teacher notes for - warren county public schools anchor codes: m8.a.1.1 represent numbers in...

GOVERNOR’S INSTITUTE FOR MATH IN CTE Lesson # 2 Building and Teaching a Math Enhancement

INTRODUCTION

Team Members: Daniel B. Plummer, (Carpentry Instructor) Tyrone Area High School Kathy Holsinger, (Math Instructor) Tyrone Area High School Title of the Lesson: Estimating line length of a common rafter PA Math Standard(s) Addressed by the Lesson: 2.01.08 A Represent and use numbers in equivalent forms (e.g., integers, fractions,

decimals, percents, exponents, scientific notation, square roots) 2.02.08 B Add, subtract, multiply and divide different kinds and forms of rational

numbers including integers, decimal fractions, percents and proper and improper fractions

2.10.08 A Compute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships

2.10.11 B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem

Assessment Anchor Codes: M8.A.1.1 Represent numbers in equivalent forms M8.A.2.2 Represent or solve problems using rates, ratios, proportions and/or percents M8.A.3.3 Compute and/or explain operations with integers, fractions and/or decimals M8.B.2.4 Construct, interpret and/or scale drawings to solve real-world problems M11.A.1.1 Represent numbers in equivalent forms M11.A.2.1 Apply ratio and/or proportion in problem solving situations M11.A.2.2 Use exponents, roots and/or absolute value to solve problems

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BUILDING A MATH ENHANCEMENT 1. Objective of the lesson.

Students will demonstrate a working knowledge of Pythagorean Theorem and its application in Carpentry (Roof Framing), while recognizing it in other contexts.

2. Identify the math, math terms and vocabulary and write out the description or

definitions. Pythagorean Theorem, (A2 X B2 = C2)

Math Terms: • Altitude = Rise (A) • Base = Run (B) • Hypotenuse = Line Length (C) • Span = The distance between structural support = 2X(B) • Run = Half of the span (B)

Pythagorean Theorem

• C2 = A2 + B2

• Allows for the exact calculation of the diagonal of a rectangle.

• This theorem can be verified with the 3-4-5 right triangle.

A

B

C

3

4

5

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3. Note the steps, rules, underlying principles of the concept or theory and summarize.

• Calculate the run or half of the span. • Determine the rise. • Locate unit rise per foot of run on the blade of framing square. • Read figure under unit rise per foot of run and multiply by the run. • Divide by 12. • Convert decimal back into feet if necessary.

• Total Rise = Unit Rise x RUN6″ x 10 = 60″

• Line Length = Unit Length x RUN13.42″ x 10 = 134.2″

10′- 0″ = 10 units of run

6″134 3/16 ″

60″134 3/16″

20′ = a run of 10

4. Develop 8-10 sample problems, moving from very specific Carpentry technology

examples to more generic problems.

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LINE LENGTH PRACTICE PROBLEMS SPAN RUN RISE PITCH SLOPE LINE

LENGTH A

24’ ½

B 10’ 5’

C 32’ 1/8

D 21 7’

E 4’ 1/6

F 16’ 6’

G 12 156"

H 18 1/3

I 6’ 1’

J 10’ 5/24

K 20’ 5/12

L 14’ 7/24

M 22’ 12’

N If the Unit Rise is 3 and the Unit Run is 4, what is the Hypotenuse? O If the Unit Rise is 6 and the Unit Run is 5, what is the Hypotenuse?

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5. Document references and supplies needed to demonstrate the math concept.

• Textbook Residential Construction Academy – Carpentry, Floyd Vogt,

2003 • Thompson/Delmar Learning, 2003 • Construction Master IV Calculator • 25’ Tape and Rafter Square w/stair gauges • Common Rafter Layout Handouts • Rafter Material • Paper & Pencil/Pen, Rafter Reference Table

6. Describe lesson adaptations for students with special needs. Peer teaching (Higher level student working with another student) Small groups (Several students working together) With an aid (One on One time with teacher assistant) 7. Provide sample handouts for students and presentation materials for teachers,

as appropriate.

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STUDENT HANDOUT - LINE LENGTH HANDOUT # 1 SPAN RUN RISE PITCH SLOPE LINE

LENGTH A

24’ ½

B 10’ 5’

C 32’ 1/8

D 21 7’

E 4’ 1/6

F 16’ 6’

G 12 156"

H 18 1/3

I 6’ 1’

J 10’ 5/24

K 20’ 5/12

L 14’ 7/24

M 22’ 12’


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TEACHING A MATH ENHANCEMENT

Title of the Lesson: Estimating Line Length of Common Rafter 1. Introduction to the lesson. Today we are going to estimate the line length of a

common rafter. This is necessary for the layout of a common rafter which is used to construct a gable and/or hip roof. We are going to use the Pythagorean Theorem for our calculation

2. Assess students’ math awareness by asking questions.

• How many students are aware of the Pythagorean Theorem? • Can you identify the terms of the Pythagorean Theorem? • Can someone give me an example of the Pythagorean Theorem?

3. Demonstrate the example problem that is embedded in the Carpentry curriculum. Example A: A slope of 9" rise per ft. run has a 15 multiplier.

Multiplying 15 times the Run will equal the Common Rafter Length.

Example B: A slope of 8" rise per ft. run has a 14.42 multiplier.

Multiplying 14.42 time the Run will equal the Common Rafter Length.

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Using the table on the framing square above (or ask your teacher if you may get a framing square from the tool crib), estimate the length of the common rafters below. Note: Round off answers to the nearest 1/16".

Run = 13'

Slope = 4" rise/ per Ft. run

Rafter Length = ______' - ______"

Run = 15'

Slope = 5" rise/ per Ft. run

Rafter Length = ______' - _______

4. Explain the math concept or theory and show students how it applies, using the

terminology of math. Pythagorean Theorem C2 =A2 +B2

Pythagorean Theorem

• C2 = A2 + B2

• Allows for the exact calculation of the diagonal of a rectangle.

• This theorem can be verified with the 3-4-5 right triangle.

A

B

C

3

4

5

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5. Demonstrate other examples as necessary.

2 2

Rafter Length = Run + Rise

Estimate the length of the common rafters for the houses listed below. Note: Round off answer to nearest 1/4".

Run = 12'

Rise = 4'

Rafter Length = ______' - ______"

Run = 16'

Rise = 9'

Rafter Length = ______' - _______"

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6. Have students explain the solutions to the problems, or demonstrate what they did to show understanding.

Student will demonstrate problem on the board, and explain step by step procedure. Students will demonstrate understanding by calculating problems with pencil paper

handout sheet. 7. Challenge students to write and solve their own example problems and demonstrate

competency in a test situation. See Handout #1

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LINE LENGTH HANDOUT #1 SPAN RUN RISE PITCH SLOPE LINE

LENGTH A

24’ ½

B 10’ 5’

C 32’ 1/8

D 21 7’

E 4’ 1/6

F 16’ 6’

G 12 156"

H 18 1/3

I 6’ 1’

J 10’ 5/24

K 20’ 5/12

L 14’ 7/24

M 22’ 12’


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Student Name:_____________ Date:___________ Test on Estimating Line Length Of Common Rafter

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