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Math-Related Credit Crosswalk for Career Technical Education Classes in Macomb County Program Information District: Warren woods Tower Program Name: Cosmetology CIP Code Number: 12.0403 Career Pathway: Human Services Instructor Name: Carroll, Daniels, Davis, Sutton, Johnson, Hofinger, Here, Fanson Date: 12/11/08 Strand STANDARDS CTE APPLICATION and PRACTICE L1 REASONING ABOUT NUMBERS, SYSTEMS AND QUANTITATIVE LITERACY L1.1 Number Systems and Number Sense L1.1.1 Know the different properties that hold in Purchasing products into negative/ making money different number systems and recognize back after service/ color formulations/estimating the that the applicable properties change in the desired length in haircutting by adding or subtracting transition from the positive integers to all whole numbers or fractions/ salon management integers, to the rational numbers, and to the business plan/ 3/4 to ¼ equals h202/ supplies and real numbers. start-up costs for a junior for semester/ mixing color L1.1.2 Explain why the multiplicative inverse of a Expenses and start-up costs/ profit and loss number has the same sign as the number, margins/using peroxide in ratio to color/ developer while the additive inverse has the opposite uses 2:1 and 1:2/ equal parts or ratios when sign. mixing/1/2 x 2/1 equals 1, positive and negative L1.1.3 Explain how the properties of associativity, Moving the numbers to regroup them/ Example: add commutativity, and distributivity, as well as sales tax individually or to whole order/ sectioning a identity and inverse elements, are used in haircut one way, but someone else sections arithmetic and algebraic calculations. differently for the same end result to a cut or style L1.1.4 Describe the reasons for the different In a salon, add up your sales and subtract booth rent, effects of multiplication by, or supplies to get profit/ sales averages/ tactics on exponentiation of, a positive number by a keeping track of overall profits number less than 0, a number between 0 and 1, and a number greater than 1. L1.2 Representations and Relationships L1.2.1 Use mathematical symbols (e.g., interval Percentages in color, such as percentage of grey/ notation, set notation, summation notation) calculate commission/ sales commission/ percentage to represent quantitative relationships and for salon/ hair color coverage situations. L1.2.2 Interpret representations that reflect Haircuts: angles and degrees have a margin of error absolute value relationships (e.g.,│x-a│< b, tolerance/ color formulations have + or – tolerance C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 1 07/27/2011 or a± b) in such contexts as error tolerance. due to manufacturers‟ formulas L1.2.3 Use vectors to represent quantities that Used in haircutting/ diagonal forward and diagonal have magnitude and direction, interpret back haircuts/ blunt or line cuts use angles/ direction and magnitude of a vector numerically, and calculate the sum and difference of two vectors. L1.2.4 Organize and summarize a data set in a Color chart/ salon management lessons/mixing table, plot, chart, or spreadsheet; find colors/ asymmetrical designs/service sales graphing/ patterns in a display of data; understand spreadsheet for sales and business plan and critique data displays in the media. L1.3 Counting and Probabilistic Reasoning L1.3.2 Define and interpret commonly used Fashion trends set by people of influence setting expressions of probability (e.g., chances of industry standards/ trendy styles from MTV affect an event, likelihood, odds). probability of customers wanting same look/ Example: What are the chances that celebrity fashion statements will be requested in salons after being seen in public? L1.3.3 Recognize and explain common probability The probability that putting bleach on brown hair and misconceptions such as “hot streaks” and it turning green is 100%/ Everyone wants Britney‟s “being due.” French manicure/ salon costs have to go down „cause we‟re due for a break Multiply and Divide Fractions N.MR.06.01 Understand division of fractions as the Instead of dividing by 2, you multiply by ½ to get inverse of multiplication. specific color N.FL.06.02 Given an applied situation involving dividing Dividing customers when someone is on vacation or fractions, write a mathematical statement to ill for the day represent the situation. N.MR.06.03 Solve for the unknown. Timesheet to total hours for the week/ sales figures for profit/ 2 oz. + 2 oz = X. What is X? Add client tickets and check spreadsheet for accuracy N.FL.06.04 Multiply and divide any two fractions, How much work have you done by noon? ½ or ¾ of including mixed numbers, fluently. your clients? Practice profit spreadsheet estimation Represent Rational Numbers as Fractions or Decimals N.ME.06.05 Order rational numbers and place them on Cash register, measure color, salon management/ the number line. sales for last year vs. this year/ Making a timeline of historical dates in cosmetology/ cutting using the comb on the scalp and measuring where to cut at what number N.ME.06.06 Represent rational numbers as fractions or Estimate hours in program for licensure 3.5 equals ½ terminating decimals when possible and day/ making correct change/ cash register translate between these representations. reconciliation N.ME.06.07 Understand that a fraction or a negative Using whole numbers. fraction is a quotient of two integers. Add and Subtract Integers and Rational Numbers N.ME.06.08 Understand integer subtraction as the Purchasing retail versus selling it. Purchasing inverse of integer addition. Understand products to us (color) then gaining the money back integer division as the inverse of integer when service is performed. We sold it for $4.00, but it multiplication. cost. . . Salon retail sales the money you get it wholesale. How much money are you making? N.FL.06.09 Add and multiply integers between -10 and Hours and points rubric. Cutting lines or degrees 10; subtract and divide integers using the relating to elevation. Now they can do it. In salon related facts. Use the number line and chip business, students must develop a business plan models for addition and subtraction. showing costs and estimate profits. