This document provides a crosswalk between math standards and their application in a Web Design career technical education program. It lists math standards related to number systems, measurement, ratios, proportions, percentages and rational numbers. For each standard, it provides an example of how the concept is applied in the Web Design program. Examples include using numbers and symbols in HTML coding, sizing and positioning images, calculating percentages for tips and taxes, and estimating sizes in pixels. The document aims to show students how math learned in other classes is relevant to their technical education and future careers by making connections between academic standards and real-world tasks in the Web Design field.

1. Math-Related Credit Crosswalk
for
Career Technical Education Classes
in Macomb County
Program Information
District: L’Anse Creuse
F. V. Pankow Center
Program Name: Web Design
CIP Code Number: 11.0801
Career Pathway: Business, Management, Marketing &
Technology
Instructor Name: Debra Schmid
Date: May 2009
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 Students learn how to change font size from negative
different number systems and recognize to positive numbers depending on their usage within
that the applicable properties change in the the webpage.
transition from the positive integers to all Ex. Font size can be specified as a relative value
integers, to the rational numbers, and to the using a + or - sign. These relative values range
real numbers. from -6 to + 6.
L1.1.2 Explain why the multiplicative inverse of a Students learn about inversion while manipulating,
number has the same sign as the number, sizing, and changing backgrounds of images.
while the additive inverse has the opposite
sign.
L1.1.3 Explain how the properties of associativity, Students learn how to plan, design and decide on the
commutativity, and distributivity, as well as layout of a webpage, its structure, images, and
identity and inverse elements, are used in layouts.
arithmetic and algebraic calculations. Ex. When designing a page layout, the commutative
law allows you to change positions of images and
text for aesthetic appeal.
L1.1.4 Describe the reasons for the different Enlarging and reducing images.
effects of multiplication by, or 100% = 1 images stays the same
exponentiation of, a positive number by a 50% = .5 reduces images by ½
number less than 0, a number between 0 150% = 1.5 enlarges image by 1 ½ times
and 1, and a number greater than 1.
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2. L1.2 Representations and Relationships
L1.2.1 Use mathematical symbols (e.g., interval The mathematical symbols of +, -, <, >, {}, ( ), %, &,
notation, set notation, summation notation) are used throughout the course.
to represent quantitative relationships and Coding HTML symbols such as copyright symbols,
situations. space symbols, and HTML tags.
Ex. <dd>: indicates that the enclosed text is a
definition in the definition list.
src = url: identifies the location of the image if
the control is set to an image.
L1.2.2 Interpret representations that reflect Webpage Development
absolute value relationships (e.g.,│x-a│< b, The concept of absolute positioning of images, lines
or a± b) in such contexts as error tolerance. of texts, paragraphs, headings on the screen is
demonstrated in most website page development.
L1.2.4 Organize and summarize a data set in a Students organize information on a webpage in
table, plot, chart, or spreadsheet; find tables using HTML tags.
patterns in a display of data; understand Ex. Students will set up spreadsheets to analyze and
and critique data displays in the media. organize client information.
L1.3 Counting and Probabilistic Reasoning
L1.3.2 Define and interpret commonly used Job and career possibilities and probabilities with
expressions of probability (e.g., chances of Web Design certifications
an event, likelihood, odds). Ex. The more training and experience one has in
Web Design the probability of getting a job
increases.
L1.3.3 Recognize and explain common probability When working with clients or students it is possible
misconceptions such as “hot streaks” and that all pages designed might be accepted and
“being due.” therefore the web designer is on a “hot streak”.
(possible but not probable)
Multiply and Divide Fractions
N.MR.06.01 Understand division of fractions as the Use of tables in HTML and Dreamweaver
inverse of multiplication. Ex. Students calculate sizing and spacing of tables
and table cells in HTML coding and
Dreamweaver.
N.FL.06.02 Given an applied situation involving dividing Ex. A designer wishes to divide the available space
fractions, write a mathematical statement to on the webpage into 3 parts. If the available
represent the situation. space is 7 ½ in by 9 inches. How many inches
are in each space?
