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Course Details:
Course Details:
Grades: 9-12
Length: two semesters
Credit: 1 (0.5 per semester)
Prerequisite: none
Course Description:
Course Description:
Math for Trades & Technical Careers emphasizes the advanced and applied algebraic topics needed for success in industry-based occupations. The course is designed to introduce students to the mathematics used in various trades and apprenticeship programs through a focus on the practical application of mathematics.
Students are expected to master skills without the use of a calculator, in addition to working with applied problems using manipulatives, calculators, spreadsheets, application software, and specialized technologies. There will be a review of the real number system, fractions, measuring tools, unit conversions, ratios, proportions, percent, plane and solid geometry, systems of equations, trigonometry, and vectors.
All concepts are applied to industry situations with the goal and focus of preparing for industry entrance exams.
Mathematical Topics
Mathematical Topics
(Recommended Order)
Semester 1
Semester 1
Numeration
Measurement
Geometry and Unit Analysis
Formulas and Equations
Semester 2
Semester 2
Ratios and Slope
Apply and Interpret Functions
Vectors
Course/ Grade Competencies
Course/ Grade Competencies
Semester 1
Semester 1
M1.9-12.1: The learner will write, apply, and provide a rationale for a mathematical model representing a given situation.
M1.9-12.2: The learner will interpret and use symbols to express relationships and justify reasoning when solving problems.
M2.9-12.1: The learner will justify how to apply properties of real number systems to variable expressions in a variety of contexts.
M3.9-12.1: The learner will use computational strategies and algorithms and provide rationale for their use.
M3.9-12.2: The learner will reason quantitatively when analyzing, representing, and solving problems.
M3.9-12.3: The learner will compare the effectiveness or logic of two plausible arguments or models.
M4.9-12.1: The learner will provide rationale for solving measurement problems that require making conversions among various units and measurement systems, or applying the effect of a scale factor.
M5.9-12.1: The learner will apply properties of arithmetic and algebra to simplify and manipulate symbolic expressions or models.
M5.9-12.2: The learner will write and apply algebraic modes to represent and answer questions about a given situation.
M5.9-12.3: The learner will interpret, analyze, and use relations and functions applied in a variety of contexts, including real-world phenomena.
Semester 2
Semester 2
M2.9-12.1: The learner will justify how to apply properties of real number systems to variable expressions in a variety of contexts.
M4.9-12.1: The learner will provide rationale for solving measurement problems that require making conversions among various units and measurement systems, or applying the effect of a scale factor.
M5.9-12.1: The learner will apply properties of arithmetic and algebra to simplify and manipulate symbolic expressions or models.
M5.9-12.3: The learner will interpret, analyze, and use relations and functions applied in a variety of contexts, including real-world phenomena.
M7.9-12.1: The learner will formulate questions to clarify the problem at hand and formulate one (or more) questions that can be answered with data.
M7.9-12.2: The learner will design and implement a plan to collect the appropriate data to answer the statistical question.
M7.9-12.3: The learner will summarize data using appropriate statistics.
M7.9-12.4: The learner will select appropriate graphical and numerical methods, and use these methods to represent the data in a way that supports interpretation.
M7.9-12.5: The learner will interpret descriptive statistics and linear models within the context of the data and the original question.
M7.9-12.6: The learner will apply probability concepts to analyze and evaluate potential decisions and strategies.
Numeration
Numeration
Graduate-Level Competency:
Graduate-Level Competency:
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.
Course/ Grade Competencies:
Course/ Grade Competencies:
M2.9-12.1
M4.9-12.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Apply rational numbers to common trade situations.
Express rational numbers as common fractions and mixed fractions.
Evaluate operations with rational numbers in applied situations.
Convert between ratios, decimals, and percents
Can be Covered:
The learner will:
Learn about and understand binary, octal, and hexadecimal numbers.
