Program Review Exemplar

Feb 14,2014 PLTW Standards and Objectives Alignment

Unit 4 [PREVIEW], Unit 5 , Unit 8

3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters. (A.REI.3)
Unit 5

4.b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the

square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real
numbers a and b. (A.REI.4.b)

-Represent And Solve Equations And Inequalities Graphically

Unit 4 [PREVIEW]
10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in
the coordinate plane, often forming a curve (which could be a line). (A.REI.l 0)

Statistics and Probability

Interpreting Categorical And Quantitative Data
-Summarize, Represent, And Interpret Data On A Single Count Or Measurement Variable

Unit 3
1. Represent data with plots on the real number line (dot plots, histograms, and box plots). (S.ID.l)
Unit 3
4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to
estimate population percentages. Recognize that there are data sets for which such a procedure is
not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal
curve. (S .ID.4)

-Summarize, Represent, And Interpret Data On Two Categorical And Quantitative Variables

Unit 4 [PREVIEW]
6.a. Fit a function to the data; use functions fitted to data to solve problems in the context of the
data. Use given functions or choose a function suggested by the context. Emphasize linear,
quadratic, and exponential models. (S.ID.6.a)
Unit 4 [PREVIEW]
6.c. Fit a linear function for a scatter plot that suggests a linear association. (S.ID.6.c)

-Interpret Linear Models

Unit 4 [PREVIEW]
7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the
context of the data. (S.ID.7)

Functions

Interpreting Functions
-Understand The Concept Of A Function And Use Function Notation

Unit 4 [PREVIEW]
1. Understand that a function from one set (called the domain) to another set (called the range)

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Feb 14,2014 PL1W Standards and Objectives Alignment

assigns to each element of the domain exactly one element of the range. Iff is a function and xis an

element of its domain, then f(x) denotes the output off corresponding to the input x. The graph off

is the graph of the equation y = f(x). (F.IF.l)

Unit 4 [PREVIEW]

2. Use function notation, evaluate functions for inputs in their domains, and interpret statements
that use function notation in terms of a context. (F.IF.2)

-Interpret Functions That Arise In Applications In Terms Of The Context

Unit 4 [PREVIEW]
5. Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes. For example, if the function h(n) gives the number of person-hours it takes
to assemble n engines in a factory, then the positive integers would be an appropriate domain for
the function.* (F.IF.5)

Unit 4 [PREVIEW]
6. Calculate and interpret the average rate of change of a function (presented symbolically or as a
table) over a specified interval. Estimate the rate of change from a graph.* (F.IF.6)

Building Functions
-Build A Function That Models A Relationship Between Two Quantities

Unit 4 [PREVIEW]
1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(F.BF.l.a)

Linear. Quadratic. And Exponential Models
-Interpret Expressions For Functions In Terms Of The Situation They Model

Unit 4 [PREVIEW] , Unit 8
5. Interpret the parameters in a linear or exponential function in terms of a context. (F.LE.5)

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©2012 Common Core State Standards Initiative

Retrieved: February 14, 2014

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Feb 14,2014 PL1W Standards and Objectives Alignment

Showing Results for:
Course: Principles Of Engineering
Units: 1, 2, 3 & 4
Lessons: Ll.l, L1.2, L1.3, L1.4, L2.1, L2.2, L2.3, L2.4, L3.1, L3.2, L3.3, L4.1 & L4.2
Common Core State Standards for Mathematical Practice (HS), Next Generation Science Standards
& Common Core State Standards for English Language Arts

Common Core State Standards for
Mathematical Practice (HS)

Number and Quantity

Quantities

-Reason Quantitatively And Use Units To Solve Problems.

Ll.ll L1.4 I L2.2 I L2.3 I L2.4 I L4.2
1. Use units as a way to understand problems and to guide the solution of multi-step problems;
choose and interpret units consistently in formulas; choose and interpret the scale and the origin in
graphs and data displays. (N.Q .1)
Ll.ll L1.4 I L2.3 I L2.4 I L4.2
2. Define appropriate quantities for the purpose of descriptive modeling. (N.Q .2)
Ll.l l L1.4 I L2.2 I L2.3 I L3.3 I L4.2
3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
(N.Q .3)

The Real Number System

-Extend The Properties Of Exponents To Rational Exponents.

L4.2
2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
(N.RN.2)

Vector And Matrix Quantities

-Represent And Model With Vector Quantities.

L4.2
1. (+) Recognize vector quantities as having both magnitude and direction. Represent vector
quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes
(e.g., v, lvl. llvll. v). (N.VM.1)
L4.2
2. (+) Find the components of a vector by subtracting the coordinates of an initial point from the
coordinates of a terminal point. (N.VM.2)
L4.2
3. (+) Solve problems involving velocity and other quantities that can be represented by vectors.
(N.VM.3)

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Feb 14,2014 PL1W Standards and Objectives Alignment

Algebra

Seeing Structure In Expressions
-Interpret The Structure Of Expressions

Ll.l I L2.3 I L4.2
1. Interpret expressions that represent a quantity in terms of its context. (A. SSE. I)
Ll.ll L2.3 I L4.2
l.a. Interpret parts of an expression, such as terms, factors, and coefficients. (A.SSE.l.a)
Ll.l I L2.3 I L4.2
l .b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For
example, interpret P(l +r)" as the product ofPanda factor not depending on P. (A.SSE.l.b)

Creating Equations
-Create Equations That Describe Numbers Or Relationships

Ll.l
1. Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational and exponential functions.
(A.CED.l)
Ll.1 1 L4.2
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving

equations. For example, rearrange Ohm's law V = IR to highlight resistance R. (A.CED.4)

L4.2
3. Represent constraints by equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or non- viable options in a modeling context. For
example, represent inequalities describing nutritional and cost constraints on combinations of
different foods. (A.CED.3)

Reasoning With Equations And Inequalities
-Solve Equations And Inequalities In One Variable

Ll.1 1 L4.2
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters. (A.REI.3)
L4.2
4. Solve quadratic equations in one variable. (A.REI.4)

Functions

Linear. Quadratic. And Exponential Models
-Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems

Ll.l
l.b. Recognize situations in which one quantity changes at a constant rate per unit interval relative
to another. (F.LE.l.b)

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Trigonometric Functions
-Model Periodic Phenomena With Trigonometric Functions

L4.2
7. (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts;
evaluate the solutions using technology, and interpret them in terms of the context.* (F.TF. 7)

Geometry

Modeling With Geometry
-Apply Geometric Concepts In Modeling Situations

Ll.l I L2.2
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a
tree trunk or a human torso as a cylinder).* (G.MG.l)
Ll.l I L4.2
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to
satisfy physical constraints or minimize cost; working with typographic grid systems based on
ratios).* (G.MG.3)
L2.2
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per
square mile, BTUs per cubic foot).* (G.MG.2)

Geometric Measurement And Dimension
-Explain Volume Formulas And Use Them To Solve Problems

L2.2
3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* (G.GMD.3)

-Visualize Relationships Between Two-Dimensional And Three- Dimensional Objects

L2.2
4. Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify
three-dimensional objects generated by rotations of two-dimensional objects. (G.GMD.4)

Similarity. Right Triangles. And Trigonometry
-Define Trigonometric Ratios And Solve Problems Involving Right Triangles

L4.2
6. Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles. (G.SRT.6)
L4.2
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.* (G .SRT.8)

Statistics and Probability

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Feb 14, 2014 PL1W Standards and Objectives Alignment

Interpreting Categorical And Quantitative Data
-Summarize, Represent, And Interpret Data On A Single Count Or Measurement Variable

L4.1
1. Represent data with plots on the real number line (dot plots, histograms, and box plots). (S.ID.l)
L4.1, L4.2
2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (interquartile range, standard deviation) of two or more different data sets. (S.ID.2)
L4.1
3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers). (S.ID.3)
L4.1
4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to
estimate population percentages. Recognize that there are data sets for which such a procedure is
not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal
curve. (S.ID.4)

Making Inferences And Justifying Conclusions
-Understand And Evaluate Random Processes Underlying Statistical Experiments

L4.1
1. Understand statistics as a process for making inferences about population parameters based on a
random sample from that population. (S.IC.l)
L4.1
2. Decide if a specified model is consistent with results from a given data-generating process, e.g.,
using simulation. For example, a model says a spinning coin falls heads up with probability 0.5.
Would a result of 5 tails in a row cause you to question the model? (S.IC.2)

-Make Inferences And justify Conclusions From Sample Surveys, Experiments, And Observational
Studies

L4.1
4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of
error through the use of simulation models for random sampling. (S.IC.4)

Conditional Probability And The Rules Qf Probability
-Understand Independence And Conditional Probability And Use Them To Interpret Data

L4.1
1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or
categories) of the outcomes, or as unions, intersections, or complements of other events ("or,"
"and," "not"). (S.CP.l)
L4.1
2. Understand that two events A and Bare independent if the probability of A and B occurring
together is the product of their probabilities, and use this characterization to determine if they are
independent. (S.CP.2)
L4.1
3. Understand the conditional probability of A given B as P(A and 8)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the same as the
probability of A, and the conditional probability of B given A is the same as the probability of B.
(S.CP.3)

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Feb 14,2014 PL1W Standards and Objectives Alignment

L4.1

4. Construct and interpret two-way frequency tables of data when two categories are associated
with each object being classified. Use the two-way table as a sample space to decide if events are
independent and to approximate conditional probabilities. For example, collect data from a random
sample ofstudents in your school on their favorite subject among math, science, and English.
Estimate the probability that a randomly selected student from your school will favor science given
that the student is in tenth grade. Do the same for other subjects and compare the results. (S.CP.4)
L4.1
5. Recognize and explain the concepts of conditional probability and independence in everyday
language and everyday situations. For example, compare the chance of having lung cancer if you
are a smoker with the chance of being a smoker if you have lung cancer. (S.CP.5)

-Use The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform
Probability Model

L4.1

6. Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A,

and interpret the answer in terms of the model. (S .CP.6)
L4.1

7. Apply the Addition Rule, P(A or B) = P(A) + P(B)- P(A and B), and interpret the answer in terms

of the model. (S.CP.7)
L4.1

8. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BIA)
= P(B)P(AIB), and interpret the answer in terms of the model. (S.CP.8)

L4.1
9. (+) Use permutations and combinations to compute probabilities of compound events and solve

problems. (S.CP.9)

Using Probability To Make Decisions
-Use Probability To Evaluate Outcomes Of Decisions

L4.1
7. (+)Analyze decisions and strategies using probability concepts (e.g., product testing, medical
testing, pulling a hockey goalie at the end of a game). (S.MD.7)

h t t p ://www.co r e s t an d a r d s . o r g/
©2012 Common Core State Standards Initiative

Retrieved: February 14, 2014

Next Generation Science Standards

High School 5/8

Engineering Design

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Feb 14,2014 PL1W Standards and Objectives Alignment

