Nutrition 331 Nutrition for Health

Study Guide

Unit 10: Water and the Minerals

Introduction

Maintenance of the body’s fluid and electrolyte balance requires proper amounts of sodium, chloride, and potassium that—along with calcium, phosphorus, sulphur, and magnesium—constitute the major minerals present in the body. Trace minerals are present in much smaller concentrations. Like vitamins, water and minerals do not yield energy, but unlike vitamins, they are inorganic in their chemical composition. Minerals are indestructible, even after being burned to ashes; they are lost from food in cooking only when leached out into the cooking water.

In this unit, we look at the functions of water in the body and at how the body maintains water balance. We discuss the importance of electrolytes in regulating the distribution, composition, and acidity of body fluids. We also briefly discuss the functions, deficiency and toxicity symptoms, and major food sources of sodium, potassium, and calcium.

Instead of providing detailed information on each trace mineral, we look at their general characteristics, such as functions, absorption, transport, excretion, and dietary sources. We cover iron in greater detail than other minerals. Finally, we discuss the need (or lack of need) for vitamin and mineral supplements.

Note: While the eText is very informative, it often provides an excessive amount of detail. Please focus on the key messages rather than the minor details. Use the objectives below to determine what you are expected to know after completing this unit.


Objectives

After completing this unit, you should be able to

  1. discuss at least seven roles of water in the body, state an adult’s daily water needs, and list beverages and foods that can help meet water needs.
  2. discuss the body’s daily requirement for sodium, the effects of excess sodium, and the major dietary sources.
  3. discuss the body’s daily requirement for potassium, the effects of inadequate potassium, and major food sources.
  4. list five factors that affect calcium absorption and list dietary sources of calcium.
  5. describe the condition of osteoporosis and explain how various dietary factors and physical activity affect bone density and the risk of developing osteoporosis.
  6. briefly describe the nutritional significance of trace minerals.
  7. describe three functions of iron and list several factors that either increase or decrease iron absorption.
  8. describe iron deficiency and state the major dietary sources of iron.
  9. discuss the appropriate use of vitamin and mineral supplements.

Section 1: Water

Reading Assignment

Chapter 8: Water and Minerals
  • chapter introduction (pp. 310–311)
  • Water (pp. 312–316, top of page, up to Are Some Kinds of Water Better for My Health Than Others?)

Often neglected as an essential nutrient, water is in fact the most indispensable and abundant component of living cells. A person can survive without food for several weeks but can live without water for only a few days. Severe malfunctions can result from loss of body fluids of 10 percent, and death can result from loss of 20 percent. Water is so important because it is involved in many biochemical reactions, and it serves as an important solvent and medium for vital materials.

On average, water comprises about 60 percent of an adult’s total body weight. The percentage is lower in the elderly, in females, and in obese people, and it is higher in children, males, and athletes. Among body tissues, muscle cells have the highest water content, while skeletal cells have the lowest. Electrolytes in the body help keep fluids at optimum levels.

The main functions of water in the body are summarized on pages 312–313 of the eText. Water is also part of the structure of macromolecules, particularly glycogen, and some of the proteins in muscle. Muscle has a much higher content of water than does body fat. Fat storage, however, requires little water, which is why obese individuals have less total body water in proportion to their weight than do muscular athletes and have more difficulty in cooling themselves during hot weather or when they have a fever.

Water helps in the softening of fecal matter because water is absorbed by dietary fibre, thereby increasing the fecal bulk for easy elimination.

Under normal conditions, the loss of water through the kidneys, lungs, feces, and skin is balanced by the intake of water from liquids and food and by metabolic water produced during energy metabolism. Since there is no water storage per se in the human body, water has to be replenished daily to replace losses. The regulation of water intake and excretion is related directly to electrolyte balance in body fluids.

A low blood volume can result from large water losses, for example, through profuse sweating, vomiting, diarrhea, bleeding, use of diuretics, and untreated diabetes. Although the kidneys provide control in homeostasis of body fluids, that mechanism is often insufficient to handle such rapid fluid and electrolyte losses. In such cases, extra fluid—and possibly extra electrolytes—should be given orally or intravenously to prevent serious dehydration and depletion of electrolytes. If a large amount of water is given without added salt, water intoxication may result.

