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(CTE) MATHEMATICS IN COMPUTER AIDED DRAFTING

Math IV

Unit Pacing Guide

Rational and Purpose:

Professional math IV is provided to enhance mathematics in high school and provide students with the math skills necessary for the current job market and/or prepare students for college entry. Curriculum that is contained within Career Technology Education (CTE) provides enhanced mathematics instruction that makes mathematics more explicit in a meaningful context and helps reinforce students’ mathematics understanding both in and out of context.

Guidelines:

All objectives must be mastered at or above a 70% efficiency level in order to receive 1 Math credit. The content/objectives to be completed in four (4) semesters are listed below in each trade specific program. Since each program contains differing content at various stages, an independent content/objective list will be constructed for each curriculum in every course. Once a designated semester worth of content/objectives (which are listed in the following table) are accomplished, .25 credits will be earned per semester for a total of 1 math credit at the end of 2 years. Failure to complete the required semester content/objectives may result in the student being removed from the Professional Math IV program.

|Competencies |

|Addition and |1st quarter 1 week |After completing this unit the |MA1, |Whole numbers |Worksheets of addition |Paper and pencil |Test of at least 10 |

|subtraction of whole | |Student will be able to calculate whole | |Real numbers |and subtraction problems |problems and software |problems in each |

|numbers | |numbers through the mathematical processes of|Goals: |Natural numbers | |demonstrational |operation to demonstrate |

| | |addition, subtraction, |G, 1.10 |Numbers Addend, Sum | |activities |mastery |

| | | | |Minuend Subtrahend | | | |

| | | |CLEs N-1B, N-1C. M-2D|Difference | | | |

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|Multiplication and |1st quarter 1 week |After completing this unit the |MA1, |Whole numbers |Worksheets of |Paper and pencil |Test of at least 10 |

|division of whole | |Student will be able to calculate whole | |Real numbers |multiplication and |problems and software |problems in each |

|numbers | |numbers through the mathematical processes of|Goals: |Natural numbers |division problems |demonstrational |operation to demonstrate |

| | |multiplication |G, 1.10 |Rational numbers, | |activities |mastery |

| | |and division. | |Multiplicand | | | |

| | | |CLEs N-1B, N-1C. M-2D|Multiplier Product | | | |

| | | | |factor, Quotient | | | |

| | | | |divisor, Dividend | | | |

|Reducing proper and |1st quarter 1 week |After completing this unit the student will |MA1 |Prime numbers Greatest|Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|improper fractions | |be able to add & subtract proper and improper| |common factor, Least |video, internet and other|problems and software |problems in each |

| | |fractions |Goals: |common multiple, |electronic sources |demonstrational |operation to demonstrate |

| | | |G, 3.3, 3.4 |Rational expression, | |activities. Peer |mastery |

| | | | |Numerator Denominator | |grouping for additional | |

| | | |CLEs |Reciprocal Equivalent | |support and interaction.| |

| | | |N-1B, N- 1C, N-2D, | | | | |

| | | |N-3E | | | | |

|Add fractions With like|1st quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers Greatest|Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|denominators and | |be able to add rational numbers with like | |common factor, Least |video, internet and other|problems and software |problems in each |

|reducing to lowest | |denominators and reduce them to lowest terms |Goals: |common multiple, |electronic sources |demonstrational |operation to demonstrate |

|terms | | |G 1.6, 1.10, 3.4 |Rational expression, | |activities. Peer |mastery |

| | | | |Numerator Denominator | |grouping for additional | |

| | | |CLEs N-1B, N-1C,N- |Reciprocal Equivalent | |support and interaction | |

| | | |2D,N- 3D, | | | | |

|Add fractions with |1st quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers Greatest|Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|unlike denominators | |be able to add rational numbers with unlike | |common factor, Least |video, internet and other|problems and software |problems in each |

| | |denominators |Goals: |common multiple, |electronic sources |demonstrational |operation to demonstrate |

| | | |G 3.3, 1.6, 3.4 |Rational expression, | |activities. Peer |mastery |

| | | | |Numerator Denominator | |grouping for additional | |

| | | |CLEs |Reciprocal Equivalent | |support and interaction | |

| | | |N-1C, N-2D, N-3D, | | | | |

| | | |N-3E | | | | |

|Add fractions With |1st quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|unlike denominators | |be able to add rational numbers with unlike | |Greatest common |video, internet and other|problems and software |problems in each |

|When neither is lowest | |denominators when neither is lowest. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

|common denominator | | |G 3.3, 1.6, 1.10, 3.4|multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs N-1B, N-1C, |Denominator Reciprocal| |support and interaction | |

| | | |N-2D, N-3D, N-3E |Equivalent | | | |

|Add mixed numbers with |1st quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|like denominators | |be able to add mixed numbers with like | |Greatest common |video, internet and other|problems and software |problems in each |

