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Embedded Credit – Content Standards and Objectives Alignment Matrix

3052 Transition Mathematics for Seniors Alignment MA1980 Welding Required Courses:

1862 Welding I1863 Welding II1864 Welding III1865 Welding IV

Recommendation that embedded credit be awarded: Yes □ No □ Provide rationale for decision

Embedded Credit Course Standards and Objectives

(Transition Math for Seniors)

Alignment to Host Course Standards and objectives

(Welding)

Content Alignment How Standards and/or objectives that do not have strong alignment will be

deliveredStrong Align-ment

Moderate

Align-ment

Weak or No Align-ment

M.TMS.1Use units as a way to understand 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.

MA.31Literacy and numeracy skills required to solve complex real world problems associated with the career/technical content areaMA.34Demonstrate accuracy in calculating and measuring graphical work required to complete career/technical assignments and projectsMA.35Analyze tables, charts, graphs, and multiple data

X Students encounter units throughout the CTE course by using and implementing units of measure in shop associated lessons and tasks directly embedded in the CTE courses.




(Welding)



Moderate

Align-ment


sources to complete career/technical assignments and projectsModule 29202 - Reading Welding Detail DrawingsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain a

welding detail drawing2. Identify and explain

lines, material fills, and sections

3. Identify and explain object views

4. Identify and explain dimensioning

5. Identify and explain notes and bill of materials

6. Interpret basic elements of a welding detail drawing

7. Sketch or draw basic welding drawings

M.TMS.2 MA.31Literacy and numeracy skills

X Students must utilize measurement and accuracy on a daily basis when performing




(Welding)



Moderate

Align-ment


Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

required to solve complex real world problems associated with the career/technical content areaMA.34Demonstrate accuracy in calculating and measuring graphical work required to complete career/technical assignments and projectsMA.35Analyze tables, charts, graphs, and multiple data sources to complete career/technical assignments and projectsModule 29202 - Reading Welding Detail DrawingsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain a



3. Identify and explain

shop related tasks and lessons direct embedded in the CTE courses.




(Welding)



Moderate

Align-ment


object views4. Identify and explain

dimensioning5. Identify and explain

notes and bill of materials



M.TMS.3Solve quadratic equations with real coefficients that have complex solutions.

MA.15 Demonstrate operating instructions before using any equipmentMA.17Follow safety and security proceduresModule 29101 – Welding SafetyObjectivesUpon completion of this module the trainee will be able to do the following:1. Identify some common

hazards in welding2. Explain and identify

proper personal

X The task associated with this standard allows students to develop a method for determining if a given perimeter will enclose a specified area. Through this contextual connection with the CTE concentration, the math instructor can open discussion for students to study the algebraic and graphic representation of quadratic equations with complex solutions and what they mean. Students will have the opportunity to practice with this mathematics concept and apply it to other contextual CTE scenarios.




(Welding)



Moderate

Align-ment


protection used in welding

3. Describe how to avoid welding fumes

4. Explain some of the causes of accidents

5. Identify and explain uses for material safety data sheets

6. Explain safety techniques for storing and handling cylinders

7. Explain how to avoid electric shock when welding

8. Describe proper material handling methods

M.TMS.4Use 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).

Module 29103 – Plasma Arc CuttingObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain the plasma arc

cutting processes2. Identify plasma arc

cutting equipment3. Prepare and set up

X Students are exposed to this standard through 3 different scenarios (pieces of evidence) Equipment Replacement has students write a formula after creating a table of values. Expansion of Metal asks students to rewrite a literal equation. Coal Silo/Funnel system asks students to write equations by combining formulas and also to identify critical properties of conic sections.




(Welding)



Moderate

Align-ment


plasma arc cutting equipment

4. Use plasma arc cutting equipment to make various types of cuts

5. Properly store equipment and clean the work area after each use

Module 29203 – Physical Characteristics and Mechanical Properties of MetalsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain the

composition and classification of base metals

2. Explain and demonstrate field identification methods for base metals

3. Identify and explain the physical characteristics and mechanical properties of metals





(Welding)



Moderate

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forms and shapes of structural metals

5. Explain metallurgical considerations for welding metals

M.TMS.5Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Factor a quadratic expression to reveal the zeros of the function it defines.

b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.







Module 29202 - Reading Welding Detail DrawingsObjectivesUpon completion of this

X The Storage Box task for this lesson should be implemented as the CTE contextual connection to this standard. Math instructors are to present this problem to students. Students are asked to share methods for solving. The mathematics instructor will insure that students are exposed to the mathematical methods involved in this standard and have students practice through extended contextual example similar to the task.

The task Coal Silo/Funnel System connects these mathematics concepts. Students must complete the square to change the form of a conic section to identify its properites.




(Welding)



Moderate

Align-ment


module, the trainee will be able to do the following:1. Identify and explain a








M.TMS.6Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.



