Course title
MATPre-requisite
Engineering I, Engineering II, Algebra II or higher concurrent enrollmentCourse description
Course Description:
Engineering I: This course is designed to introduce students to the world of Engineering Design and problem solving through the design process. The course I designed for any student who intends to pursue future training in any engineering program or technical industry. Students use problem-solving models to improve existing products while utilizing development processes to create new products. They will learn how to apply these models to solve problems in and out of the classroom setting. Students will apply mathematical and scientific concepts and models when being introduced to the fundamentals of mechanical; structural (civil; architectural and green technology); aeronautical; and robotic (VEX IQ) engineering and electrical concepts. Students will use multiple software packages; engineering poster sessions; and presentations to develop technical communication literacy skills. Computer assisted instruction; lab activities and classroom discussions will be used to create a foundation for problem solving and engineering concepts. Career and Technical Student Organization (CTSO) standards will be an integral part of this class. Dual credit may be obtained from Embry Riddle Aeronautical University for this program at high schools offering this option. An honors option is available to all students enrolled in the course. Students mathematically model the kinematics of projectile motion from a small catapult. Students perform a mathematical analysis CO2 car travel based on potential and kinetic energy on a ramp; determine the velocity at the bottom of the ramp; determine the acceleration of car and determine the force of friction between the car and the floor; students determine the force the CO2 cartridge imparts on the car and the rate of acceleration after the cartridge is spent. Students determined the mathematical relationships between the volume of a hot air balloon; pressures and ambient temperature. Students spend approximately 6 hours per week in lab.
Engineering II: This course builds on skills learned in Engineering I; while introducing students to electrical engineering; control systems; the application of green technologies; three dimensional modeling; computer aided manufacturing (CNC) and advanced robotics concepts (VEX). This class incorporates various technological processes and manufacturing technologies. Students will develop a sense of the interdependency of the various engineering disciplines. Students will also develop an understanding that engineering is a human endeavor intended to address the needs of a global society. Utilizing activities; projects and problems; students will develop the skills to solve problems using math; science; and technology in engineering processes to benefit society. The use of CAD/CAM industry based software and equipment will be an extensive part of this class. Students will be introduced to state of the art robotic software. Students will apply concepts of mechanical; electrical and control systems in various design problems. This course will continue to develop technical communication literacy (reading; writing; and speaking). Career and Technical Student Organization (CTSO) standards will be an integral part of this class. Dual credit may be obtained from Embry Riddle Aeronautical University for this program at high schools offering this option. An honors option is available to all students enrolled in the course. Students utilize three dimensional geometric relationships as they develop their skills in Computer Numeric Control. Sample problems presented in this class include:
I. When an oil company drills a new oil well they are only capable of extracting approximately 35% of the oil available. Your job is to develop a way that is economically viable and environmentally responsible; to extract at least 50% more of the oil. Requires the use of volumes; mathematical functions; statistics; and defending a mathematical argument. Students need to consider flow rates; viscosity; temperature; pump pressures; and pipe diameters.
II. The Ogallala Aquifer occupies the High Plains of the United States; extending from western Texas to South Dakota. The Ogallala Aquifer is used to water the crops and cattle that we use for food. We will no longer be able to get water from the Ogallala Aquifer sometime in next 50 years. Your job is to develop a way to continue to water the crops and cattle of the American Midwest without using the aquifer. Your solution must be economically viable and environmentally responsible. Students need to consider the possibility of geometric regression for water usage (from the aquifer); geometric growth for water usage; flow rates; volume; mathematical functions; statistics and be able to defend a mathematical argument.
III. The current EPA regulations are making it increasingly difficult to use the most abundant energy source in the United States. With the current technology; alternative energy is unreliable. This leaves nuclear energy as the best option at this time. When nuclear fuel rods are removed as “used” from the reactor; 99% of the uranium has not been used. Your job has two parts. First; you must develop a way to recycle the fuel rods so that they may be reinserted into the reactor. Second; develop a way to utilize the radiation energy being emitted from the waste material. Your solution must be economically viable and environmentally responsible. Note: The issue with storage of nuclear waste in the United States is a political issue; not one of science or technology. Students need to use exponential functions; geometric series; geometry; combinational number theory; functions and be able to defend a mathematical argument.