Ll.1 1 L3.3
HS-ETS 1-2. Design a solution to a complex real-world problem by breaking it down into smaller,
more manageable problems that can be solved through engineering. (HS.ETS1.2)
L1.4
HS-ETSl-1. Analyze a major global challenge to specify qualitative and quantitative criteria a nd
constraints for solutions that account for societal needs and wants. (HS.ETSl.l)
L2.4 I L3.2 I L3.3
HS-ETSl-3. Evaluate a solution to a complex real-world problem based on prioritized criteria and
trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics,
as well as possible social, cultural, and environmental impacts. (HS.ETS1.3)

Energy

L1.2 I L1.4 I L3.2 I L4.2
HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one
form of energy into another form of energy.* (HS.PS3.3)

Matter and Its Interactions

L2.3
HS-PS1-3. Plan and conduct an investigation to gather evidence to compare the structure of
substances at the bulk scale to infer the strength of electrical forces between particles. (HS.PS1.3)

© 2011, 2012, 2013 Achieve, Inc. All rights reserved. NEXT GENERATION SCIENCE STANDARDS
and the associated logo are trademarks of Achieve, Inc.4

Retrieved: February 14, 2014

Common Core State Standards for English
Language Arts

Reading

Key Ideas and Details

L2.2
1. Read closely to determine what the text says explicitly and to make logical inferences from it;
cite specific textual evidence when writing or speaking to support conclusions drawn from the text.
(AS.R. 1)
L2.2
2. Determine central ideas or themes of a text and analyze their development; summarize the key

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Feb 14, 2014 PL1W Standards and Objectives Alignment

supporting details and ideas. (AS.R.2)
L2.2

7. Integrate and evaluate content presented in diverse fonnats and media, including visually and
quantitatively, as well as in words. (AS.R.7)
L2.2
9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to
compare the approaches the authors take. (AS.R.9)
L2.2
10. Read and comprehend complex literary and informational texts independently and proficiently.
(AS.R. l 0)

Text Types and Purposes

L2.2
2. Write informative/explanatory texts to examine and convey complex ideas and infonnation clearly
and accurately through the effective selection, organization, and analysis of content. (AS.W.2)
L2.2
4. Produce clear and coherent writing in which the development, organization, and style are
appropriate to task, purpose, and audience. (AS.W.4)
L2.2 I L4.2
7. Conduct short as well as more sustained research projects based on focused questions,
demonstrating understanding of the subject under investigation. (AS.W. 7)
L2.2 I L4.2
8. Gather relevant infonnation from multiple print and digital sources, assess the credibility and
accuracy of each source, and integrate the information while avoiding plagiarism. (AS.W.8)
L2.2 I L4.2
9. Draw evidence from literary or infonnational texts to support analysis, reflection, and research.
(AS.W.9)
L2.2 I L4.2
10. Write routinely over extended time frames (time for research, reflection, and revision) and
shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.
(AS.W. lO)
L4.2
5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a
new approach. (AS.W.S)
L4.2
6. Use technology, including the Internet, to produce and publish writing and to interact and
collaborate with others. (AS.W.6)

Comprehension and Collaboration

L2.2 I L4.2
2. Integrate and evaluate infonnation presented in diverse media and fonnats, including visually,
quantitatively, and orally. (AS.SL.2)
L2.2
4. Present infonnation, findings, and supporting evidence such that listeners can follow the line of
reasoning and the organization, development, and style are appropriate to task, purpose, and
audience. (AS.SL.4)

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Feb 14,2014 PLTW Standards and Objectives Alignment

L2.2
5. Make strategic use of digital media and visual displays of data to express information and
enhance understanding of presentations. (AS.SL.5)

Conventions of Standard English

L2.2 I L4.2
1. Demonstrate command of the conventions of standard English grammar and usage when writing
or speaking. (AS.L.1)
L2.2 I L4.2
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and
spelling when writing. (AS.L.2)
L2.2 I L4.2
6. Acquire and use accurately a range of general academic and domain-specific words and phrases
sufficient for reading, writing, speaking, and listening at the college and career readiness level;
demonstrate independence in gathering vocabulary knowledge when considering a word or phrase
important to comprehension or expression. (AS.L.6)

http://www.corestandards.org/

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief
State School Officers. All rights reserved.

Retrieved: February 14, 2014

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Feb 14,2014 PL1W Standards and Objectives Alignment

Showing Results for:
Course: Digital Electronics
Units: 1, 2, 3 & 4
Lessons: L1.1, L1.2, L1.3, L2.1, L2.2, L2.3, L2.4, L2.5, L3.1, L3.2, L3.3, L3.4, L4.1, L4.2 & L4.3
Common Core State Standards for English Language Arts, Standards for Technological Literacy,
Common Core State Standards for Mathematical Practice (HS) & Next Generation Science
Standards

Common Core State Standards for English
Language Arts

Reading

Key Ideas and Details

Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4 I L4.11 L4.2 I
L4.3
1. Read closely to determine what the text says explicitly and to make logical inferences from it;
cite specific textual evidence when writing or speaking to support conclusions drawn from the text.
(AS.R.1)
Ll.l
2. Determine central ideas or themes of a text and analyze their development; summarize the key
supporting details and ideas. (AS.R.2)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.1
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning or
tone. (AS.R.4)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5
7. Integrate and evaluate content presented in diverse formats and media, including visually and
quantitatively, as well as in words. (AS.R.7)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.5 I L3.11 L3.2 I L3.4 I L4.11 L4.2 I L4.3
10. Read and comprehend complex literary and informational texts independently and proficiently.
(AS.R.lO)
L2.1
5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions
of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole. (AS.R.5)
L2.1
6. Assess how point of view or purpose shapes the content and style of a text. (AS.R.6)
L2.1
8. Delineate and evaluate the argument and specific claims in a text, including the validity of the
reasoning as well as the relevance and sufficiency of the evidence. (AS.R.8)

'--) Comprehension and Collaboration

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Feb 14,2014 PLTIV Standards and Objectives Alignment

L1.11 L1.3 I L2.11 L2.2 I L2 .3 I L3.3 I L4.1
2. Integrate and evaluate information presented in diverse media and formats, including visually,
quantitatively, and orally. (AS.SL.2)
L1.3 I L2.11 L2.2 I L2.3 I L3.1 I L3.2 I L3.3 I L3.4 I L4.1 I L4.2 I L4.3
6. Adapt speech to a variety of contexts and communicative tasks, demonstrating command of
formal English when indicated or appropriate. (AS.SL.6)
L2 .11 L2.2 I L2.3 I L2.4 I L2.5 I L3.4 I L4.1 I L4.3
5. Make strategic use of digital media and visual displays of data to express information and
enhance understanding of presentations. (AS.SL.5)
L2.3 I L3.4 I L4.11 L4.3
4. Present information, findings, and supporting evidence such that listeners can follow the line of
reasoning and the organization, development, and style are appropriate to task, purpose, and
audience. (AS.SL.4)
L3.1 1 L4.1
1. Prepare for and participate effectively in a range of conversations and collaborations with
diverse partners, building on others' ideas and expressing their own clearly and persuasively.
(AS.SL.l)

Text Types and Purposes

11.2 I L1.3 I 12.11 12.2 I 12.3 I 12.4 I 12.5 I L3.11 13.2 I 13.3 I 13.4 I 14.2 I 14.3
2. Write informative/explanatory texts to examine and convey complex ideas and information clearly
and accurately through the effective selection, organization, and analysis of content. (AS.W.2)
11.2 I L1.3 I 12.11 12.2 I 12.3 I 12.4 I 12.5 I L3.11 13.2 I 13.3 I 13.4
4. Produce clear and coherent writing in which the development, organization, and style are
appropriate to task, purpose, and audience. (AS.W.4)
L1.2 I 12.1 I L2.2 I L2.3 I 13.2
7. Conduct short as well as more sustained research projects based on focused questions,
demonstrating understanding of the subject under investigation. (AS.W.7)
11.2 I L1.3 I 12.1 1 12.2 I 12.3 I 12.4 I 12.5 I 13.11 13.2 I 13.3 I 13.4 I L4.2 I 14.3
9. Draw evidence from literary or informational texts to support analysis, reflection, and research.
(AS .W.9)

L1.2 I 11.3 I 12.11 12.2 I 12.3 I 13.11 L3.4
10. Write routinely over extended time frames (time for research, reflection, and revision) and
shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.
(AS .W.lO)
11.3 I L2.3 I 12.4 I 12.5 I 13.11 13.3 I 13.4 I 14.2
1. Write arguments to support claims in an analysis of substantive topics or texts, using valid
reasoning and relevant and sufficient evidence. (AS.W.1)
L2.11 L2.2 I L2.3 I 12.4 I L2.5 I 13.2 I 13 .3 I L3.4 I L4.3
3. Write narratives to develop real or imagined experiences or events using effective technique,
well-chosen details, and well-structured event sequences. (AS.W.3)
12.1 1 L2.3
5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a
new approach. (AS.W.5)
12.11 L2.4 I L4.1
8. Gather relevant information from multiple print and digital sources, assess the credibility and
accuracy of each source, and integrate the information while avoiding plagiarism. (AS.W.8)
12.2 I L2.3

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Feb 14, 2014 PL1W Standards and Objectives Alignment

6. Use technology, including the Internet, to produce and publish writing and to interact and
collaborate with others. (AS.W.6)

Conventions of Standard English

L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4 I L4.11 L4.2 I L4.3
1. Demonstrate command of the conventions of standard English grammar and usage when writing
or speaking. (AS.L.1)
L1.2 I L1.3 I L2.11 L2 .2 I L2.3 I L2.4 I 12.5 I L3. 11 L3.2 I L3.3 I L3.4 I L4.11 L4.2 I L4.3
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and
spelling when writing. (AS.L.2)
L1.2 I L2.11 L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4 I L4.11 L4.2 I L4.3
3. Apply knowledge of language to understand how language functions in different contexts, to
make effective choices for meaning or style, and to comprehend more fully when reading or
listening. (AS.L.3)
L1.2 I 11.3 I L2.11 L2.2 I L2.4 I L2.5 I L3.2 I L3.3 I L3.4 I L4.11 L4.2 I L4.3
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using
context clues, analyzing meaningful word parts, and consulting general and specialized reference
materials, as appropriate. (AS.L.4)
11.2 I L2.1 I 12.3 I 12.4 I 12.5 I 13.1 I 13.2 I 13.3 I 13.4 I L4.1 I L4.2 I L4.3
5. Demonstrate understanding of word relationships and nuances in word meanings. (AS.L.5)
L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I 13.4 I L4.11 L4.2 I L4.3
6. Acquire and use accurately a range of general academic and domain-specific words and phrases
sufficient for reading, writing, speaking, and listening at the college and career readiness level;
demonstrate independence in gathering vocabulary knowledge when considering a word or phrase
important to comprehension or expression. (AS.L.6)

http://www.corestandards.org/

©Copyright 2010. National Governors Association Center for Best Practices and Council of Chief
State School Officers. All rights reserved.

Retrieved: February 14, 2014

Standards for Technological Literacy

Students will develop an understanding of the
characteristics and scope of technology.

