A DULT B AS IC S KILLS I NSTRUCTOR T RAINING M ANUAL T EACHING M ATH IN C ONTEXT A Tool Kit for Adult Basic Skills Educators Dianne B. Barber Appalachian State University NC Community College System
Editors: Jackie McInturff, David Thompson, and Ryan Trent Graphic Design and Layout: Dianne Barber Copyright Appalachian State University exclusively grants to the North Carolina State Board of Community Colleges, its officers and employees, and volunteers affiliated with North Carolina community based literacy organizations acting within the scope of their duties a royalty-free, irrevocable license to reproduce and use the work(s) in connection with education, research, and public service functions. This manual may not, in whole or in part, be copied, photocopied, reproduced, translated, or converted to any electronic or machine readable form by any individual or organization other than the above mentioned parties without prior written consent of the Adult Basic Skills Professional Development Project acting in partnership with Appalachian State University. 2007 Adult Basic Skills Professional Development Project and Appalachian State University. Adult Basic Skills Professional Development Project Appalachian State University ASU Box 32047 Boone, NC 28608-2047 (828) 262-2269 www.abspd.appstate.edu
Table of Contents Acknowledgments Preface v vi 1 Teaching Math 1-1 Introduction Workplace Math Everyday Math Collaborative Learning Class Projects 1-3 1-5 1-6 1-8 1-8 2 Culinary Math 2-1 Introduction Seeing is Believing Equivalencies Common Abbreviations for Weights 2-5 2-7 2-11 and Measures Equivalent Measures and Weights 2-21 Card Game Standard English Equivalent Measures 2-33 and Weights Recipes More or Less Finding Recipe Yields Metric Measurements in Recipes Scooping up the Food The Mill Markup for Menu Pricing Percent Loss, Portions, and Cost Cooking with Ratios Finding Percents of Meat Cuts Check, Please Ordering Food for Large Groups 2-37 2-43 2-49 2-57 2-61 2-65 2-69 2-73 2-77 2-83 2-85 iii
3 Healthcare Math 3-1 Introduction Counting Tablets All About Measurement Measurement: Terms and Abbreviations Measurements and Approximate 3-5 3-7 3-13 3-17 3-23 Equivalents Conversion Practice & Dosage 3-31 Calculations Projecting the Need for Nurses Estimated Shortages for Registered 3-39 3-43 Nurses Healthcare Occupation Growth How Satisfied are Registered Nurses? Heart Rate, Age, and Gender Lung Capacity Understanding Medicine Labels 3-47 3-51 3-55 3-59 3-63 4 Horticulture Math 4-1 Introduction Landscape Geometry: Perimeter and Area Volume of Planting Containers Landscaping with Bricks, Blocks, and Pavers Soil, Mulch, and Stone Seeding a Lawn Hands-on Seed Mixtures Grass Seed Mixtures Cost of Seed Mixtures Sod for an Instant Lawn Insecticides and Herbicides All About Fertilizer 4-5 4-7 4-17 4-25 4-29 4-37 4-43 4-47 4-53 4-59 4-63 4-69 5 Resources and Bibliography 5-1 Internet Resources Books and Articles Bibliography 5-3 5-10 5-15 iv
Acknowledgments The Adult Basic Skills Professional Development Manual Teaching Math in Context: A Tool Kit for Adult Basic Skills Educators was made possible through the collaboration of many individuals who generously shared their expertise from years of teaching math in adult education. To them we extend our heartfelt gratitude. In addition, we extend our appreciation to the countless educators serving in instruction and training roles across the state. We thank the North Carolina Community College System for its financial and professional support. We extend thanks to President Martin Lancaster, Dr. Randy Whitfield, Ms. Katie Waters, Ms. Sillar Smith, Mr. Robert Allen, and Ms. Lou Ann Parker for continued contributions to the Adult Basic Skills Professional Development Project. Without the contributions of the Adult Basic Skills directors, instructors, and trainers this manual would be incomplete. We extend to each a hardy Thank You! A special thanks goes to Laverne Franklin who helped with ideas for lesson plans; William Barber, who reviewed, proofread, and provided answer keys for handouts; and David, Jackie, and Ryan who worked as a team to edit this manual. Without the dedication and skill of these individuals, this manual would not be possible. Thanks Team! Dianne B. Barber, Director Adult Basic Skills Professional Development Project v
Preface The purpose of this manual is to provide research-based information, lesson plans, and activities for high-quality interactive training and math programs in Adult Basic Skills. Much research and experience in math and numeracy training precedes its writing. The manual s efficacy as a reference encourages customization to meet your needs. Research concerning teaching math to adult learners is minimal. However, we have integrated research in math and numeracy, actual classroom experience with adult learners, and feedback from Adult Basic Skills instructors in the field to write this manual. Teaching plans are provided to enhance training, teaching, and learning. These plans are only samples of the types of activities that can be used for effective math instruction and training. Using this manual in conjunction with the Adult Basic Skills Professional Development Training Manual: Effective Training to plan training activities will give participants firsthand experiences in how to teach math based on students interests and needs. During training, discuss adapting the activities to reach a variety of math skill levels within the multi-level classroom. Instructors and trainers are encouraged to remain abreast of current research in the field and to conceptualize adaptations of the information and activities found in this manual. To assist in this endeavor we have included a bibliography of all works cited, works consulted, and Internet links. At the time of writing, all Website links were active. Due to the ever-changing world of technology, Internet sites may change or be deleted. You may wish to supplement these resources with your own. This manual is the 13 th volume in the Adult Basic Skills Professional Development Instructor Training Manual Series. Each manual is designed to enrich the user s knowledge base and provide opportunities for professional development. For a complete listing of training manuals, videos, and CD-ROMs visit our Website at www.abspd.appstate.edu. vi