X The Triangle Sculpture Project (in development) will have students welding a structure of steel bar in a pattern of different size triangles. The pattern of these triangles represents geometric series (Sierpinksi Triangles). The students identify presence of a geometric series and then calculate how much space the sculpture will occupy (sum




(Welding)



Moderate

Align-ment






Module 29106 – Weld QualityObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain

codes governing welding2. Identify and explain weld

imperfections and their causes

3. Identify and explain nondestructive examination practices

4. Identify and explain welder qualification tests

5. Explain the importance of quality workmanship

of the areas of the triangles and how much material they will use. See image below.

Mathematics instructors will take this opportunity to have students distinguish between arithmetic and geometric sequences. As an extension to this lesson the mathematics instructor will have students differentiate between recursive and explicit representations of those sequences.




(Welding)



Moderate

Align-ment


6. Identify common destructive testing methods

7. Perform a visual inspection of fillet welds

M.TMS.7Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of the two moving objects has greater speed.









X The Welding Rate task (in development) has students analyze the proportional relationships of the rates of welds with different types and thicknesses of materials. The welder must take into consideration the type and thickness of material as well as the type of weld/equipment used when performing the actual weld. Students will compare the different proportional relationships in various welding situations graphically and algebraically.




(Welding)



Moderate

Align-ment






4. Identify and explain forms and shapes of structural metals


M.TMS.8Use similar triangles to explain why the slope m is

Module 29203 – Physical Characteristics and Mechanical Properties of

X This standard is included in the 20% not aligned to the welding curriculum and does




(Welding)



Moderate

Align-ment


the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y=mx+b for a line intercepting the vertical axis at b.

MetalsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain the






not have to be covered in a CTE contextual manner. The implementation of this standard is dependent on the individual mathematics instructor.

M.TMS.9Solve linear equations in one variable.

Module 29105 – Base Metal PreparationObjectivesUpon completion of this module, the trainee will be

X In many instances in the Welding concentration students are tasked with finding a missing value. Many of these involve a single variable linear equation. The mathematics instructor will pinpoint this




(Welding)



Moderate

Align-ment


able to do the following:1. Clean base metal for

welding or cutting2. Identify and explain joint

design3. Explain joint design

considerations4. Mechanically bevel the

end of a mild steel plate5. Thermally bevel the end

of a mild steel plate6. Select the proper joint

design based on a welding procedure specification (WPS) or instructor direction

mathematics concept at various times and encourage students to look at the situations algebraically by setting up formal equations and providing evidence when solving them.

The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration and has students approach it from a mathematics standpoint.

As example from the evidence provided; the Coal Silo/Funnel System. Students are asked to determine the amount of material remaining in the silo after a given amount of time and a given rate. The math instructor will have students share their methods for solving this and provide justification for their answers. The instructor will insure that students can write the algebraic equation for this because they will be asked again to work with this type of equation at the end of the




(Welding)



Moderate

Align-ment


lesson.

The mathematics that revolves around this standard is required for students to complete basic welding projects within the CT curriculum.

M.TMS.10Understand 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.



proper personal protection used in welding

3. Describe how to avoid

X In Safety Enclosure students multiply binomials. Steel Plate Burnout requires students to perform operations with polynomials. In Coal Silo/Funnel System students perform operations with polynomials. The mathematics instructor will insure that students identify the polynomials and the operations performed with them. Students will apply concepts with polynomials and demonstrate their understanding mathematically through these various pieces of evidence from.




(Welding)



Moderate

Align-ment


welding fumes4. Explain some of the

causes of accidents5. Identify and explain uses

for material safety data sheets








4. Use plasma arc cutting




(Welding)



Moderate

Align-ment


equipment to make various types of cuts


Module 29105 – Base Metal PreparationObjectivesUpon completion of this module, the trainee will be able to do the following:1. Clean base metal for










(Welding)



Moderate

Align-ment


M.TMS.11Create 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.








Module 29202 - Reading Welding Detail DrawingsObjectivesUpon completion of this module, the trainee will be able to do the following:

X The mathematics instructor will utilize the evidence provided as a CTE contextual introduction to creating equations and inequalities concepts. The mathematics instructor will use mathematics resources available to them to extend the lessons to include other mathematics concepts associated with the standard. The content will encompass writing equations and inequalities of various forms as listed in the standard.




(Welding)



Moderate

Align-ment


1. Identify and explain a welding detail drawing

2. Identify and explain lines, material fills, and sections






M.TMS.12Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Module 29107 – SMAW Equipment SetupObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain

shielded metal arc welding (SMAW) safety

2. Explain welding electrical current

X In many instances in the Welding concentration students are tasked with finding a missing value. Many of these involve equations similar to those stated in the standard but not in a formal manner. The mathematics instructor will pinpoint this mathematics concept at various times and encourage students to look at the situations algebraically by setting up formal equations




(Welding)



Moderate

Align-ment


3. Identify welding power supplies and their characteristics

4. Explain how to set up welding power supplies

5. Set up a machine for welding

6. Identify tools used for weld cleaning

Module 29202 - Reading Welding Detail DrawingsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain a






6. Interpret basic elements

and providing evidence when solving them.