Standards:
Standards:
AKSS
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Make a daily goal to practice Work Keys questions so students interested in the trade unions may score well on the math portion of this test.
Measurement
Measurement
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M4.9-12.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Reason quantitatively and use units to solve problems.
Use metric and U.S. systems of measurement.
Use precision when necessary and estimate when necessary.
Use industry related scales.
Use measuring tapes (regular/landscaper’s), speed squares, carpenter’s squares, vernier caliper, micrometers
Differentiate the terms “level”, “square”, “plum”
Measure in one, two, and three dimensions
Measure angles in degrees using industry-appropriate tools
Standards:
Standards:
AKSS
N-Q.1, N-Q.2,
N-Q.3
Mathematical Practices
All mathematical practices are present in each unit.
Geometry and Unit Analysis
Geometry and Unit Analysis
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M4 - Measurement: The learner will explain reasoning when applying and modeling geometric principles.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M4.9-12.1
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Determine area & perimeter of rectangular, triangular, and circular floor layouts.
Determine volume of right rectangular prisms to find common trade volumes.
Use dimensional analysis to convert units in one, two, and three dimensions.
Use dimensional analysis to convert rates involving one, two, and three dimensions.
Standards:
Standards:
AKSS
N-Q.1, N-Q.2,
N-Q.3
Mathematical Practices
All mathematical practices are present in each unit.
Formulas and Equations
Formulas and Equations
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M5.9-12.1
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Create and solve equations that describe numbers or relationships.
Simplify, then solve equations.
Solve equations with variables on both sides.
Solve any linear equation.
Write and solve equations to model situations.
Apply the Pythagorean theorem and the converse of the Pythagorean theorem.
Standards:
Standards:
AKSS
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Use the converse of the Pythagorean theorem to create a 20 by 30 rectangle with tape on the floor.
Ratios and Slope
Ratios and Slope
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M5.9-12.1
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Create unit rates to perform quick calculations in applied problems.
Use proportions to perform any one-step unit conversion.
Use proportions to read/ create scale drawings.
Graph lines in slope-intercept form.
Find the slope of physical objects
Cite industry standards slopes for roofs, plumbing, and stairs.
Standards:
Standards:
AKSS
S‐CP.3, S‐CP.2,
S‐CP.1, S-ID.4,
S-ID.3, S-ID.2
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Hang an ABS pipe at industry standard minimum slope.
Apply and Interpret Functions
Apply and Interpret Functions
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M2 – Numbers and Number Systems: The learner will develop an applied knowledge of numbers and number systems to solve problems.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M2.9-12.1
M3.9-12.1
M3.9-12.2
M3.9-12.3
M5.9-12.1
M5.9-12.2
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Understand similarity in terms of similarity transformations.
Define trigonometric ratios and solve problems involving right triangles.
Extend the domain of trigonometric functions using the unit circle.
Apply the law of sines & law of cosines to find angles in a truss.
Can be Covered:
The learner will:
Use identities from the unit circle to perform quick calculations.
Standards:
Standards:
AKSS
G-SRT.2, G-SRT.6,
G-SRT.7, G-SRT.8,
F-TF.1, F-TF.2,
F-TF.3, G-GMD.1,
G-GMD.2, G-GMD.3,
G-MG.2, G-MG.3,
G-GPE.7
Mathematical Practices
All mathematical practices are present in each unit.
Suggested Activities, Materials, and Resources:
Suggested Activities, Materials, and Resources:
Make clinometers to find heights of tall objects outside or in school.
Vectors
Vectors
Graduate-Level Competency:
Graduate-Level Competency:
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
Course/ Grade Competencies:
Course/ Grade Competencies:
M5.9-12.1
M5.9-12.3
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Represent and model with vector quantities.
Calculate exponents, roots, and rational exponents.
Standards:
Standards:
AKSS
N-VM.1, N-VM.2,
N-VM.4, N-VM.5
Mathematical Practices
All mathematical practices are present in each unit.
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