"---) Ll.ll L1.2 I L2.11 L2.4 I L2.5 I L3.11 L3.2 I L3.3 I 13.4 I L4.ll 14.2 I L4.3

]. The nature and development of technological knowledge and processes are functions of the

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Feb 14, 2014 PLTIV Standards and Objectives Alignment

setting. (1.9-12.])
Ll.ll L1.2 I 12.11 L2.2 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4 I 14.11 L4.2 I 14.3
K. The rate of technological development is increasing rapidly. (1.9-12.K)
11.11 14.1 I L4.2 I L4.3
L. Inventions and innovations are the results of the specific, goal-directed research. (1.9-12.L)
11.11 L1.2 I L2 .11 12.2 I 14.11 L4.2 I L4.3
M. Most development of technologies these days is driven by the profit motive and the market.
(1.9-12.M)

Students will develop an understanding of the core concepts
of technology.

11.11 11.2 I 11.3 I 12.11 12.2 I 12.3 I 12.4 J 12.5 I 13.11 L3.2 I 13.3 I L3.4 I 14.11 L4.2 I
14.3
W. Systems thinking applies logic and creativity with appropriate compromises in complex real-life
problems. (2.9-12.W)
11.11 11.2 I 11.3 I 12.11 12.2 I L2.3 I L2.4 I 12.5 I 13.11 L3.2 I 13.3 I 13.4 I 14.11 L4.2 I
L4.3
X. Systems, which are the building blocks of technology, are embedded within larger technologicaL
social, and environmental systems. (2.9-12.X)
L1.1 J L1.2 I L1.3 I 12.11 L2.2 J 12.3 J L2.4 I 12.5 I 13.11 13.2 J L3.3 I L3.4 I 14.11 L4.2 J
L4.3
Y. The stability of a technological system is influenced by all of the components in the system,
especially those in the feedback loop. (2.9-12.Y)
Ll.ll L1.2 I L1.3 I 12.11 12.2 I 12.3 I L2 .4 I 12.5 I 13.11 L3.2 I L3.3 I L3.4 I 14.11 L4.2 I
L4.3
Z. Selecting resources involves trade-offs between competing values, such as availability, cost,
desirability, and waste. (2.9-12.Z)
Ll.ll L1.2 I L1.3 J 12.11 L2.3 J 12.4 J 12.5 J 13.1 J 13.2 I 13.3 J 13.4 J L4.1 J 14.2 I L4.3
M. Requirements involve the identification of the criteria and constraints of a product or system
and the determination of how they affect the final design and development. (2.9-12.M)
11.1 J 11.2 I L1.3 J 12.1 J L2.2 J L2.3 J L2.4 I L2.5 J L3.1 J L3.2 I L3.3 I L3.4 J L4.1 J L4.2 I
L4.3
BB. Optimization is an ongoing process or methodology of designing or making a product and is
dependent on criteria and constraints. (2.9-12.BB)
Ll.l J 13.11 L3.2 J 13.3 J L3.4 J L4.1 J L4.2 I 14.3
CC. New technologies create new processes. (2.9-12.CC)
11.11 L1.2 J L1.3 I 13.11 L3.2 J L3.3 I 13.4 J L4.1 J 14.2 I L4.3
DD. Quality control is a planned process to ensure that a product, service, or system meets
established criteria. (2 .9-12 .DD)
11.11 L1.2 I L1.3 I 12.11 L2.2 I L2.3 J L2.4 J 12.5 I 13.11 13.2 I L3.3 J L3.4 I 14.11 L4.2 J
L4.3
EE. Management is the process of planning, organizing, and controlling work. (2.9-1 2.EE)
Ll.ll 11.2 J L1.3 I 12.11 L2.3 J 12.4 I 13.11 L3.2 J L3.3 I L3.4 J 14.11 14.2 I 14.3
FF. Complex systems have many layers of controls and feedback loops to provide information.
(2 .9-12.FF)

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Feb 14,2014 PL1W Standards and Objectives Alignment

L2.4 I L3.1
M. Technologies systems include input, processes, output, and at times, feedback. (2 .6-8.M)
L2.4 I L3.1
N. Systems thinking involves considering how every part relates to others. (2.6-8.N)
L2.4 I L3.1
0. An open-loop system has no feedback path and requires human intervention, while a closed-loop
system uses feedback. (2.6-8.0)
L2.4 I L3.1
P. Technological systems can be connected to one another. (2.6-8.P)
L2.4 I L3.1
Q. Malfunctions of any part of a system may affect the function and quality of the system. (2 .6-8.0)
L2.4 I L3.1
R. Requirements are the parameters placed on the development of a product or system. (2.6-8.R)
L2.4 I L3.1
S. Trade-off is a decision process recognizing the need for careful compromises among competing
factors. (2.6-8.S)
L2.4 I L3.1
T. Different technologies involve different sets of processes. (2 .6-8.T)
L2.4 I L3.1
U. Maintenance is the process of inspecting and servicing a product or system on a regular basis in
order for it to continue functioning properly, to extend its life, or to upgrade its quality. (2.6-8.U)
L2.4 I L3.1
V. Controls are mechanisms or particular steps that people perform using information about the
system that causes systems to change. (2.6-8.V)

Students will develop an understanding of the relationships

among technologies and the connections between
technology and other fields of study.

Ll.ll L1.2 I L2.11 L2.4 I L2.5
]. Technological progress promotes the advancement of science and mathematics. (3.9-12.])

Students will develop an understanding of the cultural,
social, economic, and political effects of technology.

Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4 I L4.11 L4.2
H. Changes caused by the use of technology can range from gradual to rapid and from subtle to

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Feb 14,2014 PLTIV Standards and Objectives Alignment

obvious. (4.9-12.H)

Ll.ll L1.2 I L1.3 I L2.2 I L2.4 I L2.5 I L3.11 L3.3 I L3.4 I L4.1
I. Making decisions about the use of technology involves weighing the trade-offs between the
positive and negative effects. (4.9-1 2.!)
L2.1
K. The transfer of a technology from one society to another can cause culturaL sociaL economic,
and political changes affecting both societies to varying degrees. (4.9-12.K)

Students will develop an understanding of the effects of
technology on the environment.

Ll.l
H. When new technologies are developed to reduce the use of resources, considerations of
trade-offs are important. (5.9-12.H)
Ll.l
K. Humans devise technologies to reduce the negative consequences of other technologies.
(5.9-12.K)

Students will develop an understanding of the role of society
in the development and use of technology.

Ll.l
I. The decision whether to develop a technology is influenced by societal opinions and demands, in
addition to corporate cultures. (6.9-12.1)
Ll.l
]. A number of different factors, such as advertising, the strength of the economy, the goals of a
company, and the latest fads contribute to shaping the design of and demand for various
technologies. (6.9-12.])

Students will develop an understanding of the influence of
technology on history.

Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
G. Most technological development has been evolutionary, the result of a series of refinements to a
basic invention. (7.9-12 .G)

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Feb 14,2014 PLTW Standards and Objectives Alignment

Ll.ll L2.11 L2.3 I L3.1
H. The evolution of civilization has been directly affected by, and has in turn affected, the
development and use of tools and materials. (7.9-12.H)
Ll.ll L1.2 I L2.1
I. Throughout history, technology has been a powerful force in reshaping the social, cultural,
political, and economic landscape. (7.9-12.I)
L1.2 I L1.3 I L2.1
]. Early in the history of technology, the development of many tools and machines was based not on
scientific knowledge but on technological know-how. (7.9-12.])

Students will develop an understanding of the role of
troubleshooting, research and development, invention and
innovation, and experimentation in problem solving.

Ll.ll L1.3 I L2.2 I L3.11 L3.4
I. Research and development is a specific problem-solving approach that is used intensively in
business and industry to prepare devices and systems for the marketplace. (10.9-12.1)
Ll.ll L1.2 I L1.3 I L2.2 I L3.1
]. Technological problems must be researched before they can be solved. (10.9-12.])
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2
K. Not all problems are technological, and not every problem can be solved using technology.
(10.9-12.K)
L2.2
L. Many technological problems require a multidisciplinary approach. (10.9-12.L)

Students will develop the abilities to use and maintain
technological products and systems.

Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
L. Document processes and procedures and communicate them to different audiences using
appropriate oral and written techniques. (12.9-12.L)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
M. Diagnose a system that is malfunctioning and use tools, materials, machines, and knowledge to
repair it. (12.9-12.M)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
0. Operate systems so that they function in the way they were designed. (12.9-12.0)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
P. Use computers and calculators to access, retrieve, organize, process, maintain, interpret, and
evaluate data and information in order to communicate. (12.9-12.P)
L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4

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Feb 14,2014 PLTW Standards and Objectives Alignment

N. Troubleshoot, analyze, and maintain systems to ensure safe and proper function and precision.
(12 .9-12.N)

Students will develop an understanding of and be able to
select and use energy and power technologies.

Ll.1 1 Ll.2
K. Energy can be grouped into major forms: thermal. radiant, electrical, mechanical, chemical,
nuclear, and others. (16.9-1 2.K)
Ll.l I L1.2 I L1.3 I L2.1 I L2.2 I L2.3 I L2.4 I L2.5 I L3.1 I L3.2 I L3.3 I L3.4
N. Power systems must have a source of energy, a process, and loads. (16.9-12.N)
L1.2
M. Energy resources can be renewable or nonrenewable. (16.9-12.M)

L1.2
H. Power systems are used to drive and provide propulsion to other technological products and
systems. (16.6-B.H)

Students will develop an understanding of and be able to
select and use information and communication technologies.

Ll.l I L1.2 I L1.3 I L2.1 I L2.2 I L2.3 I L2.5
L. Information and communication technologies include the inputs, processes, and outputs
associated with sending and receiving information. (17.9-12.L)
Ll.l I L1.2 I L1.3 I L2.1, L2.2 I L2.3 I L2.5
M. Information and communication systems allow information to be transferred from human to
human, human to machine, machine to human, and machine to machine. (17.9-12.M)
Ll.l I L1.3 I L2.1 I L2.2 I L2.3 I L2.5
0. Communication systems are made up of source, encoder, transmitter, receiver, decoder, storage,
retrieval, and destination. (17.9-12.0)
Ll.l I L1.2 I L1.3 I L2.1 I L2.2 I L2.3 I L2.5
P. There are many ways to communicate information, such as graphic and electronic means.
(17.9-12.P)
Ll.l I L1.2 I L2.1 I L2.3 I L2.5
Q. Technological knowledge and processes are communicated using symbols, measurement,
conventions, icons, graphic images, and languages that incorporate a variety of visual, auditory,
and tactile stimuli. (17 .9-12.Q)

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L1.3 I L2.1 I L2.2 I L2.3 I L2.5
N. Infonnation and communication systems can be used to inform, persuade, entertain, control,
manage, and educate. (17 .9-12.N)

Students will develop the abilities to assess the impact of
products and systems.

L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
]. Collect information and evaluate its quality. (13.9-12.])
L2.1 1L2.4
K. Synthesize data, analyze trends, and draw conclusions regarding the effect of technology on the
individual, society, and environment. (13 .9-12.K)
L2.4
L. Use assessment techniques, such as trend analysis and experimentation, to make decisions about
the future development of technology. (13.9-12.L)

Students will develop an understanding of engineering
design.