(7 ½ x 9) ÷ 3 = n
N.MR.06.03 Solve for the unknown. In the above example
15 x 9 x 1 = n
2 3
22 ½ = n
N.FL.06.04 Multiply and divide any two fractions, Ex. A designer wishes to divide the screen into
including mixed numbers, fluently. sections for images, headlines, menus and text.
Two-thirds of the page will be designated for text
and the remaining third will be divide evenly
among images, headline and menu bar. If the
screen is 7 in. by 8 ½ in., what will be the
allotted area for each section?
(7 x 8 ½ ) = 59 ½
59 ½ x 2/3 = 39 sq inches for text
59.1/2 - 39 = 20.5
20 ½ ÷ 3 = 6 sq. in. for images, headline
and menu bar
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3. Represent Rational Numbers as Fractions or Decimals
N.ME.06.05 Order rational numbers and place them on Flash lessons use a number line
the number line. Ex. Students use the TIMELINE tool to position
images on the screen.
N.ME.06.06 Represent rational numbers as fractions or Convert using an image program
terminating decimals when possible and Ex. Students must convert from one format, such as
translate between these representations. GIF to another format, such as JPEG.
Add and Subtract Integers and Rational Numbers
N.ME.06.08 Understand integer subtraction as the Ex. A webpage developer has an 800 pixel screen
inverse of integer addition. Understand and a 400 pixel table. How many pixels will be in
integer division as the inverse of integer the margins?
multiplication. 800 – 400 = 400 / 2 = 200 pixels for margins.
N.FL.06.10 Add, subtract, multiply and divide positive Ex. When placing a table on a screen that measures
rational numbers fluently. 144 pixels by 144 pixels, what percent of the
page will this cover if the screen size is 122500
square pixels.
144x144 = 2%
122500
Find Equivalent Ratios
N.ME.06.11 Find equivalent ratios by scaling up or Enlarging and reducing images
scaling down. Ex. Students can scale images on the screen to any
scale factor to enhance appearance of the
webpage.
Solve Decimal, Percentage and Rational Number Problems
N.FL.06.12 Calculate part of a number given the Calculating amount of tip
percentage and the number. Ex. Mary’s food bill at the café was $10.55. She
wants to leave a 20% tip. How much money
should Mary give to the waitress?
N.MR.06.13 Solve contextual problems involving Calculating taxes and tips
percentages such as sales taxes and tips. Ex. John qualified for the state competition in
Lansing. The cost of the room was $115.00 per
night plus tax. If John stayed 2 nights, what was
the hotel cost?
(115 x2) = 330 x.0 6 = $19.80
$330 + $19.80 =$349.80 cost of hotel room
N.FL.06.14 For applied situations, estimate the answers Estimating image size for webpage design.
to calculations involving operations with Ex. Knowing that one inch equals 72 pixels, students
rational numbers can estimate amount of pace needed for images
or text.
N.FL.06.15 Solve applied problems that use the four Ex. Expenses for the state competition were as
operations with appropriate decimal follows: Entrance fee, $25.00, hotel room, $105
numbers. per night for 2 nights plus tax and gas, $41.00.
Find the total amount of expenses.
25 + (2 x 105) + .06(110) + 41 = $288.60
Understand Rational Numbers and Their Location on the Number Line
N.ME.06.17 Locate negative rational numbers (including Fonts can be represented as negative numbers in the
integers) on the number line. Know that Dreamweaver program.
numbers and their negatives add to 0 and Ex. -6 means a smaller font
are on opposite sides and at equal distance +6 means a larger font
from 0 on a number line. 0 means the font neither increases nor
decreases.
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4. N.ME.06.18 Understand that rational numbers are Students understand that ¼ means that the screen is
quotients of integers (non zero divided into four parts and the menu can be placed
denominators). on 1 of the four parts.
N.ME.06.19 Understand that 0 is an integer that is Point of origin
neither negative nor positive. Ex. The point of origin is the upper right hand corner
of the screen where the vertical axis intersects
the horizontal axis.
