30% of 150? (45-Add 30 [30% of 100] and 15 [30% of 50] or use any other types of reasoning explained previously.)
  
  
• What does 30% look like in decimal form? (0.30, i.e., 30/100)
  
  
• Campbell's Chicken Gumbo condensed soup has 15 calories from fat in one serving, which is 60 calories. What percent fat is that? (25%; explore/work through many methods, but particularly emphasize the first two of the following three sample solutions (use of equivalent fractions, and division to the nearest hundredth): 15/60 (i.e., 15 out of 60 calories) is equivalent to 1/4, which we know from the previous discussion is 25%; 15/60 reads from top down "15 divided by 60"-carry out the division to the hundredths place [or round to the hundredths place as needed either after dividing to the thousandths or by considering the fractional part remaining after dividing to hundredths]; set up a proportion to find the percent, which must always relate to one hundred-15/60 = x/100) Note that the fat calories fall below the 30% maximum, but Campbell's soups are too high in sodium according to recommended measures of a good diet.
  
  
• Frito Lay's potato chips have 60% calories from fat (twice the recommended maximum!). There are 150 calories in one serving (1 oz.). How many calories from fat do the chips have? (90; the question becomes "What is 60% of 150?," which is found by either using the decimal form of 60% [0.60 or 0.6] or the fraction form [60/100, 6/10, or 3/5] times 150 [again, setting up proportions for such problems will also work])
  
  
• Mr. Turkey turkey bacon has 60% of its calories from fat (imagine the fat in beef and pork bacon!), which accounts for 15 calories in every serving (1 slice). How many calories are in one serving? (25; the problem can be stated as "60% of what is 15 calories?" [0.6(0) x ___ = 15] or "15 is 60% of what?" [15 = 0.6 x ___], which is solved by the problem 15 ÷ 0.6(0). You might want to refer students to a simpler example to illustrate why the method works: 4 x ___ = 36 can be solved by the problem 36 ÷ 4. Students might also use a knowledge of proportions or formal or informal reasoning that uses fractions in their solutions.)
  
  
• Tell students that Land O' Lakes Sweet Cream Butter has 100 calories per serving (1 tablespoon) and that 100 calories per serving are from fat. Ask what percent of calories is from fat. (100%) Have them explain what 100% means. (all of a designated whole) Ask if it's possible to have more than 100% calories from fat, and why/why not. (No, there can't be more calories from fat than the total number of calories that are in the product.) What does it mean to say that a person gave 110% for some effort that she or he made, and is that possible? (No, a person cannot give more than 100% effort, which is-theoretically-the maximum amount she or he has to give. It is a saying meant to indicate that someone has exerted a tremendous effort.) Is it possible to ever have more than 100% of something? (Yes) When? (When a whole or total is capable of being exceeded, for example, if someone weighs 100 pounds and gains 15 pounds in one year. The person's weight is now 115% of the weight of one year before because it is now 100% [all] of the former whole-100 pounds-plus 15 percent more of the original 100%/whole. The percent increase is 15%.) Have students find the percent increase for a change in diet from 2000 calories daily to 2200 calories daily and then give the percent that the new caloric intake is of the former one. (The percent increase is 10%-2000 of the calories can be ignored because they represent no increase, but the 200 extra calories is 200/2000, which is 1/10 or 10%, of the original whole. The new calorie intake is 110% of the former one.)
  
  
• One serving (2 slices) of Wonder Bread is 100 calories. The calories from fat in one serving is 15. How many calories are not from fat? (85) How do you know? (Because 100 calories per serving is the total or whole, so 100 calories minus 15 calories leaves 85 calories that are accounted for by other nutrients.) Explain the saying, "Success is 10% inspiration and 90% perspiration." (It means that the total or whole of success-100%-results from a proportion of 10 of 100 equal parts (10/100, or 1/10) inspiration and 90 of 100 equal parts (90/100, or 9/10) perspiration (i.e., mostly from hard work!)

Part A

1- A.

• Answers may vary; the actual answers are Harry and David Jumbo Cashews (74%), Hershey's Kisses with Almonds (57%), Frito-Lay Cheeotos (Crunchy) (53%), and Chunky Chips Ahoy! (50%), Country Club Neapolitan Ice Cream (46%), Little Debbie Granola Bars (Chocolate Chip) (38%), Low Sodium Triscuits (32%) [Ralston Chex Mix is at but not greater than 30%].
• Methods will vary but may include different types of mental computations or estimating by looking for calorie proportions that are about 1/3 or greater of the calories per serving.
• Answers may vary; the actual answers are Harry and David Jumbo Cashews (74%), Hershey's Kisses with Almonds (57%), Frito-Lay Cheeotos (Crunchy) (53%), and Chunky Chips Ahoy! (50%).
• Methods will vary but may include different types of mental computations or estimating by looking for calorie proportions that are about 1/2 or greater of the calories per serving.
• Answers may vary; the actual answers are Harry and David Jumbo Cashews (74%) and Hershey's Kisses with Almonds (57%).
• 1st part: Answers may vary; the actual answers are Nabisco SnackWell's Devil's Food Cookie Cakes (0%) and Hostess Lights Low Fat Cup Cakes (10%). 2nd part: Answers may vary; the actual answers are Ralston Chex Mix (30%) and Low Sodium Triscuits (32%).