L1.3 I L2.11 L2.3 I L2.4 I L2.5 I L3.2 I L3.3 I L3.4
K. A prototype is a working model used to test a design concept by making actual observations and
necessary adjustments. (9.9-12.K)
L1.3 I L2.11 L2.3 I L2.4 I L2.5 I L3.4
L. The process of engineering design takes into account a number of factors. (9.9-12.L)
L2.11 L2 .3 I L2.4 I L3.11 L3.2 I L3.4
I. Established design principles are used to evaluate existing designs, to collect data, and to guide
the design process. (9.9-12.1)
L2.1 1L2.4
]. Engineering design is influenced by personal characteristics, such as creativity, resourcefulness,
and the ability to visualize and think abstractly. (9.9-12.])

Students will develop an understanding of the attributes of
design.

L2.1 9/18

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Feb 14, 2014 PLTI1' Standards and Objectives Alignment

I. Design problems are seldom presented in a clearly defined form. (8.9-1 2.1)
L3.1
]. The design needs to be continually checked and critiqued, and the ideas of the design must be
redefined and improved. (8.9-12.])
L3.3
K. Requirements of a design, such as criteria, constraints, and efficiency, sometimes compete with
each other. (8.9-12.K)

Students will develop the abilities to apply the design
process.

L2.2 , L2.3 , L2.4 , L2.5 , L3.1 , L3.2 , L3.3 , L3.4
Q. Develop and produce a product or system using a design process. (11 .9-12.0)
L2.2 , L2.4 , L2.5
R. Evaluate final solutions and communicate observation, processes, and results of the entire design
process, using verbal, graphic, quantitative, virtual, and written means, in addition to
three-dimensional models. (11.9-12.R)
L2.3, L2.4, L2.5, L3.1
P. Evaluate the design solution using conceptual, physicaL and mathematical models at various
intervals of the design process in order to check for proper design and to note areas where
improvements are needed. (11.9-1 2.P)
L2.4
N. Identify criteria and constraints and determine how these will affect the design process.
(11.9-12.N)
L2.4, L2.5
0. Refine a design by using prototypes and modeling to ensure quality, efficiency, and productivity.
of the final product. (11.9-12.0)

International Technology Education Association. (2007). Standards for technological literacy. Reston,
VA: ITEA.

Retrieved: February 14, 2014

Common Core State Standards for
Mathematical Practice (HS)

Number and Quantity 10/18

The Real Number System
-Extend The Properties Of Exponents To Rational Exponents.

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Feb 14,2014 PLTIV Standards and Objectives Alignment

Ll.ll L1.2 I L2.1
1. Explain how the definition of the meaning of rational exponents follows from extending the
properties of integer exponents to those values, allowing for a notation for radicals in terms of
rational exponents. For example, we define 5ll3 to be the cube root of5 because we want (5ll3]3 = 5°m3
to hold, so (5 113) 3 must equalS. (N.RN.1)
Ll.ll L1.2 I L2.1
2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
(N.RN.2)

Quantities
-Reason Quantitatively And Use Units To Solve Problems.

Ll.ll L1.2 I Ll.J I L2.11 L2.2 I L2.3 I LJ.ll L3.2 I L3.3 I L4.11 L4.2 I L4.3
1. Use units as a way to understand problems and to guide the solution of multi-step problems;
choose and interpret units consistently in formulas; choose and interpret the scale and the origin in
graphs and data displays. (N.Q .1)
Ll.ll L1.2 I Ll.J I L2.11 L2.2 I L2.3 I LJ.ll L3.2 I L3.3 I L4.11 L4.2 I L4.3
2. Define appropriate quantities for the purpose of descriptive modeling. (N.Q .2)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L3.11 L3.2 I L3.3 I L4.11 L4.3
3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
(N.Q .3)

Vector And Matrix Quantities
-Represent And Model With Vector Quantities.

L4.11 L4.2 I L4.3
1. (+) Recognize vector quantities as having both magnitude and direction. Represent vector
quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes
(e.g., v, lvl, llvll, v). (N.VM.l)
L4.1
3. (+) Solve problems involving velocity and other quantities that can be represented by vectors.
(N.VM.3)

-Perform Operations On Vectors.

L4.1
5. (+) Multiply a vector by a scalar. (N.VM.S)
L4.3
4.(+)Add and subtract vectors. (N.VM.4)

Algebra

Seeing Structure In Expressions 11/18
-Interpret The Structure Of Expressions

Ll.ll L1.2 I Ll.J I L2.11 L2 .2 I LJ.l, L4.11 L4.2
1. Interpret expressions that represent a quantity in terms of its context. (A.SSE.1)
L1.2 I L2.1, L2.2 I L4.11 L4.2
l.a. Interpret parts of an expression, such as terms, factors, and coefficients. (A.SSE.l.a)

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Feb 14,2014 PLHV Standards and Objectives Alignment

L1.2 I L2.2

2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 -y as (x 2 2 -
)

(j/]2, thus recognizing it as a difference ofsquares that can be factored as (x2 - y)(x2 + jl). (A.SSE.2)

L2.2

l.b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For

example, interpret P(l +r)" as the product ofPanda factor not depending on P. (A.SSE.l.b)

-Write Expressions In Equivalent Forms To Solve Problems

L1.11 L1.2 I L2.2 I L2.5 I L3.3 I 14.11 L4.2
3. Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.* (A.SSE.3)

Arithmetic With Polynomials And Rational Expressions
-Perform Arithmetic Operations On Polynomials

L1.2 I 12.11 L2.2 I 12.3 I L2.4 I L2.5 I L3.3
1. Understand that polynomials form a system analogous to the integers, namely, they are closed
under the operations of addition, subtraction, and multiplication; add, subtract, and multiply
polynomials. (A.APR.l)

-Rewrite Rational Expressions

L1.2 I L1.3 I 12.11 L2.3 I L2.4 I L2.5 I 13.4 I 14.11 L4.2 I L4.3

6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)!b(x),

where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x),
using inspection, long division, or, for the more complicated examples, a computer algebra system.
(A.APR.6)
L1.2 I L1.3 I 12.1, 12.3 I L2.4 I L2.5 I 14.1
7. (+) Understand that rational expressions form a system analogous to the rational numbers,
closed under addition, subtraction, multiplication, and division by a nonzero rational expression;
add, subtract, multiply, and divide rational expressions. (A.APR. 7)

-Understand The Relationship Between Zeros And Factors Of Polynomials

L2.1
2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder

on division by x- a is p(a), so p(a) = 0 if and only if (x- a) is a factor of p(x). (A.APR.2)

-Use Polynomial Identities To Solve Problems

L2.3 I L2.4 I L2.5 I L3.4
4. Prove polynomial identities and use them to describe numerical relationships. For example, the

=polynomial identity (x2 + y)2 (x2 -y)2 + (2xy)2 can be used to generate Pythagorean triples.

(A.APR.4)
L2.3 I 12.4 I L2.5 I L3.4
5. (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x andy for a
positive integer n, where x and y are any numbers, with coefficients determined for example by
Pascal's Triangle.1

1The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
(A.APR.5)

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Creating Equations
-Create Equations That Describe Numbers Or Relationships

L1.2 I L2.3 I L4.11 L4.2 I L4.3

1. Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational and exponential fun ctions.
(A.CED.l)

L1.2 I L4.11 L4.3
3. Represent constraints by equations or inequalities, and by systems of equations and/or

inequalities, and interpret solutions as viable or non- viable options in a modeling context. For
example, represent inequalities describing nutritional and cost constraints on combinations of
different foods. (A.CED.3)

L1.2 I L1.3 I L2 .11 L4.11 L4.3
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving

equations. For example, rearrange Ohm's law V =IR to highlight resistance R. (A.CED.4)

L4.11 14.2 I L4.3
2. Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales. (A.CED.2)

Reasoning With Equations And Inequalities
-Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning

L1.2 I L2.1 I L2.3 I L4.1 I L4.2
1. Explain each step in solving a simple equation as following from the equality of numbers asserted
at the previous step, starting from the assumption that the original equation has a solution.
Construct a viable argument to justify a solution method. (A.REI.l)
11.2 I 12.11 L4.1
2. Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise. (A.REI.2)

-Solve Equations And Inequalities In One Variable

11.2 I 12.11 L4.11 L4.2 I L4.3
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters. (A.REI.3)

-Solve Systems Of Equations

L1.2 I L2 .2 I L4.3
5. Prove that, given a system of two equations in two variables, replacing one equation by the sum
of that equation and a multiple of the other produces a system with the same solutions. (A.REI.S)
L4.2 I L4.3
6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs
of linear equations in two variables. (A.REI.6)

Functions

Interpreting Functions
· -' -Interpret Functions That Arise In Applications In Terms Of The Context

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Feb 14, 2014 PLTW Standards and Objectives Alignment

L1.2 I L4.3
4. For a function that models a relationship between two quantities, interpret key features of
graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal

description of the relationship. Key features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end
behavior; and periodicity.* (F.IF.4)

L1.2
5. Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes. For example, if the function h(n) gives the number of person-hours it takes
to assemble n engines in a factory, then the positive integers would be an appropriate domain {or
the function.* (F.IF.5)

L1.2
6. Calculate and interpret the average rate of change of a function (presented symbolically or as a
table) over a specified interval. Estimate the rate of change from a graph.* (F.IF.6)

-Analyze Functions Using Different Representations

L4.1
7. Graph functions expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.* (F. IF.7)

-Understand The Concept Of A Function And Use Function Notation

L4.2 I L4.3

1. Understand that a function from one set (called the domain) to another set (called the range)
assigns to each element of the domain exactly one element of the range. Iff is a function and x is an
element of its domain, then f(x) denotes the output off corresponding to the input x. The graph off

is the graph of the equation y = f(x). (F.IF.l)

L4.2

2. Use function notation, evaluate functions for inputs in their domains, and interpret statements
that use function notation in terms of a context. (F.IF.2)

Building Functions
-Build New Functions From Existing Functions

L1.2
4. Find inverse functions. (F.BF.4)

-Build A Function That Models A Relationship Between Two Quantities

L4.1 I L4.2 I L4.3
1. Write a function that describes a relationship between two quantities.* (F.BF.l)
L4.1

l .b. Combine standard function types using arithmetic operations. For example, build a {unction
that models the temperature of a cooling body by adding a constant {unction to a decaying
exponential, and relate these fun ctions to the model. (F.BF.l.b)

L4.1

l.c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a {unction
of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the
temperature at the location ofthe weather balloon as a fun ction of time. (F.BF.l.c)

L4.2
l.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(F.BF.l.a)

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Feb 14,2014 PLTIV Standards and Objectives Alignment

Linear. Quadratic. And Exponential Models

-Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems

L1.2 I L4.1 I L4.2
1. Distinguish between situations that can be modeled with linear functions and with exponential
functions. (F.LE.1)
L1.2
1.b. Recognize situations in which one quantity changes at a constant rate per unit interval relative
to another. (F.LE.l.b)
L1.2
2. Construct linear and exponential functions, including arithmetic and geometric sequences, given
a graph, a description of a relationship, or two input-output pairs (include reading these from a
table). (F.LE.2)