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 2 07/27/2011 N.FL.06.10 Add, subtract, multiply and divide positive Point reduction. Hours and point rubric. Practice and rational numbers fluently. repetitiveness of buying retail and selling retail. Business plan project. More students accommodating more customers, need more stations. Have them practice this like a project the salon project. Hours and points rubric. Find Equivalent Ratios N.ME.06.11 Find equivalent ratios by scaling up or Building clientele-salon mgmt chapter. If we get more scaling down. clients in here we will need more chairs and stations. How many clients or services can they handle in a 7 hour day? How much money could they make? Solve Decimal, Percentage and Rational Number Problems N.FL.06.12 Calculate part of a number given the Chemistry/elect., sales. Sales and percentages for percentage and the number. the stylist, 65 percent and 35 for salon owner. Calculate the numbers from each board and report numbers from month to month. N.MR.06.13 Solve contextual problems involving Salon mgmt chapter. State and Federal taxes. percentages such as sales taxes and tips. Applied during teaching about working in booth rent versus commission salons. Showing the student a tax form and How to use it if you are self-employed. Percentages, taxes, and tips you received--you need to claim that on the tax form. N.FL.06.14 For applied situations, estimate the answers Salon mgmt (estimation). Estimating hours and to calculations involving operations with sales. rational numbers N.FL.06.15 Solve applied problems that use the four Money. Great for multiplying and subtracting money operations with appropriate decimal for services. numbers. Understand Rational Numbers and Their Location on the Number Line N.ME.06.17 Locate negative rational numbers (including Start up cost in new business, will not see much integers) on the number line. Know that profit in the first few years of business, normally you numbers and their negatives add to 0 and will break even. A non-profit organization has to be a are on opposite sides and at equal distance zero when you add it together it is zero-will you break from 0 on a number line. even? If a hairdresser is a renter, how much money would they have to make per day to break even? N.ME.06.18 Understand that rational numbers are Fractions-color mixing and formulation. Mixing quotients of integers (non zero chemicals in hair color, mixing 9 parts of this and 3 denominators). parts = formulation. Mixing color formulations and mixing directions. Ratios 2:1 Increasing the equation for mixing additional color. Mixing color formulations and mixing directions. Ratios 2:1. Increasing the equation for mixing more color. Remember rational numbers are fractions. Mixing 3rb 10oz will be the same as using 3rb in a different--like boreal, but doubling the peroxide. When mixing color, if you need more products, how do you increase the amount of color and keep the same ratio? N.ME.06.19 Understand that 0 is an integer that is Remember that zero is a whole number. Using the neither negative nor positive. PH scale to show high acidity, or alkalinity. N.ME.06.20 Know that the absolute value of a number is Ph scale. Acids and Alkaline. Value means 3 spaces the value of the number ignoring the sign; or away from zero or minus 3 are 3 spaces away the is the distance of the number from 0. other way. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 3 07/27/2011 Understand Derived Quantities N.MR.07.02 Solve problems involving derived quantities Point system, the work performed is worth “x” such as density, velocity and weighted amount of points = grade. Syllabus. Explaining the averages. value and weighted averages of projects through the year that are given to the students. What percent of their grade each one is. Understand and Solve Problems Involving Rates, Ratios, and Proportions N.FL.07.03 Calculate rates of change including speed. Color volume and educating them on how fast volume reacts to certain hair types. Differences in hydrogen peroxide levels. 10 volume = 1 level lift, 20 = 2 levels, 30 = 3 levels, 40 = 4 levels. Hair growth changes summer vs. winter. How hot/cold affect color development. Using 40 volume using how fast it will come up with bleach comparing to use a 20- volume h202, it will have a lower speed. Summer hair grows faster in summer than the winter. Using a higher volume of peroxide will increase the speed of lift in hair color, how the level of porosity effects the processing of a perm. N.MR.07.04 Convert ratio quantities between different Converting customers per hour to customer per systems of units, such as feet per second to week, steadily building clientele. How many miles per hour. customers in an allotted amount of time? I can use the hair dryer to get the bleach up faster. How many customers in the allotted time? Figuring out how many clients you can take in one hour or per day. N.FL.07.05 Solve proportion problems using such Scaling customer down to decrease days of work methods as unit rate, scaling, finding and produce more hours in your day and make the equivalent fractions, and solving the same pay. Facial proportions in choosing make-up proportion equation a/b = c/d; know how to applications and hairstyles suitable for the client. see patterns about proportional situations in Extensions. Purchase by the track. Face portions in tables. teacher make-up and facial shapes. Using proportions in facial shapes 1/3, 1/3 and 1/3. Also, when doing hair extensions, we charge by the track. Recognize Irrational Numbers N.MR.07.06 Understand the concept of square root and Extensions add up the amount of tracks being used cube root and estimate using calculators. for clients. In formulations on the scalp on the whole using the area of the scalp as square feet and then figuring out how much that would cost. Compute with Rational Numbers N.FL.07.07 Solve problems involving operations with Very broad, covers everything. Clientele was 5 on integers. Tues and 8 on Wed. Clientele is building. Using whole numbers in sales, formula equations, hours, haircutting, etc. Today we had 4 customers yesterday we have 3, what is the difference, hours also. Figuring student hours. th N.FL.07.08 Add, subtract, multiply and divide positive Same as 6 grade strand just more involved. Building and negative rational numbers fluently. our program by adding so many more students this year, and adding another 40 students next year. Entire Cos. Curriculum. Program expansion computing. Refer back to same question in N.MR06. Entire cos. Curriculum refer back to previous question. Point‟s rubric, student hours, mixing hair color. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 4 07/27/2011 N.FL.07.09 Estimate results of computations with Desk person-amount of clients per students, and rational numbers. salon mgmt chapter. Entire. Estimate how many teachers we would need per every 20 students, in cosmetology law. Understand Real Number Concepts N.ME.08.02 Understand meanings for zero and negative Zero points this month will affect your grade in what integer exponents. way? N.ME.08.03 Understand that in decimal form, rational Calculator at desk rounded the number for the rd numbers either terminate or eventually student. No numbers in the 3 power. repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals. Solve Problems N.MR.08.07 Understand percent increase and percent Salon mgmt, retail sales. Christmas sales and we decrease in both sum and product form. discount product at a percentage. What we the mark-up? Sales comparisons between years. Percentage of sales increase or decrease. Retail mark-up, 100%. Percentage off sales. If a client was to get 20% off services before noon, how much would they save on a $50 perm? N.MR.08.08 Solve problems involving percent increases Salon mgmt, retail sales. We want to raise prices due and decreases. the cost of gas increase. Sales decrease on old retail, increase new product percentages. Students solve problems on this type of action in the salon. Our sale this 20% lower for Christmas sales. N.FL.08.09 Solve problems involving compounded Story problems. Distinguish the discount off the interest or multiple discounts. original price, of sale‟s price. Additional percentage off of products already marked down a certain percentage. Give them example of story problems to solve. An additional percentage off products of ex. 50% then 15% off that price is not 65% off that price. Teaching students to figure a 25% savings on service and a 5% off products. N.MR.08.10 Calculate weighted averages such as Calculate and average out all practical work done in course grades, consumer price indices and the semester and grade on a curve. When our costs sports ratings. go up, how do we pass that onto our clients without pricing ourselves out of the market? N.FL.08.11 Solve problems involving ratio units, such Square footage per student/client. So many students as miles per hour, dollars per pound or per licensed instructor. Square footage per student persons per square mile. and per customer. Michigan State Law. Rules and regulations and public how much square foot does the student need look up other square feet in the Cos. Book. L2 STANDARDS CTE APPLICATION and PRACTICE CALCULATION, ALGORITHMS, AND ESTIMATION L2.1 Calculation Using Real and Complex Numbers L2.1.1 Explain the meaning and uses of weighted Product cost is up, increase in cost. Grades, finals averages (e.g., GNP, consumer price index, are worth more than regular tests. grade point average). L2.1.6 Recognize when exact answers aren‟t Estimations. Ex. Wait time. Estimate how many always possible or practical. Use students will pass state board exams. Estimate wait C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 5 07/27/2011 appropriate algorithms to approximate time for a client. Senior graduate tracking grid. solutions to equations (e.g., to approximate Estimates of licensure. Senior tracking grit how many square roots). students are going up to state board? How many are passing the practical and the written portion of the state board test. When using a tracking grid, how many students who took the state board exam, will become employed in a salon? L2.2 Sequences and Iteration L2.2.1 Find the nth term in arithmetic, geometric, or Salon mgmt. other simple sequences. L2.2.2 Compute sums of finite arithmetic and Figuring pay scales and gross and net income. How geometric sequences. much percentage 50% vs. an hourly rate. In figuring commission, if they make 50% commission, how much is their gross pay in one week? L2.2.3 Use iterative processes in such examples Salon mgmt. Measuring in ounces and changing into as computing compound interest or quarts. One measurement ounces to cc‟s on the applying approximation procedures. measuring becker plastic. L3 STANDARDS CTE APPLICATION and PRACTICE MEASUREMENT AND PRECISION L3.1 Measurement Units, Calculations, and Scales L3.1.1 Convert units of measurement within and Ex. Conversions. Changing ounces to cc‟s. Changing between systems; explain how arithmetic measurements of liquid. Ounces to cc‟s. ex. operations on measurements affect units, Developer. In converting ounces to cc‟s when mixing and carry units through calculations hair color. correctly. L3.1.2 Describe and interpret logarithmic Chemistry, chemical relaxers, ex. 10 fold change in relationships in such contexts as the Richter pH scale. Acid vs. alkaline, Chemistry 10 fold. PH scale, the pH scale, or decibel Scale. Acid vs. Alkaline. Each level change is ten measurements (e.g., explain why a small fold. P.H. Scale acid to alk on the ph scale is 10 change in the scale can represent a large times the power. Ten fold with the use of litmus change in intensity). Solve applied paper. When teaching the ph scale, it increases by problems. the power of 10. L3.2 Understanding Error L3.2.1 Determine what degree of accuracy is Salon mgmt-minutes vs. seconds. What is reasonable for measurements in a given acceptable if we have to supplement a color and use situation; express accuracy through use of another formula? How much we are entitled to be significant digits, error tolerance, or percent off. of error; describe how errors in Mixing color must be accurate. No error tolerance. measurements are magnified by Haircutting must be accurate. If client requests 11/2 computation; recognize accumulated error inch off and the stylists rounds up to 2”, the outcome in applied situations. of the haircut is compromised. Error measurement for mixing tint does it have to be right on? Can you be off a little bit? Can you round off that number? When mixing hair color, students must be very accurate. If a client asks for 1 inch off in a haircut and the student removes 1.5 or 2 inches, the client may be very unhappy with the haircut. L3.2.2 Describe and explain round-off error, Yes, will it make a difference in the hair color? The rounding, and truncating. amount of inches you are taking off the hair-1 inch vs. 4 inches --the client might have a problem with that. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 6 07/27/2011 L3.2.3 Know the meaning of and interpret Create a t-shirt to advertise blondes have more fun statistical significance, margin of error, and than brunettes. Is it significant that airfare is cheaper confidence level. through the week than the weekend? Statistics say that blondes have more hairs per square inch than brunettes. State board passing rate is dependant on the statistic that those who study pass vs. those who do not. Static lies if we count on averages are fine. N/A statically saying blondes have more hair square foot approx 140,000 compared to red heads having 90,000. Students that study everyday statically will pass the tests written than whose who do not study at all. Statically speaking, blonds have more hair per square inch, than brunettes. L4.1 Mathematical Reasoning L4.1.1 Distinguish between inductive and Client consultation for hair color. Examples of why deductive reasoning, identifying and the results of a haircut were good. And why following providing examples of each. a guideline helps keep a haircut balanced. State Board inspections require the salon/school to maintain a clean environment thus if we all perform certain cleaning tasks, we will pass all future inspections and evade fines. A 100 survey results were good because we provided a good service. What does good service mean to you? Being on time taking your customers on time: A color consultation and what were the results of the color put this under comments on the client card. Is it significant that students who study consistently pass the state board at a significantly higher rate? L4.1.2 Differentiate between statistical arguments It seems that blondes have more fun than brunettes, (statements verified empirically using but statistics show that brunettes are the chosen examples or data) and logical arguments ones. This color would work for you or there is a based on the rules of logic. machine and it takes your picture and of your skin and figures the color for the hair with using the machine and not the colorist education. L4.1.3 Define and explain the roles of axioms Logical if we work harder, we can get more (postulates), definitions, theorems, customers to come in here. How do we do this if you counterexamples, and proofs in the logical bring some students in the high school in and other structure of mathematics. Identify and give students see what a good job you do good hard work examples of each. goes a long way. L4.2 Language and Laws of Logic L4.2.1 Know and use the terms of basic logic (e.g., If you use get all your hours in you can take the state proposition, negation, truth and falsity, board test. If we consistently keep our school clean implication, if and only if, contra positive, and neat, we won‟t have to worry when the state and converse). board shows up for an inspection. L4.2.2 Use the connectives “not,” “and,” “or,” and Reinforces the above. If you come to class everyday “if…, then,” in mathematical and everyday and produce work, you will graduate. If hours can settings. Know the truth table of each academic requirements are completed, you will then connective and how to logically negate graduate and get a license. If you complete your statements involving these connectives. 1500 hours by the end of the course, then you will be able to take your state board exam. L4.2.4 Write the converse, inverse, and contra If you don‟t have visual aids, student‟s engagement positive of an “If…, then…” statement. Use will not be successful. If you do hands on with the fact, in mathematical and everyday smokey eyes with other students instead of a settings, that the contra positive is logically mannequin, the student will be more productive. If we equivalent to the original while the inverse don‟t have consistent discipline, then students will and converse are not. continue to misbehave in the classroom. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 7 07/27/2011 L4.3 Proof L4.3.1 Know the basic structure for the proof of an If you take good notes then you will do well on the “If…, then…” statement (assuming the test. If there is not prior discipline installed, then we hypothesis and ending with the conclusion) will continue to have disciplinary problems within the and that proving the contra positive is program. Discipline equivalent. L4.3.2 Construct proofs by contradiction. Use This color is pretty. counter examples, when appropriate, to disprove a statement. L4.3.3 Explain the difference between a necessary Meaning: this is what I really want but I will settle for and a sufficient condition within the this. I would like to buy bulks of pre-glued extension statement of a theorem. Determine the hair for extension demo, but I will settle for used hair correct conclusions based on interpreting a to make our own extension pieces. theorem in which necessary or sufficient conditions in the theorem or hypotheses are satisfied. Convert within Measurement Systems M.UN.06.01 Convert between basic units of N/A. Converting gallons of shampoo into ounces and measurement within a single measurement diluting for extended use. Changing ounces to cc‟s. system. Repeat? Changing ounces to cc‟s. Find Volume and Surface Area M.PS.06.02 Draw patterns (of faces) for a cube and Four part chemical services.m4-part chemical rectangular prism that when cut, will cover service partings. 