Teaching Math
1-2 Teaching Math
Introduction Reluctant, apprehensive, frustrated math students can become willing, involved, and competent math students. The goal of this training manual is to help you facilitate that change in your basic skills math students. Adult Basic Skills students who have spent years fearing math or hating math, and probably failing in math, can learn to succeed in math. They can even learn to like math (Glass, 2001). How can those things possibly happen? They can happen when students learn that math can be fun, math can be practical, and math can work for them. Many students are mentally challenging you, the instructor, to show them that math has any practical value so show them! Then the only remaining obstacle for them will be their knowledge that they are not good in math. But if you guide them to successful experiences in math, and they continue to work for success because the math they are doing interests them, one day they will realize they were wrong that they can do math (Barber, Kitchens, & Barber, 1997). Many people get larger monetary rewards from their work than Adult Basic Skills instructors, but very few will ever know the elation that you can experience when you help bring about that important change in your students. People do math because math makes their lives better (Gal, 1993; Withnall, 1995). Math can protect us from being cheated or shortchanged. Math skills enhance our job opportunities. Math skills make our lives more fun. Math skills help us maintain our homes, cook, budget our money, understand the news, and plan trips and vacations. Math helps us understand our own health and can protect us from medication errors, including errors that have potentially devastating consequences. Math skills help us protect and nurture our children and care for aging family members. Math is an important, and integral, part of life. Many students try to treat math as an alien and incomprehensible subject to be avoided (Curtain-Phillips, 2004). To teach math to those students, you need to patiently, but persistently, work at discrediting that attitude. The process should begin with demonstrating how students are already using math in their own lives. By showing students there are math concepts that they have already mastered, you begin the process of verifying they can do math well. Teaching Math 1-3
Math is important because it is so useful in our both our daily lives and in the workplace (Glass, 2001). This training manual provides several lesson plans that will build on everyday applications of math for many Adult Basic Skills students. Of course, not every student will have used, or will plan to use, every application illustrated in this manual. By knowing your students and their backgrounds and experiences, you will be able to choose and emphasize those exercises that will elicit interest from the greatest number of students. A report on how Adult Basic Skills programs should tailor instruction to the workplace entitled Breaking Through: Helping Low-Skilled Adults Enter and Succeed in College and Careers advises Adult Basic Skills instructors to directly link education to economic payoffs (Liebowitz & Taylor, 2004). Their rationale is that most students are there to enhance their future job opportunities, with a goal of increased financial rewards. The report argues that the most effective educational approaches tie what students are learning to high demand occupations. Students need to be made aware there are numerous job opportunities in a particular field, and then shown applications of their education to that field. This training manual includes lesson plans that address job opportunities in culinary, healthcare, and horticulture fields as well as lesson plans that illustrate math skills that would be required for working in those jobs and for advancement. Liebowitz and Taylor (2004) recommend bringing together math and other basic skills with the ways that occupations or career paths use those skills. To enhance this effort, it is recommended that instructors focus on high demand occupations. Instructors can inspire student learning by taking time to emphasize opportunities for higher wages and increased chances for future career advancements. Another of their recommendations that you may want to implement is to engage employers in the teaching/learning process. If there is a large industry in your area, representatives of that industry may be recruited to speak to the class about their job needs and the math skills they would like their employees to have. Tying math instruction to that type of introduction from a large employer alleviates the need for the instructor to convince students that the math skills being addressed have a practical application. The same goal could be accomplished with a panel of smaller employers. 1-4 Teaching Math
This manual has two objectives. One is to provide you with lesson plans that can make math interesting, fun, and obviously applicable to your training needs and/or students lives. The second objective is to inspire you to seek out additional math applications in the workplaces and everyday lives of your students, and to develop additional lesson plans that will further encourage your students to excel at math. Please remember to share those lesson plans with other trainers and instructors, so we can all do a better job of teaching math as a fun, essential, and obtainable skill. One of the chapters in this training manual focuses on math in the healthcare industry. One of the lesson plans in that chapter encourages students to learn to evaluate the quantity of medication they are giving a family member or themselves. Another lesson plan addresses career opportunities in health professions. Some of the classroom discussions that are suggested in these and other lesson plans focus on life and career issues, thus demonstrating to all students how math is used as a tool for enhancing a person s opportunities and a person s welfare. The contexts for these exercises were deliberately chosen to encourage students to use math without making math seem to be the major focus. Students cannot doubt the value of math when it is being used in applications