| | |denominators. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs |Denominator Reciprocal| |support and interaction | |

| | | |N-1B, N-1C,N- 2D, N- |Equivalent | | | |

| | | |3D, | | | | |

|Add mixed numbers with |1st quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|unlike denominators | |be able to add mixed numbers with rational | |Greatest common |video, internet and other|problems and software |problems in each |

| | |numbers when neither rational number has a |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | |common denominator. |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs N-1B, N-1C,N- |Denominator Reciprocal| |support and interaction | |

| | | |2D, N- 3D |Equivalent | | | |

|Subtracting fractions |2nd quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|with like denominators | |be able to subtract rational numbers with | |Greatest common |video, internet and other|problems and software |problems in each |

| | |like denominators. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs N-1B, N-1C,N- |Denominator Reciprocal| |support and interaction | |

| | | |2D, N- 3D, |Equivalent | | | |

|Subtracting fractions |2nd quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|with unlike | |be able to subtract rational numbers with | |Greatest common |video, internet and other|problems and software |problems in each |

|denominators | |unlike denominators. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs |Denominator Reciprocal| |support and interaction | |

| | | |N-1B, N-1C,N- 2D, N- |Equivalent | | | |

| | | |3D, | | | | |

|Subtracting mixed |2nd quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|numbers and reducing | |be able to subtract mixed numbers and reduce | |Greatest common |video, internet and other|problems and software |problems in each |

|answers to lowest terms| |their answers to lowest terms. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs |Denominator Reciprocal| |support and interaction | |

| | | |N-1B, N-1C,N- 2D, N- |Equivalent | | | |

| | | |3D, | | | | |

|Subtracting fractions |2nd quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|when borrowing is | |be able to subtract rational numbers when | |Greatest common |video, internet and other|problems and software |problems in each |

|necessary | |borrowing is necessary. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs |Denominator Reciprocal| |support and interaction | |

| | | |N-1B, N-1C,N- 2D, N- |Equivalent | | | |

| | | |3D, | | | | |

|Multiplying fractions |2nd quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

| | |be able to multiply rational numbers. | |Greatest common |video, internet and other|problems and software |problems in each |

| | | |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs N-1B, N-1C,N- |Denominator Reciprocal| |support and interaction | |

| | | |2D, N- 3D, |Equivalent | | | |

|Multiplying fractions |2nd quarter 1 week |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|and whole numbers | |be able to multiply rational numbers and | |Greatest common |video, internet and other|problems and software |problems in each |

| | |whole numbers. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs |Denominator Reciprocal| |support and interaction | |

| | | |N-1B, N-1C,N- 2D, N- |Equivalent | | | |

| | | |3D, | | | | |

|Dividing fractions |2nd quarter 1 week |After completing this unit the student will | MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

| | |be able to divide rational numbers. | |Greatest common |video, internet and other|problems and software |problems in each |

| | | |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

| | | |G 1.6, 1.10, 3.4 |multiple, Rational | |activities. Peer |mastery |

| | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs |Denominator Reciprocal| |support and interaction | |

| | | |N-1B, N-1C,N- 2D, N- |Equivalent | | | |

| | | |3D, | | | | |

|Changing common |2nd quarter 1 weeks |After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|fractions to decimal | |be able to Change common fractions to decimal| |Greatest common |video, internet and other|problems and software |problems in each |

|fractions and decimal | |fractions and decimal fractions to common |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

|fractions to common | |fractions. |G 3.3, 1.6, 1.10, 3.4|multiple, Rational | |activities. Peer |mastery |

|fractions | | | |expression, Numerator | |grouping for additional | |

| | | |CLEs |Denominator Reciprocal| |support and interaction | |

| | | |N-1B, N-1C, M-2D, |Equivalent | | | |

| | | |M-3D, M-3E | | | | |

|Addition, subtraction, |2nd t quarter 1 week|After completing this unit the student will |MA 1, MA 5 |Prime numbers, |Hardcopy worksheets, |Paper and pencil |Test of at least 10 |

|multiplication and | |be able to add, subtract, multiply and divide| |Greatest common |video, internet and other|problems and software |problems in each |

|divisions of decimals | |decimal fractions. |Goals: |factor, Least common |electronic sources |demonstrational |operation to demonstrate |

|to recognize and | | |G 3.3, 1.6, 1.10, 3.4|multiple, Rational | |activities. Peer |mastery |

|collect data from | | | |expression, Numerator | |grouping for additional | |

|Tables and Charts and | | |CLEs N-1B, N-1C, |Denominator Reciprocal| |support and interaction | |

|use this data to | | |M-2D, M-3D, M-3E |Equivalent | | | |

|perform more advanced | | | | | | | |

|Calculations. | | | | | | | |

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|Unit Title: (Current Knowledge) Module # I Measurements, Conversions, Rotation of Angles, and Trigonometry Ratios of Acute and General Angles |

