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Embedded Credit – Content Standards and Objectives Alignment Template Teachers and Administrators who completed the template: Steve Freshour, Jared Voldness Recommendation that embedded credit be awarded: Yes □ No □ Provide rationale for decision Review of CTE Standards mentioned below: Standards in light blue are not included in the standards found in the matrix below but have been included as further reinforcement of mathematics being completed within the PLTW curriculum. IED – Introduction to Engineering Design 2461.24 Students will calculate the mean, mode, median, and range of a data set. 2461.25 Students will create a histogram of recorded measurements showing data elements or class intervals, and frequency. 2461.26 Students will demonstrate knowledge of create and assemble a prototype using CAD modeling software. 2461.36 Students will demonstrate knowledge of mathematics and dimensioning associated with CAD design software. 2461.39 Students will calculate the surface area and volume of simple geometric forms. 2461.40 Students will Identify and explain the various geometric relationships that exist between the elements of two-dimensional shapes and three-dimensional forms. 2461.61 Students will Determine ratios and apply algebraic formulas to animate multiple parts within an assembly model. 2461.65 Students will create a decision making matrix. 2461.72 Students will create a three-fold brochure marketing the designed solution for the chosen problem, such as a consumer product, a dispensing system, a new form of control system, or extend a product design to meet a new requirement. 2461.101 Students will demonstrate knowledge of design briefs and their role in the engineering design process. 2461.116 Students will create a Gantt chart to manage the various phases of their design challenge. POE – Principles of Engineering 2463.4 Students will demonstrate knowledge of engineering complexities ranging from simple machines to compound machine design 2463.5 Students will Measure forces and distances related to mechanisms. 2463.6 Students will distinguish between the six simple machines, their attributes, and components. 2463.7 Students will Calculate mechanical advantage and drive ratios of mechanisms. 2463.8 Students will Design, create, and test gear, pulley, and sprocket systems. 2463.9 Students will calculate work and power in mechanical systems. 2463.10 Students will determine efficiency in a mechanical system. 2463.11 Students will Design, create, test, and evaluate a compound machine design. 2463.15 Students will demonstrate knowledge of mathematical operations specific to electrical systems. 2463.16 Students will define the possible types of power conversion. 2463.17 Students will calculate work and power. 2463.18 Students will demonstrate the correct use of a digital multimeter. 2463.19 Students will calculate power in a system that converts energy from electrical to mechanical. 2463.20 Students will determine efficiency of a system that converts an electrical input to a mechanical output. 2463.21 Students will calculate circuit resistance, current, and voltage using Ohm’s law. 2463.22 Students will understand the advantages and disadvantages of parallel and series circuit design in an application. 2463.24 Students will Test and apply the relationship between voltage, current, and resistance relating to a photovoltaic cell and a hydrogen fuel cell. 2463.25 Students will Experiment with a solar hydrogen system to produce mechanical power. 2463.28 Students will Test and apply the relationship between R-values and recyclable insulation. 2463.29 Students will complete calculations for conduction, R-values, and radiation. 2463.32 Students will create a decision-making matrix for the design problem. 2463.34 Students will create a detailed pictorial sketch or use 3D modeling software to document the best choice, based upon the design team’s decision matrix. 2463.37 Students will create detailed flow charts utilizing a computer software application. 2463.39 Students will create system control programs that utilize flowchart logic. 2463.51 Students will calculate values in a fluid power system utilizing Pascal’s Law. 2463.54 Students will calculate values in a pneumatic system utilizing the perfect gas laws. 2463.55 Students will calculate flow rate, flow velocity, and mechanical advantage in a hydraulic system. 2463.56 Students will demonstrate knowledge of the analysis of loads on physical systems in static equilibrium (statics). 2463.57 Students will Create free body diagrams of objects, identifying all forces acting on the object. 2463.58 Students will mathematically locate the centroid of structural members. 2463.59 Students will calculate moment of inertia of structural members. 2463.60 Students will differentiate between scalar and vector quantities. 