that might help them make life-enhancing, or even lifesaving, decisions. Workplace Math Numeracy has to do not only with quantity and number but also with dimension and shape, patterns and relationships, data and chance, and the mathematics of change. Adult Basic Education and General Education Diploma (GED) mathematics instruction should be less concerned with school mathematics and more concerned with the mathematical demands of the lived-in world: the demands that adults meet in their roles as workers, family members, and community members. Therefore we need to view the new term, numeracy, not as a synonym for mathematics but as a new discipline defined as the bridge that links mathematics and the real world (Schmitt, 2000, p. 4). Most jobs require skills in basic arithmetic as well as the ability to apply those skills (Dingwall, 2000, p. 4). Cashiers need to be able to make change when the register quits working, and find discounted prices when the discounts were not properly entered in the computer. Construction Teaching Math 1-5
workers need measurement skills and often need to calculate quantities or prices. Employees need to be able to predict paycheck amounts and evaluate withholdings for taxes and social security as well as elective withholdings. Some people like for their bosses, personnel office workers, etc. to do all that math for them. However, most people aspire to job advancement and higher wages or salaries with better benefits. Math is one of the basic skills that enhance one s chances for promotion or finding a better job elsewhere. Workplace math is a good place to begin when teaching math to Adult Basic Skills students because so many students have some mastery of workplace math, plus the need to be competent in workplace math is obvious to them (Zemke & Zemke, 1981). Workplace math is an area where they have experienced success in math, and success in math builds the confidence that is so vital to overcoming math fears and phobias. Enhancing math skills will help students become better employees, experience greater job satisfaction, and advance in their chosen careers (Numeracy in Focus, 1995). Everyday Math Do you have enough money to buy lunch? Do you have enough money to pay your credit card bill this month? How much interest will you save if you pay off a loan or credit card instead of paying the minimum balance? Will you be able to take the vacation you want this year without borrowing money, and if you have to borrow money how much will you need to borrow? These are just a few of the questions that relate to the math of our personal finances. When students can relate to the questions being asked, and can see the relevance of these questions to their lives, they see the value of learning math skills (Yasukawa, Johnston, & Yates, 1995). How much fertilizer should you buy in order to fertilize your lawn? How much paint will you need to paint your house? How many posts will it take to build a fence around your property or swimming pool? How much money can you save by making these calculations and home improvements yourself rather than hiring someone else to do them? These are just a few of the many questions that illustrate how math is used to maintain personal property. Since most students aspire to becoming homeowners and living the American dream, these types of 1-6 Teaching Math
questions can help them see how math skills can make their lives more enjoyable (Sal, van Groenestign, Manly, Schmitt, & Tout, 1999). How much money will you save per month if you buy the car that is expected to get better gas mileage? How much money will you save on interest if you choose a 36-month auto loan rather than a 48-month loan? How many more weeks can you drive your car before it is time for the next scheduled maintenance? How many more miles can you drive before you will need to stop for gasoline? These and many other questions illustrate how automobile owners and drivers use math. For the vast majority of adult students, their car is an absolutely essential part of their lives. How much flour will you need to make half of the recipe? How much money will you be able to save by stocking up on a food item when it is one of the advertised specials? How much sugar will you need to borrow from a neighbor to complete a recipe (unless you really don t care about the recipe and are just borrowing because he or she is really cute)? How much of each ingredient will you need to purchase to triple a recipe for a dinner party? What time will you need to start baking if more than one item needs to go in the oven, and the items require cooking at different temperatures? These are just a few possible questions that relate to cooking and entertaining. How long will a prescription last if someone needs to take it three times a day? How much medication should you take per dose, and how much should you take if you are instructed to double the regular dose? How much will you save by purchasing a generic drug? How far apart are the contractions? What is the heart rate of an accident victim? These and many other questions can be the difference between feeling good or feeling rotten, between good health and poor health, and possibly between life and death. They offer pretty convincing reasons for learning math skills. These examples were chosen not only to illustrate the importance of math in everyday life, but also because these areas offer numerous opportunities to draw on students previous experiences. The particular life situations and perspectives that adults bring to the classroom can provide a rich reservoir for learning (Imel, 1998, p. 2). Teaching Math 1-7