The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration and has students approach it from a mathematics standpoint. As part of the Manufacturing CTE cluster standard ask that students be able to “analyze tables, charts, graphs, and multiple data sources to complete CT projects”

The mathematics that revolves around this standard is required for students to complete basic welding projects within the CT curriculum.




(Welding)



Moderate

Align-ment


of a welding detail drawing







5. Explain metallurgical considerations for




(Welding)



Moderate

Align-ment


welding metalsModule 29205 – GMAW and FCAW Equipment and Filler MetalsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain gas metal arc

welding (GMAW) and flux-cored arc welding (FCAW) safety

2. Explain the characteristics of welding current and power sources

3. Identify and explain the use of GMAW and FCAW equipment:spray transfer, globular, short circuiting, pulse

4. Identify and explain the use of GMAW and FCAW shielding gases and filler metals

5. Set up GMAW and FCAW equipment and identify tools for weld




(Welding)



Moderate

Align-ment


cleaningM.TMS.13Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.







6. Explain safety techniques

X Within the evidence provided students represent constraints by equations. The mathematics instructor will ask students to compare/contrast equations and inequalities and where each can be applied and why. The mathematics instructor will extend the lessons provided to allow students to practice with inequalities and equations.




(Welding)



Moderate

Align-ment


for storing and handling cylinders









design based on a welding procedure specification (WPS) or




(Welding)



Moderate

Align-ment


instructor directionModule 29106 – Weld QualityObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain












(Welding)



Moderate

Align-ment










M.TMS.14Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Module 29203 – Physical Characteristics and Mechanical Properties of MetalsObjectivesUpon completion of this module, the trainee will be able to do the following:

X In many instances in the Welding concentration students are tasked with finding a missing value. Many of these involve geometric formulas for perimeter, area, volume, etc.. The mathematics instructor will pinpoint this mathematics concept at various times and encourage




(Welding)



Moderate

Align-ment


1. Identify and explain the composition and classification of base metals





students to look at the situations algebraically by setting up formal equations and providing evidence when solving them.

The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration and has students approach it from a mathematics standpoint. The mathematics that revolves around this standard is required for students to complete basic welding projects within the CT curriculum.

M.TMS.15Solve simple rational and radical equations in one variable and give examples showing how extraneous solutions may arise.

MA.15 Demonstrate operating instructions before using any equipmentMA.17Follow safety and security proceduresModule 00104 – Introduction to Power Tools

X This standard is included in the 20% not aligned to the welding curriculum and does not have to be covered in a CTE contextual manner. The implementation of this standard is dependent on the individual mathematics instructor.




(Welding)



Moderate

Align-ment


1. Identify power tools commonly used in construction trades

2. Use power tools safely3. Explain how to maintain

power tools properlyModule 29101 – Welding SafetyObjectivesUpon completion of this module the trainee will be able to do the following:1. Identify some common










(Welding)



Moderate

Align-ment




M.TMS.16Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Module 00104 – Introduction to Power Tools1. Identify power tools

commonly used in construction trades


power tools properlyModule 29102 – Oxyfuel CuttingObjectives1. Identify and explain the

use of oxyfuel cutting equipment

2. Set up oxyfuel equipment3. Light and adjust an

oxyfuel torch4. Shut down oxyfuel

cutting equipment5. Disassemble oxyfuel

equipment6. Change cylinders

X By extending the concepts covered with the evidence provided for standards TMS.9, TMS.11, TMS.12 students also have the opportunity to work with the concepts involved in this standard. The mathematics instructor will insure that students practice and apply these concepts through the evidence provided and extensions of it.




(Welding)



Moderate

Align-ment


7. Perform oxyfuel cutting8. Operate a motorized,

portable oxyfuel gas cutting machine







M.TMS.17Explain each step in solving a simple equation as following from the equality of numbers asserted at the


commonly used in

X In many instances in the Welding concentration students are tasked with finding a missing value. The mathematics instructor will pinpoint this mathematics concept at various times and encourage




(Welding)



Moderate

Align-ment


previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

construction trades2. Use power tools safely3. Explain how to maintain






equipment6. Change cylinders7. Perform oxyfuel cutting8. Operate a motorized,


Module 29103 – Plasma Arc CuttingObjectivesUpon completion of this module, the trainee will be able to do the following:

students to look at the situations algebraically by setting up formal equations and providing evidence when solving them.





