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Transcript
Algebra standard 9.2.1 Understanding the concept of function, and identify important features of functions and other relations using symbolic and graphical methods. Benchmark Introduction of concepts 1.Understand the definition of a function Auto Technician 2. Distinguish between functions and other Standards 4.5, 9.1, relations defined symbolically, graphically, 11.1 or in tabular form. Application Example Diagnose electrical/electronic integrity of series, parallel and seriesparallel circuits using principles of electricity; Inspect and test gauges and gauge sending units for cause of intermittent, high, low, or no gauge readings; Diagnose incorrect operation of motor-driven accessory circuits; determine necessary action Find the voltage if the current is 10amps and the resistance is 40 Ohm’s Perform battery state-of-charge test; Perform starter current draw test; Perform charging system output test; Diagnose charging system for the cause of undercharge, no-charge, and overcharge conditions, determine necessary action What are reasonable answers for a battery charge test? 3. Find the domain of a function in a real-world context. Auto Technician Standards 5.1, 6.1, 7.1, 7.2 4. Obtain information and draw conclusions from graphs of functions and other relations. Auto Technician Standards 4.6, 6.3, 9.1 Use wiring diagrams during diagnosis of electrical circuit problems; Inspect and test starter relays and solenoids; Inspect and test gauges and gauge sending units for cause of intermittent, high, low, or no gauge readings, determine necessary action Based on the electrical diagrams, what can you conclude about the current flow? 8. Make qualitative statements about the rate of change of a function, based on its graph. Auto Technician Standards 5.1, 5.4, 6.1, 7.1, 7.2 Perform battery state-of-charge test; Inspect, clean, fill battery; Perform starter current draw test; Perform charging system output test; Diagnose charging system for the cause of undercharge, no-charge, and overcharge conditions. determine necessary action Based on the cell count in the battery displayed, what can you conclude about the total voltage? Algebra Standard 9.2.2 Recognize linear, quadratic, exponential and other common functions in real-world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context. Benchmark Introduction of concept Applications Example 1. Represent and solve problems in various contexts using linear functions Auto Technician Standards 4.5, 7.2 Diagnose electrical/electronic integrity of series, parallel and series-parallel circuits using principles of electricity; Diagnose charging system for the cause of undercharge, no-charge, and overcharge conditions Find the voltage if the current is 10amps and the resistance is 40 Ohm’s 2. Represent and solve problems in various context using exponential functions, such as investment growth, depreciation and populations growth. Auto Technician Standards 7.2 Diagnose charging system for the cause of undercharge, no-charge, and overcharge conditions When performing a alternator output test, what are the starting volts? 4. Express the terms in a geometric sequence recursively. Auto Technician Standards 4.11 Check continuity and measure resistance in electrical/electronic circuits and components using an ohmmeter; determine necessary action Determine and record the ohms as an engine starts and idles Algebra Standard 9.2.3 Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions. Benchmark 1. Evaluate polynomial and rational expressions at specified points in their domains. Introduction of concept Auto Technician Standards 4.5 Applications Example Diagnose electrical/electronic integrity of series, parallel and series-parallel circuits using principles of electricity Find the voltage if the current is 10amps and the resistance is changing Geometry Standard 9.3.1 Calculate measurements of plane and solid geometric; know that physical measurements depend on the choice of unit and that they are approximations. Benchmark Introduction of concept Applications Example 3. Understand that quantities associated with physical measurements must be assigned units. Auto Technician Standards 4.7, 4.9, 4.10, 4.11, 5.4, 5.5, 5.7 Demonstrate the proper use of a digital multimeter (DMM) during diagnosis of electrical circuit problems; Measure source voltage and perform voltage drop tests in electrical/electronic circuits using a voltmeter; Measure current flow in electrical/ electronic circuits and components using an ammeter; Check continuity and measure resistance in electrical/electronic circuits and components using an ohmmeter; determine necessary action. Measure source voltage and perform voltage drop tests in electrical/electronic circuits using a voltmeter 5. Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements. Auto Technician Standards 4.14, 4.15, 4.16.4.19, 5.1, 5.2, 6.1, 6.2, 6.3, 6.5, 7.1, 7.2, 7.5, 8.1, 8.3, 8.4, 9.1. 10.1. 10.2, 11.1, 11.2, 11.3 Measure and diagnose the cause(s) of excessive key-off battery drain (parasitic draw); Inspect and test fusible links, circuit breakers, and fuses; Repair wiring harness (including CAN/BUS systems). determine necessary action Inspect and test fusible links, circuit breakers, and fuses; determine necessary action. Geometry Standard 9.3.2 Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry. Benchmark 1,Understand the role of definitions in logical arguments. Introduction of concept Applications Example Auto Technician Standards 4.5 Diagnose electrical/electronic integrity of series, parallel and series-parallel circuits using principles of electricity Talking to the customer, the technician must be able to define the terms to the customer Auto Technician Standards 4.8, 4.9, 4.10, 4.11, 4.14, 5.2, 6.4, 7.4, Check electrical circuits with a test light; Measure source voltage and perform voltage drop tests in electrical/electronic circuits using a When talking to the customer, technicians will speak in a logical, easy to follow manner. 1. Understand the role of undefined terms in logical arguments. 2. Accurately interpret and use words and phrases in geometric proofs such as “if…then,” “if and only if,” “all,” and “not.” 8.2 voltmeter; determine necessary action 3. Assess the validity of a logical argument or give counterexamples to disprove a statement. Auto Technician Standards 4.8,4.9, 4.10, 4.11, 4.14, 5.2, 6.4, 7.4, 8.2 Check electrical circuits with a test light; Measure and diagnose the cause(s) of excessive key-off battery drain (parasitic draw); determine necessary action Often times customers will come up with their own theories of what is wrong, or challenge what the technician is telling them. 4. Express proofs in a form that clearly justifies the reasoning, such as twocolumn proofs, paragraph proofs, flow charts or illustrations. Auto Technician Standards 4.2, 4.8,4.9, 4.10, 4.11, 4.14, 5.2, 6.4, 7.4, 8.2 Identify and interpret electrical/electronic system concern; determine necessary action. When talking to the customer, technicians will speak in a logical, easy to follow manner. 5. Use technology tools to develop mathematical reasoning skills in multistep problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets. Auto Technician Standards 4.14, 6.4, 6.6, 7.4 Measure and diagnose the cause(s) of excessive key-off battery drain (parasitic draw); Remove and install starter in a vehicle; Differentiate between electrical and engine mechanical problems that cause a slow-crank or no-crank condition; Remove, inspect, and install generator (alternator); determine necessary action. By using data from technology tools, the technician will arrive at a logical conclusion as the root of excessive key-off battery drain. Geometry Standard 9.3.3 Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. Benchmark 6. Apply the properties of congruent and similar figures to solve problems and logically justify results. Introduction of concept Auto Technician Standards 5.4 Applications Example Inspect, clean, fill, and replace battery How is the construction of a 12V and 24V battery differ even though they look the same? Data Analysis and Probability Standard 9.4.1 Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships. Benchmark Introduction of concept Applications Example 1. Describe and compare data sets using summary statistics, including measures of center, location and spread. Auto Technician Standards 4.2, 4.7, 4.13, 6.2, 7.4, 7.5 Identify and interpret electrical/electronic system concern; Demonstrate the proper use of a digital multimeter (DMM) during diagnosis of electrical circuit problems; Locate shorts, grounds, opens, and resistance problems in electrical/electronic circuits; Perform starter circuit voltage drop tests determine necessary action. What is the possible spread of DMM readings? 