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|Core Concepts: Students will learn: How to accurately interpret different measurements using different scales and units of measure; Differentiate between standard English and Metric conversions; Assess different|

|directions and rotations of angles in reference to the unit circle; and discover the relationships between acute and general angles. |

|Comp. # 1 |3rd quarter 2 weeks |After completing this unit the student will |MA 1, MA 2, MA 4, MA |Architect Rule |Dividers/compass |Classroom demonstration |Students will be given a |

| | |know all fraction and decimal incremental |5 |Angles |Protractors |of how to use various |50 question test |

|Be able to accurately | |equivalents on an exploded view of an inch; | |Degrees |Rulers |measuring devices |involving the recognition|

|interpret different | |understand and identify all ratios, scales, |Goals: |(Fractional Degree) |Meter sticks | |of fraction to decimal |

|units of measure using | |actual size, and smallest calibrations found |G 1.6, 1.10, 2.7 |Numerator |Yard sticks |Lecture on how to |conversions, decimal to |

|different scale | |on an architect rule; be able to measure with| |Denominator |Angle finder |interpret various scales|fraction conversions, |

|measuring devices. | |any of the 12 different scales on an |CLEs |Vertex |Architect Rule |and units of measure |fill in ratios when given|

|(Architect Scale) | |architect rule : |N-3D, N-3E, G 4B, |Side |Elmo |using an Elmo Zoom |a scale, and fill in |

| | | |M-2Dc |(Center Mark) |Projector |overhead projector |scale when given a ratio.|

| | | | |Unit Circle | | | |

| | | | |Units of Measure | |The students will be | |

| | | | |Smallest Calibration | |given guided practice on|There will be a written |

| | | | |Ratios | |how to complete a table |test on measuring and |

| | | | |Scales | |of all ratios, scales, |accuracy. |

| | | | | | |actual size, and | |

| | | | | | |smallest calibrations | |

| | | | | | |found on an architect | |

| | | | | | |rule. | |

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| | | | | | |The students will | |

| | | | | | |complete an extensive | |

| | | | | | |assignment on scale | |

| | | | | | |interpretation and | |

| | | | | | |actual measuring | |

| | | | | | |practices | |

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|Comp. # 2 |3rd quarter 1 week |After completing this unit the student will |MA 1, MA 2, MA 5 |English system |Access to an on-line |On-line conversion |. |

| | |be able to compare equivalent measurement | |Metric system |computer source |programs |The students will be |

|Differentiate between | |units and conversions to interpret proper |Goals: |Equivalent | | |asked to measure several |

|Standard English and | |dimensioning. |G-1.10, 1.7, 3.4. |Meter |Paper and pencils |Short lecture using and |objects using a standard |

|Metric conversions | | | |Decimeter | |explaining the metric |and metric measuring |

| | | |CLEs |Centimeter |Chart of metric |system |device to formulate |

| | | |N-1C, M-2D |Millimeter |conversions | |their own conversion |

| | | | |Kilometer | |Review of how to find |factor |

| | | | |Feet |Worksheets which contain|and calculate a | |

| | | | |Inches |conversion problems |conversion factor. |They will then be given a|

| | | | |Yard | | |written test |

| | | | | |Chart of |Worksheets handed out | |

| | | | | |Metric-Customary |for guided practice | |

| | | | | |Equivalents | | |

|Comp. # 3 |3rd quarter 2 weeks |After completing this unit the student will |MA-1, MA-2, MA-4 |Trigonometry |Handouts of Trigonometry|Class will watch a video|There will be a written |

| | |understand angles and angle measurements, | |Angles |examples in reference to|lesson about the unit |test to check for |

|Assess different types | |know the difference between terminal and co |Goals: |Terminal |the unit circle and |circle and how terminal |comprehension concerning|

|of angles and their | |terminal angles, and differentiate between |G-1.8 |Co terminal |terminal/co terminal |and co terminal angles |positive and negative |

|measure of rotation. | |degrees, minutes, and seconds. | |Rotation |illustrations |change directions. |angle direction as well |

|(Positive and Negative | | |CLEs |Unit Circle | | |as angle measurement in |

|rotation/Terminal and | | |N-3E, G-1A, M-1B. |Standard- Position |Software presentation of|Short class lecture with|degrees, minutes, and |

|Co terminal) Understand| | | |Quadrennial |how angle direction |corresponding worksheet |seconds |

|the relationship | | | |Radians |change from positive to |examples for guided | |

|between deg/min/seconds| | | |Reference-Angles |negative |practice | |

| | | | |Degrees | | | |

| | | | |Minutes | | | |

| | | | |Seconds | | | |

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|Comp. # 4 |3rd quarter 2 weeks |After completing this unit the student will |MA-1, MA-2, MA-5. |Functions |Scientific Calculators |Short lecture |Paper and pencil test to |

