Food for Thought, Notes

Numbers Institute, PO Box 1320, Shepherdstown WV 25443, LR@NumbersInstitute.com

These teaching notes accompany a poster which shows data on 150 foods.

There are several ways to look at the poster:

A. You can study one food at a time, and see what nutrients it has. For example the first food, Acerola, has an extremely long line for Vitamin C, since it has a high concentration of Vitamin C. None of the other lines for Acerola is particularly long, so it has little concentration of any other nutrient. The unshaded section in the center circle takes about 90% of the circle, so the food is 90% water. Most of the rest is carbohydrate. A good dictionary, encyclopedia or nutrition book may list Acerola; it is also called Barbados cherry. It is sometimes found in health food stores, as a good source of Vitamin C.

B. You can study one nutrient at a time, and see what foods are good sources. For example the thick line near the bottom of each circle shows Vitamin A. The longest lines for Vitamin A are for carrot, chicken liver, and sweet potato.

The thick line near the top of each circle shows Calories. The longest lines are for butter, margarine, and oils, especially oils, since each of these is largely fat. Fat has 9 calories per gram; protein and carbohydrate about 4 calories per gram; and water 0 calories per gram. Therefore the foods with the highest concentration of fat have the most calories, and the foods that are mostly water have very few calories (like Acerola).

C. You can study a group of nutrients at a time. For example the lines at the upper left corner of each circle show amino acids. Therefore meats, cheeses, and some beans and grains have a cluster of long lines at the upper left. Lines in the lower left show vitamins, and various foods are strong in these. Lines in the lower right show minerals, and grains are often a good source of these.

D. You can compare groups of foods on particular nutrients. For example meats are often strong in vitamin B12, which is the thick line in the middle of the vitamins (lower left corner of each circle). B12 is found in animal products and fermented soy products. Vegetarians often need supplements to have enough Vitamin B12, since it primarily comes from meats. Lack of it causes anemia and other problems.

E. You can understand some traditional dietary advice with the help of the poster. Very few foods have a full range of vitamins, hence the advice to eat a variety. Beans and rice are considered complementary proteins, so the standard recommendation is to eat both, in order to have a full range of amino acids: Beans are higher in Lysine than Methionine, and rice is higher in Methionine than Lysine. These 2 amino acids are shown by a thick line and a thin line near the middle of the amino acids (upper left corner of each circle). You will see that among beans, the thick line is always longer than the thin line of this pair. In rice, both lines are short, since cooked rice is mostly water and carbohydrate, but the thick line is shorter than the thin line in this pair. Therefore beans and rice are complementary. Note also that you can get substantial quantities of Methionine even from beans, if you eat enough of them.

F. You can decide which foods would be interesting to eat together, to create balanced menus, either for one meal, or for a day's or week's meals. You can balance amino acids, or vitamins, or all nutrients. Remember at the same time to minimize fat, especially saturated fat and cholesterol. For example peanut butter has more potassium than bananas or potatoes, but it is much higher in fat, so bananas and potatoes are better in most diets.

G. You can use the poster for practice with graphs. The pie charts and bar charts on the poster can be converted into numbers (see below). People can draw similar graphs for other foods, using the nutrition labels on the foods. You can ask students, alone or in groups of 2-3 to design a new graph on some topic every week, perhaps letting them rotate among categories like: bars, pies, lines, time series, very dense (over 40 numbers graphed), very simple, etc. They can find data on the web, in textbooks and newspapers (weather, sports, financial pages).

Help in Interpreting the Poster

The foods on the poster are compared in equal quantities, gram for gram, or ounce for ounce.

The curved marks around each food serve 2 purposes:

(a) Like marks on a clock, they help you find each line, and help compare the same lines on different foods.

(b) The curved marks also show scale. They mark twice the average level of nutrients, in all foods on the poster.

Lines which go halfway to the curved marks, show average levels of nutrients. Lines which go all the way to the curved marks show nutrients that are present at twice the average level.