9-part perm sectioning. The make- the solid exactly (nets). up prism looks Pamela. Gauge for a facial wax cut the muskin for underneath the eyebrow you take this poster and fold it in four part chemical services. Sectioning a head for a four part chemical service procedure. A1 STANDARDS CTE APPLICATION and PRACTICE EXPRESSIONS, EQUATIONS, AND INEQUALITIES A1.1 Construction, Interpretation, and Manipulation of Expressions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric) A1.1.1 Give a verbal description of an expression The verbal expression would be everything that is that is presented in symbolic form, write an added up in the products list of all the items in the algebraic expression from a verbal stock room total number would be “x " for c.i.p. description, and evaluate expressions given review. values of the variables. A1.1.2 Know the definitions and properties of Length time and width how much square feet does exponents and roots and apply them in the state or c.i.p. require? This will help the square algebraic expressions. feet. A1.2 Solutions of Equations and Inequalities (linear, exponential, logarithmic, quadratic, power, polynomial, and rational) A1.2.1 Write and solve equations and inequalities Used in profit and loss equations. Cost vs. sales. See with one or two variables to represent A.1.1. Used in profit and loss equations. H mathematical or applied situations. A1.2.7 Solve exponential and logarithmic equations How many hours per day, then per week, then per x (e.g., 3(2 ) = 24), 2 ln(x + 1) = 4), and justify month? steps in the solution. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 8 07/27/2011 A1.2.9 Know common formulas (e.g., slope, Calculating hours per week, or commissions that distance between two points, quadratic they will be paid. Commission percentages in sales. formula, compound interest, distance = rate · time), and apply appropriately in contextual situations. A2 STANDARDS CTE APPLICATION and PRACTICE FUNCTIONS A2.4 Lines and Linear Functions A2.4.2 Graph lines (including those of the form x = Color graphs and the conversion charts for h and y = k) given appropriate information. formulating colors. Graph tonality of a color. Use color chart and conversion charts. Graph product use from the time they learn about professional products until the end of class. Conversion chart. Graphing profits and losses. Sales and cost. Color equations graphing. Graphs. How much money this month compared to that month? Is the client‟s floor getting busier? Two parts a chart to 4 parts conversion chart. Color graphs and conversion charts for formulating color. A3 STANDARDS CTE APPLICATION and PRACTICE MATHEMATICAL MODELING A3.1 Models of Real-world Situations Using Families of Functions Example: An initial population of 300 people grows at 2% per year. What will the population be in 10 years? A3.1.1 Identify the family of functions best suited Different speed on the blow dryers for optimum for modeling a given real-world situation usage. [e.g., quadratic functions for motion of an object under the force of gravity or exponential functions for compound interest. In the example above, recognize that the appropriate general function is t exponential (P = P0a )]. Calculate Rates - Algebra A.PA.06.01 Solve applied problems involving rates, Volume of peroxides with the different rates of color including speed. development or speed. Volume of peroxides develops at different rates or speed. The learner would learn this concept to learn wattage and speed on blow dryers. Volumes of peroxide will develop at a different rate, or speed. Use Variables, Write Expressions and Equations, and Combine Like Terms A.FO.06.03 Use letters with units, to represent Peroxide volumes. 20-40 developing at higher and quantities in a variety of contexts. lower rates. A.FO.06.04 Distinguish between an algebraic Color formulation and calculation of hours. The expression and an equation. learner would use color formulation and hour‟s calculation to learn this concept. Color formulation and hours calculated. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 9 07/27/2011 A.FO.06.06 Represent information given in words using Give them a real world color formulation to correct algebraic expressions and equations. the color problem. Used in the formulation of commissions of formulating color. The teacher would give them a color correction example and have them write out the formulation for the color. A story problem using algebra and show me your work. Translate English into math. Used in the formulation of commissions, or formulating color. Give them color correction formulas. A.FO.06.07 Simplify expressions of the first degree by You are running a fund raiser-a book of tickets you combining like terms and evaluate using need to sell. How many books did you sell? How specific values. many tickets did you want to sell? Tickets--not books x and y. Our budget in your class figure out how much product we are using that month. Represent Linear Functions Using Tables, Equations, and Graphs A.RP.06.08 Understand that relationships between Time line. quantities can be suggested by graphs and tables. A.RP.06.10 Represent simple relationships between Get some numbers from story problem to graph. quantities using verbal descriptions, formulas or equations, tables and graphs. Solve Equations A.FO.06.11 Relate simple linear equations with integer Sales of service minus the till money at the end of coefficients. the day. And the completion of the deposit forms. Sales, minus till money equals profit. By complete a deposit form. Sales minus the till money equals our profit by completing a deposit form. A.FO.06.12 Understand that adding or subtracting the To get an exact color formulation we would use this same number to both sides of an equation concept. The learner will use this concept to get an creates a new equation that has the same exact color formulation--we would use this concept. solution. To get an exact color formulation, we would use this concept. A.FO.06.13 Understand that multiplying or dividing both Product mark up from cost to retail percentage. The sides of an equation by the same non-zero learner would use this concept to learn product mark- number creates a new equation that has the up from cost to retail percentage. same solutions. Understand and Represent Linear Functions A.PA.07.06 Calculate the slope from the graph of a The slope of the graph. A little more profit by the linear function as the ratio of “rise/run” for a slope of the graph. Your wealth will increase. pair of points on the graph and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change. Understand and Solve Problems about Inversely Proportional Relationships A.PA.07.09 Recognize inversely proportional High end salons versus medium priced salons. And relationships in contextual situations; know how the price ranges go up and down. Salon that quantities are inversely proportional if Management chapter requires students to factor their product is constant. raising the price of a service or product and relating the inverse proportion to the increase or decrease of clientele. In sales, if price goes down--do sales go up? The learner will use word problems to teach this concept. The difference in price between a high-end C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 10 07/27/2011 and low-end salon. Price concepts. Salon Management chapter Service prices resemble area in which you work. Such as students in higher priced cities can charge more for services than in a smaller, lower priced area. Something is going up while something is going down. Maybe by lowering the price, we will get more customer supply and demand. If the price of services goes down, will the client base rise? If the cost of products is reduced, will we be selling more products? A.RP.07.10 Know that the graph of y = k/x is not a line, Add up all the items and multiply by 6 percent or add know its shape and know that it crosses up all the items separate and the results will be the neither the x nor the y-axis. same. Just like a one to one ratio -- is the same as a two to two ratio? Apply Basic Properties of Real Numbers in Algebraic Contexts A.PA.07.11 Understand and use basic properties of real Students will understand the sales and the taxes and numbers: additive and multiplicative how to apply it to the salon retails. They will also identities, additive and multiplicative learn how to apply it to their commissions and hourly inverses commutativity, associativity, and pay. How to calculate their taxes. the distributive property of multiplication over addition. Combine Algebraic Expressions and Solve Equations A.FO.07.12 Add, subtract and multiply simple algebraic Students will add sales tax at the end or for each expressions of the first degree. item purchased. Both methods should be the same. G1 STANDARDS CTE APPLICATION and PRACTICE FIGURES AND THEIR PROPERTIES G1.1 Lines and Angles; Basic Euclidean and Coordinate Geometry G1.1.1 Solve multi-step problems and construct We use angles in hair cutting. Roller sets. Curling proofs involving vertical angles, linear pairs iron placements, facials for proper hand placements. of angles, supplementary angles, The learner would use angles to demonstrate a complementary angles, and right angles. proper hair cut. Also to teach roller placement and perming-rod placement. Using the protractor. We use angles in haircutting, roller sets and curling iron placement. G1.1.2 Solve multi-step problems and construct Using the circumference of the head design, a proofs involving corresponding angles, haircut with the required angles. Using the protractor alternate interior angles, alternate exterior will use angle a 45 degree angle and 180 degree angles, and same-side (consecutive) angle using the perimeter of the hairline. Using the interior angles. circumference of the head, design a haircut using required angles. G1.1.4 Given a line and a point, construct a line Dealing with two different triangles. through the point that is parallel to the original line using straightedge and compass. Given a line and a point, construct a line through the point that is perpendicular to the original line. Justify the steps of the constructions. G1.2 Triangles and Their Properties G1.2.2 Construct and justify arguments and solve Using the angles of the cuts and the circumference of multi-step problems involving angle the head in designing hair cuts. The learner would C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 11 07/27/2011 measure, side length, perimeter, and area learn this concept to design a 45*, 90* or 180* of all types of triangles. haircut. G1.2.5 Solve multi-step problems and construct Salon design project. proofs about the properties of medians, altitudes, and perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle. Using a straightedge and compass, construct these lines. G1.4 Quadrilaterals and Their Properties G1.4.1 Solve multi-step problems and construct Design a floor plan in a beauty salon. The students proofs involving angle measure, side length, are required to design it to scale. Salon Business diagonal length, perimeter, and area of project requires students to draw and build a scale squares, rectangles, parallelograms, kites, model of a salon they have designed. Construct a and trapezoids. salon floor plan to scale. The learner would learn this concept while creating a floor plan in salon design. Salon project to scale and angles to construct a floor plan. G1.6 Circles and Their Properties G1.6.1 Solve multi-step problems involving We use circle placement in pins curls and rollers and circumference and area of circles. perm rods. Using the circumference of the pin curls or roller, determine the size needed. The different shape bases of the pin curls arc, half moon and triangle and rectangle base. Using the circumference of the pin curl, or roller to determine. G1.6.4 Know and use properties of arcs and The learner will learn this concept in roller placement, sectors and find lengths of arcs and areas arc and other shaped bases in the designing of pin of sectors. curls. G1.8 Three-dimensional Figures G1.8.1 Solve multi-step problems involving surface When we are going into wiggery we measure the area and volume of pyramids, prisms, head forms to customize the wigs for the perfect fit. cones, cylinders, hemispheres, and Using a 3D head, form measure the circumference of spheres. the head for wiggery. The learner will learn this concept in wiggery by measuring the mannequin for a proper fitting wig. Wigs with a 3-D head form with a tape measure with a head form. Using a 3D head form to measure the circumference of the head. G1.8.2 Identify symmetries of pyramids, prisms, When