Good Nutrition

Activity 4: Formulas and Equations
(Teacher Copy)

• calculators

Students will use nutrition formulas to learn more about their own health and nutrition, while learning to apply mathematical formulas and solve equations.

• To identify and define mathematical formulas and equations.
• To use appropriate terminology in working with formulas and equations.
• To set up and solve mathematical equations.

### Introduction

Ask students to tell you anything they know about formulas. Ask them to do the same for equations. See if students can give examples of these, define them in their own words, tell when or in what context they've heard of them, and so forth. (A mathematical formula is a rule or principle that usually contains symbols and which can be used to find a particular numerical piece of information. An equation is a number sentence that contains an equal sign. A = l x w is a formula for finding the area of a rectangle, whereas 45 = 5 x w is an equation that might represent the area of a rectangle in which area and length measures are known.)

Tell students that they just used formulas--though not in symbolic form--in the last activity. Have students try to guess what formulas ("rules" for finding given information) they used (determining percent calories of total calories for the three macronutrients in given food products). Once this is established, have students try to create a formula--a general rule in words or symbols, or preferably both--for finding the percent fat of total calories, using the number of grams of fat and the total calories for a given food product serving. You might want to have students first work on this in pairs or in small groups. Students should develop any formula such as the following:

%F = (G x 9) ÷ TC or F = 9G/C,

where the symbol on the left represents percent fat and the expression on the right means grams of fat times 9 calories divided by total calories (in that order). Be sure students understand the meaning of "formula," a generalized rule that can always be applied to finding a numerical value for a particular type of information.

You might want to review or teach the following here or at an appropriate place:

1. Symbolic language. For example, multiplication can be represented by the "x" sign, by a raised dot, or by absence of a symbol (as in 4n), whereas division can be shown by a "÷" sign, by a "/" sign (front slash), or by a fraction bar. Include use of variables.
2. Rules for order of operations in solving equations.
3. Key terminology, showing examples of each term and attending to meaning more than to formal definitions. A variable is a symbol that represents one or more numbers. A number that a variable represents is a value. An expression that contains a variable (e.g., y x 2.4) is called a variable expression. An expression that represents a particular number (e.g., 3.6 x 5) is a numerical expression, and the number named by a numerical expression (e.g., "7" is named by 6 + 1) is the value of the expression. Placing a numerical expression in its simplest form (again, "7" for 6 + 1) is called simplifying the expression.

Distribute calculators. Assuming that students have decided on F = (9 x G) ÷ C as their formula for percent fat calories of total calories, work together as a class to find the percent fat calories for two ounces of chunk light Star-Kist tuna canned in oil, which has 170 calories and 13 grams of fat (69% fat). Students should understand why they substitute 170 for C and 13 for G, getting F = (9 x 13) ÷ 170. Help students to see that this is also an equation. In many cases a formula will also be an equation. However, "area of a rectangle is found by taking length times width" is a formula (in words, in this case) but not an equation (which uses symbols), and 53 = m + 39 is an equation but not necessarily a formula (e.g., it might simply be the solution to a particular word problem).

Ask students if they think tuna canned in water would be lower in fat. If so, how much? Using their formula, ask students how they would find the number of grams of fat in two ounces of chunk light Star-Kist tuna canned in water, which is 60 calories and 15% fat. Have students work in pairs or small groups to find the answer (1 gram) by substituting known values for the appropriate variables and computing the answers using their calculators. Work through the problem as a class. Note the very large difference in fat content between the same amount of tuna canned in oil versus that canned in water.

Have students find the total calories for a medium-sized order of McDonald's french fries, which has 17.1 grams of fat, making up 48% of the total calories. Work through the problem as above to arrive at an answer (321 total calories). You might want to ask students what fraction of a typical person's maximum daily fat intake the 17.1 grams of fat is (more than one-fourth of the 65-gram maximum for a person on a 2000-calorie diet).

Ask students if their formula could be written as (9 x G) ÷ C = F. (Yes, the entire expression on the left of an equal sign can be exchanged with the entire expression on the right without affecting the outcome.)

• females (example): W = 100 + (5 x I) (where W is desirable body weight and I is height in inches over 5 feet)

• males (example): W = 105 + (6 x I) (where W is desirable body weight and I is height in inches over 5 feet

1. Example: P = (W - D) ÷ D (where P is percent difference between actual and desirable body weight, W is actual body weight, and D is desirable body weight)

2. See chart below. Spend adequate time discussing how students estimated percent differences. For the third row, note that some students might avoid working with negative numbers by using the absolute value of (W - D) in their formula above (which they should reflect in the formula) and then using common sense to determine if the percent difference is above or below the actual body weight.

Actual
Body Weight
Desirable
Body Weight
Percent Difference
(estim./actual)
Body Weight
Classification
177 lb. 140 lb. (varies) / 26% mildly obese
131 lb. 122 lb. (varies) / 7% normal
171 lb. 195 lb. (varies) / -12% underweight

1. Example: P = 0.8 x W (where P is an adult's RDA for protein and W is weight in kilograms) [Note that students must first convert their desirable weight in pounds to its equivalent in kilograms.]

1. Example: C = 0.73 x W x M (where C is the number of calories expended, W is body weight in pounds, and M is number of miles)

2. Example: C = 4 x (0.73 x W x M) (where C is the number of calories expended, W is body weight in pounds, and M is number of miles)

3. Example: C = 1/3 x (0.73 x W x M) or C = (0.73 x W x M) ÷ 3 (where C is the number of calories expended, W is body weight in pounds, and M is number of miles)

1. Answers will vary, but they should be expressed in calories or calories per day.

• Answers may vary, but the most obvious method probably is to find 2% of the calories in the BMR in letter A and subtract it from the BMR, then repeat this step two more times, each time using the newer/newest and not the original BMR. Ask students if the answer can be found by taking 6% of the BMR and subtracting (doing one step only). Discuss why this method will not yield the same answer (be sure students fully understand this).

• Even if a person consumes the same amount of calories daily and gets the same amount of exercise across time, she or he will gain weight with age. To maintain weight while aging, a person must eat less and/or exercise more.