Objectives Chapter 1 Use symbols to complete a math statement Write number statements Find the sum of whole numbers Subtract whole numbers Multiply whole numbers Factor whole numbers Divide whole numbers Solve for the unknown in whole number operations Round to specific place value Estimate using whole numbers Calculate an arithmetic mean, median, mode, and range Convert between Roman numerals and Arabic numerals Convert between standard time and military time Apply whole numbers to critical thinking exercises

Whole Number Review Pages 11 - 35 This unit will serve as a review for most learners. Critical to their success in later units is a solid understanding of borrowing in subtraction (to be used in the subtraction of fractions) and multiplication and division (to be used in all other units). These basic skills need to be mastered so that the learner is able to accurately and efficiently complete other math calculations. I do not recommend the use of calculators in this or any other unit of the text because learners tend to become reliant on them. Mental math skills will help learners become confident in their math computations. Memorizing the multiplication tables is essential. The tables can be drilled with a learner’s children or as a group activity in class. Blank multiplication tables are included in Appendix E, and students should be encouraged to copy this form and practice with it to build their speed and accuracy. This practice goes hand in hand with their learning the divisibility facts. Rounding is another critical skill because it is used with decimals, standard and metric measurement conversions, and apothecary and dosage calculations. The unit provides the three steps to rounding. Use the technique of underlining what unit the learner is to round to and circling the unit to its right. This focuses the learner on the numbers involved and also helps the learner avoid rounding to the wrong number. Keeping the focus on what the learner is rounding to is vital. The learner who takes a few extra seconds to underline and circle the involved numbers will make fewer mistakes. Pages 11 - 35

Chapter 1 Appendix E Help This appendix includes several tools to help you learn math. These tools have been used by other students who have reported that using these tools helped them learn math and streamline their learning and memorization of math concepts and formulas. The appendix includes two copies of the blank forms so that you can make your own copies and place them in a binder. Continue to next slide

Whole Number Overview Page 1 Key skill of health care workers Accuracy is important Being competent in whole number concepts will form the basis for successful computations This chapter will form the foundation for the daily math functions you will use in the workplace. Continue to next slide

Whole Numbers Page 2 What is a whole number? It is a positive number. (not included are fractions or decimals) Whole numbers are used in our everyday lives to add calories, count medicine capsule, calculate wages, arrive at a total cost of a purchase, and measure our weight in pounds. Examples – page 3-4 – practice 1-2 go over as a class No Group Work

Integers Page 5 Whole number and their opposites are called integers. 7 and -7 = integers and opposite of each other Number line is used to visualize integers and their relationships with other integers. Line labeled with the integers in increasing order from left to right. The number line extends in both directions: REMEMBER that any integer is always greater than the integer to its left. In negative numbers, the closer a negative number is to 0 on the number line, the larger the number is. For example, -3 is larger than -19 because -3 is closer to 0 on the number line than -19 is. -1 1 2 3 4 -7 -6 -5 -4 -3 -2 5 6 7

Symbols and Number Statements Page 5 Symbols and Number Statements Symbols are used to show the relationship among numbers. Symbol = > < ≤ ≥ Meaning is equal to is greater than is less than is equal to or less than is equal to or greater than Example 1 + 7 = 8 19 > 6 5 < 12 age ≤ 5 weight ≥ 110 pounds A number statement or simple equation shows the relationship between numbers, operations, and/or symbols. Examples - page 5 - practice 3 No group work

Page 6 Addition In addition problems, the total, or answer is called the sum. Addition involves finding a total, sum, by combining two or more numbers. To add, line up the numbers in a vertical column (make sure place values match up) and add to find the total. Examples page 6 – practice 5 Group work – page 7 – practice 6

Page 8 Subtraction Subtraction involves taking one number away from another number. To subtract, line up the numbers according to place value. Start with the right side of the math problem and work your way toward the left side, subtracting each column. Fewer errors occur if the subtraction problem is set up vertically. Place value shows the ones, tens, hundreds, and so on, column.