| | |be able to understand and use the concepts of|1.10 |Acute Angles | | |demonstrate mastery of |

|Apply concepts | |trigonometric ratios to find the values of | |Trigonometric-ratios |Detailed Lesson Plan |Hand out worksheets for |trigonometric functions |

|concerning the | |the six trigonometric functions for angles |Goals: |Degrees | |guided practice |concerning common angles |

|functions of acute and | |that measure 30, 45, and 60 degrees. |G-3.4, G-2.3, G-2.7. |Radians |Work sheets | | |

|general angles (Trig | | | |Reference-Triangles | |Examine a CAD drawing |Provide a CAD drawing |

|ratios for 30, 45, and | | |CLEs |Sine |CAD drawings |that provide examples of|that has unknown line |

|60 degree angles) | | |N-1B, N-3D, G-1A, |Cosine | |trigonometric ratios |lengths to be found using|

| | | |G-4B, M-1B, M-2D |Tangent | |being used to find |trigonometric ratios |

| | | | |Cosecant | |unknown measurements | |

| | | | |Secant | | | |

| | | | |Cotangent | |Assign math problems to | |

| | | | | | |check for understanding | |

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|Unit Title: (Current Knowledge) Module # II Right triangles, General triangles, Transversals, and Area of Triangles |

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|Core Concepts: Students will investigate: Right triangles using the functions sine, cosine, tangent, secant, cosecant, cotangent, and Pythagorean’s theorem; The Law of Sines and Cosines to solve acute or obtuse |

|triangles; general triangles SSS, SAS, ASA, AAS, and SSA; Problems of angle measure in reference to parallel lines cut by a transversal; and use appropriate formulas to calculate the area of a triangle. |

|Comp. # 1 |4th quarter 2 weeks |After completing this unit the student will |MA-1, MA-2, MA- 4, |Ratio |Pencil |The class will analyze |A test will be given to |

| | |be able to make a distinction between the |MA-5 |Proportions |Paper |several different |check for student’s |

|Be able to solve right | |trigonometric ratios of sine, cosine, secant,| |Hypotenuse | |triangles ranging from |understanding of how to |

|triangles using the | |cosecant, tangent and cotangent and know the |Goals: |Right triangle |Scientific Calculator |30 to 90 degrees and |solve right triangles by |

|functions of sine, | |proper application of each one and apply |G-1.6, G-1.8, G-1.10,|Sine | |fill in a table of all |hand and by using the |

|cosine, tangent, | |Pythagorean’s theorem to any right triangle | |Cosine |Blank table or |ratios of sides. The |trigonometric functions |

|secant, cosecant, and | |to find unknown sides and angles. |G-3. 4. G-4.1 |Tangent |Spreadsheet |class will then use a |on a scientific |

|cotangent in addition | | | |Secant | |scientific calculator to|calculator. |

|to using Pythagorean’s | | |CLEs |Cosecant |CAD drawings of |find trigonometric |Students will also be |

|theorem | | |N-1B, N-3D, N-3E, |Cotangent |non-right triangles |ratios of all angles. |given a blueprint with |

| | | |A-1B, A-1C, G-1A, |Pythagorean’s theorem | |The class will discover |unknown measurements to |

| | | |G-4B, and M-2D. | | |that the functions on |find and calculate and |

| | | | | | |the calculator are only |will solve several |

| | | | | | |ratios of the sides of a|different measurement |

| | | | | | |triangle. The class |exercises using CAD |

| | | | | | |will then do problems |drawings of non-right |

| | | | | | |using Pyth. Theor. |triangles |

|Comp. # 2 |4th quarter 2 weeks |Be able to construct any acute or obtuse | MA-1, MA-2, MA- 4 |Proportions |Pencil |The student’s will solve|A test will be given to |

| | |angle and solve for unknown sides or angles | |Direct |Paper |several triangles using |check for student’s |

|Be able to manipulate | |with existing given information using the Law|Goals: |Indirect | |the law of Sines and |understanding of how to |

|formulas such as the | |of Sines and the Law of cosines. |G-1.6, G-1.8, G-1.10,|Law of Sines |Scientific Calculator |Cosines. |solve non-traditional |

|Law of Sines and | | | |Law of Cosines | | |triangles by using the |

|Cosines to solve any | | |G-3. 4. G-4.1 |Altitude |CAD drawings of |The student’s will then |law of Sines and cosines |

|triangle whether right,| | | |Acute |non-right triangles |develop a real-life |by hand and students will|

|acute, or obtuse in | | |CLEs |Obtuse | |scenario using the law |also be given a blueprint|

|addition to using | | |N-1B, N-3D, N-3E, | |Poster board |of Sines and cosines to |with unknown measurements|