Collaborative Learning You will see that the lesson plans in this training manual call for students to work in pairs or groups. Many lesson plans also suggest that students report their findings to the entire class, and that the class members have numerous opportunities to learn from each other. In this manual, much emphasis has been placed on collaborative learning because collaborative learning works, especially with Adult Basic Skills students (Leonelli & Schwendeman, 1994). Students who have experienced failures in more traditional math classrooms need a different approach; repeating the instructional methods that failed in the past is likely to result in more failure and more frustration. Students are often more willing to learn from each other than from a power figure. This helps the student who is being taught by a peer, but often helps the peer much more. Learning something well enough to explain it, and therefore teach it, requires a level of understanding that students seldom achieve otherwise. Furthermore, explaining a math concept or procedure to a peer helps the student put that concept or procedure into their own long term memory bank. Then the student teacher will be more likely to be able to use those concepts and procedures well into the future (Gardner, 1999). Look for additional ways and opportunities to incorporate collaborative learning into math instruction. Share your successes with other Adult Basic Skills instructors. Both you and the other instructors will benefit from that interaction, which is, in itself, a form of collaborative learning. Class Projects Although this manual does not make suggestions for class projects, some of the lesson plans could easily be expanded to projects that would help a family in need or make a major difference in the community. If your students suggest that a particular lesson plan topic could be used in this manner, encourage them to explore the costs and benefits of such a project. Whether or not they actually initiate the work phase of the project, the planning phase would require a lot of practice in math applications. At the very least, they would all get to see math in real-life applications. 1-8 Teaching Math
Culinary Math
2-2 Culinary Math
Culinary Math Table of Contents Introduction Seeing is Believing Equivalencies Common Abbreviations for Weights and Measures Equivalent Measures and Weights Card Game Standard English Equivalent Measures and Weights Recipes More or Less Finding Recipe Yields Metric Measurements in Recipes Scooping up the Food The Mill Markup for Menu Pricing Percent Loss, Portions, and Cost Cooking with Ratios Finding Percents of Meat Cuts Check, Please Ordering Food for Large Groups 2-5 2-7 2-11 2-21 2-33 2-37 2-43 2-49 2-57 2-61 2-65 2-69 2-73 2-77 2-83 2-85 Culinary Math 2-3
2-4 Culinary Math
Introduction The food service industry has shown phenomenal growth over the last 50 years. As Americans become more and more dependent on that industry, job opportunities in the culinary arts continue to increase at a rapid pace that shows no sign of slowing down. While many see working at a fastfood franchise as a dead-end job, those who obtain the math skills required for management aspects of the food service industry will have many opportunities for advancement. Measurement skills are required in many occupations, but especially in the culinary arts. Chefs, short-order cooks, etc. must be able to determine quantities of ingredients when recipes are being modified and when fractions or multiples of recipes are required. Food preparation often requires conversion of one unit of measurement to another. Units of measurement in recipes do not always correspond to those on ingredient labels. This chapter includes lesson plans designed to help students learn math by practicing measurement skills in this context. Many students who will not work as a professional chef will become amateur chefs because they enjoy entertaining or simply enjoy cooking. Whether as a hobby or a profession, food preparation can be a fun activity for those who have the math and measuring skills to become good at it. Advancement opportunities are plentiful for good cooks and chefs. They can advance in careers such as restaurant management or ownership. Of course, the business aspect of the food service industry requires additional math skills. Restaurants and other businesses that specialize in food preparation are very focused on the profit margin. Ingredients must be ordered or purchased in the most cost-effective manner. Determining and comparing costs is an important application of math skills. Profit becomes dependent on menu or product pricing, which also requires math skills. The applications of math to the ability to compete and earn a profit in the food service industry are obvious. Culinary Math 2-5
Price and quantity calculations must be made to order supplies and maintain adequate inventory of ingredients. Cost and income analysis can make the difference between success and failure in this competitive industry. Those who desire advancement in this aspect of culinary arts need to improve their math skills. If they do so, rewarding and lucrative careers may be in their future. 2-6 Culinary Math
Materials: Seeing is Believing Equivalencies Goal: Students will be able to see, work with, and recognize differences between units of measurement and their equivalents. A variety of different size containers (pints, quarts, and gallons), measuring cups and spoons, and food scales to measure ounces, pounds, grams, and kilograms Colored liquid such as tea (1-2 gallons) Dry beans, rice, or other dry ingredient to measure Paper and markers (for preparation only) Handout: Standard English and Metric Equivalent Measures and Weights Preparation: 1. Collect measuring instruments needed to make the measurements listed on the handout. Note: If you do not have the instruments to actually allow students to do all of the measurements, make samples of each measurement so students can see exactly how much each measurement is, then adjust the remainder of the activity. 2. Make 1-2 gallons of tea or other colored liquid. 3. Using the handout as a guide, set up several measuring stations around the classroom such as stations to measure ingredients using cups, pints, quarts, milliliters, liters, etc.; a second station to measure ingredients using measuring spoons and grams; a third station that includes measuring spoons and cups; and a fourth station with scales for pounds, ounces, grams, and kilograms. Be sure to include ingredients, liquid and/or dry, for students to measure. Culinary Math 2-7