1- B

1. Ralston Chex Mix (Traditional): 30%
2. Frito-Lay Cheeotos (Crunchy): 53%
3. Nabisco SnackWell's Devil's Food Cookie Cakes: 0%
4. Little Debbie Granola Bars (Chocolate Chip): 38%
5. Hershey's Kisses with Almonds: 57%
6. Hostess Lights Low Fat Cup Cakes: 10%
7. Chunky Chips Ahoy!: 50%
8. Country Club Neapolitan Ice Cream: 46%
9. Low Sodium Triscuits: 32%
10. Harry and David Jumbo Cashews: 74%
    Answers will vary; see fourth bullet (regarding Campbell's Chicken Gumbo soup) in the Introduction for possible solution strategies
    
    

• at least 70%
• 47%

It is probably best to work through and discuss Part A with students before moving on to Part B so that errors and misunderstandings in figuring percents as well as the notion of rounding error can be addressed before students reinforce or compound errors in the next section.

Part B

Note: Because of the fact that there are about and not exactly 9 calories in one gram of fat, further incongruencies (beyond rounding error as discussed in #'s 1D above and 1B below) can occur between figures on labels and those that students compute based on general nutrition guidelines. The same holds true for the calories per gram for other nutrients. As an example, note that for Post Raisin Bran (letter K on p. 4 of R3) 4 x 46 carbohydrate grams is 184 calories, 4 x 4 protein grams is 16 calories, and 10 calories from fat totals 210 calories, but the product lists only 190 calories per serving. Therefore, all percents figured computationally are approximate.

1 - A

• Yes, 5x 9 = 45 calories.
• No, because 13 x 9 = 117, and the total calories is 120. Also accept "yes" answers by those who recognize that rounding error has occurred.
• Same idea as the last bullet (7 x 9 = 63, but the total calories is 60...)

1 - B: Answer might be yes or no. See second bullet in #1A (rounding error). Grams listed are rounded to the nearest whole number. Even if the number was only rounded off by one or two tenths, this "error" is magnified 9 times when the rounded number is multiplied by 9. 2 - A

• Possible answers include: Post Raisin Bran (K)-8%,Philadelphia Brand Cream Cheese (N)-8%, Kroger Yogurt (U)-13%, Prairie Farms French Onion Dip (P)-7%, Olde Tyme Whipping Cream (S)-less than 8% [Little Charlie's Pizza(P)-15%, Stove Top Stuffing (Q)-15%, Lender's Bagels (R)-15%]
• Possible answers include: Post Raisin Bran (K)-97%, Thomas' English Muffins (L)-87%, Tropicana Orange Juice (M)-98%, Lender's Bagels (R)-78%, Healthy Choice Bean and Ham Soup (T)-76%, Kroger Yogurt (U)-74% [Stove Top Stuffing (Q) is 47% carbohydrate as prepared, which more important for health purposes than is the dry mix composition]

1. For fat, multiply the percent (third column) in decimal form times the total calories (middle column), then divide by 9. [The first step finds the number of calories that fat comprises of one serving of the product. Each gram of fat is about nine calories, which the second step addresses.] The same method is used for finding grams of carbohydrates and protein, except that the second step involves dividing by 4 rather than 9. Explore other methods. For example, for the Subway sub, which is 25% fat, a student might divide total calories by 4 for the first step.
   
   
2. Multiply fat grams times 9 calories and carbohydrate and protein grams times 4 calories each, then add the three numbers. Explore other methods. For example, a student might multiply 27 fat grams for the Big Mac times 9 calories to get 243 calories, then multiply that times 2 (because fat is 50% of the calories) to get 486 calories. Note that different methods will yield different answers, which is acceptable based on room for error as discussed previously.
   
   
3. One solution is to add the other two percents in the box and subtract the sum from 100%. Another solution is to multiply a nutrient in the first column times its equivalent number of calories (4 or 9) and then to divide it by the total calories (and round to the nearest hundredth). Again, different methods will yield different acceptable answers.

1. 300. 60% (recommended daily intake of carbohydrates) times 2000 calories (assumed diet) equals 1200 calories from carbohydrates, which is 300 grams because there are 4 calories in each gram.
   
   
2. • 8%. 96 calories (24 grams of carbohydrates) divided by 1200 calories that come from carbohydrates in a healthful 2000-calorie diet.
   • 92%
   
   
   
3. • 11%. 7 grams of fat times 9 calories each is 63 calories, which- divided by the maximum daily caloric intake of 600 calories (30% of 2000 calories)-is 10.5 percent. Another method is to simply divide 7 grams of fat by 65 grams (the maximum recommended daily grams of fat for a 2000-calorie diet, as noted at the beginning of Part C), which is about 10.8%.
   • About 1/9.
   • 58 grams. 65 grams (maximum recommended fat intake in grams for a 2000-calorie diet) minus 7 grams (one serving of Doritos).
   • 89%. 100% (total percent of fat calories for a particular diet) minus 11% (determined in first item in letter C for 7 grams of fat).

1. Correct answer is water (bottled spring water).
2. Answers will vary.
3. Yes. Percent Daily Value's are based on a 2000-calorie diet. If you are on a 2500-calorie diet, you can consume 25% more calories (1/4 of the 2000-calorie base), and, therefore, the %DV's found on food labels may add up to 125% for your daily intake. For example, the Daily Value for saturated fat is 20 grams, or 100%, for a 2000-calorie diet, but a person on a 2500-calorie diet may consume another 5 grams, or 25% of the base amount, for a total of 125% of the Daily Value, which is always based on a 2000-calorie diet.
4. 1/2% of something is one-half of 1%. Since that is one-half of one part out of 100 parts, it means one out of every 200 parts. (You might want to work through some examples of this.)
5. 7 calories per gram of alcohol.