You may find Consumer Corner: Bottled Water in Canada (p. 319) interesting. (You will not be tested on this material.) As the eText points out, millions of people pay grossly inflated prices for bottled water. By a miracle of modern marketing, people pay two or three times more for bottled water than they pay for gasoline (measured as dollars per litre).

Water (i.e., more or less pure water) is not the only way to meet fluid needs. The eText discusses suitable water needs for adult women and men as 11.4 cups (2.7 L) or 15.6 cups (3.7 L) per day, respectively. This includes tap water, fluids from milk and juices, tea, and coffee. Some beverages that are not encouraged, such as soft drinks or sweetened fruit drinks, also contribute to fluid needs. Water needs increase during hot weather and are higher for endurance athletes.

Tap water is a good choice for meeting fluid needs because it is calorie free, inexpensive, and refreshing, especially if chilled.


Section 2: Sodium

When we talk about electrolytes in body fluids, three of the major minerals involved are sodium, chloride, and potassium. They are provided in the diet and are readily absorbed by the small intestine into the blood. They are filtered by the kidneys and then either reabsorbed into the body or excreted in the urine.

The great majority of ingested sodium, potassium, and chloride is excreted in the urine. The rest is lost in the feces, and small amounts of sodium and chloride are lost in sweat, assuming there is no excessive sweating or diarrhea.

Reading Assignment

Chapter 8: Water and Minerals
  • Sodium (pp. 327–331)

Sodium is (by far) the most abundant positively charged electrolyte in the extracellular fluid, where it is involved in maintaining the fluid and acid-base balance. It also functions in conduction of nerve impulses and control of muscle contraction.

Since sodium is abundant in the food supply and humans tend to consume more than is required, dietary deficiency of sodium is very unlikely.

Evidence strongly indicates that excess intake of sodium, in the form of sodium chloride, is a major cause of hypertension, one of the most common chronic health problems in industrialized countries. Hypertension is a major factor in coronary heart disease, stroke, and renal failure. It is thought that salt-sensitive or sodium-sensitive people are particularly prone to develop hypertension if they consume a lot of salt. This issue is discussed in more depth in Unit 12.

About 80 percent of dietary sodium comes from processed foods and only 15 percent of typical sodium intake comes from the salt shaker. Many of the processed foods listed in Figure 8-8: Sources of Sodium in the Canadian Diet (p. 330) are significant sources of sodium in the Canadian diet. While processed cheeses are specifically mentioned, block cheeses are also fairly high in sodium. Cheddar and mozzarella cheese contain about 250 to 300 milligrams per 50-gram serving. Grain products also deserve a special mention as about 20 percent of sodium comes from grain products, such as bread and cold cereals. It is common for grain products to emerge as one of the top three sources of sodium in a diet.

In general, the more processed a food, the more sodium is added and the less potassium is present. For instance, some canned chicken and rice soups contain more salt than chicken!

Frozen vegetables (without sauces) and high-sugar processed foods tend to be low in sodium. Sugar is virtually sodium free, as are foods such as soft drinks and candy. Ice cream and homemade desserts are also quite low in sodium.

An acceptable daily intake of sodium is 1500 milligrams. Requirements may be higher for endurance athletes, especially during hot weather. For many people, an achievable goal is the upper limit of 2300 milligrams. Many Canadians would be challenged to keep sodium levels below this level, as typical intakes are 2400 to 5000 milligrams per day.


Section 3: Potassium

Reading Assignment

Chapter 8: Water and Minerals
  • Potassium (pp. 331–333)

Potassium is the major positively charged electrolyte in the intracellular fluid. As an electrolyte, it maintains the fluid and acid-base balance. Like sodium, potassium is important for neuromuscular activity, including that of the heart muscle. It also promotes cellular growth in protein synthesis and acts as a biological catalyst in energy metabolism.

If injected into the bloodstream, potassium can stop the heart from beating. Special care must be taken when using salt substitutes containing potassium chloride, especially by people with kidney failure. However, a high intake of potassium from foods does not cause toxicity because of its slow absorption through the intestine. The kidneys can normally control blood levels of potassium by increasing urinary excretion.

Numerous studies have demonstrated an inverse correlation between dietary potassium and blood pressure. This topic is further discussed in Unit 12. In view of this important potential benefit, it is prudent to include more potassium-rich foods in the diet. Diets high in potassium are generally low in sodium (an additional benefit).