|Pythagorean’s theorem | | |A-1B, A-1C, G-1A, | | |solve for unknowns in |to find and calculate and|

| | | |G-4B | | |their example. |will solve several |

| | | | | | | |different measurement |

| | | | | | |Presentation of their |exercises using CAD |

| | | | | | |example |drawings of non-right |

| | | | | | | |triangles |

|Comp. # 3 |4th quarter 2 weeks |After completing this unit the student will |MA 1, MA 2, MA 5 |Congruent |Compass |Short in class lecture |The students will be |

| | |be able to solve for the unknown parts of a | |Right triangle | |with illustrations drawn|given a CAD drawing that |

|Solving general | |triangle by using the known parts of that |Goals: |Correspondences |Protractor |on the board |requires a working |

|triangles SSS, SAS, | |same triangle using the SSS, SAS, ASA, and |G- 1.10, 2.3, 3.4, |SSS | | |knowledge of the SSS, |

|ASA, AAS, and SSA and | |AAS postulates of congruence. |4.1, 4.6. |ASA |Scientific- Calculator |In class math problems |SAS, ASA, and AAS |

|problems of angle | |The students will also learn that special | |SSA | |with worksheet |postulates and the theory|

|measure in reference to| |relationships exist between pairs of angles |CLEs |SAS |Illustrations on |illustrations |of transversals to |

|parallel lines cut by a| |formed when parallel lines are cut by a |N-1B, N-3D, G-1A, |Postulates |Worksheets | |complete. |

|transversal | |transversal. These concepts will be |G-4A, G-4B, M-2B, |Planes | |The students will work | |

| | |illustrated, proven, and drawn on one or more|M-2D |Lines |Architect ruler |individually and in |The students will be |

| | |CAD drawings. | |Parallel lines | |pairs on CAD drawing |given a written test to |

| | | | |Converses |Common- Triangles |that illustrate the use |check for mastery of all |

| | | | |Transversal | |of these principal of |concepts reviewed in this|

| | | | |Acute |Paper/Pencil |analytical geometry |lesson plan |

| | | | |Obtuse |CAD drawings | | |

| | | | |Alternate interior | | | |

| | | | |Alternate exterior | | | |

| | | | |Complementary | | | |

| | | | |Supplementary | | | |

| | | | |Corresponding | | | |

|Comp. # 4 |4th quarter 3 weeks |After completing this unit the student will |MA 1, MA 2, MA 4. |Area |Scientific- Calculator |Lecture entailing all |Paper and Pencil Test to |

| | |be able to calculate the area of a triangle | |Equilateral | |knowledge needed to |illustrate competency in |

|Be able to identify and| |by using the formulas K=1/2 bh and herons |Goals: |Reference-triangle |Poster Example of a |master comprehension of |finding the area of |

|use the appropriate | |formula of K= √s(s-a)(s-b)(s-c) were s is |G- 1.8, 1.10, G-2.1, |Semi perimeter |possible business |triangular area & |several different |

|formulas for | |equal to ½ perimeter of the triangle. |2.3, G-3.4, 3.8, |Heron (Hero) |venture calculating lot |Choose a private |triangle figures. |

|calculating the areas | | |G-4.6. |Formula |size |business venture to | |

|of triangles. (Heron’s| | | | | |calculate all associated|The students will be |

|Formula) | | |CLEs | |Flash cards of a |costs which will include|asked to draw an aerial |

| | | |N-1B, N-3D, G-1B, | |business scenario |purchasing a triangular |view of their business on|

| | | |G-4A, G-4B, G-2D, | | |lot. The surface area |CAD and include all the |

| | | |D-1C. | |Spread sheets for cost |of the lot will have to |measurements to their |

| | | | | |justification |be covered with such |drawing |

| | | | | | |material as marble, sod,| |

| | | | | | |or tile. | |

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|Unit Title: (Current Knowledge) Module # III Graphing trigonometric functions, calculating volumes in English and Metric units, understanding vectors, and studying the mechanics of gears and pulleys. |

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|Core Concepts: Student will be able to: Recognize trigonometric functions and graph them on a graphing calculator; Calculate volumes in English and Metric units; understand the principals of vectors; and |

|calculate the various arrangements and uses of gears and pulleys. |

|Comp. # 1 |5th quarter 2 weeks |After completing this unit the student will |MA 1, MA 2, MA 4 |Radius |Graphing-calculator |Lecture illustrating the|Written test |

| | |be able to recognize trigonometric function, | |Degrees | |differing trigonometric |demonstrating competency |

|To interpret graphs of | |their basic position represented by Cartesian|Goal: |Radians |Geometer’s-sketchpad |function. |in recognizing the |

|trigonometric functions| |coordinates and graph the function on a |G 1.10, 3.4, 3.6 |Trig-functions | | |different trigonometric |