Subtraction (Cont’d) Page 8 If a number cannot be subtracted from the number directly above it, then increase the value of the smaller number by borrowing. This is a two-step process: Subtract 1 from the top number in the column directly to the left of the number that is too small. Add 10 to the column that needs to be larger. This process may be repeated as many times as needed to complete the subtraction. Examples – page 8-9 – practice 7 Group work – page 9 – practice 8

Page 9 Multiplication To multiply, line up the numbers according to place value. By putting the largest numbers on top of the problem, you will avoid careless errors. Remember that you are multiplying not adding Remember to move the numbers from the second & succeeding lines over one column to the left – use a zero to indicate theses movements (these zeros are often called “place holder zeros”) Multiplication is repeated addition. For example: 5 x 3 = 5 + 5 + 5 = 15. Memorizing the multiplication tables is essential to sound mental math. If you are dependent on a calculator or have forgotten some of the tables, practice memorizing the multiplication tables using the chart show in the Student Resource Appendix at the front of the text. It is important that you memorize the multiplication tables for the numbers 1 through 12 and also those for number 15. Students in health care use the number 15 frequently in dosage calculations, such as the conversions of medications from the apothecary system to metric and vice versa. Examples – page 10 – practice 9 – odds Group Work – page 10 – practice 9 evens and all of practice 10

Prime Factorization Page 11 Factor = a number which divides exactly into another number. When two or more factors are multiplied, they form a product. Prime factor = a number that can only be the product of 1 and itself. We review prime factorization in this unit because it is a foundation skill that will help you complete other math functions. For example, factoring helps you figure out divisible numbers for division, arrive at common denominators, and find equivalent fractions. Knowing these terms will help you when you are reading math problems and on exams. It can be helpful to use factor trees to illustrate prime factors of a number. **** Examples – page 11-12 – practice 11 48 = 3x2x2x2x2 = 3 x 24 124 = 2x2x31 = 31 x 2^2 75 = 5x5x3 = 3 x 5^2 92 = 2x2x23 = 23x2^2 *** No group work in book 625 = 5^4 = 5x5x5x5 64 = 2^6 = 2x2x2x2x2x2 39 = 3x13 81 = 3^4 = 3x3x3x3 100 = 2^2x5^2 = 2x2x5x5

Page 12 Division Division is the act of splitting numbers or amounts into equal parts or groups. To divide whole numbers, determine what number is being divided into smaller portions the size of the portions Division can appear in three different forms of 27 ÷ 3 3 27 Examples – page 13 – practice 12 Group work – page 14 – practice 13-14 27 3 x

Solving for the Unknown Number With Basic Mathematics Page 15 Solving for the Unknown Number With Basic Mathematics Sometimes number statements ask for the unknown number. Looking for an unknown number is an aspect of algebra. To solve these problems, you must understand the relationship between the numbers. Opposite operations Examples – pages 15-16 – practice 15-18 Group work – pages 15-16 – practice 15-18: the rest

Pages 16 – 17 Rounding Whole numbers have place values. The number three thousand one hundred ninety-five has four specific place values: thousands 3,195 ones hundreds tens By using the place values in a number, we can round the number to a particular and specific place unit. Rounding means reducing the digits in a number while keeping the value similar. Rounding is valuable because it helps to estimate supplies, inventory, & countable items to the nearest unit. Rounding is accomplished in three steps: 1. Locate the place you are asked to round and underline it. 2. Circle the number to the right of the underlined digit. 3. If the circled number is 5 or greater, add 1 to the underlined number and change the number(s) to the right of the underline number to zero(s). If the number is 4 or less, round to the next number that is smaller. Use Zeros as place holders for the digits. *** Examples – page 17 – practice 19: odds Group Work – page 17 – practice 19: evens

Page 17 Estimation Estimation = a method of coming up with a math answer that is general, not specific. When we estimate, we rely on rounding to help us get to this general answer. For example, with money rounding is done to the nearest dollar. If an amount has 50 cents or more, round to the nearest dollar and drop the cent amount. If the amount is under 50 cents, retain the dollar amount and drop the cent amount. Examples – page 18 – practice 20 Group work – page 18 – practice 20: rest

Basics of Statistical Analysis Page 18 Basics of Statistical Analysis The basics of statistical analysis includes topics of mean (average), median, mode, and range. Each of these topics deals with groups or subsets of numbers and their relationships to each other and the set as a whole. Continue to next slide