Snapshot 8-4: Potassium (p. 332) gives some major food sources of potassium. Highly processed foods such as cured meats, frozen dinners, ready-to-eat cereals, crackers, baked pies, and pastries have far more sodium and less potassium than do fresh fruits, vegetables, and legumes. Achieving the AI for potassium is easily achieved by consuming generous amounts of vegetables and fruits and adequate milk products. Dietary deficiency of potassium is rare in normal diets because potassium is widely distributed in food. However, a relatively poor intake is common because most people do not consumer enough unprocessed foods such as vegetables and fruits.


Section 4: Calcium

Reading Assignment

Chapter 8: Water and Minerals
  • Calcium (pp. 320–322)
  • Calcium in Canadian Foods (pp. 322–324)
  • Controversy 8: Osteoporosis: Can Lifestyle Choices Reduce the Risks? (pp. 353–362)

Note: You will not be tested on the following details: bone structure, protein (in relation to calcium), homocysteine, diagnosis and medical treatment of osteoporosis, and different types of calcium supplements.

Calcium is the most abundant mineral in the body. Ninety-nine percent of the body’s calcium is found in bones and teeth. The remaining one percent is distributed as calcium ions in the blood, extracellular fluids, and soft tissue, where it regulates many metabolic functions.

The role of calcium in bone strength is well known. However, if dietary calcium is inadequate, the body turns to the bones, the body’s calcium storage site. The body gives higher priority to maintaining the level of functional calcium in the blood and tissues than in bone. When blood calcium levels are low, hormones and vitamin D send messages to bone cells to release calcium. If the diet is consistently short of calcium, bone calcium slowly disappears. Calcium can be withdrawn almost without limit from bone as the severe bone loss in osteoporosis demonstrates.

Physiological and dietary factors affecting calcium balance include the following:

  • the presence of lactose – The absorption of calcium can be improved 15 to 50 percent by lactose. Hence, calcium from milk and milk products has a higher bioavailability than calcium from other sources.
  • vitamin D status – If the level of active vitamin D is low, the amount of calcium absorbed from the gut will be low, regardless of how much calcium is in the diet. Vitamin D need not be consumed at the same time as calcium-rich foods to facilitate calcium absorption.
  • calcium binders such as oxalic acid – Calcium binders, which inhibit calcium absorption, are found naturally in some foods, including some high-calcium foods. For example, fresh spinach has 60 milligrams of calcium per 250 millilitre serving, but the oxalic acid in spinach binds calcium, leaving as little as 6 milligrams of calcium available for absorption. Thus, spinach is not a good source of calcium. Other foods containing oxalic acid are Swiss chard and rhubarb. Some dark green, leafy vegetables with calcium and little or no oxalic acid are turnip greens and kale.
  • the relative need for calcium – Several periods during the life cycle, including infancy, childhood, adolescence, pregnancy, and lactation, are characterized by an increased calcium requirement. To meet these additional demands, the body becomes more efficient at absorbing dietary calcium; absorption increases from the average of 10 to 30 percent to as high as 50 percent. When demand for calcium is lower, the rate of absorption decreases proportionally.
  • physical activity – An important factor enhancing calcium balance is one’s degree of physical activity. Bed rest or immobilization of bones causes loss of bone calcium as does the weightlessness experienced by astronauts. It is thought that bone requires the stress of weight to maintain a balance between deposition and resorption. Without the stress of body weight and exercise, bone resorption exceeds deposition resulting in a net loss of bone.

Milk products are the best sources of calcium, both qualitatively and quantitatively. In the Canadian diet, milk products provide about 60 percent of the total calcium intake. The calcium in milk is readily available because lactose is present and milk is fortified with vitamin D. Other comparably rich calcium sources include sardines (especially with the bones) and shrimp. Clams, canned salmon (with bones), almonds, soybeans, and calcium-set tofu are also sources, although they are less rich.

Calcium-fortified orange juice and soy milk provide alternative calcium sources for some. Note that orange juice does not provide the other nutrients typically found in milk, such as vitamin D, protein, and riboflavin. Soy milk may or may not be fortified with nutrients, so read the nutrition facts table to assess your choice.

