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# Building and Teaching a Math Enhancement

 INTRODUCTION

Team Members:
George Fetch : Industrial Arts and Drivers Ed. @ Benton Area School District
Jeremy Chapin: Special Ed. Math and English @ Benton Area School District

Title of the Lesson: Making a Trivet

PA Math Standard(s) Addressed by the Lesson:

2.3.8 A – Develop formulas and procedures for determining measurements (e.g. area,
volume, distance)

2.3.8 D – Estimate, use and describe measures of distance, rate, perimeter, area, volume,
weight, mass, and angles.

Assessment Anchor Codes:

M8.B.2 - Apply appropriate techniques, tools, and formulas to determine measurements

 BUILDING A MATH ENHANCEMENT

1. Objective of the lesson.
Students will demonstrate a working knowledge of

Adding and dividing fractions (math concept) and its application in Wood
Working (technical field), while recognizing it in other contexts.

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

a. Planing- A process by which a board is smoothed and dimensioned to adjust the
thickness by use of a planing machine.

b. Denominator- The bottom number in a fraction.

c. Numerator- The top number in a fraction.

d. Reciprocal- a fraction written upside down.

e. Cross-cut- Cutting a board across the grain.

f. Rip-cut- Cutting a board with the grain.

g. Jointing- Planing the edge of a board.

• Fraction addition – (remember to use a common denominator)
• Fraction Subtraction- (remember to use a common denominator)
• Fraction Division- (remember to use the reciprocal)

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

The following steps must be followed in sequential order:
1. Plane the board
2. Joint edges of board
3. Cross cut board
4. Rip cut board
5. Notch the board
6. Sand and assemble board

4. Develop 8-10 sample problems, moving from very specific wood working
technology examples to more generic problems.

1. Given a 1 inch thick board, how many times would it have to be run through a
planer that planes of an inch per cut to make the board of an inch thick?

2. Given a 1 inch thick board, how many times would it have to be run through a
planer that planes of an inch per cut to make the board of an inch thick?

3. With 15 students in a class, is a board that is 8 ft. in length, long enough for each
student to have a 6 in. long piece?

4. How long would a board have to be to make a trivet with each section being 2
inches long.
5. If a board is cut into three equal pieces, what would be the length of each
piece?
6. Pick any 5 boards from the lumber pile and measure them to the nearest inch.
7. What is half of ?
8. What is ?
9. What is ?

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

FUNDAMENTALS OF MATH with Career Applications. Copyright 2002 Pearson
Education Inc.
Curriculum based practice problems directly from lesson
Dry-Erase board
Various boards from lumber pile for the students to measure

6. Describe lesson adaptations for students with special needs.

- Give students written directions and frequently repeat oral directions
- Work with a partner
- Break assignments into smaller steps

7. Provide sample handouts for students and presentation materials for teachers,
as appropriate.

 TEACHING A MATH ENHANCEMENT

Title of the Lesson: Making a Trivet

1. Introduction to the lesson.

I am going to introduce the lesson by showing them a finished trivet and briefly
telling them how we are going to go about making one from a rough piece of lumber.

2. Assess students’ math awareness by asking questions.

How do you add fractions with uncommon denominators?
How do you subtract fractions with uncommon denominators?
How do you divide fractions with uncommon denominators?
How do you convert feet to inches?

3. Demonstrate the example problem that is embedded in the Wood-working
technology curriculum.

Question

- Given a 1 inch thick board, how many times would it have to be run through a
planer that planes of an inch per cut to make the board of an inch thick?

Solution

- Step #1 – Find a common denominator for our fractions, which would be - Step #2 – Determine how many 16ths are in 1 inch and in of an inch.

- Step #3 – Set up the equation as follows and solve: - Step #4 – After determining the difference between 1 inch and of an
inch in 16ths is 4, we can know we have to run it through the planer 4
times.

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

*Adding Fractions (ex. )→When adding fractions, add the
numerators together while keeping the denominators the same; reduce when
necessary.

*Subtracting fractions (ex. )→When subtracting fractions, subtract the
numerators while keeping the denominators the same; reduce when necessary.

*Dividing fractions (ex. )→When dividing fractions we use the
reciprocal of the divisor and simply multiply the numerators and the denominators.

5. Demonstrate other examples as necessary.
a. If a board is cut into three equal pieces, what would be the length of each
piece?
b. Pick any 5 boards from the lumber pile and measure them to the nearest inch.
c. What is half of ?

d. What is ?

6. Have students explain the solutions to the problems, or demonstrate what they
did to show understanding. Correct answers are in ( ).

A. Given a 1 inch thick board, how many times would it have to be run
through a planer that planes of an inch per cut to make the board of
an inch thick? (4 times)

B. Given a 1 inch thick board, how many times would it have to be run
through a planer that planes of an inch per cut to make the board of
an inch thick? (8)

C. With 15 students in a class, is a board that is 8 ft. in length, long enough
for each student to have a 6 in. long piece?
(8ft.=96in. 6in.x15students=90 –Yes)

D. How long would a board have to be to make a trivet with each section
being 2 inches long? (6in.)

E. If a in. board is cut into three equal pieces, what would be the length
of each piece? ( in.)

F. Pick any 5 boards from the lumber pile and measure them to the
nearest inch. (Answers will vary)

G. What is half of ? H. What is 7. Challenge students to write and solve their own example problems and
demonstrate competency in a test situation.

• At this point I would have the students come up with ten of their own
problems and solutions relating to the math that we are doing in our shop
class.

e.g. I would be looking for any math problem the kids could come up on
their own that involved anything along the lines of adding, subtracting, or
dividing fractions.