Arithmetic Mean (Average) Pages 18 – 19 Arithmetic Mean (Average) Average = a number that represents a group of the same unit of measurement. It provides a general number that represents this group of numbers as long as all the numbers are the same units. You will use addition and division skills to compute averages. To compute a mean (average), follow these two steps: Add the individual units of measure Divide the sum of the units of measure by the number of individual units. Averages are useful in health occupations because they provide general trends and information. **** Example – page 19 – practice 21: evens Group Work – page 19 – practice 21: odds

Pages 19 – 20 Median Median = the middle number in a list of numbers that are arranged in order from the smallest to the largest. To determine the median, follow these steps: Step 1: Sort the list of numbers from smallest to largest Step 2: Cross off one number from each end of the line of numbers until one number is reached in the middle. (if two numbers are left over add them then divide by 2) The median is useful in health care when we are looking at data information that has a lot of variance or extreme values because the median helps group that information around the center number. One example is looking at data from a flu outbreak. The median would help generalize or center the data. *** Examples – page 20-21 – practice 22: even Group work – page 20-21 – practice 22: odds

Page 21 Mode Mode = the “most popular” value or the most frequently occurring item in a set of numbers. To locate the mode in a series or listing of numbers, identify the number(s) that occurs the most. Examples – page 21-22 – practice 23: even Group work – page 21-22 – practice 23: odds

Page 22 Range The range of a set of numbers is the largest value in the set minus the smallest value in the set. Note that the range is a single number, not many numbers. The range is the difference between the largest and the smallest numbers. Examples – page 22 – practice 24: even Group work – page 22 – practice 24: odds

Page 23 Roman Numerals In our daily lives, we use Arabic numerals 0 to 9 and combinations of these digits to do most of our mathematical activities. In the health care field, Roman numerals are sometimes use along with Arabic numerals. Roman numerals are often found in prescriptions and in medical records and charts. Roman numerals consists of lower- and uppercase letters that represent numbers. For medical applications, Roman numerals are written in lowercase letters for the numbers 1 to 10. However, use uppercase letters when smaller numbers (0-9) are part of a number larger than 30 such as 60: LX not lx. Do not use commas in Roman numerals.

Roman Numerals (Cont’d) Page 23 Roman Numerals (Cont’d) Roman numerals are formed by combining the numbers. 1 = i or I 6 = vi or VI ½ = ss 2 = ii or II 7 = vii or VII 50 = L 3 = iii or III 8 = viii or VIII 100 = C 4 = iv or IV 9 = ix or IX 500 = D 5 = v or V 10 = x or X 1,000 = M Mnemonic Device – Note the pattern: 50-100-500-1000 L = 50 Lovely Lucky C = 100 Cates Charms D = 500 Don’t Dunked in M = 1,000 Meow! Milk This will help you to remember the order and value of each Roman numeral. *** Roman numeral letters are arranged from the largest value to the smallest value. Each letter’s value is added to the previous letter’s value. Only powers of ten (I, X, C, M) can be repeated; however, these letters cannot be repeated more than three times in a row. USE the following basic Roman numeral concepts to accurately read and write Roman numerals.

Converting Roman Numerals Pages 23 – 26 Converting Roman Numerals Add Roman numerals of the same or decreasing value when they are placed next to each other. Read these from left to right. Subtract a numeral of decreasing or lesser value from the numeral to its right. When converting long Roman numerals to Arabic numerals, it is helpful to separate the Roman numerals into groups and work from both ends. Examples – page 24 – practice 25: even Group work – page 24 – practice 25: odds *** Examples – page 24 – practice 26: even Group work – page 24 – practice 26: odds **** Examples – page 25 – practice 27: even Group work – page 25 – practice 27: odds Examples – page 25-26 – practice 28-29: even Group work – page 25-26 – practice 28-29: odds

Time in Allied Health Page 26 Universal (military) time is used in many health care facilities. Based on the 24-hour clock Begins at 0001, which is one minute after midnight It avoids confusion over a.m. and p.m. and colons are not used between these numbers. Examples – page 27 – practice 30-31: some Group work – page 27 – practice 30-31: rest