Unfortunately, most Canadians do not consume enough calcium. Only young men consistently consume adequate levels of calcium. According to one estimate, the average 19- to 30‑year-old female consumed about 87 percent of the calcium AI; 51- to 70‑year-old men consumed 86 percent of the AI (Forster-Coull et al., 2004). A summary of calcium sources and suggestions for increasing calcium intake are found in the eText, pages 350–353.

Consuming calcium from food sources is by far the best way of meeting calcium needs. However, in situations of allergy, lactose intolerance, food dislikes, poor appetite, or illness, some people may find it difficult to consume enough calcium from foods. In such cases, a calcium supplement is necessary. The eText presents an interesting discussion of calcium supplements on pages 359–361. (You will not be tested on this topic.)

The failure to deposit sufficient calcium in the bone can cause growth retardation in children and bone loss in adults. Suboptimal and marginal intakes of calcium throughout life can result in osteoporosis, mainly in post-menopausal women. Although this disease of bone loss is multifactorial in origin, a growing body of evidence suggests that a low calcium intake is a significant factor. A person with osteoporosis has a long history of being in negative calcium balance: much calcium was withdrawn from bone, making the bone porous and of low mass. As a result, bones become more susceptible to fracture, especially at the wrist, spine, and hip. The level of peak bone mass at approximately 30 years of age is a major factor in determining the risk of developing osteoporosis. A diet that meets the recommended intakes of all bone nutrients, most notably calcium, phosphorus, and vitamin D, is important throughout life. The eText discusses some risk factors of osteoporosis and identifies preventive measures (pp. 354–359).

Many people believe that osteoporosis results simply from a lack of calcium. This is an oversimplification; the condition is multifactorial. While a convincing body of evidence demonstrates that much of the Canadian population has an inadequate intake of calcium, evidence also indicates that many Canadians have an inadequate intake of vitamin D, and that both of these nutrients are critically important for bone health. Also, several factors increase calcium loss in urine, including excess intake of sodium and caffeine. Smoking also increases the risk of osteoporosis. Conversely, adequate potassium intake lowers calcium loss in urine. Exercise is also protective against osteoporosis.

The upper limit for calcium is 2500 milligrams per day. Some health problems that may develop at this level include milk alkali syndrome, identified by high blood calcium levels, blood alkalosis, and poor kidney function.


Section 5: General Characteristics of Trace Minerals

Although present in only minute amounts in the body (less than 0.01% of body weight), trace minerals are essential for many vital functions.

The trace minerals known to be essential for humans include iron, zinc, iodine, selenium, copper, manganese, fluorine, and chromium.

Each nutrient has an optimum effect only at a particular level of intake. That too much or too little of a nutrient may be equally harmful is particularly true of trace minerals. Because of the minuscule amounts required, each has a rather narrow range of safe intake, outside of which lies a real possibility of deficiency or toxicity. Many body systems might be affected.

Unlike excess water-soluble vitamins, excess trace minerals are not excreted efficiently but tend to accumulate in tissues. Consequently, the best way of obtaining safe and adequate amounts is through a balanced diet rather than through supplements. Trace minerals are widely available in food.

Trace minerals are known to be involved in many enzyme and hormone systems as well as being constituents of some body compounds.

Examples of minerals and their functions are listed in the following table:

Mineral Substance Function
iodine thyroxin regulation of energy metabolism
iron hemoglobin oxygen transport
zinc insulin glucose utilization
fluoride fluorapatite strengthening of teeth

Table 10.1: Mineral functions

The absorption of trace minerals is generally regulated at the mucosa of the small intestine. Absorption depends greatly on the physiological need; that is, if more is required, more will be absorbed. Oxalic and phytic acids, present in some foods, can interfere with the absorption of trace minerals by binding with them to form insoluble complexes. Furthermore, nutrient interactions can also affect the absorption of trace minerals. For example, excessive iron intake can depress the absorption of zinc, while large amounts of zinc can interfere with copper absorption.

The amounts of trace minerals present in plants depend, to some extent, on the mineral content of the soils in which the plants are grown. Soils deficient in a mineral may produce plants containing low amounts of that mineral. As a rule, however, our foods come from many different geographical areas; thus, a balanced mixed diet should provide adequate amounts of all the essential trace minerals.

In grains, trace minerals are usually concentrated in the outer bran coating and in the germ (whole grains). Milling of whole grains to produce refined white flours removes a significant portion of trace minerals from the diet. Boiling foods in large amounts of water will lower trace mineral content through leaching.