For example the average level of potassium in all the foods on the poster is 278 milligrams of potassium per 100 grams of food. (The numbers are given in the text at the bottom of the poster.) The curved marks show twice this level, or 556mg of potassium per 100g of food.

The potassium line for chili con carne goes about halfway to the curved marks, since chili con carne has 273mg of potassium per 100g, nearly the average level. On the other hand, the potassium line for spinach goes all the way to the curved marks, since spinach has 558mg of potassium per 100g of food. The potassium line for molasses goes far outside the curved marks, since molasses has 1464mg of potassium per 100g of food, or 2.6 times the level shown by the curved marks.

The scale on the poster is a technique to have all the nutrients scaled in a similar way.

The text at the bottom of the poster shows the average concentration, per 100 grams, of every nutrient on the poster. Since the curved marks are always at twice this level, you can interpret the scale given by the curved marks.

For ounces you can convert the text at the bottom of the poster. Concentration per ounce is always .28 times the level per 100 grams (because an ounce is 28 grams, or .28 times 100 grams). Therefore the average potassium on the poster is .28 x 278mg = 78mg, per ounce of food. If you use cup measures, concentration per cup is generally 2.27 times the level per 100g. (A cup of food usually weighs 8 ounces or 227g.) Therefore the average potassium is 2.27 x 278mg = 631mg, per cup of food. (This 2.27 does not apply to foods like cereals, where a cup includes a lot of air, and is lighter than 227g.)

Daily Reference Values The text at the bottom of the poster shows the Daily Reference Value for each nutrient (except Manganese and amino acids, where DRVs have not been established). The DRVs are generally recognized values, published by the US government. They replace what used to be called 'minimum daily requirements'. Pregnant women and some other groups of people need somewhat different values. DRV is also called Daily Value (DV).

The DRVs are in parentheses at the bottom of the poster. They show how much you need to eat, to reach the reference values. For example the DRV for potassium is 3500mg, which is 12.6 times the average concentration in the foods on the poster (average is 278mg per 100g). You would reach this level with 12 servings per day, at 100g each, of foods like chili that have average levels of potassium, or 6 servings of foods like spinach, potato skins, or buckwheat flour that have twice the average level.

Food packages show the number of grams in a serving. (Some liquids are labeled in milliliters (ml): a milliliter is about a gram.) Packages also show the nutrients in each serving, in milligrams or as a percent of the DRV.

You can use the poster's figure for DRV to convert percentages into milligrams. For example suppose you have a loaf of bread which is labeled as having 6% of the DRV of iron, in a 38g slice. The DRV for iron is 18mg, so this bread has .06 times 18mg, or 1.08mg, of iron in that 38g slice.

You can compare a food label to foods on this poster if you convert milligrams per serving to milligrams per 100g: Your 38g slice of bread has 1.08mg of iron, so 100g of the bread would have ¹⁰⁰/38 times as much, or 2.8mg of iron. This 2.8mg is a bit more than the average iron (2.0mg) for all foods on the poster, so the iron line would extend a bit more than halfway to the curved marks. If you look at the various breads on the poster, you will see that their lines for iron vary somewhat, but they do go a bit more than halfway to the curved marks.

Readings. Books on nutrition are in libraries under Dewey Decimal numbers 641 and 664. Topics range from analysis to advice. For example: Nutritive Value of Foods, (US Government Printing Office stock#oo1-ooo-oo475-o $4, fax telephone 1-2o2-512-225o) lists major minerals, vitamins, and other nutrients for many foods. Many similar private books exist, although most cover fewer nutrients and fewer foods, and cost more. Nutrition Desk Reference, by Garrison and Somer, describes each nutrient thoroughly, the foods that contain it, and the risks from over- or under-consumption. Other encyclopedias on nutrition or nursing cover similar topics. Keeping Food Fresh, by Bailey, does not show nutrients, but lists many common and rare foods, and how to buy and store them. There are similar general books, and books on specific types of foods. Rules on nutrition labeling and Daily Reference Values are in volume 21 of the Code of Federal Regulations, parts 101 and 104 (especially 101.3 and 101.9), which is published by the US government and available on the web and in large libraries.