the student is involved in hair cutting each side cones, cylinders, hemispheres, and needs to be the same length. When performing a spheres. comb out the set need to be symmetrical. Hair is distributed evenly/symmetrically between the quadrants of the client‟s head. G2 STANDARDS CTE APPLICATION and PRACTICE RELATIONSHIPS BETWEEN FIGURES G2.2 Relationships Between Two-dimensional and Three-dimensional Representations G2.2.1 Identify or sketch a possible three- When the teacher is demonstrating on the dimensional figure, given two-dimensional mannequin the students will then copy the views (e.g., nets, multiple views). Create a demonstration on their mannequin. The learner will two-dimensional representation of a three- learn this concept during a demonstration by the dimensional figure. teacher where the teacher will demonstrate on a mannequin and the student will copy the concept on C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 12 07/27/2011 a paper head form. Wiggery with the measuring tape. On a head form sheet. When the teacher is demonstrating on the mannequin, the students will copy the demonstrations on their mannequins. G3 STANDARDS CTE APPLICATION and PRACTICES TRANSFORMATIONS OF FIGURES IN THE PLANE G3.1 Distance-preserving Transformations: Isometrics G3.1.1 Define reflection, rotation, translation, and While practicing hairstyling and haircutting. The glide reflection and find the image of a learner will learn this concept while practicing figure under a given isometric. hairstyling and haircutting. Making a floor plan all the rooms are 10 by 13--but it is the exact same shape but it is turned around facing the opposite direction. While practicing hairstyling and haircutting. G3.1.2 Given two figures that are images of each Put zoom times one. other under an isometric find the isometric and describe it completely. G3.2 Shape-preserving Transformations: Isometrics G3.2.1 Know the definition of dilation and find the The students will take hair samples and look at them image of a figure under a given dilation. through a microscope and see the hair cuticle. The shaft and the bulb of the hair. The learner will use this concept when we are analyzing the hair strand under the microscope. The students will take hair samples and look at them through a microscope and see the cuticle of the hair strand and hair bulb. Understand the Concept of Congruence and Basic Transformations G.GS.06.02 Understand that for polygons, congruence When looking at facial shapes to match to a specific means corresponding sides and angles hair cut or style. In haircutting, all sides of the clients have equal measures. head should match evenly. (4 inches in length at top, sides and back). The learner would use this concept, face shape analysis when preparing for a client hair cut. When looking at facial shapes to make a specific haircut or style. G.TR.06.03 Understand the basic rigid motions in the By changing the facial features when in styling and in plane (reflections, rotations, translations). cutting the hair. In make-up application, make all Relate these to congruence, and apply faces appear oval by highlighting and low lighting them to solve problems. using make-up. By changing the facial features when styling and in cutting the hair. Construct Geometric Shapes G.SR.06.05 Use paper folding to perform basic Using typing paper and double end papers, show geometric constructions of perpendicular bookend papers and the spiral paper these are big lines, midpoints of line segments and angle examples so all can see them. bisectors; justify informally. Draw and Construct Geometric Objects - Geometry G.SR.07.01 Use a ruler and other tools to draw squares, The student will use drawings in salon projects. They rectangles, triangles and parallelograms will draw the cuts they are about to perform. Using with specified dimensions. angles and lines. The student would use this concept to prepare a salon layout. Students construct images C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 13 07/27/2011 using lines, squares and other shapes when making food pyramids, salon layouts, hair follicle diagrams, skin and nail diagrams, etc. Understand the Concept of Similar Polygons and Solve Related Problems G.TR.07.04 Solve problems about similar figures and When doing their salon project they will use graph scale drawings. paper and layout a salon using the square footage and how many stations the size of the station. Then they will be required to price the items need to fulfill their salon project. The student would use this concept to calculate the actual size of a salon based on the drawing they have created. When designing the salon for their future, figure in cost and sizes of relative equipment. The layout you want is the picture to represent that how do we know how to represent that? How much will the salon cost including all the chairs, mirrors and supplies? When doing their salon project, students will use graph paper to layout a salon using the square footage. How many stations for the size of the station, and what is the cost? Solve Problems about Geometric Figures G.SR.08.03 Understand the definition of a circle; know Using the roller and its placements and what the wand use the formulas for circumference comb out will look like. and area of a circle to solve problems. G.SR.08.05 Solve applied problems involving areas of Develop a floor plan, figure the square footage, and triangles, quadrilaterals and circles. determine the cost. Visualize Solids G.SR.08.08 Sketch a variety of two-dimensional Floor plan of the salon project. Showing the front of representations of three-dimensional solids the salon the inside of the salon. In haircutting, including orthogonal views (top, front and making all sides the same. The learner will use this side) picture views (projective or isometric) concept on an on-going basis during teacher lecture and nets; use such two-dimensional and demonstration on a mannequin. The student representations to help solve problems. would sketch the details of the lesson or concept being taught. Floor plan of the salon project, showing the front of the salon and the inside of the salon. Understand and Apply Concepts of Transformation and Symmetry G.TR.08.10 