(Welding)



Moderate

Align-ment


1. Explain the plasma arc cutting processes

2. Identify plasma arc cutting equipment

3. Prepare and set up plasma arc cutting equipment







end of a mild steel plate




(Welding)



Moderate

Align-ment


5. Thermally bevel the end of a mild steel plate

6. Select the proper joint design based on a welding procedure specification (WPS) or instructor direction











(Welding)



Moderate

Align-ment



M.TMS.18Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form ( x−p )2=q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., x2=49), taking square roots, completing the square, the quadratic formulas 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.







X The Safety Enclosure task associated with this standard allows students to develop a method for determining if a given perimeter will enclose a specified area. Through this contextual connection with the CTE concentration, the math instructor can open discussion for students to study the algebraic and graphic representation of quadratic equations with complex solutions and what they mean. The discriminant of the Quadratic Formula will be discussed which leads students to develop and understand the derivation of Quadratic Formula (which includes completing the square) and complex numbers. The mathematics instructor will insure this connection is made with students and they have the opportunity to practice with these mathematics concepts and apply it to other contextual CTE scenarios.




(Welding)



Moderate

Align-ment





Module 29102 – Oxyfuel CuttingObjectives1. Identify and explain the







Module 29103 – Plasma Arc Cutting




(Welding)



Moderate

Align-ment


ObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain the plasma arc






M.TMS.19Prove 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 produced a system with the same solutions.




X Students solve a system of equations in Steep Plate Shipment. Equipment Replacements also has students solve a system of equations. The mathematics instructor will use mathematics resources available to them as an extension to the evidence to give the students an opportunity to apply various methods for solving systems of equations (algebraically and graphically). Students will have the opportunity to decide




(Welding)



Moderate

Align-ment











design based on a welding procedure

the best method to use when working with systems of equations and apply their justification to CT concepts (i.e. the mathematics instructor will alter the tasks to include the same concepts but different solutions).




(Welding)



Moderate

Align-ment


specification (WPS) or instructor direction









M.TMS.20Solve a simple system consisting of a linear

Module 29103 – Plasma Arc CuttingObjectives

X This standard is included in the 20% not aligned to the welding curriculum and does not have to be covered in a CTE contextual




(Welding)



Moderate

Align-ment


equation and a quadratic equation in two variables algebraically and graphically.

Upon completion of this module, the trainee will be able to do the following:1. Explain the plasma arc






manner. The implementation of this standard is dependent on the individual mathematics instructor.

M.TMS.21Explain 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 solutions approximately, e.g., using technology to graph the functions, make tables of values, or find




plasma arc cutting

X This standard is encompassed by the evidence and extensions from standard TMS.19 because the mathematics concepts within this standard describe a way of solving system of equations graphically. This concept is especially useful in the lesson Equipment Replacement because the lessons creates a good situation for the mathematics instructor to utilize technology tools available to them such as graphing




(Welding)



Moderate

Align-ment


successive approximations. equipment4. Use plasma arc cutting

equipment to make various types of cuts


calculators or spreadsheet programs.

M.TMS.22Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables.







design based on a welding procedure specification (WPS) or

X This standard is encompassed by the evidence and extensions from standard TMS.19 and TMS.21 because the mathematics concepts within this standard describe methods of solving systems of equations. This concept is especially useful in the evidence provided because the lessons create a good situation for the mathematics instructor to discuss and apply algebraic methods for solving systems of equations as well as utilize technology tools available to them such as graphing calculators or spreadsheet programs.




(Welding)



Moderate

Align-ment


instructor directionModule 29202 - Reading Welding Detail DrawingsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain a








M.TMS.23Graph the solutions to a linear inequality in two variables as a half-plane

X This standard is included in the 20% not aligned to the welding curriculum and does not have to be covered in a CTE contextual manner. The implementation of this standard




(Welding)



Moderate

Align-ment


(excluding the boundary in the case of a strict inequality) and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

is dependent on the individual mathematics instructor.

M.TMS.24Understand 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. If f is a function and x in an element of its domain, them f (x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f (x ).







design based on a

X In many instances in the Welding concentration students work with functions in an informal manner. They understand and use the idea of domain and range (input and output). The mathematics instructor will pinpoint this mathematics concept at various times and encourage students to look at the situations mathematically.

The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration and has students approach it from a mathematics standpoint. The mathematics that revolves around this standard is required




(Welding)



Moderate

Align-ment


welding procedure specification (WPS) or instructor direction









Module 29107 – SMAW Equipment Setup

for students to complete basic welding projects within the CT curriculum.