Understand Derived Quantities
N.MR.07.02 Solve problems involving derived quantities Determining weighted grades and students averages
such as density, velocity and weighted 1st quarter = 40%
averages. 2nd quarter = 40%
Exam = 20%
Understand and Solve Problems Involving Rates, Ratios, and Proportions
N.FL.07.03 Calculate rates of change including speed. Rate of Work
Ex. It takes designer A 30 hours to design 2 web
pages and designer B 24 hours to design 3 web
pages. What is the rate per hour of designers A
and B?
N.MR.07.04 Convert ratio quantities between different Milliseconds to days to determine time between
systems of units, such as feet per second to current date and a future date.
miles per hour. To convert milliseconds to days divide the number of
milliseconds stored in the daysTOGO variables by
the product of 1000 x 60 x 60 x 24. This expression
represents to 1000 milliseconds on one second, the
60 seconds in a minute, the 60 minutes in an hour
the 24 hours in a day.
N.FL.07.05 Solve proportion problems using such Inches to Pixels
methods as unit rate, scaling, finding Ex. 1 in = 72 pixels
equivalent fractions, and solving the 3 in n pixels
proportion equation a/b = c/d; know how to n = 216 pixels
see patterns about proportional situations in
tables.
Compute with Rational Numbers
N.FL.07.07 Solve problems involving operations with Calculating profit for BPA fundraiser
integers. Ex. One box of candy costs the club $12.00 and
holds fifty candy bars. If Mike sells 5 boxes of
candy for $0.50 per bar, how much profit did Mike
make for the club?
5 x 50 x .50 = $125
5 x 12 = $ 60
$125 - $ 60 = $ 65 profit.
N.FL.07.09 Estimate results of computations with Students estimate image size for placement on the
rational numbers. screen.
Understand Real Number Concepts
N.ME.08.03 Understand that in decimal form, rational Students understand that ½ = .5 and 1/3 = .333…
numbers either terminate or eventually
repeat, and that calculators truncate or
round repeating decimals; locate rational
numbers on the number line; know fraction
forms of common repeating decimals.
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5. Solve Problems
N.MR.08.08 Solve problems involving percent increases Enlarging and reducing images
and decreases. Ex. In Dreamweaver, the percent of increase /
decrease can be found for image sizing.
N.MR.08.10 Calculate weighted averages such as Determining weighted grades and students averages
course grades, consumer price indices and 1st quarter = 45%
sports ratings. 2nd quarter = 45%
Exam = 10%
N.FL.08.11 Solve problems involving ratio units, such Inches to Pixels
as miles per hour, dollars per pound or Ex. 1 in. = 72 pixels
persons per square mile. 8 in n pixels
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 Determining weighted grades and students averages
averages (e.g., GNP, consumer price index, 1st quarter = 30%
grade point average). 2nd quarter = 30%
Final Project = 20%
Exam = 20%
L2.1.6 Recognize when exact answers aren’t Webpage Design
always possible or practical. Use Design images do not have exact specifications,
appropriate algorithms to approximate therefore designers estimate size of images for
solutions to equations (e.g., to approximate aesthetic purposes.
square roots). Ex. Approximate areas of screen dedicated to
specifics areas on the webpage such as menus,
text, heading and images.
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 Decide on the best unit of measurement: pixels,
between systems; explain how arithmetic points, inches etc.
operations on measurements affect units, Ex. Pixels to inches : 1 inch = 72 pixels
and carry units through calculations Inches to points: 1 inch = 12 points
correctly. 72 pixels = 12 points
L3.2 Understanding Error
L3.2.2 Describe and explain round-off error, Round and estimate image size for visual placement.
rounding, and truncating.
L3.2.3 Know the meaning of and interpret Understand margin of error in image sizing, image
statistical significance, margin of error, and mapping, and page layout
confidence level.
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6. L4.1 Mathematical Reasoning
L4.1.1 Distinguish between inductive and Deductive:
deductive reasoning, identifying and If a client wants a blue and red webpage, then the
providing examples of each. designer will accommodate the clients wishes.
