# Cos Volume Profit

Document Sample

```					                                    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
01/12/2011
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
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.
01/12/2011
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.
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.

01/12/2011
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
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.

01/12/2011
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.
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
01/12/2011
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.

01/12/2011
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.
01/12/2011
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,
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.
01/12/2011
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.

01/12/2011
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

01/12/2011
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
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

01/12/2011
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.

G1.4.1               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
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
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
01/12/2011
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

01/12/2011
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?

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

01/12/2011
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.
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

01/12/2011
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.
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.