(Welding)



Moderate

Align-ment


ObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain







Module 29109 – SMAW Beads and Fillet WeldsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Set up shielded metal arc

welding (SMAW) equipment

2. Describe methods of




(Welding)



Moderate

Align-ment


striking an arc3. Properly strike and

extinguish an arc4. Describe causes of arc

blow and wander5. Make stringer, weave,

and overlapping beads6. Make fillet welds in the

following positions: horizontal, vertical, overhead

Module 29110 Joint Fit-Up and AlignmentObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain job

code specifications2. Use fit-up gauges and

measuring devices to check joint fit-up

3. Identify and explain distortion and how it is controlled

4. Fit up joints using plate and pipe fit up tools

5. Check for joint




(Welding)



Moderate

Align-ment


misalignment and poor fit up before and after welding










(Welding)



Moderate

Align-ment


Module 29205 – GMAW and FCAW Equipment and Filler MetalsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain gas metal arc





5. Set up GMAW and FCAW equipment and identify tools for weld cleaning




(Welding)



Moderate

Align-ment


Module 29403 GTAW Aluminum PipeObjectivesUpon completion of this module, the trainee will be able to do the following:1. Prepare GTAW

equipment for V-groove and modified U-groove welds on aluminum pipe

2. Identify and explain V-groove and modified U-groove welds on aluminum pipe with GTAW equipment

3. Perform V-groove and modified U-groove welds on aluminum pipe in the following positions using GTAW equipment: 2G, 5G, 6G

Module 29404 GMAW Aluminum PipeObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain GMAW




(Welding)



Moderate

Align-ment


preparations associated with making V-groove welds on aluminum pipe

2. Perform V-grove welds on aluminum pipe with backing in the following positions using GMAW equipment, aluminum wire, and shielding gas: 2G, 5G, 6G

M.TMS.25Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.






5. Properly store equipment and clean the work area

X The Triangle Sculpture Project (in development) will have students welding a structure of steel bar in a pattern of different size triangles. The pattern of these triangles represents geometric series (Sierpinksi Triangles). The students identify presence of a geometric series and then calculate how much space the sculpture will occupy (sum of the areas of the triangles and how much material they will use. See image below.




(Welding)



Moderate

Align-ment


after each useModule 29106 – Weld QualityObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain








Mathematics instructors will take this opportunity to have students distinguish between arithmetic and geometric sequences. As an extension to this lesson the mathematics instructor will have students differentiate between and work with recursive and explicit representations of those sequences.

M.TMS.26Interpret the parameters in a linear or exponential function in terms of a

Module 29103 – Plasma Arc CuttingObjectivesUpon completion of this

X Students must interpret and apply parameters inherent within the welding curriculum but mostly informally. Evidence provided for this standard also asks students to interpret




(Welding)



Moderate

Align-ment


context. module, the trainee will be able to do the following:1. Explain the plasma arc









3. Identify and explain nondestructive

parameter in a more formal manner. The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration and has students approach it from a mathematics standpoint. The mathematics that revolves around this standard is required for students to complete basic welding projects within the CT curriculum.




(Welding)



Moderate

Align-ment


examination practices4. Identify and explain

welder qualification tests5. Explain the importance

of quality workmanship6. Identify common

destructive testing methods


M.TMS.27For 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.







X As part of the Manufacturing CTE cluster, a standard asks that students be able to “analyze tables, charts, graphs, and multiple data sources to complete CT projects” The mathematics instructor will pinpoint these mathematics concepts at various times and encourage students to look at the situations algebraically and graphically by setting up formal equations.

There are several pieces of evidence provided for this standard that formally address this standard and allow sufficient opportunities for the instructor to extend concepts and students to apply them.




(Welding)



Moderate

Align-ment











Module 29203 – Physical Characteristics and Mechanical Properties of





(Welding)



Moderate

Align-ment


MetalsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain the






Module 29205 – GMAW and FCAW Equipment and Filler MetalsObjectivesUpon completion of this module, the trainee will be




(Welding)



Moderate

Align-ment


able to do the following:1. Explain gas metal arc





5. Set up GMAW and FCAW equipment and identify tools for weld cleaning

M.TMS.28Distinguish between situations that can be modeled with linear functions and with exponential functions.

Module 29103 – Plasma Arc CuttingObjectivesUpon completion of this module, the trainee will be able to do the following:

X Evidence provided for this standard that allows the instructor to utilize resources available to them to extend the mathematics concepts of the standard and give students




(Welding)



Moderate

Align-ment


1. Explain the plasma arc cutting processes

2. Identify plasma arc cutting equipment




the opportunity to apply them.

M.TMS.29Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.



2. Explain and demonstrate field identification





(Welding)



Moderate

Align-ment


methods for base metals3. Identify and explain the

physical characteristics and mechanical properties of metals



M.TMS.30Describe qualitatively the functional relationship between two quantities by analyzing a graph.

MA.34Demonstrate accuracy in calculating and measuring graphical work required to complete career/technical assignments and projectsMA.35Analyze tables, charts, graphs, and multiple data sources to complete career/technical assignments and projectsModule 29106 – Weld QualityObjectivesUpon completion of this module, the trainee will be

X As part of the Manufacturing CTE cluster, a standard asks that students be able to “analyze tables, charts, graphs, and multiple data sources to complete CT projects” The mathematics instructor will pinpoint these mathematics concepts at various times and encourage students to look at the situations algebraically and graphically by setting up formal equations.