If the webpage is blue and red then the client will
be happy.
If the client is happy, then he will be a returning
customer.
If the business has customers that return, then it’ll
be a successful business.
Inductive:
If clients are happy they will continue to do
business with the company and the company will
be successful.
L4.1.2 Differentiate between statistical arguments Logic shows clients may choose one design because
(statements verified empirically using of a certain preference when statistics might show
examples or data) and logical arguments the opposite choice would be more appropriate.
based on the rules of logic. Ex. Statistics show that web designs that are
colorful and easily readable are more apt to be
used by potential customers, but some web
designs are more of a personal preference
L4.2 Language and Laws of Logic
L4.2.3 Use the quantifiers “there exists” and “all” in At all times, you must plan and sketch your design
mathematical and everyday settings and according to the client’s specifications before
know how to logically negate statements beginning to design on the computer.
involving them.
L4.2.4 Write the converse, inverse, and Discuss cause and effect of studying and doing well.
contrapositive of an “If…, then…” statement. Ex. If I score well on all projects, then I
Use the fact, in mathematical and everyday will understand the concepts of web
settings, that the contrapositive is logically design.
equivalent to the original while the inverse Converse: If I understand all concepts of web
and converse are not. design, then I will score well on all
projects.
Inverse: If I do not score well on the projects,
then I do not understand the
concepts of web design.
Contrapositive; If I do not understand the concepts
of web design, then I will not score
well on the projects.
L4.3 Proof
L4.3.2 Construct proofs by contradiction. Use Statement: If I study, I will pass the exam.
counter examples, when appropriate, to Contradiction: I studied, but I failed the exam.
disprove a statement. Conclusion: I did not study.
L4.3.3 Explain the difference between a necessary Working with clients and timetables. What might start
and a sufficient condition within the out necessary could end up sufficient
statement of a theorem. Determine the Ex. A client wants the web page design by a certain
correct conclusions based on interpreting a date(sufficient), but really needs the design by a
theorem in which necessary or sufficient later date.(necessary)
conditions in the theorem or hypotheses are
satisfied.
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7. 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 HTML Coding
that is presented in symbolic form, write an Students are able to interpret all HTML coding
algebraic expression from a verbal symbols.
description, and evaluate expressions given Ex. Data = url identifies the location of the object’s
values of the variables. data.
A1.2 Solutions of Equations and Inequalities (linear, exponential, logarithmic,
quadratic, power, polynomial, and rational)
A1.2.9 Know common formulas (e.g., slope, Formulas used in web design
distance between two points, quadratic Ex. Area = l x w Length times width
formula, compound interest, distance = rate Circumference = 2πr radius calculations
· time), and apply appropriately in contextual Diameter = 2r diameter of a circle
situations.
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 Templates are used as formulas to format pages for
for modeling a given real-world situation consistency throughout the project design.
[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 exponential
(P = P0at)].
A3.1.2 Adapt the general symbolic form of a Ex. Template could be as follows.
function to one that fits the specifications of ¼ of the page used for headings
a given situation by using the information to ¼ of the page used for images
replace arbitrary constants with numbers. ¼ of the page for content
In the example above, substitute the given ¼ of the page for menu bar.
values P0 = 300 and a = 1.02 to obtain P =
300(1.02)t.
Calculate Rates – Algebra
A.PA.06.01 Solve applied problems involving rates, Rate of work
including speed. Ex. Ben can design 3 web pages in 15 hours and
45 minutes. How many web pages can he design
in 8 hours.
3 = x
945 480
x = 1.5 web pages
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8. Understand the Coordinate Plane
A.RP.06.02 Plot ordered pairs of integers and use A digital image is a rectangular array of numbers.
ordered pairs of integers to identify points in Each pixel has an x & y location and a value.
all four quadrants of the coordinate plane. Ex. In a project for a floor design the PAINT program
is used to find the x & y coordinate.
