Math-in-CTE Lesson Plan Template
Lesson Title: Calculating Board Feet
Lesson # 6
Author(s):
Frank Flood
E-mail Address(es):
fflood@cumberland.tec.nj.us
Phone Number(s):
856-451-9000, x 260
Ted Archer
856-451-9000, x 261
tarcher@cumberland.tec.nj.us
Occupational Area: Construction Trades
CTE Concept(s): Calculating Board Feet
Math Concepts: Equations – Substituting Data into Equation
Lesson Objective:
The student will be able to correctly calculate board footage using decimal numbers.
Supplies Needed:
One (1) foot pieces of: 2” x 4”, 2” x 6”, 2” x 8”, 2” x 10”, 2” x 12”, and 4” x 4”
One (1) 8’ pierce of 2” x 12”, and one (1) 8’ pierce of 4” x 4”.
TEACHER NOTES
(and answer key)
THE "7 ELEMENTS"
1. Introduce the CTE lesson.
a. We have a budget to build a house. Do we have enough
money?
b. What do we need to know before we can tell if we have enough
money?
a. We can’t tell!
b. Solicit student responses that could include:
-what do we have to buy?
-how much (quantity)?
-what does each part cost?
-what is the total when you add each part?
Direct student answers to get to the fact that you need to know
something called ‘board feet’.
2. Assess students’ math awareness as it relates to the CTE
lesson.
A.. You know the formula for perimeter of a rectangle is P = 2l + 2w,
if the length of the rectangle is 6” and the width is 4”, then
P =(2 x 6) + (2 x 4) → P = 12 + 8 → P = 20”
The student math assessment is for variable substitution in an
expression.
B. Similarly, the formula for the area of a rectangle is A = l x w,
Using the same rectangle,
A = 6 X 4 → A = 24sq.in.
3. Work through the math example embedded in the CTE lesson.
**Each piece has already been labeled: 2” on one edge, 1’ foot on
the other end, appropriate width on one face, 1’ on one end, 12” on
a. Pick up the 2” x 4” x 1’ sample. Explain the thickness (edge), the
the other end, the appropriate board foot measurement on the
width (face), and the length of the piece showing the labels for
remaining face.
each. (Do not show the board foot measurement yet!)
b. Explain that the formula is the sum of
b. As explanation is developing, it is preferable to write the
thickness (T) x width (W) x Length (L) divided by 12
formula on the board.
BF = T” x W” x L’ / 12” or BF = T” x W” x L’
c. Write:
BF = T” x W” x L’ / 12”
12”
BF = 2” x 4” x 1’ / 12”
c. Calculate the BF for the 2” x 12” sample piece.
BF = 2” x 4” x 12” / 12”
(cancel 12” from numerator and denominator)
BF = 2” x 4”
BF = 8”
BF = 8” / 12” (per foot) {verbal discussion}
BF = .667 bf - this is the first answer on #3.1
Complete Worksheet 3.1 – this worksheet will be used as a
reference sheet for the remainder of the lesson.
2nd - BF = T” x W” x L’ / 12”
BF = 2” x 6” X 1’ / 12” → 1.0 bf
rd
3 - BF = T” x W” x L’ / 12”
BF = 2” x 8” x 1’ / 12” → 1.33 bf
Distribute Worksheet 3.1
4th - BF = T” x W” x L’ / 12”
BF = 2” x 10” x 1’ / 12” → 1.667bf
5th - BF = T” x W” x L’ / 12”
BF = 2” x 12” x 1’ / 12” → 2.0bf
6th - BF = T” x W” x L’ / 12”
BF = 4” x 4” x 1’ / 12” → 1.33bf
d. Calculate the BF for the 2” x 12” x 8’ sample piece
e. One – 8’ 0” length of 2” x 4”
f.
One – 14’ 0” length of 2” x 6”
g. One – 8’ 0” length of 2” x 8”
h. One – 12’ 0” length of 2” x 10”
i.
One – 12’ 0” length of 2” x 12”
j.
Two - 10’ 0” length of 4” x 4”
k. Five – 12’ 0” length of 2” x 10”
l.
Four – 10’ 0” length of 4” x 4”
d. BF = T” x W” x L’ / 12” is 2 board feet
Based on the previous calculation on #3.1,
the BF measurement for a 1’ piece of 2” x 12” is
2 board feet
Therefore, an 8’ piece of 2” x 12” is 8 times as long.
BF = 8’ x 2’
BF = 16bf
Distribute Worksheet #3.2 – the first 2 columns of #3.2 are actually
transferred from #3.1
e. BF = T” x W” x L’ / 12”
BF = .667 x 8’ → 5.336bf
f. BF = T” x W” x L’ / 12”
BF = 1.0 X 14’ → 14.0bf
g. BF = T” x W” x L’ / 12”
BF = 1.33 x 8’ → 10.64bf
h. BF = T” x W” x L’ / 12”
BF = 1.667 x 12’ → 20.004bf
i. BF = T” x W” x L’ / 12”
BF = 2.0 x 9’ → 18.0bf
j. BF = T” x W” x L’ / 12”
BF = 1.33 x 10’ → 13.33bf
k. Based on the answer to letter ‘h’, one 12’ length has a bf
of 20.004, therefore 5 pieces is
BF = 20.004 x # pieces → 20.004 x 5 = 100.02bf
l. Based on the answer to letter ‘j’, one 10’ length has a
bf of 13.33, therefore 4 pieces is
BF = 13.33 x # pieces → 13.33 x 4 = 53.32bf
4. Work through related, contextual math-in-CTE examples.
a. Have students work cooperatively in small groups to complete
worksheet 4.1
a. See answer key #4.1 for calculations.
5. Work through traditional math examples.
#1: n2 – m ; use m = 7 & n = 8
Distribute Worksheet 5.1
82 – 7 → 64 – 8 = 57
Do #1 & #2 as large group. Then have students complete remaining
problems as cooperative group and/or complete as a homework
assignment.
#2: 8( x – y); use x = 5, and y = 2
8( 5 – 2) → 8(3) = 24
6. Students demonstrate their understanding.
Have students work cooperatively in small groups to complete
worksheet 6.1
7. Formal assessment.
The formal assessment of the skills will be part of a complete building
project. The building project could be anything from a small framing
project to a complete house.
NOTES:
See answer key #6.1 for calculations.