| | |graphing calculator. | |Scale |Pencil and Paper |Graph some |functions |

| | | |CLEs N-1B, N-3D, |Arcs | |trig-functions on graph | |

| | | |N-3E, Alg-2B, Alg-3A,|Equivalencies |Graph paper |paper |Written test to prove |

| | |Solve vectors and how they relate to gears |G-2A- G-4B |Proportional | | |that each student can |

| | |and pulleys | |Central-angles |Handouts with graphic |Use graphing calculator |successfully graph a |

| | | | |Periodic |examples |to make graphs of |trigonometric function on|

| | | | |Symmetric | |different trig-functions|a graphing calculator and|

| | | | |Vectors | | |once given a graph of a |

| | | | |Vector quantity | | |function the student will|

| | | | |Terminal point | | |have to write the proper |

| | | | |Directed line segment | |Math worksheet problems |corresponding |

| | | | |Initial point | | |trigonometric function |

| | | | |Magnitude | | | |

| | | | |Components | | | |

|Comp. # 2 |5th quarter 2 weeks |After completing this unit the student will |MA 1, MA 2, MA 5 |Volume |Many various size and |Review volume formulas |Students will be given a |

| | |be able to observe 3-D objects and complex | |English system |shaped containers to |for various geometric |written test over volume |

|To observe different | |containers to calculate their volumes in |G 1.10, 2.3, 3.4, |Metric system |represent various |shapes and sized |and a container will be |

|shaped 3-D object and | |English and Metric units |3.6 |Area |volumes | |given to each one to |

|calculate their volumes| | | |Circumference | |The students will do |measure and calculate the|

|in English and Metric | | |CLEs |Length |Several measuring |some paper and pencil |volume |

|units | | |N-1B, N-3B, G-1B, |Width |devices |problems | |

| | | |G-4B G-3C, M-2C, M-2D|Height | | | |

| | | | |Depth |List of formulas |The students will be | |

| | | | |Special Prisms | |asked to measure | |

| | | | |Polygon |Worksheets with various |containers they brought | |

| | | | |Base |volume problems to solve|in and calculate the | |

| | | | |Lateral faces | |volume for each one | |

| | | | |Cylinder |Scientific calculator |using different | |

| | | | |Cone | |measuring devices | |

| | | | |Sphere |Have students bring an | | |

| | | | | |odd shaped container | | |

| | | | | |from home | | |

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|Comp. # 3 | |After completing this unit the student will |MA-1, MA-2, MA-4 |Vector quantity |Chapter handout that |Short video showing the |Written test to prove |

| |5th quarter 2 weeks |understand vectors and their components and | |Directed line-segment |explains vector |motion of vectors from |successful comprehension |

|To understand vectors | |be able solve problems that entail the use of|Goals: |Initial point |operations, vectors in |Math Advantage software |of vector concepts |

|and their components | |vectors. |G-1.7, 1.10, 2.1, |Terminal point |the rectangular | | |

|and use vectors to | | |2.3, 3.5, 4.6 |Geometric vector |coordinate system, and |Lecture explaining |The students will present|

|solve problems | | | |Magnitude |the properties of |chapter handouts and |a real life application |

| | | |CLEs |Norm |vectors |lesson plan |of using a vector with |

| | | |N-1B, 3D, 3E, G-2A, |Zero Vector | | |ropes, pulleys, and |

| | | |G- 4B, M-2B |Equivalent –vector |Math Advantage Software |Guided practice of |weights and then prove |

| | | | |Resultant | |solving problems. |their findings |

| | | | |Velocity vector |Scientific graphic | |mathematically |

| | | | |Bearing |calculators |Real examples ill. | |

| | | | |Component-vector | |Tension and compression | |

| | | | |Projections | | | |

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|Comp. # 4 |5th quarter 3 weeks |After completing this unit the student will |MA-1, MA-2, MA-4, |Torque |Bock & Tackle |The students will be |The students will print |

| | |be able to understand the phenomenon of |MA-5 |Pulleys | |given a ratio such as a |their set of CAD drawn |

|To study the phenomenon| |mechanics involving gears and pulleys | |Gears |Ropes |(4:11 rear end to an |gears and transform their|

|of mechanics involving | | |Goals: |Block | |automobile) and be asked|two dimensional drawing |

|gears and pulleys | | |G-1.4, 1.8, 1-10, |Force |Coma long |to design a set of gears|into three dimensional |

| | | |G-2.3, 3.4, 4.1, 4.6,|Mass | |from this ratio and then|figures to demonstrate |

| | | | |Velocity |List of Definitions and |make a drawing of their |their drawing, of the |

| | | | |Gravitational- force |Formulas |design on CAD with |gears, to be of the |

| | | |CLEs |Freebody- diagram | |associated mathematic |correct scale and |

| | | |N-1B, 3D, 3E, G-1A, |Tension |Working drawing of bevel|computations on drawing |workable. |