Use Variables, Write Expressions and Equations, and Combine Like Terms
A.FO.06.03 Use letters with units, to represent In the Hexadecimal Code for color, all RGB values in
quantities in a variety of contexts. the browser-safe palette are combinations of the
same six colors in 20% increments of Red, Green
and Blue.
Ex. #33 66 99 means a little red(20%), more
green(40%) and even more blue(60%)
A.FO.06.04 Distinguish between an algebraic Expression: <color> Sets the color
expression and an equation. Equation: newAmt = ++oldAmt
Increase an operand by one
A.FO.06.05 Use standard conventions for writing All operations are performed in standard order of
algebraic expressions. preference for Java Script which is: parentheses,
negation, multiply and divide, add and subtract.
A.FO.06.06 Represent information given in words using Web designers use a variety of equations and
algebraic expressions and equations. expressions for coding.
Ex. Evaluate/Return right+ Ret = (x--,z)*(y--,q)
means evaluate two expressions and returns the
second one.
Represent Linear Functions Using Tables, Equations, and Graphs
A.RP.06.08 Understand that relationships between Creating tables in XML documents and HTML web
quantities can be suggested by graphs and pages.
tables. Ex. Given the data for a train schedule, students can
create a table in an XML file and HTML webpage
for the train service.
A.RP.06.10 Represent simple relationships between Ex. marginwidth = value
quantities using verbal descriptions, Sets the margin between the contents of the
formulas or equations, tables and graphs. frame and its top and bottom border values in
pixels.
Understand and Apply Directly Proportional Relationships and Relate to
Linear Relationships - Algebra
A.AP.07.01 Recognize when information given in a Sizing Images
table, graph or formula suggests a directly Ex. Students understand that as the height of an
proportional or linear relationship. image is increased/decreased, that the width
must increase/decrease proportionately.
Understand and Solve Problems about Inversely Proportional Relationships
A.PA.07.09 Recognize inversely proportional Students understand that increasing the size of an
relationships in contextual situations; know image, or frameset will reduce the amount of
that quantities are inversely proportional if surrounding screen space.
their product is constant.
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9. Understand the Concept of Non-linear Functions Using Basic Examples
A.PA.08.02 For basic functions, describe how changes Students make changes to tables, framesets, and
in one variable affect the others. images to affect surrounding size of screen space on
the page layout for visual appeal.
Understand Solutions and Solve Equations, Simultaneous Equations and
Linear Inequalities
G1.6.1 Solve multi-step problems involving Image mapping
circumference and area of circles. Ex. Students must know the circumference and area
of circles to determine the size of map
positioned over an image.
G3 STANDARDS CTE APPLICATION and PRACTICES
TRANSFORMATIONS OF FIGURES IN THE PLANE
G3.1 Distance-preserving Transformations: Isometries
G3.1.1 Define reflection, rotation, translation, and Students use the rotate and transform buttons in
glide reflection and find the image of a Macromedia Flash program to enhance webpage
figure under a given isometry. designs.
G3.1.2 Given two figures that are images of each Students are able to identify the isometry used on a
other under an isometry, find the isometry particular image in the webpage design.
and describe it completely. Ex. Students can identify a rotation or a reflections of
the original image.
G3.1.3 Find the image of a figure under the Students often use more than one isometry.
composition of two or more isometries and Ex. Students can rotate and/or reflect an image to
determine whether the resulting figure is a enhance webpage design appearance.
reflection, rotation, translation, or glide
reflection image of the original figure.
G3.2 Shape-preserving Transformations: Isometries
G3.2.1 Know the definition of dilation and find the The Zoom feature allows for a dilation of an image on
image of a figure under a given dilation. webpages to enhance the design.
Understand the Concept of Congruence and Basic Transformations
G.GS.06.02 Understand that for polygons, congruence Students understand that reproducing an image
means corresponding sides and angles (copying or moving) that the size of the angles and
have equal measures. sides do not change.
G.TR.06.03 Understand the basic rigid motions in the Students use rigid motion of images to solve layout
plane (reflections, rotations, translations). problems.
Relate these to congruence, and apply them
to solve problems.