Note: You may wish to read more about iodine, zinc, selenium, fluoride, chromium, copper, and other trace minerals (pp. 333–335 and 341–346). You will not be tested on the details of these trace minerals.


Section 6: Iron

Reading Assignment

Chapter 8: Water and Minerals
  • Iron (pp. 335–340)

Note: You will not be tested on the material in Table 8-10: Calculation of Iron Absorbed from Meals.

Iron deficiency is the most common nutritional deficiency worldwide, affecting all socioeconomic groups. Infants, children, and women in their childbearing years are the groups most affected.

Present in all cells of the body, iron plays an important role in many biochemical reactions. In a healthy adult, about 70 to 80 percent of iron is found in hemoglobin.

The iron in the body can be divided into two forms: functional iron and stored iron. Functional iron serves a metabolic role in hemoglobin and myoglobin and an enzymatic role in enzymes containing iron as a cofactor.

The functions of iron include the following:

  • oxygen transport from lungs to body tissues – Iron, a component of hemoglobin in the red blood cells, combines with oxygen in the lungs, where the oxygen concentration is high, and releases it in tissues where the oxygen concentration is low. Muscle myoglobin picks up the oxygen and holds it for use during muscle contraction.
  • energy production – Lack of energy is symptomatic of an iron deficiency.
  • assistance in a wide variety of biochemical reactions

The body loses iron in a number of ways, although most body systems tend to preserve body iron. It is present in minute amounts in every cell; thus, any cell loss represents a small loss of iron. Blood loss represents a significant iron loss because most of the body’s iron is found in hemoglobin. Therefore, hemorrhages or blood donation can result in a major loss of iron; hemorrhages, of course, seldom occur in healthy adults. Women, however, experience significant iron loss monthly through menstruation; the amount lost is highly variable, but the average is about 0.3 to 1.0 milligrams per day. Besides the iron needed to replenish daily losses, extra iron is needed during cellular growth. Thus, infants, children, adolescents (especially girls), women in their childbearing years, and pregnant women have higher iron requirements and are more prone to iron deficiency than others.

The absorption rate of iron can range from 2 to 35 percent, with a typical average of 10 to 15 percent. The most influential determinant of iron absorption is the iron status of the individual; that is, the amount of iron present in body stores. When a person’s requirement increases, iron is initially withdrawn from stores. Low iron stores signal the mucosal cells to absorb more iron from the gut. But when intake has been high, absorption drops, leaving the large majority of dietary iron to be excreted in the feces.

Under normal circumstances, the body can maintain a normal iron balance. However, a consistently low intake of iron coupled with high iron requirements can exceed the body’s ability to maintain a balance. Body stores will eventually become depleted, causing hemoglobin levels to drop, resulting in iron deficiency anemia. Deficiency symptoms are described in the eText (pp. 336–337).

Iron deficiency progresses through two stages. The first stage, known simply as iron deficiency, occurs when iron stores are depleted. About 20 percent of women and 3 percent of men in Canada and the United States have iron deficiency. As the eText points out, people can be iron deficient without being anemic.

The second stage, anemia, occurs when iron stores are completely exhausted and hemoglobin levels begin to drop. About 8 percent of women and 1 percent of men have this condition.

Anemia can easily be treated by iron supplementation if it is caused by iron deficiency alone. Nutritional anemia may also be caused by various other deficiencies.

Sources of dietary iron are shown in Snapshot 8-5: Iron (p. 338). There are two forms of iron in foods: heme iron and non-heme iron. Each is absorbed differently by the gut. Heme iron is found in hemoglobin and myoglobin and makes up about 40 percent of the total iron in animal tissues. The absorption of heme iron is relatively high, occurring at a constant rate of about 23 percent. The major sources are meat, fish, and poultry. Non-heme iron is found in most meats, fish, poultry, legumes, and whole and enriched grain products. Dark green leafy vegetables also tend to be high in non-heme iron. Iron supplements are also non-heme. Non-heme iron is absorbed at a lower rate than is heme iron—about 2 to 20 percent. Its absorption depends on the presence of enhancing or inhibiting factors in the food, such as phytates and tannins. People with low iron stores absorb both heme and non-heme iron more efficiently than do people with normal iron stores.

