Math Standards-You’re Teaching Them- Does Anyone Know?

Why Did We Take On This Project?

• Trouble retaining students– Falling behind in math credits at their home

schools– Students still need to pass the MCA and

BST/GRAD tests

What Did We DoHow Did We Accomplish It?

• Went through the state math standards– Erick explained the math standards and Pete gave

examples from the world of automotive technology.

Initial Step

What Did We DoHow Did We Accomplish It?

• Went through curriculum to identify math standards taught.

• To Pete’s surprise, very few of the standards are NOT covered…

Curriculum Sheet with Math Standards• NORTHEAST METRO CAREER & TECHNICAL CENTER• Career and Technical Academic Standards and Benchmarks• Program: Automotive Technology• Course: Brakes (AUST 100)• Course Description: This course covers basic automotive brake system theory including hydraulic systems, drum brakes and disk brake

systems. Student will learn to diagnose brake systems, machine brake drums and rotors, remove and replace drum and disc brake system parts, and overhaul brake cylinders and calipers and the understanding of micrometer parts and readings. Students will learn automotive tools, shop equipment, and basic safety procedures.

• Academic Standards and Benchmarks:• The student will: • Standard 1.0: Investigate career opportunities and career paths within the automotive industry.

1. Explain the roles and functions of individuals engaged in the automotive industry.

2. Investigate employment opportunities and five-year career outlook. • Standard 2.0: Identify and apply ethical and safe practices used in the automotive industry.

1. Describe shop safety rules.

2. Wear safety glasses when in lab.

3. Demonstrate safe and courteous behavior at all times.• Standard 3.0: Demonstrate a positive work ethic and employability skills required in the automotive industry.

1. Work as a team member in shop.

2. Develop and demonstrate time management.

3. Demonstrate safe and courteous behavior at all times.• Standard 4.0: Properly test, diagnose, service, and repair general brake systems.

1. Complete work order to include customer information, vehicle identifying information, customer concern, related service history, cause, and correction. 9412,9431,8248,9422

2. Identify and interpret brake system concern; determine necessary action. 8241,8324,9411

3. Research applicable vehicle and service information, such as brake system operation, vehicle service history, service precautions, and technical service bulletins. 9.4.2.1,9422,9438

4. Locate and interpret vehicle and major component identification numbers (VIN, vehicle certification labels, calibration decals). 8.2.2.1• Standard 5.0: Properly test, diagnose, service, and repair hydraulic systems.

1. Diagnose pressure concerns in the brake system using hydraulic principles (Pascal's Law). 9421,9422,9218,9242,9.2.1.1,9221,9222,8211,9212,8241,9212,9423,9431,9438

Strand Standard No. Benchmark Curriculum Assessment

9, 10, 11

Geometry &

Measurement

Calculate measurem

ents of plane and

solid geometric figures;

know that physical

measurements

depend on the choice of a unit and that they are

approximations.

9.3.1.3

Understand that quantities associated with physical measurements must be assigned

units; apply such units correctly in expressions, equations and problem solutions

that involve measurements; and convert between measurement systems.

For example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600

seconds = 88 feet/second.

9.3.1.4

Understand and apply the fact that the effect of a scale factor k on length, area and volume

is to multiply each by k, k2 and k3, respectively.

9.3.1.5

Make reasonable estimates and judgments about the accuracy of values resulting from

calculations involving measurements. For example: Suppose the sides of a rectangle

are measured to the nearest tenth of a centimeter at 2.6 cm and 9.8 cm. Because of measurement errors, the width could be as

small as 2.55 cm or as large as 2.65 cm, with similar errors for the height. These errors affect calculations. For instance, the actual

area of the rectangle could be smaller than 25 cm2 or larger than

26 cm2, even though 2.6 × 9.8 = 25.48.

Socket Sizes

• Pete says……• Erick says……. Math Standard 8112- Compare

real numbers and be able to locate it on a number line– Math Standard 9313-Understand that quantities

associated with physical measurement must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems.