IV. The average family in the United States deposits 4.3 pounds of solid waste into landfills every day. This creates a large impact on open spaces and land resources. Your job is to develop a way (other than recycling) to reduce the impact of the amount of waste that is placed in these landfills. Your solution must be economically viable and environmentally responsible. Students need to consider exponential growth; geometry; and statistics and be able to defend a mathematical argument.
V. The current scientific theories claim that global climate change is the result of human activity in the form of releasing carbon dioxide into the atmosphere. It is necessary to continue using the energy that creates the carbon dioxide in order to maintain the global economy. Your job is to develop an economically viable and environmentally responsible way to sequester the carbon dioxide that is being emitted into the atmosphere. Students need to consider geometric series; geometry; statistics and algebraic functions as well as being able to defend a mathematical argument.
VI. One sixth of the world’s population does not have access to potable drinking water. Your job is to develop a way to provide a sustainable method to provide safe; clean drinking water to these populations. You may assume that a water source is available. Your solution must be economically viable and environmental responsible. Students need to consider population growth; statistics; flow rates; algebraic functions and be able to defend a mathematical series.
VII. In 2005; Hurricane Katrina devastated the city of New Orleans. Despite many overtones; not much has been done to prevent a repeat of the event. Your job is to develop an economically viable and environmentally responsible way to safeguard the people and the property of New Orleans against a repeat of a Katrina-like disaster. Students need to use geometry; statistics; probability; and algebraic functions as well as be able to defend a mathematical argument.
VIII. Approximately 12.5% of the global population suffers from chronic malnourishment. While there are many reasons for this; the primary reason is access to food. Your job is to develop a way to provide healthy food to these people. Your solution should be economically viable; environmentally responsible and sustainable. Students need to consider population growth; geometry; and statistics and be able to defend a mathematical function.
Students spend approximately 6 hours per week working on projects/labs.
Engineering III: This course applies engineering technology and skills to the manufacturing processes while recognizing that engineering is a human endeavor intended to address the needs of a global society. This course will examine the relationship of manufacturing and process development to the world of engineering. Students will use advanced engineering design; production; and programming techniques for Mobile robotics (VEX); Robotic Arm; 3 Dimensional Modeling; and Computer Numerical Control (CNC). Students will incorporate mathematical and scientific modeling and processes in order to solve real world manufacturing and production problems. Students will identify the impact of various engineering disciplines on manufacturing processes. Students will continue to utilize and improve technical communication skills (reading; writing; and speaking). Students will investigate the impact of manufacturing and robotics on both local and global societies. Career and Technical Student Organization (CTSO) standards will be an integral part of this class. Dual credit may be obtained from Embry Riddle Aeronautical University for this program at high schools offering this option. An honors option is available to all students enrolled in the course.
IX. When an oil company drills a new oil well they are only capable of extracting approximately 35% of the oil available. Your job is to develop a way that is economically viable and environmentally responsible; to extract at least 50% more of the oil. Requires the use of volumes; mathematical functions; statistics; and defending a mathematical argument. Students need to consider flow rates; viscosity; temperature; pump pressures; and pipe diameters.
X. The Ogallala Aquifer occupies the High Plains of the United States; extending from western Texas to South Dakota. The Ogallala Aquifer is used to water the crops and cattle that we use for food. We will no longer be able to get water from the Ogallala Aquifer sometime in next 50 years. Your job is to develop a way to continue to water the crops and cattle of the American Midwest without using the aquifer. Your solution must be economically viable and environmentally responsible. Students need to consider the possibility of geometric regression for water usage (from the aquifer); geometric growth for water usage; flow rates; volume; mathematical functions; statistics and be able to defend a mathematical argument.
XI. The current EPA regulations are making it increasingly difficult to use the most abundant energy source in the United States. With the current technology; alternative energy is unreliable. This leaves nuclear energy as the best option at this time. When nuclear fuel rods are removed as “used” from the reactor; 99% of the uranium has not been used. Your job has two parts. First; you must develop a way to recycle the fuel rods so that they may be reinserted into the reactor. Second; develop a way to utilize the radiation energy being emitted from the waste material. Your solution must be economically viable and environmentally responsible. Note: The issue with storage of nuclear waste in the United States is a political issue; not one of science or technology. Students need to use exponential functions; geometric series; geometry; combinational number theory; functions and be able to defend a mathematical argument.