-Interpret Expressions For Functions In Terms Of The Situation They Model

L4.1
5. Interpret the parameters in a linear or exponential function in terms of a context. (F.LE.5)

Trigonometric Functions

-Extend The Domain Of Trigonometric Functions Using The Unit Circle

L4.11 L4.2 I 14.3
1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by
the angle. (F.TF. 1)
14.1
2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise
around the unit circle. (F.TF.2)

Geometry

Congruence

-Experiment With Transformations In The Plane

L4.1 114.2
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line, distance along a line, and distance around a circular
arc. (G.C0.1)
L4.1
2. Represent transformations in the plane using, e.g., transparencies and geometry software;
describe transformations as functions that take points in the plane as inputs and give other points
as outputs. Compare transformations that preserve distance and angle to those that do not (e.g.,
translation versus horizontal stretch). (G.C0.2)
L4.1
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments. (G.C0.4)

-Make Geometric Constructions

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Feb 14,2014 PLHV Standards and Objectives Alignment

L4.1
12. Make formal geometric constructions with a variety of tools and methods (compass and

straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a
segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular
lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a
given line through a point not on the line. (G.C0.12)

Circles
-Understand And Apply Theorems About Circles

L4.1
4. (+) Construct a tangent line from a point outside a given circle to the circle. (G.C.4)
L4.3

2. Identify and describe relationships among inscribed angles, radii, and chords . Include the
relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter
are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects
the circle. (G .C.2)

-Find Arc Lengths And Areas Of Sectors Of Circles

L4.2
5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional
to the radius, and define the radian measure of the angle as the constant of proportionality; derive
the formula for the area of a sector. (G.C .S)

Statistics and Probability

Interpreting Categorical And Quantitative Data
-Summarize, Represent, And Interpret Data On Two Categorical And Quantitative Variables

L4.2
6. Represent data on two quantitative variables on a scatter plot, and describe how the variables
are related. (S .ID.6)

-Interpret Linear Models

L4 .2
8. Compute (using technology) and interpret the correlation coefficient of a linear fit. (S.ID.8)

Making Inferences And Justifying Conclusions
-Understand And Evaluate Random Processes Underlying Statistical Experiments

L4.2
1. Understand statistics as a process for making inferences about population parameters based on a
random sample from that population. (S.IC.l)

Using Probability To Make Decisions 16!18
-Calculate Expected Values And Use Them To Solve Problems

L4.2 I L4.3

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Feb 14, 2014 PLTW Standards and Objectives Alignment

1. (+) Define a random variable for a quantity of interest by assigning a numerical value to each
event in a sample space; graph the corresponding probability distribution using the same graphical
displays as for data distributions. (S.MD.1)
L4.2
2. (+) Calculate the expected value of a random variable; interpret it as the mean of the probability
distribution. (S.MD.2)

-Use Probability To Evaluate Outcomes Of Decisions

L4 .3
5. (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and
finding expected values. (S.MD.5)

http://www.corestandards.org/
©2012 Common Core State Standards Initiative

Retrieved: February 14, 2014

Next Generation Science Standards

High School

Matter and Its Interactions

Ll.l
HS-PSl-1. Use the periodic table as a model to predict the relative properties of elements based on
the patterns of electrons in the outermost energy level of atoms. (HS.PS1.1)

Motion and Stability: Forces and Interactions

Ll.l
HS-PS2-6. Communicate scientific and technical information about why the molecular-level
structure is important in the functioning of designed materials.* (HS.PS2.6)

Energy

Ll.l
HS-PS3-2. Develop and use models to illustrate that energy at the macroscopic scale can be
accounted for as either motions of particles or energy stored in fields. (HS.PS3.2)
Ll.ll L1.2' L1.3' L2.1' L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4 I L4.11 L4.2 I
L4.3
HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one

Project Lead The Way, Inc. ©2014 17/18

Feb 14,2014 PLTIV Standards and Objectives Alignment

form of energy into another form of energy.* (HS.PS3.3)

Engineering Design

Ll.l I L1.2 I L1.3 I L2.1 I L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
HS-ETSl-3. Evaluate a solution to a complex real-world problem based on prioritized criteria and
trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics,
as well as possible social, cultural, and environmental impacts. (HS.ETS1.3)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
HS-ETSl-4. Use a computer simulation to model the impact of proposed solutions to a complex
real-world problem with numerous criteria and constraints on interactions within and between
systems relevant to the problem. (HS.ETS1.4)
L1.3 I L2.11 L2.2 I L2.3 I L2.4 I L2.5 I L3.11 L3.2 I L3.3 I L3.4
HS-ETSl-2. Design a solution to a complex real-world problem by breaking it down into smaller,
more manageable problems that can be solved through engineering. (HS.ETS1.2)

Waves and their Applications in Technologies for Information Transfer

L1.2
HS-PS4-l. Use mathematical representations to support a claim regarding relationships among the
frequency, wavelength, and speed of waves traveling in various media. (HS.PS4.1)

© 2011, 2012, 2013 Achieve, Inc. All rights reserved. NEXT GENERATION SCIENCE STANDARDS
and the associated logo are trademarks of Achieve, Inc.4

Retrieved: February 14, 2014

Project Lead The Way, Inc. @201 4 1 8/ 1 8

Feb 14,2014 PL1W Standards and Objectives Alignment

Showing Results for:
Course: Computer Integrated Manufacturing
Units: 1, 2, 3 & 4
Lessons: L1.1, L1.2, L1.3, L2.1, L2.2, L2.3, L3.1, L3.2, L3.3, L4.1 & L4.2
Common Core State Standards for English Language Arts, Standards for Technological Literacy,
Next Generation Science Standards & Common Core State Standards for Mathematical Practice (HS)

Common Core State Standards for English
Language Arts

Reading

Key Ideas and Details

Ll.l, L2.1, L2.2 I L4.1
1. Read closely to determine what the text says explicitly and to make logical inferences from it;
cite specific textual evidence when writing or speaking to support conclusions drawn from the text.
(AS.R.l)
Ll.l, L1.3 I L2.1, L2.2 I L4.1
2. Determine central ideas or themes of a text and analyze their development; summarize the key
supporting details and ideas. (AS.R.2)
Ll.l , L1.2 [OPTIONAL], L1.3 I L2.1, L2.2 I L2.3 I L3.1, L4.1
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning or
tone. (AS.R.4)
Ll.l, L1.2 I L1.3 I L2.1, L2.2 I L2.3 I L3.1, L3.2 I L3.3
7. Integrate and evaluate content presented in diverse formats and media, including visually and
quantitatively, as well as in words. (AS.R.7)
Ll.l, L2.1, L2.2
9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to
compare the approaches the authors take. (AS.R.9)
Ll.l, L2.1, L2.2 I L4.1
10. Read and comprehend complex literary and informational texts independently and proficiently.
(AS.R.10)

Text Types and Purposes

Ll.l, L1.2 [OPTIONAL], L1.3 I L2.1, L2.2 I L2.3 I L4.1
2. Write informative/explanatory texts to examine and convey complex ideas and information clearly
and accurately through the effective selection, organization, and analysis of content. (AS.W.2)
Ll.l, L1.2 [OPTIONAL], L1.3 I L2.1, L2.2 I L3.2 I L4.1 I L4.2
4. Produce clear and coherent writing in which the development, organization, and style are
appropriate to task, purpose, and audience. (AS.W.4)

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Feb 14,2014 PLTW Standards and Objectives Alignment

11.11 12.11 L2.2 I L4.1
8. Gather relevant information from multiple print and digital sources, assess the credibility and
accuracy of each source, and integrate the information while avoiding plagiarism. (AS.W.8)
11.11 12.11 L2.2 I L4.1
9. Draw evidence from literary or informational texts to support analysis, reflection, and research.
(AS.W.9)
Ll.2 [OPTIONAL], Ll.3 I L3.2 I L3.3 I L4.2
3. Write narratives to develop real or imagined experiences or events using effective technique,
well-chosen details, and well-structured event sequences. (AS.W.3)

Comprehension and Collaboration

Ll.ll Ll.3 I 12.11 L2.2 I L3.2 I L3.3 I L4.2
1. Prepare for and participate effectively in a range of conversations and collaborations with
diverse partners, building on others' ideas and expressing their own clearly and persuasively.
(AS.SL.1)
L1.1, L1.2 [OPTIONAL], L1.3 I L2.1, L2.2 I L2.3 I L3.1, L3.2 I L3.3 I L4.11 L4.2
2. Integrate and evaluate information presented in diverse media and formats, including visually,
quantitatively, and orally. (AS.SL.2)
L1.11 12.11 L2.2 I L4.1
4. Present information, findings, and supporting evidence such that listeners can follow the line of
reasoning and the organization, development, and style are appropriate to task, purpose, and
audience. (AS.SL.4)
11.11 L2.11 L2.2 I L4.1
5. Make strategic use of digital media and visual displays of data to express information and
enhance understanding of presentations. (AS.SL.5)
Ll.1 112.1 1 L2.2
6. Adapt speech to a variety of contexts and communicative tasks, demonstrating command of
formal English when indicated or appropriate. (AS.SL.6)

Conventions of Standard English

L1.11 L1.2 [OPTIONAL], L1.3 I 12.11 L2.2 I L2.3 I L3.11 L3.2 I L3.3 I L4.1, L4.2
1. Demonstrate command of the conventions of standard English grammar and usage when writing
or speaking. (AS.L.1)
11.1, 11.2 [OPTIONAL], 11.3 I 12.1, 12.2 I 12.3 I 13.1 I 13.2 I 13.3 I 14.1, 14.2
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and
spelling when writing. (AS.L.2)
11.1, 11.3 I 12.1, 12.2
3. Apply knowledge of language to understand how language functions in different contexts, to
make effective choices for meaning or style, and to comprehend more fully when reading or
listening. (AS.L.3)
11.1, L1.2 [OPTIONAL], 11.3 I L2.1, 12.2 I 13.11 L3.2
4. Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using
context clues, analyzing meaningful word parts, and consulting general and specialized reference
materials, as appropriate. (AS.L.4)
11.11 Ll.2 I L1.3 I L2.1 I L2.2 I L2.3 I L3.11 L3.2 I L3.3 I L4.11 L4.2
6. Acquire and use accurately a range of general academic and domain-specific words and phrases

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Feb 14,2014 PL1W Standards and Objectives Alignment

sufficient for reading, writing, speaking, and listening at the college and career readiness level;
demonstrate independence in gathering vocabulary knowledge when considering a word or phrase
important to comprehension or expression. (AS. L.6)

http://www.corestandards.org/

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief
State School Officers. All rights reserved.

Retrieved: February 14, 2014

Standards for Technological Literacy

Students will develop an understanding of the
characteristics and scope of technology.

11.1
K. The rate of technological development is increasing rapidly. (1.9-12.K)

Students will develop an understanding of the core concepts
of technology.