Brake Pads• Pete Says….• Erick Says….Math Standard 9322-Accurately interpret

and use phrases in geometric proofs such as “if-then”, “all”, and “not.”– Math Standard 9421- Evaluate reports based on data

published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed.

– Math Standard 9323-Asses the validity of a logical argument and give counter examples to disprove a statement.

Also Math Standards-9324, 9336, 9438

Rotors and Micrometers

• Pete Says….• Erick Says….Math Standard 9311- Determine the

surface area and volume of pyramids, cones, and spheres. Use measuring devices or formulas as appropriate.– Math Standard 9315- Make reasonable estimates and

judgments about the accuracy of values resulting from the calculations involving measurements.

– Also Math Standards 9313 & 9338

Torque Wrench

• Pete Says….• Erick Says….Math Standard 8221-Represent

arithmetic sequences using equations, tables, graphs, and verbal descriptions, and use them to solve problems.– Math Standard 9218- Make qualitative statements

about the rate of change of a function, based on its graph or table of values.

– Also Math Standards 9313 & 9315

We’ve Identified the Math, Now What?

• Look to enhance the lessons– Larry’s Truck– Embed math examples into the CTE – Hands on examples

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Larry’s New Truck

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What Parts Control the Stopping of the Truck?

• Master Cylinder• Brake Hoses/Lines• Wheel Cylinders• Brake Calipers

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Before we apply Pascal’s Law

We must first review and be familiar with…• Diameter of a Piston• Radius of the Piston• Area of the top surface of the Piston

Mathematically speaking…Diameter: The width of a circular or cylindrical object. Radius: The radius of a circle is half the diameter Area: Any particular extent of space or surface

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Math – Hands on Practice • Measure across the

top of the piston, through the center and record the diameter (inches)

• Calculate the radius of the piston

• Calculate the area of the top of the piston

A = π · r · r orA = πr2

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Area Example

• Diameter = 7 inches• Radius = 3 1/2 inches• Area = ?

A= π·r2

3.14 · (3 ½ in)2 = 38.465 in2

Area = 38.465 in2

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Did Larry have brake failure?

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Remember Larry’s Truck ……..• The truck has a major

braking problem.• You suggested earlier

that we replace it with bigger brake parts…

• What do we need to know about the original braking system?

GIT-R-DONE

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Facts about Larry’s Truck

• ¼ in brake lines• ½ in bore master cylinder• 7/8 in bore wheel cylinders• 2 in caliper pistons

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Can you fix Larry’s truck?

• Devise a plan to fix Larry’s truck based on Pascal’s Law and your knowledge of automotive systems that will remedy Larry’s braking problems.– Be sure to show all calculations and justify your

solution plan in a written paragraph.

Remember Larry doubled the size of the original tire size…..

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Be thorough..Larry is depending on you…

• How would you

–“Git-R-Done”?

GIT-R-DONE

Auto Related Worksheets

Embedded Math Example

Provide groups of 2 to 4 students with a piston and have them do the following.

• 1.Measure the diameter of a piston• 2. Using your measured value of diameter,

calculate the radius of the piston.• 3. Using the formula for area of a circle, A = πr2 ,

find the area of the top of the piston.

*After these auto examples, we could increase the rigor by adding “traditional math” examples*

Sample Test Questions From AYES• 9. Which measuring instrument should you use to measure rotor parallelism?• ( )Feeler gauge ( )Micrometer• ( )Vernier caliper ( )Dial indicator• 10. While obtaining diagnostic trouble codes (DTCs) to diagnose ABS systems• ( )DTCs indicate a defect in a specific• component• ( )On some systems cycle the ignition• switch three times to obtain DTCs• ( )Some ABS systems do not provide• flash codes• ( )Flash codes must be obtained with the• engine running• 11. If a small piston acts upon a larger piston, the force of the larger piston will• ____________________ but the distance it travels will _______________.• ( )Decrease, not change ( )Increase, not change• ( )Decrease, increase ( )Increase, decrease

Response From Partnering Schools

• In front of school relations committees for approval as we speak…..