XII. The average family in the United States deposits 4.3 pounds of solid waste into landfills every day. This creates a large impact on open spaces and land resources. Your job is to develop a way (other than recycling) to reduce the impact of the amount of waste that is placed in these landfills. Your solution must be economically viable and environmentally responsible. Students need to consider exponential growth; geometry; and statistics and be able to defend a mathematical argument.
XIII. The current scientific theories claim that global climate change is the result of human activity in the form of releasing carbon dioxide into the atmosphere. It is necessary to continue using the energy that creates the carbon dioxide in order to maintain the global economy. Your job is to develop an economically viable and environmentally responsible way to sequester the carbon dioxide that is being emitted into the atmosphere. Students need to consider geometric series; geometry; statistics and algebraic functions as well as being able to defend a mathematical argument.
XIV. One sixth of the world’s population does not have access to potable drinking water. Your job is to develop a way to provide a sustainable method to provide safe; clean drinking water to these populations. You may assume that a water source is available. Your solution must be economically viable and environmental responsible. Students need to consider population growth; statistics; flow rates; algebraic functions and be able to defend a mathematical series.
XV. In 2005; Hurricane Katrina devastated the city of New Orleans. Despite many overtones; not much has been done to prevent a repeat of the event. Your job is to develop an economically viable and environmentally responsible way to safeguard the people and the property of New Orleans against a repeat of a Katrina-like disaster. Students need to use geometry; statistics; probability; and algebraic functions as well as be able to defend a mathematical argument.
XVI. Approximately 12.5% of the global population suffers from chronic malnourishment. While there are many reasons for this; the primary reason is access to food. Your job is to develop a way to provide healthy food to these people. Your solution should be economically viable; environmentally responsible and sustainable. Students need to consider population growth; geometry; and statistics and be able to defend a mathematical function.
The following are used to satisfy the dual enrollment requirements for Engineering III.
1. Helicopter Lab—Students create mathematical models using linear programming based on four equations and four unknowns in order to predict the height at which a helicopter with rotor blades between the extremes will hover; given all other variables are constant. Students utilize Excel for this lab.
2. Catapult Lab--Students create mathematical models to predict the distance a projectile will travel based on extremes of throwing arm travel distance. Students utilize Excel for this lab.
3. Solar Oven Lab—Students create a mathematical model; using linear programming; to predict the temperature of the cooking chamber based on a number of variables; including cooking chamber volume; size of reflectors; albedo of reflectors; incident angle of the reflectors and cooking chamber window with the sun; and the amount of solar energy available at the surface of the earth when the ovens are tested. Students utilize Excel for this lab.
Students spend approximately 6 hours per week working on projects and/or labs.
Upon successful completion of this course; students can earn an embedded 4th math credit needed for graduation as determined by State Board of Career & Technical Education and the PUSD Governing Board. This credit may not transfer to colleges or universities as a math credit and students are encouraged to work with the counselors and post-secondary admissions representative for that determination.
Course Sequence: Engineering I; Algebra II or above math course; Engineering II; Engineering III; Engineering IV; CTE Internship
Course Outline and Standard Alignment:
Introduction to Engineering Design Engineering Course Unit 1.0—Career/Portfolio
1. Career/Portfolio
A. Objective: Create electronic portfolio
1. Why it is important and content
a. Multi media
b. Samples of work
c. Resume
d. Cover letter
e. Networking - Myspace/Facebook/LinkedIn/etc.