G.TR.06.04 Understand and use simple compositions of Student often use more than one transformation in
basic rigid transformations. design of webpages.
Draw and Construct Geometric Objects - Geometry
G.SR.07.01 Use a ruler and other tools to draw squares, Students use rulers extensively in both Dreamweaver
rectangles, triangles and parallelograms MX software and Flash MX for design purposes.
with specified dimensions.
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10. Understand the Concept of Similar Polygons and Solve Related Problems
G.TR.07.03 Understand that in similar polygons, Enlarging and reducing images
corresponding angles are congruent and the Students understand that when re-sizing an image,
ratios of corresponding sides are equal; that the resulting image is similar to the original
understand the concepts of similar figures image, that is, the sides are proportional to the
and scale factor. inputted scale factor.
G.TR.07.04 Solve problems about similar figures and Enlarging and reducing images to a certain scale
scale drawings. factor to solve layout problems.
Solve Problems about Geometric Figures
G.SR.08.03 Understand the definition of a circle; know Image mapping explains and uses the theory of
wand use the formulas for circumference circumference of circles, and radius of circles
and area of a circle to solve problems.
G.SR.08.05 Solve applied problems involving areas of Students must calculate the radius and
triangles, quadrilaterals and circles. circumference of circles when image mapping.
Visualize Solids
G.SR.08.08 Sketch a variety of two-dimensional When planning a webpage, students first sketch their
representations of three-dimensional solids design and page layout.
including orthogonal views (top, front and
side) picture views (projective or isometric)
and nets; use such two-dimensional
representations to help solve problems.
Understand and Apply Concepts of Transformation and Symmetry
G.TR.08.09 Understand the definition of dilation from a Scaling images and image maps demonstrate
point in the plane and relate it to the dilation from a point in a plane.
definition of similar polygons.
G.TR.08.10 Understand and use reflective and rotational Students can rotate images to fit the layout of various
symmetries of two-dimensional shapes and web pages and to solve layout problems to enhance
relate them to transformations to solve readability and appearance of the web page.
problems.
S2 STANDARDS CTE APPLICATION and PRACTICE
BIVARIATE DATA - EXAMINING RELATIONSHIPS
S2.1 Scatterplots and Correlation
S2.1.4 Differentiate between correlation and There exists a strong correlation between the
causation. Know that a strong correlation designer’s preferences and the client’s preferences.
does not imply a cause-and-effect Sometime a positive correlation and sometimes a
relationship. Recognize the role of lurking negative correlation.
variables in correlation.
S3 STANDARDS CTE APPLICATION and PRACTICE
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11. SAMPLES, SURVEYS, AND EXPERIMENTS
S3.1 Data Collection and Analysis
S3.1.1 Know the meanings of a sample from a Target Audience: Popularity of certain types of web
population and a census of a population, design.
and distinguish between sample statistics Ex. Students discuss this year's clients preferences
and population parameters. to draw conclusion on the preferences of future
customers
S3.1.2 Identify possible sources of bias in data Client Preference or Bias
collection and sampling methods and simple Ex. The client may have certain preferences(bias)
experiments; describe how such bias can with graphic design wishes versus what web
be reduced and controlled by random design standards might suggest
sampling; explain the impact of such bias on
conclusions made from analysis of the data;
and know the effect of replication on the
precision of estimates.
S3.1.3 Distinguish between an observational study Observing a particular demographic, may suggest
and an experimental study, and identify, in that people like certain types of web design pages,
context, the conclusions that can be drawn but findings from experimental data show that the
from each. purpose of the webpage is more important.
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 more designs presented to a client, the more
situations, in such settings as finance, choices that client will have and the higher the
health, ecology, or epidemiology, to make probability that the client will purchase the webpage
informed decisions. designs from your company.
Draw, Explain and Justify Conclusions Based on Data
D.AN.08.02 Recognize practices for collecting and Students collect data from projects concerning length
displaying data that may bias the of time to create a web design, fees, number of
presentation or analysis. designers needed etc. and analyze to display to
clients.
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