| | | |1.B, 4.A, 4B, M-1B, |Compression |gears | | |

| | | |2D. |Acceleration | |The students will design|The students will print |

| | | | |Pitch diameter |Illustrations of CAMS |a pulley system with CAD|their three dimensional |

| | | | |Pitch circle |and shafts |software and print their|pulley system, add ropes |

| | | | |Addendum | |drawings on a 3-D |and weights to each |

| | | | |Base |Displacement diagrams |printer |pulley, place scales on |

| | | | |Root |with typical curves | |every rope going through |

| | | | |Radial | | |every pulley, then check |

| | | | |Dedendum |Disk CAM profile | |to see if their measured |

| | | | |Involute |constructions | |weights match their |

| | | | |Throat diameter | | |calculated weights. If |

| | | | |Face radius |CAD software | |they do not the students |

| | | | |Bevel gear | | |will identify errors and |

| | | | |Central distance |CAM gear | |make corrections |

| | | | |Spur gear | | | |

| | | | |Worm gear |CAM shaft | | |

| | | | |Gear ratio | | | |

| | | | | |3-D printer | | |

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|Unit Title: (Current Knowledge) Module # IV Electrical theory, ergonomic design, load bearing capacity, and characteristics of the geometric circle |

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|Core Concepts: The Student will be able to Calculate volts, amps, watts, and ohms, create ergonomic designs such as cabinets and stairways, calculate load bearing capacity of beams and support systems, and |

|understand the characteristics of a geometric circle. |

|Comp. # 1 |6th quarter 2 weeks |After completing this unit the student will |MA 1, MA 5 |Volts |Calculator |Introduce the lesson by |Written test containing |

| | |have a general understanding of where | |Ohms | |explaining how energy |problems similar to the |

|(Electrical Theory)– to| |electrical energy originates and how such |Goals: |Current |Worksheets |changes form from |ones worked in class |

|calculate volts, amps, | |energy changes forms. The student will be |G-1.10, 2.3, 2.7, |Resistance | |mineral (stored) energy,| |

|watts, and ohms as | |able to recognize electrical symbols on a |3.4, 3.8 |Watts |Board examples |through a process of |Students will be asked to|

|direct and indirect | |blueprint, calculate total voltage, current, | |Gauge of wire | |transformations until it|draw a detailed |

|proportional units | |ohms, and watts using an ohm’s power wheel, |CLEs |Voltage drop |Wire gauge chart |becomes electrical |electrical diagram in CAD|

| | |review color codes, draw electrical symbols |N-1A, 1C, 3D, 3E, |Schematics | |energy. |and calculate the size of|

| | |on a CAD drawing, calculate available current|M-2D, D-1C |Blueprints |Electrical CAD drawings | |their entry cable, |

| | |vs. maximum rating of current breaker source,| |Kilowatts |and blueprints |Class lecture explaining|breaker box, and estimate|

| | |compare total amperage used by devices, | |Ohm’s Law | |Ohm’s law and how to do |their monthly bill in |

| | |appliances, and air conditioning units to | |Conductance | |electrical calculations |kilowatts |

| | |total available amperage of breaker box, use | |Outlets | | | |

| | |information of calculations to determine what| |Fixtures | |Work through some | |

| | |size of entry cable to use, and estimate a | |Switches | |drawing that have | |

| | |dwelling’s monthly utility bill by kilowatt | | | |numbers assigned to | |

| | |usage. | | | |electrical voltages, | |

| | | | | | |current, and resistance | |

| | | | | | |and calculate unknowns | |

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|Comp. # 2 |6th quarter 2 weeks |After completing this unit the student will |MA1, MA 2 |Tread |International |Instructor will do a |Students will take a |

| | |be able to Create a set of stairs so the rise| |Riser |Residential Stair Codes |demonstration of a wall |paper and pencil test |

|Create ergonomic | |and run will meet the International |Goals: |Step | |structure and go from |designed from information|

|designs involving | |Residential Code (IRS) to accommodate a given|G-1.2, 1.4, 1.7, |Headroom |Auto CAD 2009 |1st floor to basement. |taught in the lesson. |

|stairways and cabinets | |set of conditions such as a basement floor to|1.10, 2.4, 2.7, 3.2, |Layout | | | |

| | |1st level floor. The student will also be |4.5, 4.7 |Handrail |Architectural Drafting |Student will consult the|Students will draw a |

| | |able to design an ergonomically accessible | |Studs |and Design Text |(IRS) to consider and |specified set of steps on|

| | |and/or usable set of cabinets for a person’s |CLEs |Elevation | |calculate all acceptable|CAD according to (IRS) |

| | |specific stature with an ergonomic design |N-1A, 3-D, A-1C, |Ergonomics | |rise heights and tread |Codes. |