f. Internships
2. Create portfolio
a. Online tutorial (Front Page/Publisher/Other)
b. Upload samples of work
3. Bridges
a. Interest inventory
4. Cover letter
a. Resources
5. Resume
Introduction to Engineering Design Engineering Course Unit 2.0—Civil
2. Civil
A. Technical drawing
B. Technical writing
C. History of engineering
D. Engineering types
E. Careers
F. Presentation
G. Materials
H. Understanding how/why things work
I. Science > Math
J. Critical thinking
Engineering Standards:
4.3; 4.4; 5.1
4.3; 4.5; 52
1.3; 2.3; 4.2; 4.4; 5.2; 6.2; 6.3
2.5; 3.1; 3.2; 3.3; 4.1; 4.3; 4.5
2.4; 4.1
4.4; 4.5
3.4
2.1; 2.5; 2.6
2.5; 4.1; 4.2; 4.4
Math Standards:
HS.N-Q.1
HS.N-Q.2
HS.N-Q.3
HS.A-SSE.1
HS.A.SSE.3
HS.A-REI.3
HS.G-MG.2
HS.G-MG.3
HS.S-ID.6
Introduction to Engineering Design Engineering Course Unit 3.0—Aerospace
3. Aerospace
A. Technical drawing
B. Technical writing
C. History of engineering
D. Engineering types
E. Careers
F. Presentation
G. Materials
H. Understanding how/why things work
I. Science > Math
J. Critical thinking
Engineering Standards:
4.3; 4.4; 5.1
4.3; 4.5; 52
1.3; 2.3; 4.2; 4.4; 5.2; 6.2; 6.3
3.2; 3.3; 3.4; 4.3; 4.4; 4.5
2.4; 4.3; 5.1
2.5; 3.1; 3.2; 3.3; 4.1; 4.3; 4.5
4.4; 4.5
2.1; 4.1; 4.3; 4.5
2.4; 3.1; 3.2; 4.1; 4.4; 4.5; 5.1
3.1; 3.3; 3.4; 3.5; 4.1; 4.2; 4.4; 4.5
2.1; 2.5; 2.6
2.5; 4.1; 4.2; 4.4
Math Standards:
HS.N-Q.1
HS.N-Q.2
HS.N-Q.3
HS.N-VM.3; HS.N-VM.4
HS.N-VM.5
HS.A-SSE.1
HS.A-REI.3
HS.F-IF.2
HS.F-IF-6; HS.F-IF.9
HS.F-BF.1
HS.G-MG.3
HS.S-ID.6
Introduction to Engineering Design Engineering Course Unit 4.0—Mechanical
4. Mechanical (catapult)
A. Technical drawing
B. Print reading
C. Technical writing
D. History of engineering
E. Engineering types
F. Careers
G. Presentation
H. Materials
I. Understanding how/why things work
J. Science > Math
K. Critical thinking
Engineering Standards:
4.3; 4.4; 5.1
4.3; 4.5; 52
1.3; 2.3; 4.2; 4.4; 5.2; 6.2; 6.3
3.2; 3.3; 3.4; 4.3; 4.4; 4.5
2.4; 4.3; 5.1
2.5; 3.1; 3.2; 3.3; 4.1; 4.3; 4.5
3.1; 3.2; 3.3; 3.4; 3.5
4.4; 4.5
2.1; 4.1; 4.3; 4.5
2.1;4.1; 4.3; 4.5
2.4; 3.1; 3.2; 4.1; 4.4; 4.5; 5.1
3.1; 3.3; 3.4; 3.5; 4.1; 4.2; 4.4; 4.5
2.1; 2.5; 2.6
2.5; 4.1; 4.2; 4.4
3.1; 3.2
4.1; 4.2
Math Standards:
HS.N-Q.1
HS.N-Q.2
HS.N-Q.3
HS.N-VM.1; HS.N-VM.3; HS.N-VM.4
HS.N-VM.5
HS.A-SSE.1
HS.A-CED.1
HS.A-REI.3
HS.F-IF.2
HS.F-IF.4
HS.F-IF-6; HS.F-IF.9
HS.F-BF.1
HS.G-MG.3
HS.S-ID.6
HS.S-ID.7
HS.S-ID.8
Principles of Engineering Course Unit 1.0
1. Career/Portfolio
A. Objective: Update electronic portfolio
1. Review importance and content
a. Multi media
b. Samples of work
c. Resume
d. Cover letter
e. Networking - Myspace/Facebook/LinkedIn/etc.
f. Internships
2. Update portfolio
a. Upload samples of work
b. Revisit Bridges
c. Update resume
d. Update cover letter
3. Filling out a job application
4. Preparing for an interview
a. Questions
1) What do they ask you?