4. Make a list of the measurements students are to make at each station and tape it to the table or post it on the wall above the table. Be sure it is large enough to be easily read. 5. Make copies of the Standard English and Metric Equivalent Measures and Weights handout for each student. Procedure: 1. Ask students how measurement plays a role in their daily lives. Allow time for students to share their knowledge and experience. 2. Advise students that today s activity is about measurement. Ask students questions such as, How much is a cup? a teaspoon? a quart? a bushel? Then ask about common metric measurements such as a gram, liter, and kilogram. Note: A gram is about the weight of a regular size paper clip and a kilogram is about the weight of a big book or dictionary. 3. Advise students that everyone will have a better understanding of these measurements as well as mental images to take with them. 4. Distribute the Standard English and Metric Equivalent Measures and Weights handout. 5. Allow students to choose a partner. 6. Advise students they are to work with their partner to prove each of the equivalent measures listed at each station using the ingredients, containers, and measuring instruments provided. As they complete each measurement, they should mark it on their handout. You may need to demonstrate how to use some of the instruments, especially the scales. 7. Allow time for students to complete the indicated measurements. Assessment: Observe students as they make the assigned measurements. Allow time for students to reflect on what they learned from this activity. 2-8 Culinary Math
Standard English and Metric Equivalent Measures and Weights 1 pinch = 1/8 teaspoon 1 teaspoon = 5 milliliters 3 teaspoons = 1 tablespoon 1 tablespoon = 15 milliliters 2 tablespoons = 1 ounce 1 ounce = 28 grams 4 tablespoons = ¼ cup 8 tablespoons = ½ cup 12 tablespoons = ¾ cup 16 tablespoons = 1 cup 1 cup = 240 milliliters or 0.24 liters 2 cups = 1 pint 1 pint =.047 liters 4 cups = 1 quart 1 quart = 0.95 liters 16 cups = 1 gallon 2 pints = 1 quart 4 quarts = 1 gallon 5 fifths = 1 gallon 2 quarts = 1 magnum 8 quarts = 1 peck 4 pecks = 1 bushel 8 ounces = 1 fluid cup 16 ounces = 1 pound 1 pound = 454 grams or 0.45 kilograms 1 pound = 1 fluid pint 2 pounds = 1 fluid quart 8 pounds = 1 fluid gallon 12 dozen = 1 gross 32 ounces = 1 quart 64 ounces = ½ gallon 128 ounces = 1 gallon 1 gram = 0.035 ounces 1 kilogram = 2.2 pounds Culinary Math 2-9
2-10 Culinary Math
Materials: Common Abbreviations for Weights and Measures Goal: Students will be able to play games that require the matching of common measurement terms with their abbreviations. Through playing the games, students learn and/or review abbreviations used for measurement. Sets of Measurement Terms and Abbreviations cards Preparation: 1. Review the measurement terms and abbreviations provided on the cards at the end of this activity. You may wish to delete or add cards to the set given. Blank cards are provided. 2. Make a copy of the Measurement Terms and Abbreviations cards on cardstock. Cut the cards apart to make one set. Make enough sets of cards so each group of 2-4 students can have a set. 3. Be sure each card set is thoroughly shuffled. 4. Review the rules given on the following page and decide which game (Matching or Concentration) the students will play. Procedure: 1. Briefly review the measurement terms and abbreviations students will be using to play the game. 2. Explain the rules for the game that the students are to play. 3. Allow students to form groups of 2-4 players. Give each group one set of the Measurement Terms and Abbreviations cards. 4. Allow students to play until all groups finish at least one game. 5. Be sure to collect the cards for future use. Culinary Math 2-11
Assessment: As students play the game, observe their participation and involvement. Extension: Allow students to make different rules for the games. Allow students to make rules for a new game. Rules for Matching Card Game: 1. Tell students that when you say, GO, they are to spread the cards on the table, face up, so that all students can look for matches. 2. Students within each group work together to pair up each term with its correct abbreviation as quickly as possible. When they have finished, they should announce they are done. 3. When a team announces they have finished, all groups stop working while their matches are checked for correctness. If there are errors, all groups continue to play. 4. Repeat until one group has correctly matched all their cards. This team is the winner. Rules for Concentration Card Game: 1. Have one student place the cards face down on the table so the rows and columns of cards make a rectangle. Space should be left between rows and columns so that cards can easily be turned over. 2. Students take turns choosing two cards. For each turn, the student turns two cards face up to see if they match. If the cards match, the student keeps the two cards. If not, the student replaces the cards face down in the same position. 3. Students continue to take turns until all the cards have been matched. 4. The winner is the student with the most pairs. 2-12 Culinary Math
Measurement Terms and Abbreviations tsp (t) teaspoon tbsp (T) tablespoon c cup pt pint Culinary Math 2-13
Measurement Terms and Abbreviations qt quart gal gallon oz ounce lb pound 2-14 Culinary Math
Measurement Terms and Abbreviations bch bunch doz dozen ea each crt crate Culinary Math 2-15
Measurement Terms and Abbreviations meter m decimeter dm centimeter cm millimeter mm 2-16 Culinary Math
Measurement Terms and Abbreviations kilometer km hectometer hm decameter dam cubic centimeter cm 3 Culinary Math 2-17
Measurement Terms and Abbreviations cubic meter m 3 milliliter ml liter l gram g 2-18 Culinary Math
Measurement Terms and Abbreviations kilogram kg degrees Celsius ºC degrees Fahrenheit ºF Culinary Math 2-19
2-20 Culinary Math
Materials: Equivalent Measures and Weights Card Game Goal: Students will be able to play games that require matching equivalencies used in the food service industry. Through playing the games, students learn and/or review the equivalencies. Sets of Equivalent Measurements cards Preparation: 1. Review the equivalent measures and weights provided on the cards at the end of this activity. You may wish to delete or add cards to the set given. Blank cards are provided. 2. Make a copy of the Equivalent Measurements cards on cardstock. Cut the cards apart to make one set. Make enough sets of cards so that each group of 2-4 students can have a set. 3. Be sure each card set is thoroughly shuffled or have students shuffle the cards prior to using them. 4. Review the rules given on the following page and decide which game (Matching or Concentration) the students will play. Procedure: 1. Briefly review the equivalent measures and weights students use to play the game. 2. Explain the rules for the game. 3. Allow students to form groups of 2-4 players. Give each group one set of the Equivalent Measurements cards. 4. Allow students to play until all groups finish at least one game. 5. Be sure to collect the cards for future use. Culinary Math 2-21