2. Analyze the effects on summary statistics of changes in data sets. Auto Technician Standards 4.1 Complete work order to include customer information, vehicle identifying information, customer concern, related service history, cause, and correction What will happen the charge time when you change the resistance in a battery charger? 3.Use scatterplots to analyze patterns Auto Technician Standards 5.4 Inspect, clean, fill, and replace battery Graph the battery reserves for different batteries based on similar ampere ratings. Data Analysis and Probability Standard 9.4.2 Explain the uses of data and statistical thinking to draw inferences make predictions and justify conclusions. Benchmark Introduction of concept Applications Example 1. Evaluate reports based on data published in the media by identifying the source of the data. Auto Technician Standards 4.1, 4.2, 4.17, 4.18, 4.19, 5.1, 5.2, 5.3, 5.5, 5.8, 6.1, 6.2, 6.4, 6.5, 7.1, 7.2, 7.3, 7.5, 8.1, 8.2, 8.3, 8.4, 9.1, 9.2, 10.1, 10.2, 11.1, 11.2, 11.3, 11.4, 11.5 Complete work order to include customer information, vehicle identifying information, customer concern, related service history, cause, and correction; Research applicable vehicle and service information, such as electrical/electronic system operation, vehicle service history, service precautions, and technical service bulletins; Remove and replace terminal end from connector; Perform battery stateof-charge test; determine necessary action. Every battery company claims to be the best battery, so how can we tell which one is best? 2. Explain misleading uses of data. Auto Technician Standards 4.1, 4.2, 5.1, 5.2, 5.3, 5.4, 6.1, 6.4, 6.5. 6.6, 7.1, 7.2, Complete work order to include customer information, vehicle identifying information, customer concern, related service history, cause, and correction; Research applicable vehicle and service information, such as electrical/electronic system operation, vehicle service history, service precautions, and technical service bulletins; Many customers will come in with their hearts set on getting the biggest battery possible because they saw it on a sommercial, why is this not a good idea? 3. Explain the impact of sampling methods during data collection. Auto Technician Standards 4.3, 54 Diagnose electrical/electronic integrity of series, parallel and series-parallel circuits using principles of electricity; Inspect, clean, fill, and replace battery. In order to figure out what claims are valid, we need to figure how they got their data and who is paying the celebrities to endorse them. Data Analysis and Probability Standard 9.4.3 Calculate probabilities and apply probability concepts to solve real-world and mathematical problems. Benchmark 1. Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes). Introduction of concept Auto Technician Standards 4.1, 4.5, 4.13, 5.4 Applications Example Complete work order to include customer information, vehicle identifying information, customer concern, related service history, cause, and correction; Diagnose electrical/electronic integrity of series, parallel and seriesparallel circuits using If you just carry 2 brands of batteries that come in 2 different sizes with 7 different cold cranking amps, how many batteries is that total? principles of electricity 8. Apply probability concepts to realworld situations to make informed decisions. Auto Technician Standards 4.3, 4.5, 4.8, 4.9, 4.10, 4.11, 4.13, 4.14, 4.15, 5.4, 6.3, 7.4, 11.1 Research applicable vehicle and service information, such as electrical/electronic system operation, vehicle service history, service precautions, and technical service bulletins; Diagnose electrical/electronic integrity of series, parallel and seriesparallel circuits using principles of electricity; Check electrical circuits with a test light ; Measure source voltage and perform voltage drop tests in electrical\ electronic circuits using a voltmeter; determine necessary action What are the probability that a customer would come in with a blown horn fuse twice given that your first diagnosis was a short in the after market stereo wiring? 9. Use the relationship between conditional probabilities and relative frequencies in contingency tables. Auto Technician Standards 5.1, 6.1, 6.6, 7.1 Perform battery state-ofcharge test; determine necessary action; Perform starter current draw tests; Differentiate between electrical and engine mechanical problems that cause a slow-crank or nocrank condition; Perform charging system output test; determine necessary action If 1 out of 1000 batteries is defective, what is the probability that the same customer would come in with 2 defective batteries?