Understand and use reflective and Balance and symmetries of a hairstyle and hair cut. rotational symmetries of two-dimensional Students are engaged in utilizing balance and shapes and relate them to transformations symmetry in the curriculum textbook. The learner to solve problems. would use this concept during the balance and symmetry lesson application. Students study symmetry in Chapter 9. Principals of Design. You are rotated on a 90 degree angle. Balance and symmetry of a hairstyle or cut. S1 STANDARDS CTE APPLICATION and PRACTICE UNIVARIATE DATA - EXAMINING DISTRIBUTIONS S1.1 Producing and Interpreting Plots C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 14 07/27/2011 S1.1.1 Construct and interpret dot plots, Explaining the ph scale in perming hair products, histograms, relative frequency histograms, etc… bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics. S1.1.2 Given a distribution of a variable in a data The learner will compare and contrast the incomes of set, describe its shape, including symmetry career opportunities with in the cosmetology field. or skewness, and state how the shape is The learner will compare and contrast the incomes of related to measures of center (mean and career opportunities within the Cosmetology field. median) and measures of variation (range The learner will compare and contrast the incomes of and standard deviation) with particular career opportunities within the cosmetology field. attention to the effects of outliers on these measures. S1.2 Measures of Center and Variation S1.2.1 Calculate and interpret measures of center Students will calculate the average incomes using including: mean, median, and mode; explain mean, median and mode. Without using a graph. uses, advantages and disadvantages of each measure given a particular set of data and its context. S1.2.3 Compute and interpret measures of With curving the gages inter grade pro. variation, including percentiles, quartiles, interquartile range, variance, and standard deviation. S2 STANDARDS CTE APPLICATION and PRACTICE BIVARIATE DATA - EXAMINING RELATIONSHIPS S2.1 Scatter plots and Correlation S2.1.1 Construct a scatter plot for a bivariate data A plot of data, ages, people as customer base. set with appropriate labels and scales. S2.1.4 Differentiate between correlation and The difference between gas pricing in the summer; is causation. Know that a strong correlation the season really the cause? does not imply a cause-and-effect relationship. Recognize the role of lurking variables in correlation. S3 STANDARDS CTE APPLICATION and PRACTICE SAMPLES, SURVEYS, AND EXPERIMENTS S3.1 Data Collection and Analysis S3.1.1 Know the meanings of a sample from a The learner will learn this concept during the salon population and a census of a population, interview portion of the program. They will interview and distinguish between sample statistics salon owners to get a consensus on certain data. and population parameters. The learner will learn this concept during the salon interview portion of the program. They will interview salon owners to get a consensus on certain data. Jennifer Aniston hair cut friends. The learner will learn this concept during the salon interview portion of the program. They will interview salon owners to C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 15 07/27/2011 get a consensus on certain data. S3.1.3 Distinguish between an observational study The learner will use this concept during hair coloring and an experimental study, and identify, in lesson they will identify the underling pigment and context, the conclusions that can be drawn tonal value. Students are given a sample hairstyle from each. and expected to identify the techniques needed to duplicate that style. Using the media and magazines vs. clients, determine the trends of the current times. Students are given a sample hairstyle and expected to identify techniques used to duplicate the style. Chemistry vinegar and oil suspensions, solvents, etc. The learner will use this concept during hair coloring lessons. They will identify the underlying pigment and tonal value. S4 STANDARDS CTE APPLICATION and PRACTICE PROBABILITY MODELS AND PROBABILITY CALCULATION S4.2 Application and Representation S4.2.2 Apply probability concepts to practical The learner will use this concept during client situations, in such settings as finance, consultation. The client might ask for the most health, ecology, or epidemiology, to make popular cuts or styles that they have seen on TV, informed decisions. magazines. Or in the entertainment business. Represent and Interpret Data D.RE.07.01 Represent and interpret data using circle Pie shaped in hair cutting and in pin curl placements, graphs, stem and leaf plots, histograms, roller placements and in our comb outs and styles. and box-and-whisker plots and select Using radial designs. In hairstyling, use a pie shaping appropriate representation to address for roller placement. The learner will use this concept specific questions. in learning radial design during hairstyling. D.AN.07.02 Create and interpret scatter plots and find Triangular base bangs, triangular base pin curl line of best fit; use an estimated line of best bases. Color wheels. fit to answer questions about the data. Draw, Explain and Justify Conclusions Based on Data D.AN.08.02 Recognize practices for collecting and The students will give their evaluation of how the did displaying data that may bias the on their benchmarks. Weather it was good or bad. presentation or analysis. And where they could improve. Students evaluate their own benchmark. Student evaluations of each other or of their own work. In a benchmark, ask the student to first evaluate their own work and the teachers. The students will be evaluated by using a standard benchmark. Understand Probability Concepts for Simple and Compound Events D.PR.08.05 Find and/or compare the theoretical The students will work in the computer lab finding probability, the experimental probability hair related events and writing reports on their and/or the relative frequency of a given findings. event. C:\Docstoc\Working\pdf\1775920e-0cb6-4d5c-8cb4-9eca65b1a21f.doc 16 07/27/2011

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