Assessment: As students play the game, observe their involvement. Extension: Allow students to make different rules for the games. Allow students to make rules for a new game. Rules for Matching Card Game: 1. Tell students that when you say GO, they are to spread the cards on the table, face up, so that all students can look for matches. 2. Students within each group work together to pair up each equivalent but different measurement as quickly as possible. When they have finished, they should announce they are done. Note: Do not pair cards with same measurements. 3. When a team announces they have finished, all groups stop working while their matches are checked for correctness. If there are errors, all groups continue to play. 4. Repeat until one group has correctly matched all their cards. This group is the winner. Rules for Concentration Card Game: 1. Have one student place the cards face down on the table so that the rows and columns of cards make a rectangle. Space should be left between rows and columns so that cards can easily be turned over. 2. Students take turns choosing two cards. The student turns two cards face up to see if they match. If the cards match (different measurement but equivalent), the student keeps the two cards. If not, the student replaces the cards face down in the same position. 3. Students continue to take turns until all the cards have been matched. 4. The winner is the student with the most equivalent pairs. 2-22 Culinary Math
Equivalent Measurements 1 pinch 1/8 teaspoon (approximately) 3 teaspoons 1 tablespoon 2 tablespoons 1 ounce 4 tablespoons ¼ cup Culinary Math 2-23
Equivalent Measurements 8 tablespoons ½ cup 12 tablespoons ¾ cup 16 tablespoons 1 cup 2 cups 1 pint 2-24 Culinary Math
Equivalent Measurements 4 cups 1 quart 16 cups 1 gallon 2 pints 1 quart 4 quarts 1 gallon Culinary Math 2-25
Equivalent Measurements 5 fifths 1 gallon 2 quarts 1 magnum 8 quarts 1 peck 4 pecks 1 bushel 2-26 Culinary Math
Equivalent Measurements 8 ounces 1 fluid cup 16 ounces 1 pound 1 pound 1 fluid pint 2 pounds 1 fluid quart Culinary Math 2-27
Equivalent Measurements 8 pounds 1 fluid gallon 12 dozen 1 gross 32 ounces 1 quart 64 ounces ½ gallon 2-28 Culinary Math
Equivalent Measurements 128 ounces 1 gallon 1 gram 0.035 ounces 1 kilogram 2.2 pounds 28 grams 1 ounce Culinary Math 2-29
Equivalent Measurements 454 grams or 0.45 kg 1 pound 5 milliliters 1 teaspoon 15 milliliters 1 tablespoon 240 milliliters or 0.24 liters 1 cup 2-30 Culinary Math
Equivalent Measurements.047 liters 1 pint 0.95 liters 1 quart 1 liter 1.06 quarts Culinary Math 2-31
2-32 Culinary Math
Materials: Standard English Equivalent Measures and Weights Goal: Students will be able to read and interpret tables of equivalent measures to solve food service industry related situations involving conversions. Handouts: (1) Standard English Equivalent Measures and Weights (2) Make it Equal Calculators Preparation: 1. Make copies of the handouts for each student. 2. If students have not completed the Seeing is Believing Equivalencies activity earlier in this chapter, obtain measuring containers and samples of the different measurements so that students can see the similarities and differences. Procedure: 1. Give each student a copy of the Standard English Equivalent Measures and Weights handout. 2. Explain the different measurements used on the handout. Demonstrate several equivalent measures if students have not completed the Seeing is Believing Equivalencies activity earlier in this chapter. 3. Discuss the importance of accurate conversions and calculations in the food service industry. Be sure the discussion includes why (1) accurate measurements allow for consistency in food preparation and (2) weight is the most accurate measure for dry ingredients. A cup can hold different amounts based on how packed or loose the item in the cup is, whereas one pound will always be one pound. Culinary Math 2-33
4. Give each student a copy of the Make it Equal handout. Review the concepts of ratio and proportion. Demonstrate several examples and then allow students to work together or independently to solve the remainder of the problems. 5. Allow students to share solutions and discuss areas of difficulty in solving the problems. Assessment: Ask students to write and solve a realistic word problem similar to one of the problems on the handout. Collect, review, and give students feedback. Extension: Use the student-written word problems for practice and review. Invite a guest speaker from a culinary arts program and/or another food service industry employee to visit and share how equivalencies and other math concepts are used in their jobs. Allow time for questions and discussion. Answers for Handout: 1. 1 quart 17. 1 pint 2. 2 quarts 18. 1 quart 3. 4 pounds 19. ½ gallon 4. 4 quarts 20. 2 fluid quarts 5. 2 cups 21. 1 gallon 6. 1 cup 22. 80 quarts 7. 1 pint 23. 8 quarts 8. 1 quart 24. ¼ teaspoon 9. 64 ounces 25. 30 gallons 10. 1 ½ quarts 26. 2 quarts 11. 1 gallon 27. 2 quarts 12. 9 pints 28. 4 pecks 13. 1 tablespoon 29. 3 ½ cups or 1 ¾ pints 14. 3 tablespoons 30. 5 cups or 2 ½ pints 15. 1 cup 31. 6 cups or 3 pints or 1 ½ quarts 16. ½ cup 32. 8 cups or 4 pints or 2 quarts 2-34 Culinary Math
Standard English Equivalent Measures and Weights 1 pinch = 1/8 teaspoon 3 teaspoons = 1 tablespoon 2 tablespoons = 1 ounce 4 tablespoons = ¼ cup 8 tablespoons = ½ cup 12 tablespoons = ¾ cup 16 tablespoons = 1 cup 2 cups = 1 pint 4 cups = 1 quart 16 cups = 1 gallon 2 pints = 1 quart 4 quarts = 1 gallon 5 fifths = 1 gallon 2 quarts = 1 magnum 8 quarts = 1 peck 4 pecks = 1 bushel 8 ounces = 1 fluid cup 16 ounces = 1 pound 1 pound = 1 fluid pint 2 pounds = 1 fluid quart 8 pounds = 1 fluid gallon 12 dozen = 1 gross 32 ounces = 1 quart 64 ounces = ½ gallon 128 ounces = 1 gallon Culinary Math 2-35