The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration




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able to do the following:1. Identify and explain








and has students approach it from a mathematics standpoint. The mathematics that revolves around this standard is required for students to complete basic welding projects within the CT curriculum.

M.TMS.31Identify the effect on the graph of replacing f (x) by f ( x )+k , kf ( x ) , f (kx ) , and f (x+k ) for specific values of k (both positive and negative); find the value of k given the graphs.



cutting equipment

X The lesson Three Phase Power included as evidence for this standard makes the CT contextual connection of transformations of functions (the lesson specifically involves translations and dilations of a trigonometric function). The math instructor will extend the mathematics introduced in the lesson to include the remaining transformations and using mathematics resources available to




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6. Identify tools used for

them give students the opportunity to practice identifying the transformations graphically and algebraically with various functions.




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weld cleaningModule 29205 – GMAW and FCAW Equipment and Filler MetalsObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain gas metal arc





5. Set up GMAW and FCAW equipment and identify tools for weld




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cleaningM.TMS.32Graph functions expressed symbolically and show key features of he graph, by hand in simple cases and using technology for more complicated cases.

a. Graph linear and quadratic functions

and show intercepts, maxima, and minima.b. Graph polynomial

functions, identifying zeros when suitable factorizations are available, and showing end behavior.










X The Storage Box task for this lesson should be implemented as the CTE contextual connection to this standard. Math instructors are to present this problem to students. Students are asked to share methods for solving. The mathematics instructor will insure that students are exposed to the mathematical methods involved in this standard and have students practice through extended contextual examples similar to the task.




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M.TMS.33Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.



X Through the evidence cited for this standard students explore exponential functions through CTE (welding) contextual scenarios. To develop further understanding of exponential functions mathematics instructors will extend the mathematics concepts within these lessons to give students the opportunity to compare and




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contrast exponential functions with other functions (namely quadratic and linear).




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M.TMS.34Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a. Use the process of factoring and completing the square in a quadratic function to show zeroes, extreme values, and symmetry of the graph, and to interpret these in terms of a context.






X The Storage Box task for this lesson should be implemented as the CTE contextual connection to this standard. Math instructors are to present this problem to students. Students are asked to share methods for solving. The mathematics instructor will insure that students are exposed to the mathematical methods involved in this standard and have students practice through extended contextual examples similar to the task.

The Safety Enclosure task associated with this standard allows students to develop a method for determining if a given perimeter will enclose a specified area. Through this contextual connection with the CTE concentration, the math instructor can open discussion for students to study the algebraic and graphic representation of quadratic equations with complex solutions and what




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5. Identify and explain notes and bill of

they mean. The discriminant of the Quadratic Formula will be discussed which leads students to develop and understand the derivation of Quadratic Formula (which includes completing the square) and complex numbers. The mathematics instructor will insure this connection is made with students and they have the opportunity to practice with these mathematics concepts and apply it to other contextual CTE scenarios.




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materials6. Interpret basic elements

of a welding detail drawing


M.TMS.35Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

MA.31Literacy and numeracy skills required to solve complex real world problems associated with the career/technical content areaMA.34Demonstrate accuracy in calculating and measuring graphical work required to complete career/technical assignments and projectsMA.35Analyze tables, charts, graphs, and multiple data sources to complete career/technical assignments and projectsModule 29203 – Physical Characteristics and Mechanical Properties of Metals

X As part of the Manufacturing CTE cluster, a standard asks that students be able to “analyze tables, charts, graphs, and multiple data sources to complete CT projects” The mathematics instructor will pinpoint these mathematics concepts at various times and encourage students to look at the situations algebraically and graphically and compare multiple sets of data.

The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration and has students approach it from a mathematics standpoint. The mathematics that revolves around this standard is required for students to complete basic welding




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ObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain the






projects within the CT curriculum.

M.TMS.36Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-


X Through the evidence cited for this standard students explore the mathematics concepts through CTE (welding) contextual scenarios. To develop further understanding of the functions included in this standard and to include all mathematical aspects of this




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output pairs (include reading these from a table). (CCSS.Math.Content.HSF-LE.A.2)











standard mathematics instructors will extend the mathematics concepts within these lessons to give students the opportunity to use and justify relationships involved in the functions (and sequences) included in the standard.




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M.TMS.37Write a function that

Module 29106 – Weld Quality

X While the individual pieces of evidence do not robustly expose students to this standard.




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describes a relationship between two quantities.

a. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to a model.

b. Compose functions. For example, if T ( y )is the temperature in the atmosphere as a function 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 of the weather balloon as a function of time.

ObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain








Together they give the students the opportunity to apply the mathematical concepts within the standard. Mathematics instructors will implement the lessons. The mathematics instructor will insure students identify the composition of functions in the lesson Steel Plate Burnout. These pieces of evidence once implemented allow the mathematics instructor to make the CTE contextual connection of the mathematics concepts and then extend them to accurately and wholly insure students have the opportunity to practice and apply the concepts within this standard.




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M.TMS.38Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s Principle, and informal limit arguments.


commonly used in construction trades









Module 29103 – Plasma

X Students are applying the concepts of perimeter, area, and volume continually within the welding curriculum. However they aren’t formally given the opportunity to give an informal argument for the formulas. The evidence cited for this task will give students the opportunity to do so.

The Winter Wonderland task has been reworked to include students deriving and justify the formula for volume of the snowman if filled with snow.

The Coal Silo/Funnel system project asks students to derive the formula for a truncated cone and justify their reasoning. Also within the mathematics connection of the project students work through the derivation for the volume of a cone and cylinder.




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Arc CuttingObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain the plasma arc











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M.TMS.39Give an informal argument using Cavalieri’s Principle for the formulas for the volume of a sphere and other solid figures.







design based on a welding procedure

X Students are applying the concept of continually within the welding curriculum. However they aren’t formally given the opportunity to give an informal argument for the formulas. The evidence cited for this task will give students the opportunity to do so.

The Winter Wonderland task is being reworked to include students deriving and justifying the formula for volume of the snowman if filled with snow.

The Coal Silo/Funnel system project asks students to derive the formula for a truncated cone and justify their reasoning. Also within the mathematics connection of the project students work through the derivation for the volume of a cone and cylinder.




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specification (WPS) or instructor direction









M.TMS.40Use coordinates to prove simple geometric theorems

Module 29109 – SMAW Beads and Fillet WeldsObjectives

X The mathematics instructor, when implementing the Bolt Circles task, will insure that students understand they are




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algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1 ,√3) lies on the circle centered at the origin and containing the point (0 ,2).

Upon completion of this module, the trainee will be able to do the following:1. Set up shielded metal arc

welding (SMAW) equipment

2. Describe methods of striking an arc

3. Properly strike and extinguish an arc

4. Describe causes of arc blow and wander

5. Make stringer, weave, and overlapping beads

6. Make fillet welds in the following positions: horizontal, vertical, overhead

Module 29110 Joint Fit-Up and AlignmentObjectivesUpon completion of this module, the trainee will be able to do the following:1. Identify and explain job

code specifications2. Use fit-up gauges and

measuring devices to

finding short cuts for proving/disproving that a point lies on a circle in a CTE contextual manner. The task is being reworked so that students don’t focus on the term “short cut”. The mathematics instructor will also utilize mathematics resources available to them to have students practice with proving the above and other theorems.

In the Coal Silo/Funnel system project the mathematics instructor will take the opportunity to prove theorems of similar triangles when deriving the formula for a truncated cone.

The Coal Silo/Funnel System project connects the derivation of the formula for a cone with the centroid of the right triangle whose profile is revolved around a leg of the triangle to form the cone. Students prove and locate that the centroid of a triangle is the intersection of the medians of the triangle.




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check joint fit-up3. Identify and explain

distortion and how it is controlled

4. Fit up joints using plate and pipe fit up tools

5. Check for joint misalignment and poor fit up before and after welding

M.TMS.41Use coordinates to compute perimeters and areas of triangles and rectangles, e.g. using the distance formula.

X

This standard is included in the 20% not aligned to the welding curriculum and does not have to be covered in a CTE contextual manner. The implementation of this standard is dependent on the individual mathematics instructor.

M.TMS.42Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with topographic grid systems based on ratios).

MA.15 Demonstrate operating instructions before using any equipmentMA.17Follow safety and security proceduresModule 29101 – Welding SafetyObjectives

X The reason for strong alignment of this standard is that students apply this concept regularly in the Welding shop but not necessarily formally therefore the mathematics instructor takes curriculum already inherent in the CTE concentration and has students approach it from a mathematics standpoint. The mathematics that revolves around this standard is required for students to complete basic welding




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Upon completion of this module the trainee will be able to do the following:1. Identify some common









Module 29105 – Base Metal PreparationObjectivesUpon completion of this

projects within the CT curriculum. The evidence provided for this standard supports this conclusion.