2463.61 Students will identify magnitude, direction, and sense of a vector. 2463.62 Students will calculate the X and Y components given a vector. 2463.63 Students will calculate moment forces given a specified axis. 2463.64 Students will Use equations of equilibrium to calculate unknown forces. 2463.65 Students will Use the method of joints strategy to determine forces in the members of a statically determinate truss. 2463.69 Students will Calculate weight, volume, mass, density, and surface area of selected common household product. 2463.73 Students will obtain measurements of material samples. 2463.74 Students will tensile test a material test sample. 2463.75 Students will identify and calculate test sample material properties using a stress strain curve. 2463.105 Students will demonstrate knowledge of the principles of statistics to calculate the theoretical probability that an event will occur 2463.106 Students will Calculate the experimental frequency distribution of an event occurring. 2463.107 Students will apply the Bernoulli process to events that only have two distinct possible outcomes. 2463.108 Students will Apply AND, OR, and NOT logic to probability. 2463.109 Students will Apply Bayes’ theorem to calculate the probability of multiple events occurring. 2463.110 Students will create a histogram to illustrate frequency distribution. 2463.111 Students will Calculate the central tendency of a data array, including mean, median, and mode. 2463.112 Students will Calculate data variation, including range, standard deviation, and variance. 2463.113 Students will demonstrate knowledge of the principles of kinematics and statistics to design and present a workable solution to a design problem associated with bodies in motion. 2463.114 Students will calculate distance, displacement, speed, velocity, and acceleration from data. 2463.115 Students will Design, build, and test a vehicle that stores and releases potential energy for propulsion. 2463.116 Students will calculate acceleration due to gravity given data from a free fall device. 2463.117 Students will calculate the X and Y components of a projectile motion. 2463.118 Students will determine the needed angle to launch a projectile a specific range given the projectile’s initial velocity. EDD – Engineering Design and Development 2464.9 Students will explain the feasibility of his or her solution based on his or her research. 2464.15 Students will Conduct research and perform a trend analysis on a technical problem. 2464.17 Students will demonstrate knowledge of performing and graphically representing an evaluation of proposed design solutions using specific criteria, including product specifications. 2464.35 Students will demonstrate knowledge of evaluating and selecting appropriate testing methodologies for testing the product, conduct product testing, refine the design as needed, and document the process and results. 2464.43 Students will apply the appropriate statistical analysis tools to the test results to ensure validity. Embedded Credit Course Standards and Objectives (Advanced Mathematical Modeling) Alignment to Host Course Standards and Objectives Content Alignment Strong Moderate Weak or Alignment Alignment No Alignment M.AMM.1 Demonstrate reasoning skills in developing, explaining and justifying sound mathematical arguments and analyze the soundness of mathematical arguments of others. M.AMM.2 Communicate with and about mathematics orally and in writing as part of independent and collaborative work, including making accurate and clear presentations of solutions to problems. M.AMM.3 Gather data, conduct investigations and apply mathematical concepts and models to solve problems in mathematics and other disciplines. All projects and activities IED 2461.72 EDD 2464.17,35,43 x All projects and activities IED 2461.72 EDD 2464.9 x All projects and activities IED 2461.36, 72 x M.AMM.4 Determine, represent and analyze mathematical models for loan amortization and the EDD 2464.9 x How Standards and/or objectives that do not have strong alignment will be delivered Students will be provided a financial unit which will supplement the EDD course and allow students an opportunity effects of different payments and/or finance terms (e.g., Auto, Mortgage, and/or Credit Card). M.AMM.5 Determine, represent and analyze mathematical models for investments involving simple and compound interest with and without additional deposits. (e.g., Savings accounts, bonds, and/or certificates of deposit.) M.AMM.6 Determine, represent, and analyze mathematical models for Inflation and the Consumer Price Index using concepts of rate of change and percentage growth. M.AMM.7 Research and analyze personal budgets based on given parameters (e.g., Fixed and discretionary expenses, insurance, gross vs. net pay, types of