Make it Equal 1. 32 ounces = quart(s) 15. 16 tablespoons = cup(s) 2. 64 ounces = quart(s) 16. 8 tablespoons = cup(s) 3. 64 ounces = pound(s) 17. 1 pound = pint(s) 4. 128 ounces = quart(s) 18. 2 pounds = quart(s) 5. 16 ounces = cup(s) 19. 4 pounds = gallon(s) 6. 8 ounces = cup(s) 20. 4 pounds = fluid quart(s) 7. 2 cups = pint(s) 21. 8 pounds = gallon(s) 8. 4 cups = quart(s) 22. 20 gallons = quart(s) 9. 8 cups = ounce(s) 23. 1 peck = quart(s) 10. 6 cups = quart(s) 24. 2 pinches = teaspoon(s) 11. 16 cups = gallon(s) 25. 120 quarts = gallon(s) 12. 18 cups = pint(s) 26. 4 pints = quart(s) 13. 3 teaspoons = tablespoon(s) 27. 1 magnum = quart(s) 14. 9 teaspoons = tablespoon(s) 28. 1 bushel = peck(s) In the food service industry, liquids and solids are often measured by weight. If a scale is not available and a recipe calls for the following, how much liquid measure would you use? 29. 1 ¾ pounds of water 31. 3 pounds of apple juice 30. 2 ½ pounds of 2% milk 32. 4 pounds of skimmed milk 2-36 Culinary Math
Materials: Recipes More or Less Goal: Students will be able to multiply and divide whole numbers and fractions to convert recipes to obtain a specified number of servings. Handouts: (1) Changing Recipes (2) Recipes (3) Standard English Equivalent Measures and Weights from the Standard English Equivalent Measures and Weights lesson (optional) Additional recipes (ask students to bring in recipes or use recipes from books or magazines) Preparation: 1. Review the handouts and decide if you need to provide students with a copy of the Standard English Equivalent Measures and Weights. 2. Make copies of the handout(s), one for each student. 3. Ask each student to bring in a recipe or provide recipes from books or magazines. Procedure: 1. Begin with a discussion about how most of us have learned to follow a recipe at some point and the fact that ingredients have relationships to each other is an important concept in cooking. Most recipes are written to serve a certain number of people. What if you have a recipe that makes 3 dozen cookies and you only want 1 dozen, or maybe you need 6 dozen for the bake sale? Ask students if they have ever doubled or halved a recipe. Allow time for students to share their knowledge and experience. 2. Explain that, in the food service industry, it is often necessary to convert a recipe to make very large batches. For instance, a bakery Culinary Math 2-37
may sell over a hundred pumpkin pies at Thanksgiving. Someone has to determine the amount of ingredients needed to make all those pies while making sure the relationships between all the ingredients stay the same. 3. Tell students that today it is going to be their turn to convert recipes for more or less servings. 4. Distribute the Changing Recipes handout (and the Standard English Equivalent Measures and Weights handout if you decide to use it), one per student. 5. Demonstrate how to find the working factor and convert several ingredients. 6. Allow time for students to complete the handout and ask questions. 7. Examine the answers for the handout. Discuss how hard it would be to get exact measures for some of the ingredients in the Oatmeal Raisin Cookie recipe, i.e. 2/3 egg, 5/12 cup, etc. However, when recipes are given in pounds and ounces, it is much easier to obtain exact measures, which is important for recipe consistency. 8. Distribute the Recipes handout. 9. Let students choose a partner. Explain that they are to work together to: Assessment: a. Copy their recipes onto the blank Recipes handout, being sure to include step-by-step directions. b. Half the recipe. c. Double the recipe. d. Carefully check their work, i.e. copying and math. Allow time for discussion of the math used to complete the task. Ask questions such as, What happens to the denominator of a fraction when you half it? Allow students to self-assess their work through sharing of answers. 2-38 Culinary Math
Extension: Let students publish a recipe book from the recipes they brought in by adding additional recipes. Answers for Handout: Oatmeal Raisin Cookies 3 dozen 1 dozen 10 dozen* granulated sugar 1 cup 1/3 cup 3 1/3 cups shortening ½ cup 1/6 cup or 3 tbsp 1 2/3 cups eggs 2 2/3 egg or 1 6 2/3 eggs or 7 milk ¼ cup 4 teaspoons 5/6 cups flour 1 ½ cups ½ cup 5 cups raisins 1 ¼ cups 5/12 cup 4 1/6 cups oatmeal 1 2/3 cups 5/9 cup 5 5/9 cups salt ½ tsp 1/6 tsp 1 2/3 tsp cinnamon 1 tsp 1/3 tsp 3 1/3 tsp baking soda 1 tsp 1/3 tsp 3 1/3 tsp Soft Dinner Rolls 4 dozen 1 ½ dozen 6 dozen granulated sugar 5 oz 1 7/8 oz 7 ½ oz shortening 5 oz 1 7/8 oz 7 ½ oz salt ½ oz 3/16 oz ¾ oz dry milk 1 ½ oz 9/16 oz 2 ¼ oz eggs 2 oz ¾ oz 3 oz flour 2 lbs ¾ lb or 9 oz 3 lbs water 1 lb 3/8 lb or 6 oz 1 ½ lbs yeast 2 ½ oz 15/16 oz 3 ¾ oz 9 Lemon Pies 4 Pies 1 Pie 15 Pies granulated sugar 1 lb 12 oz 7 oz 6 lbs 9 oz butter 2 oz ½ oz 7 ½ oz salt ¼ oz 1/16 oz 15/16 oz lemon juice 9 oz 2 ¼ oz 33 ¾ oz or 2 lbs 1 ¾ oz egg yolks 6 oz 1 ½ oz 22.5 oz or 1 lb 6 ½ oz corn starch 4 oz 1 oz 15 oz water 2 lbs ½ lb or 8 oz 7 ½ lbs grated lemon peel 1 ½ oz 3/8 oz 5 5/8 oz Culinary Math 2-39
Changing Recipes In the food service industry, recipes often need to be converted to feed a specific number of people. One way to do this is to find a working factor which is used to find the new amount of each ingredient. Steps to changing the portion size of recipes: 1. Find a working factor: working factor = new yield old yield. 2. Multiply each ingredient by the working factor to find the amount of each ingredient needed for the indicated portions. Determine the amount of each ingredient needed to prepare the indicated portions. Oatmeal Raisin Cookies Ingredient 3 dozen 1 dozen 10 dozen* granulated sugar shortening 1 cup ½ cup eggs 2 milk flour raisins oatmeal salt cinnamon ¼ cup 1 ½ cups 1 ¼ cups 1 2/3 cups ½ tsp 1 tsp baking soda 1 tsp *Even though you probably would not mix 10 dozen at one time, you may want to know how much of each ingredient to purchase to make 10 dozen for a bake sale or to sell at a bakery. 2-40 Culinary Math