Vegetarians are advised to consume 14 milligrams and 32 milligrams of iron daily for men and women, respectively.

The dietary factors that enhance or inhibit iron absorption are described on pages 339–341 of the eText.


Section 7: Vitamin and Mineral Supplements

Reading Assignment

Chapter 7: The Vitamins
  • Controversy 7: Vitamin Supplements: Who Benefits? (pp. 295–303)

Note: You will not be tested on the information in Table C7‑2: Dietary Supplement Terms (p. 298) or the information specific to the United States (pp. 297–299).

Vitamin and mineral supplements are not usually necessary for people who eat a well-balanced diet. In fact, only through foods can the 50 or more nutrients be provided for the daily needs of the body. Even the best supplement does not contain the as-yet uncategorized substances present in natural food that are believed to possess health benefits. Above all, we eat foods—not nutrients—to live.

The eText provides an informative account of the situations where supplements may be justified (Table C7‑1, p. 296), the potential hazards of using supplements, and some of the misleading claims used to increase the sales of supplements (pp. 302–303).

A strong case for supplementation can be made for folic acid and vitamin D:

  • folic acid (i.e., the form of folate used in supplements) to prevent neural tube defects (for women of childbearing age)
  • vitamin D, which may be valuable for people in northern latitudes—which includes all of Canada—during the winter. This is recommended by many health experts for people over the age of 50.

Does taking a supplement lead to improved health for the general population? The answer appears to be a clear no. Our best evidence for this comes from studies that have examined whether use of vitamin-mineral supplements reduce the risk of death. Five cohort studies followed large groups of adults, usually aged between 50 and 70, for long periods (8 to 10 years) and reported that total mortality (the risk of death from any cause) was no lower among regular users of multivitamins than among non-users. These findings are supported by the results of randomized controlled trials. Several such trials have taken place in order to determine whether supplements have any value in the areas of all-cause mortality, cardiovascular disease, cancer, or cognitive impairment. The findings have been clearly negative (Guallar et al., 2013).

The hazards of supplementation are well illustrated by the antioxidant vitamins: beta-carotene (see eText, pp. 300–301), vitamin E (see eText, p. 301), and vitamin C (see eText, p. 268). The eText explains that supplements of these vitamins seldom supply any health benefit. Beta-carotene supplements may actually increase the risk of lung cancer. What is especially interesting (not mentioned in the eText) is the effect that taking these supplements for several years has on total mortality. After all, it is hardly important whether the death rate from a single disease falls (cancer or heart disease) if the risk of death from any cause is unchanged. Bjelakovic et al. (2012) conducted a study that pooled together data from numerous clinical trials in which the amount of the vitamins given was typically several times higher than the RDA. The investigators reported that supplementing with these vitamins led to an increase of about 2 to 5 percent in total mortality.

While supplements of particular vitamins and minerals have their place, a large volume of supplements is taken for no good reason. Health food stores make most of their profits from the sale of a vast range of dietary supplements. Although sales staff freely offer advice to support the value of supplements, such advice is seldom accurate and seldom based on credible information (Temple et al., 2009; Temple, 2010). Most often, it is based on testimonials or on a distorted version of nutrition science. Health food stores also sell products promoted as treatments for obesity. However, few users lose more than a trivial amount of weight. In recent years, many products, often mixtures of herbs, have been marketed for their “detoxification” qualities. Such products are claimed to stimulate the liver to remove toxins, thereby improving health. This concept, however, lacks any kind of scientific support. Another popular type of dietary supplement is protein supplements for body builders. Use of such supplements to improve muscle mass is also without scientific basis. Amino acids, which are the building blocks of proteins, are also often commonly sold in health food stores. As explained on page 225 of the eText, there is a lack of acceptable scientific evidence supporting their value.

For some supplements, solid evidence exists to justify their value; for example, vitamin D. Supplements of proven value typically cost around $3 per month. But if a person walks into a health food store and complains about not having enough energy, having headaches, and fearing death by cancer, they will probably be advised to take several different supplements, each costing between $20 and $60 per month (based on recommended usage). Following that advice could easily cost the user up to $100 to $200 per month, and the benefit to health is likely to be trivial at best. Indeed, the net effect on health might be more negative than positive.


Review Questions

See eText Chapter 8, Self-Check:

  • questions 1, 2, 5, 6, 7, 8, and 9 (p. 362)