11.1, L3.1, 14.1
W. Systems thinking applies logic and creativity with appropriate compromises in complex real-life
problems. (2.9-12.W)
11.1, L4.1
X. Systems, which are the building blocks of technology, are embedded within larger technological,
social, and environmental systems. (2.9-12.X)
11.1,L1.2
Y. The stability of a technological system is influenced by all of the components in the system,
especially those in the feedback loop. (2.9-12.Y)
11.1, 11.2 [OPTIONAL], 11.3 I 12.2 I 13.1, 14.1, 14.2
Z. Selecting resources involves trade-offs between competing values, such as availability, cost,
desirability, and waste. (2.9-12.Z)
11.1 , 11.2 [OPTIONAL], 11.3 I 12.2 I 13.2 I 14.1, 14.2
BB. Optimization is an ongoing process or methodology of designing or making a product and is
dependent on criteria and constraints. (2.9-12.BB)

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Feb 14,2014 PLTit' Standards and Objectives Alignment

Ll.l
CC. New technologies create new processes. (2.9-12.CC)
Ll.ll L1 .3 I L2 .3 I L4.1
DD. Quality control is a planned process to ensure that a product, service, or system meets
established criteria. (2.9-12.DD)
Ll.1 1 L4.1
EE. Management is the process of planning, organizing, and controlling work. (2.9-12.EE)
Ll.l I L1.2 I L1.3
FF. Complex systems have many layers of controls and feedback loops to provide information.
(2.9-12.FF)
L1.2 [OPTIONAL] I L4.1
M . Requirements involve the identification of the criteria and constraints of a product or system
and the determination of how they affect the final design and development. (2.9-12.M)

Students will develop an understanding of the relationships
among technologies and the connections between
technology and other fields of study.

Ll.l
G. Technology transfer occurs when a new user applies an existing innovation developed for one
purpose in a different function. (3.9-12.G)

Students will develop an understanding of the cultural,
social, economic, and political effects of technology.

Ll.ll L2.1, L2.2 I L3.1, L4.1, L4.2
I. Making decisions about the use of technology involves weighing the trade-offs between the
positive and negative effects. (4 .9-12.1)
L2.1, L3.1

J. Ethical considerations are important in the development, selection, and use oftechnologies.

(4.9- 12.])

Students will develop an understanding of the role of society
in the development and use of technology.

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Feb 14,2014 PL1W Standards and Objectives Alignment

Ll.l

H. Different cultures develop their own technologies to satisfy their individual and shared needs,
wants, and values. (6.9-12.H)
Ll.l

J. A number of different factors, such as advertising, the strength of the economy, the goals of a

company, and the latest fads contribute to shaping the design of and demand for various
technologies. (6.9-12.])
L3.1
I. The decision whether to develop a technology is influenced by societal opinions and demands, in
addition to corporate cultures. (6.9-12.1)

Students will develop an understanding of the influence of
technology on history.

Ll.l
G. Most technological development has been evolutionary, the result of a series of refinements to a
basic invention. (7.9-12.G)
Ll.l
H. The evolution of civilization has been directly affected by, and has in turn affected, the
development and use of tools and materials. (7.9-12.H)
Ll.l
I. Throughout history, technology has been a powerful force in reshaping the social, cultural,
political, and economic landscape. (7.9-12.1)
Ll.l
N. The Industrial Revolution saw the development of continuous manufacturing, sophisticated
transportation and communication systems, advanced construction practices, and improved
education and leisure time. (7.9-12.N)
Ll.l
0. The Information Age places emphasis on the processing and exchange of information. (7.9-12.0)

Students will develop an understanding of engineering
design.

Ll.l, L1.2 [OPTIONAL], L1.3 I L4.2
]. Engineering design is influenced by personal characteristics, such as creativity, resourcefulness,
and the ability to visualize and think abstractly. (9. 9-12.])
L1.2 [OPTIONALL L1.3 I L2.2 I L2.3 I L3.2 I L3.3 I L4.2
K. A prototype is a working model used to test a design concept by making actual observations and
necessary adjustments. (9 .9-12.K)
L1.2 [OPTIONALL L1.3 I L2.3 I L3.2 I L4.2

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Feb 14,2014 PL1W Standards and Objectives Alignment

L. The process of engineering design takes into account a number of factors. (9.9-12.L)
L1.3 I L4.2
I. Established design principles are used to evaluate existing designs, to collect data, and to guide
the design process. (9.9-12.0

Students will develop an understanding of the role of
troubleshooting, research and development, invention and
innovation, and experimentation in problem solving.

Ll.l
I. Research and development is a specific problem-solving approach that is used intensively in
business and industry to prepare devices and systems for the marketplace. (10.9-12.!)
Ll.l
K. Not all problems are technological, and not every problem can be solved using technology.
(10.9-12.K)
Ll.l
L. Many technological problems require a multidisciplinary approach. (10.9-12.L)

Students will develop an understanding of and be able to
select and use info~mation and communication technologies.

Ll.l
L. Information and communication technologies include the inputs, processes, and outputs
associated with sending and receiving information. (17.9-12.L)
Ll.l 1Ll.3
M. Information and communication systems allow information to be transferred from human to
human, human to machine, machine to human, and machine to machine. (17.9-12.M)
L1.2 I L2.11 L2.2 I L3.2 I L4.1 I L4.2
N. Information and communication systems can be used to inform, persuade, entertain, control,
manage, and educate. (17.9-12.N)
L1.2 I 11.3 I L2.11 L2.2 I L2.3 I L3.11 L3.2 I 13.3 I L4.11 L4.2
P. There are many ways to communicate information, such as graphic and electronic means.
(17.9-12.P)
L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L3.1, L3.2 I 13.3 I L4.11 L4.2
Q. Technological knowledge and processes are communicated using symbols, measurement,
conventions, icons, graphic images, and languages that incorporate a variety of visual, auditory,
and tactile stimuli. (17.9-12.0)

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Feb 14,2014 PL1W Standards and Objectives Alignment

Students will develop an understanding of and be able to
select and use manufacturing technologies.

Ll.l, L2.2 I L2.3 I L4.1, L4.2
0. Manufacturing systems may be classified into types, such as customized production, batch
production, and continuous production. (19.9-12.0)
Ll.l
P. The interchangeability of parts increases the effectiveness of manufacturing processes.
(19.9-12.P)
L2.2
N. Durable goods are designed to operate for a long period of time, while non-durable goods are
designed to operate for a short period oftime. (19.9-12.N)

Students will develop an understanding of the attributes of
design.

L1.2 [OPTIONAL], Ll.J I L2.3 I L3.2 I L4.2
H. The design process includes defining a problem, brainstorming, researching and generating
ideas, identifying criteria and specifying constraints, exploring possibilities, selecting an approach,
developing a design proposal, making a model or prototype. (8.9-12.H)
L1.2 [OPTIONALL L2.1, L2.3 I L3.2 I L4.2
]. The design needs to be continually checked and critiqued, and the ideas of the design must be
redefined and improved. (8.9-12.])
L1.2 [OPTIONALL Ll.J I L2.1, L2.3 I L3.2 I L4.2
K. Requirements of a design, such as criteria, constraints, and efficiency, sometimes compete with
each other. (8.9-12.K)
L2.1, L4.2
I. Design problems are seldom presented in a clearly defined form. (8.9-12.1)

Students will develop the abilities to apply the design
process.

L1.2 [OPTIONALL Ll.J I L3.2 7/12
M. Identify the design problem to solve and decide whether or not to address it. (11.9-12.M)
L1.2 I Ll.J I L2.3 I L3.2 I L3.3 I L4.2
N. Identify criteria and constraints and determine how these will affect the design process.

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Feb 14,2014 PLIW Standards and Objectives Alignment

(11.9-12.N)
L1.2 [OPTIONAL], L1.3 I L3.2
0. Refine a design by using prototypes and modeling to ensure quality, efficiency, and productivity
of the final product. (11.9-12.0)
Ll.3 I L2.3 I L3.2 I L3.3 I L4.2
Q. Develop and produce a product or system using a design process. (11.9-12.0)
Ll.3 I L2 .2 I L2.3 I L3.2 I L3.3 I L4.2
R. Evaluate final solutions and communicate observation, processes, and results of the entire design
process, using verbal, graphic, quantitative, virtual, and written means, in addition to
three-dimensional models. (11.9-12.R)
L2.11 L2.3 I L3.2 I L4.2
P. Evaluate the design solution using conceptual, physical, and mathematical models at various
intervals of the design process in order to check for proper design and to note areas where
improvements are needed. (11.9-12.P)

Students will develop an understanding of the effects of
technology on the environment.

.9.:.12

L2.2 I L4.1
L. Decisions regarding the implementation of technologies involve the weighing of trade-offs
between predicted positive and negative effects on the environment. (5.9-12.L)
L3.1 1 L4.1
H. When new technologies are developed to reduce the use of resources, considerations of
trade-offs are important. (5.9-12.H)

Students will develop an understanding of and be able to
select and use energy and power technologies.

.9.:.12

L3.2
N. Power systems must have a source of energy, a process, and loads. (16.9-12 .N)

International Technology Education Association. (2007). Standards for technological literacy. Reston,
VA: ITEA.

Retrieved: February 14, 2014

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Feb 14,2014 PLTIV Standards and Objectives Alignment

Next Generation Science Standards

High School

Engineering Design

Ll.l
HS-ETSl-1. Analyze a major global challenge to specify qualitative and quantitative criteria and
constraints for solutions that account for societal needs and wants. (HS.ETSl.l)

L1.2 I L1.3 I L2.3 I L3.11 L3.2 I L3.3 I L4.2
HS-ETSl-2. Design a solution to a complex real-world problem by breaking it down into smaller,
more manageable problems that can be solved through engineering. (HS.ETS1.2)
L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L3.11 L3.2 I L3.3 I L4.11 L4.2
HS-ETSl-3. Evaluate a solution to a complex real-world problem based on prioritized criteria and
trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics,
as well as possible social, cultural, and environmental impacts. (HS.ETS1.3)
L1.2 I L1.3 I L2.3 I L3.11 L3.2 I L3.3 I L4.2
HS-ETSl-4. Use a computer simulation to model the impact of proposed solutions to a complex
real-world problem with numerous criteria and constraints on interactions within and between
systems relevant to the problem. (HS.ETS1.4)

Earth and Human Activity

L1.3
HS-ESS3-1. Construct an explanation based on evidence for how the availability of natural
resources, occurrence of natural hazards, and changes in climate have influenced human activity.
(HS.ESS3.1)
L1.3
HS-ESS3-2. Evaluate competing design solutions for developing, managing, and utilizing energy
and mineral resources based on cost-benefit ratios.* (HS.ESS3.2)
L2.1 1L3.1
HS-ESS3-4. Evaluate or refine a technological solution that reduces impacts of human activities on
natural systems.* (HS.ESS3.4)

Energy

L3.2

HS-PS3-1. Create a computational model to calculate the change in the energy of one component in

a system when the change in energy of the other component(s) and energy flows in and out of the

system are known. (HS.PS3.1)

L3.2 I L4.2

__;I HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one
form of energy into another form of energy.* (HS.PS3.3)

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Feb 14,2014 PLTW Standards and Objectives Alignment

© 2011, 2012, 2013 Achieve, Inc. All rights reserved. NEXT GENERATION SCIENCE STANDARDS
and the associated logo are trademarks of Achieve, Inc.4