income, wage, salary, commission), career choice, geographic region, retirement and/or investment planning, etc.). M.AMM.8 Research and analyze taxes including payroll, sales, to study the feasibility of the financial aspects of their design project. EDD 2464.9 x Students will be provided a financial unit which will supplement the EDD course and allow students an opportunity to study the feasibility of the financial aspects of their design project. EDD 2464.9 x EDD 2464.9 x Students will be provided a financial unit which will supplement the EDD course and allow students an opportunity to study the feasibility of the financial aspects of their design project. Students will be provided a financial unit which will supplement the EDD course and allow students an opportunity to study the feasibility of the financial aspects of their design project. EDD 2464.9 x Students will be provided a financial unit which will supplement the EDD course and personal property, real estate and income tax returns. M.AMM.9 Use the Fundamental Counting Principle, Permutations and Combinations to determine all possible outcomes for an event; determine probability and odds of a simple event; explain the significance of the Law of Large Numbers. M.AMM.10 Determine and interpret conditional probabilities and probabilities of compound events by constructing and analyzing representations, including tree diagrams, Venn diagrams, two-way frequency tables and area models, to make decisions in problem situations. M.AMM.11 Use probabilities to make and justify decisions about risks in everyday life. M.AMM.12 Calculate expected value to analyze mathematical fairness, payoff and risk. M.AMM.13 Identify limitations or lack of POE 2463.105-106 x allow students an opportunity to study the feasibility of the financial aspects of their design project. POE Lesson 4.1 Statistics POE 2463.108-109 x POE Lesson 4.1 Statistics 2463.105-109 x POE Lesson 4.1 Statistics 2463.105, 112 IED 2461.24, 25 POE 2463.105 x x Students will calculate expected values as an extension to POE Lesson 4.1.2 Candy Statistics. IED Unit 3 Measurement and Statistics information in studies reporting statistical information, especially when studies are reported in condensed form. M.AMM.14 Interpret and compare the results of polls, given a margin of error. M.AMM.15 Identify uses and misuses of statistical analyses in studies reporting statistics or using statistics to justify particular conclusions, including assertions of cause and effect versus correlation. M.AMM.16 Describe strengths and weaknesses of sampling techniques, data and graphical displays and interpretations of summary statistics and other results appearing in a study, including reports published in the media. M.AMM.17 Identify the population of interest, select an appropriate sampling technique and collect data. EDD 2464.43 IED 2461.24, 25 POE 2463.105 EDD 2464.15, 17, 35, 43 x IED Unit 3 Measurement and Statistics IED Unit 4 Modeling Skills EDD Component 0 Lesson g2.4 M.AMM.18 Identify the variables to be used in a study. IED 2461.24, 25 POE 2463.105 EDD 2464.17, 35 x IED Unit 4 Modeling Skills IED Unit 5 Geometry of Design POE 2463.105, 112 IED Unit 4 Modeling Skills POE Lesson 4.1 Statistics EDD Component 0 Lesson g2.4 x POE Lesson 4.1 Statistics POE 2463.105, 112 EDD 2464.35, 43 x POE Lesson 4.1 Statistics EDD Design project POE 2463.105, 112 EDD 2464.17, 35, 43 x POE Lesson 4.1 Statistics EDD Component 0 Lesson g2.4 EDD Design Project M.AMM.19 Determine possible sources of statistical bias in a study and how such bias may affect the ability to generalize the results. M.AMM.20 Create data displays for given data sets to investigate, compare, and estimate center, shape, spread and unusual features. M.AMM.21 Determine possible sources of variability of data, both those that can be controlled and those that cannot be controlled. M.AMM.22 Report results of statistical studies to a particular audience, including selecting an appropriate presentation format, creating graphical data displays and interpreting results in terms of the question studied. M.AMM.23 Communicate statistical results in both oral and written formats using appropriate statistical and nontechnical language. M.AMM.24 IED 2461.24, 25 POE 2463.105 EDD 2464.43 x IED 2461.24, 25 POE 2463.110, 111, 112 EDD 2464.17, 43 x IED 2461.24,25 POE 2463.105 EDD 2464.9,17,63 x IED Unit 3 Measurement and Statistics IED Unit 4 Modeling Skills EDD Design Project IED Unit 3 Measurement and Statistics IED Unit 4 Modeling Skills IED Unit 5 Geometry of Design EDD Component 0 Lesson g2.4 EDD Design Project IED Unit 3 Measurement and Statistics IED Unit 4 Modeling Skills EDD Design Project IED 2461.24, 25 POE 2463.105 EDD 2464.17, 43 x IED Unit 3 Measurement and Statistics IED Unit 4 Modeling Skills IED Unit 5 Geometry of Design EDD Design