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module, the trainee will be able to do the following:1. Clean base metal for








composition and




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classification of base metals





Module 29403 GTAW Aluminum PipeObjectivesUpon completion of this module, the trainee will be able to do the following:1. Prepare GTAW

equipment for V-groove and modified U-groove welds on aluminum pipe

2. Identify and explain V-groove and modified U-groove welds on




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aluminum pipe with GTAW equipment

3. Perform V-groove and modified U-groove welds on aluminum pipe in the following positions using GTAW equipment: 2G, 5G, 6G

Module 29404 GMAW Aluminum PipeObjectivesUpon completion of this module, the trainee will be able to do the following:1. Explain GMAW

preparations associated with making V-groove welds on aluminum pipe

2. Perform V-grove welds on aluminum pipe with backing in the following positions using GMAW equipment, aluminum wire, and shielding gas: 2G, 5G, 6G

M.TMS.43Represent data on two quantitative variables on a

Module 29106 – Weld QualityObjectives

X The task Quality Control asks students to create a scatter plot and interpret the data




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scatter plot, and describe how the variables are related. Interpret linear models.

Upon completion of this module, the trainee will be able to do the following:1. Identify and explain








represented.

Based on the Quality Control task, as an extension, students will also collect their own data over a given amount of time from projects being completed in their shop. They will then create their own statistical analysis lesson including an answer key. Thus students are exposed to the statistics concepts included in the statistics standards and have work for the mathematics instructor to compare and check for comprehension. The mathematics instructor may implement additional statistics lessons if needed based on the students understanding.

M.TMS.44Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of data.


codes governing welding

X The task Quality Control is being reworked to included the statistical terms of rate of change/correlation coefficient and constant versus the typical terms used when writing a linear equation.




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2. Identify and explain weld imperfections and their causes







M.TMS.45Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points on the line.




3. Identify and explain nondestructive





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examination practices4. Identify and explain





M.TMS.46Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.











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M.TMS.47Represent data with plots on the real number line (dot plots, histograms, and box plots).

MA.12Recognize the main causes of accidentsMA.13Research agencies that are responsible for emergencies in the workplaceModule 29101 – Welding SafetyObjectivesUpon completion of this module the trainee will be able to do the following:1. Identify some common





X The task Quality Control is being reworked to allow students to be exposed to different ways of visually representing and analyzing data. The students will create a box plot of the data where they will also analyze and chose the best measure of central tendency (mean, median, mode). Based on the Quality Control task, as an extension, students will also collect their own data over a given amount of time from projects being completed in their shop. They will then create their own statistical analysis lesson including an answer key. Thus students are exposed to the statistics concepts included in the statistics standards and have work for the mathematics instructor to compare and check for comprehension. The mathematics instructor may implement additional statistics lessons if needed based on the students understanding




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The task Safety Statistics also has students develop and analyze a box plot on page 2 of the actual task. They also use excel to analyze the data collected from OSHA. Safety is covered at the beginning of each year for students within the CTE concentration. Students will collect their own data over the year and compare their statistics the next.

M.TMS.48Use 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.

MA.12Recognize the main causes of accidentsMA.13Research agencies that are responsible for emergencies in the workplaceModule 29101 – Welding SafetyObjectivesUpon completion of this module the trainee will be able to do the following:1. Identify some common


proper personal

X The task Quality Control is being reworked to allow students to be exposed to different ways of visually representing and analyzing data. The students will create a box plot of the data where they will also analyze and chose the best measure of central tendency (mean, median, mode). Based on the Quality Control task, as an extension, students will also collect their own data over a given amount of time from projects being completed in their shop. They will then create their own statistical analysis lesson including an answer key. Thus students are exposed to the statistics concepts included in the statistics standards and have work for the mathematics instructor to compare and




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protection used in welding







check for comprehension. The mathematics instructor may implement additional statistics lessons if needed based on the students understanding

The task Safety Statistics also has students develop and analyze a box plot on page 2 of the actual task. They also use excel to analyze the data collected from OSHA. Safety is covered at the beginning of each year for students within the CTE concentration. Students will collect their own data over the year and compare their statistics the next.

M.TMS.49Interpret differences in shape, center, and spread in the context of the data sets, accounting got possible effects of extreme data points (outliers).

MA.12Recognize the main causes of accidentsMA.13Research agencies that are responsible for emergencies in the workplaceModule 29101 – Welding SafetyObjectivesUpon completion of this

X The task Safety Statistics also has students develop and analyze a box plot on page 2 of the actual task. They also use excel to analyze the data collected from OSHA. Safety is covered at the beginning of each year for students within the CTE concentration. Students will collect their own data over the year and compare their statistics the next.




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module the trainee will be able to do the following:1. Identify some common









M.TMS.50Compute (using technology) and interpret the correlation coefficient of a linear fit.

Module 29106 – Weld QualityObjectivesUpon completion of this module, the trainee will be

X The task Quality Control is being reworked to included the statistical terms of rate of change/correlation coefficient and constant versus the typical terms used when writing a




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able to do the following:1. Identify and explain








linear equation.


M.TMS.51Distinguish between correlation and causation. (CCSS.Math.Content.HSS-ID.A.3)



imperfections and their





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causes3. Identify and explain

nondestructive examination practices





M.TMS.52Understand statistics as a process for making inferences about population parameters based on a random sample from that population.










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