Changing Recipes, continued Ingredients for recipes used in the food service industry are often given by weight. Soft Dinner Rolls Ingredient 4 dozen 1 ½ dozen 6 dozen granulated sugar 5 oz shortening salt dry milk eggs flour water yeast 5 oz ½ oz 1 ½ oz 2 oz 2 lbs 1 lb 2 ½ oz 9 Lemon Pies Ingredient 4 Pies 1 Pie 15 Pies granulated sugar 1 lb 12 oz butter salt lemon juice egg yolks cornstarch water grated lemon peel 2 oz ¼ oz 9 oz 6 oz 4 oz 2 lbs 1 ½ oz Culinary Math 2-41
Recipes Title: Ingredient Serves Serves Serves Preparation and cooking directions: Use back if additional space is needed. 2-42 Culinary Math
Materials: Finding Recipe Yields Goal: Handout: What is the Yield? Calculators Preparation: Students will be able to add, multiply, and divide to find the number of servings for a given recipe by finding the total weight or measurement of the ingredients, converting the total to the desired units, and dividing by a portion size to find the recipe yield. 1. Review the handout to determine if you want to add additional practice problems or recipes. 2. Make copies of the handout, one for each student. Procedure: 1. Explain the definition of yield. Yield is the amount of portions, servings, or units a particular recipe will produce. Explain that most recipes give an approximate yield. However, in the food service industry, the serving may be larger or smaller, thus requiring the chef or business owner to determine a new yield. 2. Ask students if they have ever developed a new recipe. If so, how did they determine the yield? Explain that finding the yield for recipes is important in the food service industry. The business owner uses the yield to determine how much must be charged for each individual serving. 3. Advise students they will be finding the yield for several recipes. Explain that recipes may be written in two different ways, i.e., using either measurements or weights for ingredients. To find the yield, the total weight or measurement of all the ingredients must be Culinary Math 2-43
determined and converted to the same units as the portion size, and then divided by the desired portion size. 4. To find the yield, students must be able to easily convert from pounds to ounces and from quarts, pints, teaspoons, and tablespoons to cups. Review these equivalencies and conversions. Remind students that only like ingredients can be added. 5. Distribute the What is the Yield? handout and calculators. 6. Demonstrate how to find the yield of the first recipe on the handout. The serving size and ingredients are given in weight. To find the yield: a. Find the total weight for all the ingredients. b. Convert total weight to ounces. c. Divide the total weight (ounces) by the serving portion weight. d. The result is the yield or number of portions. 7. Demonstrate how to find the yield of the second recipe on the handout. The serving size and ingredients are given in measurement. To find the yield: a. Find the total measurement for all the ingredients. b. Convert total measurement to cups. c. Divide the total measurement by the serving portion measurement. d. The result is the yield or number of portions. 8. Allow students to find the yield of the other recipes given on the handout. Assessment: As students complete the handout, check their work to see if they found the correct yields. If not, allow time for students to work with peers to find errors. 2-44 Culinary Math
Extension: Allow students to find additional recipes on the Internet where ingredients are given in weight so they can find the yield. Allow students to make a recipe that a bakery might use by converting a traditional recipe into weights and then doubling or tripling the ingredients. Students could exchange recipes to determine yields. Answers for Handouts: 1. 165 dinner rolls 2. 42 servings of fruit salad 3. 14 coffee cakes 4. 20 servings of cheese vegetable spread/dip Culinary Math 2-45
What is the Yield? 1. How many 1½ oz dinner rolls can be made from the recipe below? 1 lb 4 oz 1 lb 4 oz 2 oz 6 oz 6 oz 7 lbs 8 oz 4 lbs 10 oz Dinner Rolls granulated sugar shortening salt dry milk whole eggs flour water yeast 2. How many ½ cup servings can be made from the recipe below? 2 quarts 1 pint 1 pint 1 cup 3 cups 1 cup 1 quart Fruit Salad cranberries, chopped apples, chopped oranges, chopped pineapple, chopped sugar lemon flavored gelatin hot water 2-46 Culinary Math
What is the Yield?, continued 3. How many 12 oz coffee cakes can be made from the recipe below? 1 lb 1 lb 1 oz 3 lbs 1½ lb 12 oz 4 oz 2 lbs 8 oz 1 lb ¼ oz 1 oz Coffee Cakes granulated sugar shortening salt bread flour pastry flour whole milk dry milk water yeast chopped pecans mace vanilla 4. How many ¼ cup servings can be made from the recipe below? Cheese Vegetable Spread/Dip 2 cups cream cheese 1 cup blue cheese 4 T green pepper, minced 8 T onion, minced 8 T celery, minced 4 T pimiento, chopped 2 t hot sauce 2 t worcestershire sauce ½ cup mayonnaise Culinary Math 2-47
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Materials: Metric Measurements in Recipes Goal: Students will be able to convert recipes from the metric system to the U.S. customary system and from the U.S. customary system to the metric system when given a table of equivalents. Handouts: (1) Weights and Measures: U.S. Customary and Metric System Equivalents (2) Metric and U.S. Customary Recipes (3) Our Favorite Recipes Recipes Calculators Preparation: 1. Ask students to bring in a copy of their favorite recipes. You may want to collect these before you actually plan to use them to be sure you have an ample supply. If not, add some of your favorites. 2. Decide if students will need a review of common abbreviations used for measurements. If so, consider having them play the games from the Common Abbreviations for Weights and Measures lesson, or at least review the abbreviations prior to completing this lesson. 3. Make copies of the handouts, one for each student. Procedure: 1. Discuss how the United States uses one system of measurement while most of the rest of the world uses the metric system. 2. Distribute and explain the Weights and Measures: U.S. Customary and Metric System Equivalents handout. Distribute calculators. Demonstrate how to complete several of the conversion problems using ratios and proportions, and then allow students to complete the handout. Culinary Math 2-49