Retrieved: February 14, 2014

Common Core State Standards for
Mathematical Practice (HS)

Algebra

Reasoning With Equations And Inequalities
-Solve Equations And Inequalities In One Variable

L1.2 I L2.3 I L3.1 ' L3.2 I L4.2
3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters. (A.RE1.3)

-Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning

L2.3
1. Explain each step in solving a simple equation as following from the equality of numbers asserted
at the previous step, starting from the assumption that the original equation has a solution.
Construct a viable argument to justify a solution method. (A.REI.1)

-Represent And Solve Equations And Inequalities Graphically

L2.3
10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in
the coordinate plane, often forming a curve (which could be a line). (A.REI.l 0)

Creating Equations
-Create Equations That Describe Numbers Or Relationships

L2.1 I L2.3

1. Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational and exponential functions.
(A.CED.l)

L2.3 I L3.1 I L3.2
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving

equations. For example, rearrange Ohm's law V =IR to highlight resistance R. (A.CED.4)

Seeing Structure In Expressions 10!12
-Interpret The Structure Of Expressions

L2 .3
l.a. Interpret parts of an expression, such as terms, factors, and coefficients. (A.SSE .l.a)

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Feb 14,2014 PL1W Standards and Objectives Alignment

Functions

Linear. Quadratic. And Exponential Models
-Interpret Expressions For Functions In Terms Of The Situation They Model

L1.2 I L1.3 I L2.11 L2.3 I L3.1
5. Interpret the parameters in a linear or exponential function in terms of a context. (F.LE.5)

Interpreting Functions
-Understand The Concept Of A Function And Use Function Notation

L2.1 1L2.3
2. Use function notation, evaluate functions for inputs in their domains, and interpret statements
that use function notation in terms of a context. (F.IF.2)

Building Functions
-Build A Function That Models A Relationship Between Two Quantities

L2.1 1L2.3
l.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(F.BF.l.a)

Number and Quantity

Quantities
-Reason Quantitatively And Use Units To Solve Problems.

L2.11 L2.2 I L2.3 I L3.11 L3.2
1. Use units as a way to understand problems and to guide the solution of multi-step problems;
choose and interpret units consistently in formulas; choose and interpret the scale and the origin in
graphs and data displays. (N.Q .1)
L2.11 L2.2 I L2.3 I L3.11 L3.2 I L4.2
3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
(N.Q .3)
L2.3
2. Define appropriate quantities for the purpose of descriptive modeling. (N.Q .2)

Geometry

Geometric Measurement And Dimension
-Visualize Relationships Between Two-Dimensional And Three- Dimensional Objects

L2.1, L2.3 I L3.11 L3.3 I L4.2
4. Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify
three-dimensional objects generated by rotations of two-dimensional objects. (G.GMD.4)

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Modeling With Geometry
-Apply Geometric Concepts In Modeling Situations

L2.1, L2.3
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a
tree trunk or a human torso as a cylinder).* (G.MG. l)
L2.1
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per
square mile, BTUs per cubic foot).* (G.MG.2)
L2 .1, L2.3 I L3.1, L3.2
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to
satisfy physical constraints or minimize cost; working with typographic grid systems based on
ratios).* (G.MG.3)

Similarity. Right Triangles. And Trigonometry
-Define Trigonometric Ratios And Solve Problems Involving Right Triangles

L2 .3 I L3.1
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.* (G.SRT.8)

Circles
-Understand And Apply Theorems About Circles

L2.3
4. (+) Construct a tangent line from a point outside a given circle to the circle. (G.C.4)

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©2012 Common Core State Standards Initiative

Retrieved: February 14, 2014

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Feb 14,2014 PL111' Standards and Objectives Alignment

Showing Results for:
Course: Aerospace Engineering
Units: 1, 2, 3 & 4
Lessons: Ll.l, L1.2, L1.3, L2.1, L2.2, L2.3, L3.1 , L3.2, L4.1, L4.2 & L4.3
Common Core State Standards for English Language Arts, Standards for Technological Literacy,
Next Generation Science Standards & Common Core State Standards for Mathematical Practice (HS)

Common Core State Standards for English
Language Arts

Reading

Key Ideas and Details

Ll.l l L2.2 I L2.3 I L3.11 L3.2 I L4.3
1. Read closely to determine what the text says explicitly and to make logical inferences from it;
cite specific textual evidence when writing or speaking to support conclusions drawn from the text.
(AS.R.l)
Ll.ll L2.2 I L3.11 L3.2 I L4.3
2. Determine central ideas or themes of a text and analyze their development; summarize the key
supporting details and ideas. (AS.R.2)
Ll.ll L2.2 I L2.3 I L3.11 L3.2 I L4.11 L4.2 I L4.3
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning or
tone. (AS.R.4)
Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L3.11 L3.2 I L4.11 L4.2 I L4.3
7. Integrate and evaluate content presented in diverse formats and media, including visually and
quantitatively, as well as in words. (AS.R.7)
Ll.ll L2.2 I L3.11 L4.3
9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to
compare the approaches the authors take. (AS.R.9)
Ll.ll L2.2 I L2.3 I L3.11 L3.2 I L4.3
10. Read and comprehend complex literary and informational texts independently and proficiently.
(AS.R.lO)

Text Types and Purposes

Ll.ll L1.2 I L2.2 I L2.3 I L3.11 L3.2 I L4.11 L4.3
2. Write informative/explanatory texts to examine and convey complex ideas and information clearly
and accurately through the effective selection, organization, and analysis of content. (AS.W.2)
Ll.ll L1.2 I L2.2 I L2.3 I L3.11 L4.11 L4.3
4. Produce clear and coherent writing in which the development, organization, and style are
appropriate to task, purpose, and audience. (AS.W.4)

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Feb 14,2014 PLTW Standards and Objectives Alignment

11.1
7. Conduct short as well as more sustained research projects based on focused questions,
demonstrating understanding of the subject under investigation. (AS.W.7)
11.1, 12.2, 13.2, 14.3
8. Gather relevant information from multiple print and digital sources, assess the credibility and
accuracy of each source, and integrate the information while avoiding plagiarism. (AS.W.8)
11.1, 12.2, 12.3, 13.1, 13.2, 14.3
9. Draw evidence from literary or informational texts to support analysis, reflection, and research.
(AS.W.9)
11.2 1 12,3 1 13,1 1 13,2 1 14,1 1 14,3
3. Write narratives to develop real or imagined experiences or events using effective technique,
well-chosen details, and well-structured event sequences. (AS.W.3)
13.2
1. Write arguments to support claims in an analysis of substantive topics or texts, using valid
reasoning and relevant and sufficient evidence. (AS.W.1)

Comprehension and Collaboration

11.1, 12.2, 13.2 I 14.1 I 14.3
1. Prepare for and participate effectively in a range of conversations and collaborations with
diverse partners, building on others' ideas and expressing their own clearly and persuasively.
(AS.SL.1)
11.1, 11.2, 11.3, 12.2, 13.1 I 13.2, 14.1, 14.2, 14.3
2. Integrate and evaluate information presented in diverse media and formats, including visually,
quantitatively, and orally. (AS .SL.2)
11.1, 12.2, 12.3, 13.1 I 13.2, 14.3
4. Present information, findings, and supporting evidence such that listeners can follow the line of
reasoning and the organization, development, and style are appropriate to task, purpose, and
audience. (AS.SL.4)
11.1 I 12.2, 12.3, 13.1 , 13.2, 14.3
5. Make strategic use of digital media and visual displays of data to express information and
enhance understanding of presentations. (AS.SL.5)
11.1 I 12.2, 12.3 I 13.1 , 13.2, 14.3
6. Adapt speech to a variety of contexts and communicative tasks, demonstrating command of
formal English when indicated or appropriate. (AS.SL.6)

Conventions of Standard English

11.1, 11.2, 11.3, 12.1 I 12.2 I 12.3 I 13.1 I 13.2 I 14.1 I 14.2 I 14.3
1. Demonstrate command of the conventions of standard English grammar and usage when writing
or speaking. (AS.L.1)
11.11 11.2 I 11.3 I 12.11 12.2 I 12.3 I 13.11 13.2 I 14.11 14.2 I 14.3
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and
spelling when writing. (AS.L.2)
11.1, 11.2
3. Apply knowledge of language to understand how language functions in different contexts. to
make effective choices for meaning or style, and to comprehend more fully when reading or
listening. (AS.L.3)

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Feb 14,2014 PL1WStandards and Objectives Alignmen t

11.1 111.2 1 11.3 1 12,11 12,2 1 12,3 1 13,11 13,2 1 14,11 14,2
4. Detennine or clarify the meaning of unknown and multiple-meaning words and phrases by using
context clues, analyzing meaningful word parts, and consulting general and specialized reference
materials, as appropriate. (AS.L.4)
11.1 111.2 1 11.3 1 12,11 12,2 1 12,3 1 13.1 1 13,2 1 14,11 14,2 1 14,3
6. Acquire and use accurately a range of general academic and domain-specific words and phrases
sufficient for reading, writing, speaking, and listening at the college and career readiness level;
demonstrate independence in gathering vocabulary knowledge when considering a word or phrase
important to comprehension or expression. (AS .L.6)

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©Copyright 2010. National Governors Association Center for Best Practices and Council of Chief
State School Officers. All rights reserved.

Retrieved: February 14, 2014

Standards for Technological Literacy

Students will develop an understanding of the
characteristics and scope of technology.

11.11 13.2
]. The nature and development of technological knowledge and processes are functions of the

setting. (1.9-1 2.J)

11.1 111.3
K. The rate of technological development is increasing rapidly. (1.9-12.K)
11,2 1 11,3
L. Inventions and innovations are the results of the specific, goal-directed research. (1.9-12.L)

Students will develop an understanding of the core concepts
of technology.

11.11 11.2 I 11.3 I 12.11 12.2 I 12.3 I 13.2 I 14.1 114.2
Z. Selecting resources involves trade-offs between competing values, such as availability, cost,
desirability, and waste. (2.9-12.2)
11.11 11.2 1 11,3 1 12,11 12,2 1 12,3 1 13,1 114,1 114,2

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Feb 14,2014 PLTIV Standards and Objectives Alignment

BB. Optimization is an ongoing process or methodology of designing or making a product and is
dependent on criteria and constraints. (2.9-12.BB)
Ll.l
CC. New technologies create new processes. (2.9-12.CC)
L1.2 I L1.3 I L2.11 L2.2 I L3.2 I L4.1
M. Requirements involve the identification of the criteria and constraints of a product or system
and the determination of how they affect the final design and development. (2.9-12.M)
L1.3 I L2.2 I L2.3 I L4.2
W. Systems thinking applies logic and creativity with appropriate compromises in complex real-life
problems. (2.9-12.W)
L1.3 I L2.2 I L2.3 I L4.11 L4.2
X. Systems, which are the building blocks of technology, are embedded within larger technologicaL
social, and environmental systems. (2.9-12.X)
L2.1
DD. Quality control is a planned process to ensure that a product, service, or system meets
established criteria. (2 .9-12.DD)
L2.2 I L4.2
FF. Complex systems have many layers of controls and feedback loops to provide information.
(2.9-12.FF)

Students will develop an understanding of the relationships
among technologies and the connections between
technology and other fields of study.