2) What do you ask them?
b. Answers
c. Appearance
d. Etiquette
1) Timeliness
2) Manners
3) Presence
4) Attitude
5) Preparedness
e. Company Research
f. Mock interview
Principles of Engineering Course Unit 2.0
2. SkillsUSA
Electrical/Computer
Engineering Standards:
2.5; 3.1; 3.2; 3.3; 4.1; 4.3; 4.5
4.3; 4.5; 52
1.3; 2.3; 4.2; 4.4; 5.2; 6.2; 6.3
4.3; 4.4;4.5
4.4; 4.5
2.1;4.1; 4.3; 4.5
3.1; 3.3; 3.4; 3.5; 4.1; 4.2; 4.4; 4.5
3.1; 3.3; 3.4; 3.5; 4.1; 4.2; 4.4; 4.5
4.1; 4.2; 4.3; 4.4; 4.5
4.1
3.1; 3.2
3.5; 4.1; 4.3; 4.4; 5.1; 5.2; 6.1; 6.2
2.5; 4.1; 4.2; 4.4
Math Standards:
HS.A-SSE.1
HS.N-Q.2
HS.N-Q.3
HS.A-SSE.2
HS.A-REI.3
HS.F-IF.4
HS.F-BF.1
HS.F-BF.1
HS.F-LE.2
HS.F-LE.3
HS.S-ID.7
HS.F-TF.5
HS.S-ID.6
Principles of Engineering Course Unit 3.0
Technical drawing
Technical writing
History of engineering
Engineering types
Careers
Presentation
Materials
Understanding how/why things work
Science > Math
Critical thinking
Engineering Standards:
4.3; 4.4; 5.1
4.3; 4.5; 52
1.3; 2.3; 4.2; 4.4; 5.2; 6.2; 6.3
3.2; 3.3; 2.4; 4.3; 4.4; 4.5
2.4; 4.3; 5.1
2.5; 3.1; 3.2; 3.3; 4.1; 4.3; 4.5
4.4; 4.5
2.1; 4.1; 4.3; 4.5
2.5; 3.1; 3.2; 3.3; 4.1; 4.3; 4.5
2.1;4.1; 4.3; 4.5
2.4; 3.1; 3.2; 4.1; 4.4; 4.5; 5.1
Math Standards:
HS.N-Q.1
HS.N-Q.2
HS.N-Q.3
HS.N-VM.1; HS.N-VM.3; HS.N-VM.4
HS.N-VM.5
HS.A-SSE.1
HS.A-REI.3
HS.F-IF.2
HS.A-SSE.1
HS.F-IF.4
HS.F-IF-6; HS.F-IF.9
HS.F-BF.1
Engineering and Manufacturing Course Unit 1.0
1. Career/Portfolio
A. Objective: Update electronic portfolio
1. Review importance and content
2. Update portfolio
a. Upload samples of work
b. Revisit Bridges
c. Update resume
d. Update cover letter
3. College research
a. Review admissions requirements/cost
b. Review program prerequisites/availability
c. Check scholarships/grants/FAFSA
Principles of Engineering Course Unit 2.0
Mechanical/Industrial
Engineering Standards:
4.3; 4.4; 5.1
4.3; 4.5; 52
1.3; 2.3; 4.2; 4.4; 5.2; 6.2; 6.3
3.2; 3.3; 3.4; 4.3; 4.4; 4.5
2.4; 4.3; 5.1
2.5; 3.1; 3.2; 3.3; 4.1; 4.3; 4.5
2.4; 4.1
3.1; 3.2; 3.3; 3.4; 3.5
2.1; 4.1; 4.3; 4.5
2.1;4.1; 4.3; 4.5
2.4; 4.1; 5.1
2.4; 3.1; 3.2; 4.1; 4.4; 4.5; 5.1
3.1; 3.3; 3.4; 3.5; 4.1; 4.2; 4.4; 4.5
2.1; 2.5; 2.6
2.5; 2.6; 4.1; 4.2; 4.4
4.1; 4.2
2.5; 4.1; 4.2; 4.4
3.1; 3.2
4.1; 4.2
Math Standards:
HS.N-Q.1
HS.N-Q.2
HS.N-Q.3
HS.N-VM.1; HS.N-VM.3; HS.N-VM.4
HS.N-VM.5
HS.A-SSE.1
HS.A-SSE.3
HS.A-SSE.4
HS.F-IF.2
HS.F-IF.4
HS.F-IF.4
HS.F-IF-6; HS.F-IF.9
HS.F-BF.1
HS.G-MG.3
HS.S-ID.4
HS.S-ID.5
HS.S-ID.6
HS.S-ID.7
HS.S-ID.8
Engineering Design and Development Course Unit 1.0
1. Capstone Project
A. Objective: Creating a project that will be presented to a panel of judges
1. Promoting themselves/portfolio
2. Add Capstone Project to portfolio geared toward a certain job/field
Outcomes:
1. Help for future success
2. Adapt/transfer skills/be flexible
3. Why is it important to learn a software to meet needs/objective?
4. Culminating project/Capstone
5. Resume
6. Hands-on projects in various engineering areas
7. Engineering concepts
8. Critical thinking - CTSO
9. Economic impact of engineering
10. Engineering design
11. Environmental impact
a. Waste
b. Soil
c. Water
d. Roads
e. Nuclear
12. Engineering materials
a. Weights/measures
b. Processes materials
c. Procedures
d. Plastics
e. Metals
f. Woods
g. Welding
13. Mechanics
a. Gravity
b. Forces
c. Math stuff
Arizona
State Mathematical Standard or Benchmark with Engineering Standard Connections:
HS.N-Q.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.
Connections:
SCHS-S1C4-02;SSHS-S5C5-01HS.N-Q.2. Define appropriate quantities for the purpose of descriptive modeling.
Connection: SSHS-S5C5-01
HS.N-Q.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
HS.N-VM.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; |v|; ||v||; v).
HS.N-VM.3. Solve problems involving velocity and other quantities that can be represented by vectors.
Connections: 11-12.RST.9 SCHS-S5C2-01;SCHS-S5C2-02;SCHS-S5C2-06;11-12.WHST.2d
a. Understand vector subtraction v – w as v + (–w); where –w is the additive inverse of w; with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order; and perform vector subtraction component-wise.
Connection: ETHS-S6C1-03
HS.N-VM.5. Multiply a vector by a scalar.
a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise; e.g.; as c(vx; vy) = (cvx; cvy). Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0; the direction of cv is either along v (for c > 0) or against v (for c
HS.N-VM.8. Add; subtract; and multiply matrices of appropriate dimensions.
b. Connections: 9-10.RST.3;ETHS-S6C2-03
c. HS.N-VM.9. Understand that; unlike multiplication of numbers; matrix multiplication for square matrices is not a commutative operation; but still satisfies the associative and distributive properties.
Connections: ETHS-S6C2-03;9-10.WHST.1e
HS.A-SSE.1. Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression; such as terms; factors; and coefficients.
Connection: 9-10.RST.4
nterpret complicated expressions by viewing one or more of their parts as a single entity. For example; interpret P(1+r)n as the product of P and a factor not depending on P.
HS.A-SSE.2. Use the structure of an expression to identify ways to rewrite it. For example; see x4 – y4 as
(x2)2 – (y2)2; thus recognizing it as a difference of squares that can be factored as
(x2 – y2)(x2 + y2).
HS.A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Connections: 9-10.WHST.1c;
11-12.WHST.1c
Factor a quadratic expression to reveal the zeros of the function it defines.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
HS.A-SSE.4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1); and use the formula to solve problems. For example; calculate mortgage payments.
Connection: 11-12.RST.4
HS.A-CED.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.
HS.A-CED.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.
HS.A-REI.2. Solve simple rational and radical equations in one variable; and give examples showing how extraneous solutions may arise.
HS.A-REI.3. Solve linear equations and inequalities in one variable; including equations with coefficients represented by letters.
HS.A-REI.8. Represent a system of linear equations as a single matrix equation in a vector variable.
HS.A-REI.9. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 ´ 3 or greater).
Connection: ETHS-S6C2-03
HS.A-REI.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).
HS.A-REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the
School country
United StatesSchool state
ArizonaSchool city
GlendaleSchool / district Address
6330 West Thunderbird RoadSchool zip code
85306Date submitted
Approved
YesApproved competency code
- MTHA
- 4 years of Math