Red Rocks Community CollegeConstruction Technology

Technical Education Pathways Project – Integrating math standards with

real-world applications

NSF DUE 0202263

Educational Goals

“The Project’s overriding goal is to build a partnership with construction industry, high schools,

and workforce development agencies to:

• Foster increased interest in construction careers

• Define and improve the education and training pathways to success in those careers

• To provide support to those who choose to learn and teach along those pathways.”

The goals of the Technical Education Pathways Project and RRCC:

Program Highlights

• RRCC is currently partnered with 13 Colorado and 1 California high schools for the 2005/06 school year– Geometry Principles (Math)– Introduction to Construction (CTE)– Alternative Energy (CTE/Science)

• Curriculum based on state content standards

• Courses are part of the Construction Academy program, with curriculum developed via the Technical Education Pathways Project (TEPP)

• Partially funded by the National Science Foundation to increase academic core competencies through the integration of technical education and academic curriculum in the classroom

Increasing Core Competencies

• Improve the academic preparation of high school students with real-world technical applications of mathematics

• Review academic and technical curriculum to define joint learning objectives, course sequence and articulation requirements

• Provide professional development activities to achieve these competencies

Academic Integration With Technical Education

The GOAL is to improve the skill adaptability of the student – integrating the real-world application of scientific, mathematics and

communication content taught in the classroom with mentored workplace

internships and apprenticeships

Mathematics in Colorado

• The percentage of students meeting math standards has declined on the Colorado Student Assessment Program in the higher grade levels

32.431.6

32.9

26.627.128.3

0

5

10

15

20

25

30

35

2002 2003 2004

Grade 9

Grade 10

Source: Colorado Department of Education

Increased Math Requirements

Colorado Commission on Higher Education (CCHE): Revised requirements for admission to a state 4 year college and university include –

• High School Class of 2008 – 3 years of math (Algebra 1 or higher)

• High School Class of 2010 – 4 years of math (Algebra 1 or higher)

Schools with Strong Math Gains

• Common Factors for schools with strong math gains:

– Math teachers knew the math standards and the math content

– Math lessons in textbooks were supplemented with practical activities

– Teachers focused on student outcomes rather than just on the math lesson

– Teachers asked students questions and made adjustments based on feedback

Source: Colorado Department of Education – “The State’s Prime Numbers”

Geometry Principles – Jefferson County Math Performance Matrix

Geometry Principles Jefferson County Public Schools Grades 9-12 Math Performance Expectations Matrix

Developed and Distributed by the Technical Education Pathways Project

Source: RRCC – Technical Education Pathways Project

Standard Benchmark

Description Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Unit 7

Unit 8

Unit 9

Unit 10

3G3 Probability using counting techniques 4A1 Creates and interprets two and three dimensional objects D D 4A2 Geometric construction 4A3 N-gons and polyhedra D 4B1 Makes conjectures using induction and deduction I 4B2 Geometric proof 4C1 Pythagorean Theroem D D D D 4C2 Areas D D D D D D 4C3 Volume and surface area of solids D D D 4C4 Uses known properties in real world applications 4D1 Similar and congruent figures I 4D2 Symmetry and transformations D 4D3 Uses coordinate geometry and/or tessellations to solve

problems using geometric transformations

4D4 Solids of revolution 4E1 Right triangle trig I I I 4E2 Special right triangles I I 4E3 Recognizes the relationship of slope and the tangent ratio I 5A1 Solves problems involving multi-dimensions and expresses

them in the appropriate unit of measure

D

D

5A2 Uses the appropriate unit of measure to determine volume and surface area

D

D

5A3 Distance formula 5B1 Compares and contrasts the concepts of precision,

accuracy, and error of measurement

I

5B2 Applies Precision, accuracy, and error or measurement to real world problems

I

I

Sta

ndar

d #4

Introduce

Develop

Lesson Example – Unit 6

Unit 6 Lesson # 1 Title: Sine and Cosine Ratios Performance Expectation: 4E1 Uses right triangle trigonometry to solve real world problems Lesson Overview: In this lesson students will continue to use the tangent ratio and will be introduced to the sine and cosine ratios. Applications will be directed to everyday construction models.

Materials: Math Concepts Taught: Use of trig ratios in real situations. Construction Concepts Taught: The use of the trig ratios to find dimensions of roof

trusses, stairway and ramps, ladders, etc. Vocabulary Math Construction Sine, cosine, and tangent ratios Journal Activity Identify the trig ratio you would use to find the missing parts of this right triangle. 1. You would use _________ when you know <A and a to find c. 2. You would use _________ when you know <B and b to find a. 3. You would use _________ when you know <A and c to find b.

C

A

B a

c

b

Truss

Lesson Example – Unit 6

2. When using an extension ladder you must maintain an angle of 75º to the ground. Determine the length of the ladder if must be placed 4 feet from the base of the building.

Since the 4’ side is the adjacent side of the right triangle and the angle of elevation is 75º and the hypotenuse is the length we wish to find, we must use the cosine ratio.

h

4º75cos

h cos 75º = 4 h 15.5’ or 15’ -6”

3. A ramp is constructed to the front door of a house. The angle of elevation of the ramp is 10º. How long must the ramp be if it must span a distance of 15 feet.

Since the 15’ side is adjacent to the 10º angle, we will use the cos ratio.

h

1510cos

h cos 10º = 15 h 15.2’ or 15’ -2”

75º

4’ -0”

h

10º

15’ -0”

ramp (h)

Pathway

• Algebra Principles – high school

• Geometry Principles – high school

• Introduction to Construction – dual credit with community college

• Alternative Energy – dual credit with community college• Work, apprenticeship, community college, university

What the Students are Saying . . .

“As a student who has struggled with math, this is the first math class that has ever interested me. The subject matter is more realistic, and the work is more hands on.”

“This class has actually made me realize what I would like to do as a college student and for a career.”

Math Students in Action

What the Students are Saying . . .

“This class puts math into real situations that are useful. Regular math seems useless compared to this.”

“The field trips make it more fun and interesting.”

“I like this class because the work is realistic stuff that we use in real life after we graduate. It is actual job preparation.”

Math Students in Action

“The material is easier to understand and is more realistic than traditional geometry class.”

“The class is challenging but fun.”

“This class helps for students who aren’t strong at math and helps them better understand it.”

What the Students are Saying . . .

Math Students in Action

“In this class I have approximately three or four students (mainly female) that have shown a considerable change in attitude about math. This by far has been the most exciting class I have been a part of in my 7 years of teaching math. The hands-on approach has a large effect on class participation, which in turn leads to no classroom management problems, everyone is busy!”

Jefferson County Schools – Geometry Principles Teacher

What the Teachers are Saying . . .

Math Students in Action

What the Teachers are Saying . . .

“The attendance of this class is well above the rest of my classes, approximately 98%.”

“So far, every lesson has just invigorated me to teach the next lesson better. To a student, every student said that they not only would recommend this class to a friend but have already done so. Next year I have two sections because the word is getting out that math can be fun and interesting!”

Jefferson County Schools – Geometry Principles Teacher

Math Students in Action

What Industry is Saying . . .

“We like to have kids out here so they can see how many different types of careers there are in construction.”

“Construction is desperate for younger workers.”

“OK, I get it…!”

Construction Academy industry partners

Math Students in Action

Red Rocks Community CollegeConstruction Technology

Technical Education Pathways Project – Integrating math standards with

real-world applications

NSF DUE 0202263