Ll.l
G. Technology transfer occurs when a new user applies an existing innovation developed for one
purpose in a different function. (3.9-12.G)
Ll.l
H. Technological innovation often results when ideas, knowledge, or skills are shared within a
technology, among technologies, or across other fields. (3.9-12 .H)
Ll.1 1Ll.3

J. Technological progress promotes the advancement of science and mathematics. (3.9-12.])

Students will develop an understanding of the cultural,
social, economic, and political effects of technology.

Ll.l
H. Changes caused by the use of technology can range from gradual to rapid and from subtle to
obvious. (4.9-12.H)
L1.2 I L1.3 I L2.2 I L3.2 I L4.11 L4.2

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Feb 14, 2014 PL1W Standards and Objectives Alignment

I. Making decisions about the use of technology involves weighing the trade-offs between the
positive and negative effects. (4.9-12.1)
L3.1
]. Ethical considerations are important in the development, selection, and use of technologies.
(4 .9-12.])
L3.1
K. The transfer of a technology from one society to another can cause cultural, social, economic,
and political changes affecting both societies to varying degrees. (4.9-12.K)

Students will develop an understanding of the role of society
in the development and use of technology.

Ll.l, L3.1
H. Different cultures develop their own technologies to satisfy their individual and shared needs,
wants, and values. (6.9-12.H)
Ll.l, L3.1
I. The decision whether to develop a technology is influenced by societal opinions and demands, in
addition to corporate cultures. (6.9-12.1)

Students will develop an understanding of the influence of
technology on history.

Ll.l, L1.3 I L3.2
G. Most technological development has been evolutionary, the result of a series of refinements to a
basic invention. (7.9-12.G)
Ll.l, L3.2
H. The evolution of civilization has been directly affected by, and has in turn affected, the
development and use of tools and materials. (7.9-12.H)
Ll.l, L3.1, L3.2
I. Throughout history, technology has been a powerful force in reshaping the social, cultural,
political, and economic landscape. (7.9-12.1)
L3.2
L. The Middle Ages saw the development of many technological devices that produced long-lasting
effects on technology and society. (7.9-12.L)
L3.2
M. The Renaissance, a time of rebirth of the arts and humanities, was also an important
development in the history of technology. (7.9-12.M)

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Feb 14,2014 PL1W Standards and Objectives Alignment

Students will develop an understanding of engineering
design.

11.11 11.3 I 13.11 14.1

J. Engineering design is influenced by personal characteristics, such as creativity, resourcefulness,

and the ability to visualize and think abstractly. (9.9-12.])
11.11 11.2 I 11.3 I 12.11 12.2 I 13.11 13.2 I 14.11 14.2
L. The process of engineering design takes into account a number of factors. (9.9-12.L)
11.2 1 14,2
I. Established design principles are used to evaluate existing designs, to collect data, and to guide
the design process. (9.9-12.1)
11.2 1 12,11 12,2 1 13,11 14,11 14,2
K. A prototype is a working model used to test a design concept by making actual observations and
necessary adjustments. (9.9-12 .K)

Students will develop the abilities to assess the impact of
products and systems.

11.1 112.1 112.2

J. Collect information and evaluate its quality. (13.9-12.])

11.1 112.1 112.2
K. Synthesize data, analyze trends, and draw conclusions regarding the effect of technology on the
individuaL society, and environment. (13.9-12.K)

Students will develop an understanding of and be able to
select and use information and communication technologies.

11.11 11.3 I 13.11 13.2 I 14.11 14.2 I 14.3
N. Information and communication systems can be used to inform, persuade, entertain, controL
manage, and educate. (17.9-12.N)
11.11 11.2 I 11.3 I 12.11 12.2 I 12.3 I 13.11 13.2 I 14.11 14.2 I L4.3
P. There are many ways to communicate information, such as graphic and electronic means.
(17.9-12.P)
11.2 1 11.3 1 12,11 12,2 1 12,3 1 13,11 13,2 1 14,11 14,3
Q. Technological knowledge and processes are communicated using symbols, measurement,
conventions, icons, graphic images, and languages that incorporate a variety of visuaL auditory,

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Feb 14,2014 PL1W Standards and Objectives Alignment

and tactile stimuli. (17.9-12.Q)
11.3 1 12,3
M. Information and communication systems allow information to be transferred from human to
human, human to machine, machine to human, and machine to machine. (17.9-12.M)
14.2
L. Information and communication technologies include the inputs, processes, and outputs
associated with sending and receiving information. (17.9-12.L)

Students will develop an understanding of and be able to
select and use transportation technologies.

11.11 12,2 1 13,1
M. The design of intelligent and non-intelligent transportation systems depends on many processes
and innovative techniques. (18-9-12.M)

Students will develop an understanding of the attributes of
design.

11.2 1 12,11 12,2 1 13,11 14,1
H. The design process includes defining a problem, brainstorming, researching and generating
ideas, identifying criteria and specifying constraints, exploring possibilities, selecting an approach,
developing a design proposal, making a model or prototype. (8.9-12.H)
11,2 1 12,11 12,2 1 13,11 14,11 14,2
]. The design needs to be continually checked and critiqued, and the ideas of the design must be
redefined and improved. (8.9-12.])
11.2 1 11.3 1 12,11 12,2 1 13,11 13,2 1 14,11 14,2
K. Requirements of a design, such as criteria, constraints, and efficiency, sometimes compete with
each other. (8.9-12.K)
12,2 1 13,11 14,1
I. Design problems are seldom presented in a clearly defined form. (8.9-12.1)

Students will develop the abilities to apply the design
process.

11.2 1 11.3 1 12,11 12,2 1 12,3 1 13,11 14,1 1 14,2 7!14

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Feb 14,201 4 PLTW Standards and Objectives Alignment

N. Identify criteria and constraints and determine how these will affect the design process.
(1 1.9-1 2.N)
11.2 1 12,1 1 12,2 1 13.11 14 ,1 114,2
0. Refine a design by using prototypes and modeling to ensure quality, efficiency, and productivity
of the final product. (11.9-1 2.0)
11.2 1 12,11 12,2 1 13,2 1 14,1
P. Evaluate the design solution using conceptual, physical, and mathematical models at various
intervals of the design process in order to check for proper design and to note areas where
improvements are needed. (11.9-12.P)
11.2 1 12,1 1 12,2
Q. Develop and produce a product or system using a design process. (11.9-12.0)
11.2 1 12.2
R. Evaluate final solutions and communicate observation, processes, and results of the entire design
process, using verbal, graphic, quantitative, virtual, and written means, in addition to
three-dimensional models. (11.9-12.R)
13.1
M. Identify the design problem to solve and decide whether or not to address it. (1 1.9-12.M)

Students will develop an understanding of the role of
troubleshooting, research and development, invention and
innovation, and experimentation in problem solving.

11.3 I 12.2 I 13.1
]. Technological problems must be researched before they can be solved. (1 0.9-12.])
11.3 I 12.3 I 13.1
L. Many technological problems require a multidisciplinary approach. (10.9-12.L)
12.2
I. Research and development is a specific problem-solving approach that is used intensively in
business and industry to prepare devices and systems for the marketplace. (10.9-1 2.1)
13.1
K. Not all problems are technological, and not every problem can be solved using technology.
(1 0.9-12.K)

Students will develop the abilities to use and maintain
technological products and systems.

12.1 8/ 14
L. Document processes and procedures and communicate them to different audiences using
appropriate oral and written techniques. (12.9-12.L)
12.1

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Feb 14,2014 PL1W Standards and Objectives Alignment

P. Use computers and calculators to access, retrieve, organize, process, maintain, interpret, and
evaluate data and information in order to communicate. (12.9-12.P)

Students will develop an understanding of the effects of
technology on the environment.

L2.2 I LJ.l, L3.2 J L4.1
L. Decisions regarding the implementation of technologies involve the weighing of trade-offs
between predicted positive and negative effects on the environment. (5.9-12.L)
L4.1
H. When new technologies are developed to reduce the use of resources, considerations of
trade-offs are important. (5.9-12.H)

Students will develop an understanding of and be able to
select and use energy and power technologies.

L3.2
]. Energy cannot be created nor destroyed; however, it can be converted from one form to another.
(16.9-12.])

International Technology Education Association. (2007) . Standards for technological literacy. Reston,
VA: ITEA.

Retrieved: February 14, 2014

Next Generation Science Standards

High School

Engineering Design

Ll.l, L3.1 , L4.1
HS-ETS1-1. Analyze a major global challenge to specify qualitative and quantitative criteria and
constraints for solutions that account for societal needs and wants. (HS.ETS1.1)

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Feb 14,2014 PLTIV Standards and Objectives Alignment

Ll.ll L1.2 I L1.3 I L2.11 L2.2 I L2.3 I L3.11 L3.2 I L4.11 L4.2
HS-ETS1-3. Evaluate a solution to a complex real-world problem based on prioritized criteria and
trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics,
as well as possible social, cultural, and environmental impacts. (HS.ETS1.3)
L1.2 I L1.3 I L2.11 L2.2 I L3.11 L3.2 I L4.11 L4.2 I L4.3
HS-ETS1-2. Design a solution to a complex real-world problem by breaking it down into smaller,
more manageable problems that can be solved through engineering. (HS.ETS1.2)
L1.2 I L1.3 I L2.11 L2.2 I L3.2 I L4.11 L4.2
HS-ETS1-4. Use a computer simulation to model the impact of proposed solutions to a complex
real-world problem with numerous criteria and constraints on interactions within and between
systems relevant to the problem. (HS.ETS1.4)

Motion and Stability: Forces and Interactions

L1.2 I L2.2 I L3.2 I L4.1
HS-PS2-l. Analyze data to support the claim that Newton's second law of motion describes the
mathematical relationship among the net force on a macroscopic object, its mass, and its
acceleration. (HS.PS2 .1)
L3.2
HS-PS2-4. Use mathematical representations of Newton's Law of Gravitation and Coulomb's Law to
describe and predict the gravitational and electrostatic forces between objects. (HS.PS2.4)

Energy

L1.2 I L2.2 I L4.1
HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one
form of energy into another form of energy.* (HS.PS3.3)
L2.2 I L4.1
HS-PS3-1. Create a computational model to calculate the change in the energy of one component in
a system when the change in energy of the other component(s) and energy flows in and out of the
system are known. (HS.PS3.1)
L3.2
HS-PS3-2 . Develop and use models to illustrate that energy at the macroscopic scale can be
accounted for as either motions of particles or energy stored in fields. (HS.PS3.2)
L3.2
HS-PS3-5. Develop and use a model of two objects interacting through electric or magnetic fields to
illustrate the forces between objects and the changes in energy of the objects due to the interaction.
(HS.PS3.5)

Earth's Systems

L1.2
HS-ESS2-4. Use a model to describe how variations in the flow of energy into and out of Earth's
systems result in changes in climate. (HS.ESS2.4)

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