Project IED 2461.101 EDD 2464.9, 17, 22, 35 x x IED Unit 3 Measurement and Statistics IED Unit 4 Modeling Skills IED Unit 5 Geometry of Design EDD Design Project The CTE Math Instructor and Solve problems involving large quantities that are not easily measured. M.AMM.25 Use arrays to efficiently manage large collections of data and add, subtract, and multiply matrices to solve applied problems. M.AMM.26 Determine or analyze an appropriate model for problem situations - including linear, quadratic, power, exponential, logarithmic and logistic functions (e.g., stopping distance, period of a pendulum, population growth, Richter Scale, and/or Fujita Tornado Scale). M.AMM.27 Determine or analyze an appropriate cyclical model for problem situations that can be modeled with trigonometric functions (e.g., predator-prey models, tide heights, diurnal cycle, and/or music). M.AMM.28 Determine or analyze an appropriate piecewise model for problem situations (e.g., postal rates, phase change x IED 2461.61 POE 2463.4-11, 15-22, 24, 25, 28, 29, 51, 54, 55, 74, 75 EDD 2464.15 x IED Unit 4 Modeling Skills IED Unit 5 Geometry of Design EDD Component 0 Lesson g2.4 Testing Instrumentation and Logger Pro Software POE 2463.113 POE 2463.15 the PLTW Instructor will provide an extension for students. The CTE Math Instructor and the PLTW Instructor will provide an extension for students. x x Students will be provided an extension Lab to coincide with POE Lesson 3.1 Machine Control. Students will use Vernier Probes to analyze light waves using the supplied Light Sensor. POE Unit 1 Energy and Power POE Unit 1 Lesson 1.4 Renewable Electrical Energy Design graphs, sales tax, and/or utility usage rates). M.AMM.29 Solve problems using recursion or iteration (e.g., fractals, compound interest, population growth or decline, and/or radioactive decay). M.AMM.30 Collect numerical bivariate data; use the data to create a scatter plot; determine whether or not a relationship exists; if so, select a function to model the data, justify the selection and use the model to make predictions. M.AMM.31 Solve problems involving scheduling or routing situations that can be represented by a vertex-edge graph; find critical paths, Euler paths, Hamiltonian paths, and minimal spanning trees (e.g., Konigsberg bridge problem, mail vs. Fed Ex delivery routes, kolam drawings of India, traveling salesman problem, and/or map coloring). M.AMM.32 Construct, analyze, and interpret flow charts in order to develop and describe problem EDD 2464.9 POE 2463.4-11, 15-22, 24, 28, 29, 75 EDD 2464.15, 17 x Students will be provided a financial unit which will supplement the EDD course and allow students an opportunity to study the feasibility of the financial aspects of their design project. IED Unit 4 Modeling Skills IED Unit 5 Geometry of Design x EDD Component 0 Lesson g2.4 Testing Instrumentation and Logger Pro Software EDD Design Project x IED 2461.65,115 POE 2463.32,37,39 x The CTE Math Instructor and the PLTW Instructor will provide an extension for students. IED Unit 2 Technical Sketching and Drawing IED Unit 7 Documentation IED Unit 9 Design Team solving procedures. M.AMM.33 Apply and analyze various ranking algorithms to determine an appropriate method for a given situation (e.g., fair division, apportionment, and/or search engine results). M.AMM.34 Analyze various voting and selection processes to determine an appropriate method for a given situation (e.g., preferential vs. nonpreferential methods, and/or weighted voting). M.AMM.35 Create and use two- and threedimensional representations of authentic situations using paper techniques or dynamic geometric environments for computer-aided design and other applications. x x IED 2461.26,36 POE 2463.34 x POE Lesson 1 EDD uses flow charts throughout the course to steer students through the design process. (Engineering Design Process Flow Chart, Gantt charts, Product Development Process) PLTW Design Process EDD Design Project The CTE Math Instructor and the PLTW Instructor will provide an extension for students. The CTE Math Instructor and the PLTW Instructor will provide an extension for students. IED Unit 2 Technical Sketching and Drawing IED Unit 4 Modeling Skills IED Unit 5 Geometry of Design IED Unit 7 Documentation IED Unit 8 Advanced Computer Modeling IED Unit 9 Design Team IED Unit 10 Design Challenges POE West Point Bridge Builder M.AMM.36 Solve geometric problems involving inaccessible distances. M.AMM.37 Use vectors to represent and solve applied problems. M.AMM.38 Use matrices to represent geometric transformations and solve applied problems. x POE 2463.56-65, 113-118 x x EDD Design Project The CTE Math Instructor and the PLTW Instructor will provide an extension for students. POE Lesson 2.1 Statics The CTE Math Instructor and the PLTW Instructor will provide an extension for students.