| | |within a feasible work triangle. |G-4A, 4B, M-2D |Human motion | |lengths. A comparison | |

| | | | |Rise | |will be made to make |Students will design and |

| | | | |Run | |students aware of rise, |draw a cabinet according |

| | | | |Slope | |run, slope and |to specifications. |

| | | | |y-intercept | |y-intercept | |

| | | | |y = mx + b | | | |

| | | | | | |Students will establish | |

| | | | | | |a median height for a | |

| | | | | | |family and design a | |

| | | | | | |cabinet layout to | |

| | | | | | |accommodate their | |

| | | | | | |physical attributes. | |

|Comp. # 3 |6th quarter 2 weeks |After completing this unit the student will |MA-1, MA-2 |KIPS- 1000s of lbs |Text on Architecture |The students will decide|An assessment will be |

| | |be able to calculate sizes of I beams, grades| |Live loads |residential drawing and |the most economical way |given that requires the |

|To calculate load | |and spans to determine load capability. |Goals: |Dead loads |design |to build a basement by |student to compare values|

|bearing capacity of | | |G-1.7, 1.8, 1.10, |Span | |comparing alternate |of different |

|beams and support | | |2.7, 3.4, 4.6 |Joist | |configurations and |configurations of load |

|systems | | | |Beams | |calculating various |bearing materials on a |

| | | |CLEs N-1B, N-3D, 3E, |I Beams | |arrangements of load |paper and pencil test. |

| | | |G- 4A, 4B, M-2D |Wide flange | |bearing materials. | |

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|Comp. # 4 |6th quarter 3 weeks |After completing this unit the student will |MA-1, MA-2, MA-5 |Circumference |Compass |The students will be |The students will be |

| | |be able to calculate the circumference of a | |Pi | |asked to draw several |given a written test to |

|To study the | |circle by using the radius and pi, calculate |Goals: |Radius |Protractor |circles with a compass |show competency in how to|

|characteristics of | |the diameter of a circle using circumference |G-1.6, 1.8, 1.10, |Diameter | |and measure the diameter|calculate circle |

|geometric circles such | |and pi, calculate the area of a circle using |2.3, 3.5, |Chord |Geometry worksheets |and circumference of the|measurements and will be |

|as the centra, radius, | |πr², and be able to identify the difference |4.1, |Segment |demonstrating circles |circles and fill out a |asked to draw several |

|diameter, | |between a sector, segment, or arc. | |Arc | |table with these |sized circles in a |

|circumference, sectors,| | |CLEs |Tangent |Scientific calculator |measurements. They will|practical drawing |

|segments, arcs, | | |N-1B, 3D, 3E, G-1B, |Segment | |then find a common ratio|application according to |

|Tangents, chords, and | | |4B, M-2D, |Centra | |between the two known as|specified instructions |

|secants | | | | | |pi. | |

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| | | | | | |The students will then | |

| | | | | | |be given several | |

| | | | | | |examples in industry of | |

| | | | | | |circle measurements that| |

| | | | | | |are required to complete| |

| | | | | | |a job | |

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|Unit Title: (Post Knowledge) Higher education/career prep project |

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|Core Concept: To unite in a project with at least one other program to utilize mathematical concepts learned in previous mathematics curriculum to provide evidential proof of mastery. |

|To conduct a project |4th Semester |After completing this unit the student will |MA 1, MA 2, MA 3, MA |determine, compare |All material and |Project jointly agreed |Assessment will be |

|designed and prepared | |be able to unite with fellow students to |4, MA 5. |agree, support, prove, |resources available from|upon by trade specific |designed and designated |

|by a joint effort | |complete a real world situational workplace |G 1.1, 1.2, 1.4, |influence, estimate, |the Cass Career Center |instructor, CCC |at the beginning of each |

|between Program | |endeavor or task. |1.8, 1.10, 2.1, |choose decide justify, | |administration, and core|project. |

|Instructor and Math | | |2.2, 2.3, 2.7, 3.1, |appraise, interpret, | |resource teachers. | |

|instructor to | | |3.2, 3.3, 3.5, 3.6, |build disprove, test, | | | |

|demonstrate mastery of | | |3.7, 3.8, 4.1, 4.4, |compile, invent, solve,| | | |

|previously learned | | |4.5, 4.6, 4.7. |perceive, influence, | | | |

|competencies and to | | |CLEs N-1B, N-1C, |plan, conclude, defend,| | | |

|demonstrate mastery of | | |N-3D, N-3E, G-1A, |evaluate, predict, | | | |

|applicable | | |G-1B, G-2A, G- 4B, M-|measure, rate, design, | | | |

|Concepts of | | |2C, M- 2D, |select prioritize | | | |

|mathematics. | | | |explain, criteria, | | | |

| | | | |assess value deduct. | | | |

| | | | |construct, and | | | |

| | | | |theorize. | | | |

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