Math-in-CTE Lesson Plan Template
Lesson Title: Board Feet
Author(s):
Bob Pearce
Lesson #5
Phone Number(s):
406-324-2703
Paul Nickels
269-468-8540
E-mail Address(es):
bpearce@helena.k12.mt.us
paulnikels@sbcglobal.net
Occupational Area: Building and Trades
CTE Concept(s): Board Feet
Math Concepts: Formulas for figuring board feet. Order of Operations, rates, percent increase, unit analysis
Lesson Objective:
Students will be able to figure how much wood is need for a project along with the cost of the lumber.
Supplies Needed:
Pencil and calculator
TEACHER NOTES
(and answer key)
THE "7 ELEMENTS"
1.
Introduce
the
CTE lesson.
Answers will vary. Try to lead the students to what the wood will cost.
Have a alder door and
Cost of material will depend on the type of wood and the amount of wood.
a oak door, ask
Raised panel will have an elk or a skater dude logo design on them, made with the cnc router.
students what they
Prefer.
2. Assess students’ math
awareness as it relates
1. Pieces x thickness x width x length / 144 = total bd.ft.
to the CTE lesson.
1.Figure how to do Board
Feet
2. 1’’ x12’’x12’’
2. “What is a BD. FT.?
Board foot examples:
3.“How many square
inches are in a BD. FT.?
4. “How thick is a BD.
FT.?
5. What is the difference
between a board foot
and a square foot?
6. Why is figuring a
Board Foot important.
7. How is the percent
3. 144 square inches
added to total?
4. 1 inch?
5. Board foot you take the thickness into account. Such as 4/4, 5/4, 6/4. It is a volume.
5. Square foot you disregard the thickness, mostly used for plywood or manmade material. This is like finding
surface are.
6. To see how much lumber is needed to build something and the cost of the lumber.
7. 0.20 x the total plus the total, or 1.2 times the total
3.
Work through the
math
example
embedded in the CTE
lesson.
1. 15 PIECES 1x 6’’ x 10’
shelves for garage.
2. 4 pieces 1x 6’’ x 52’’
stiles for a kitchen
cabinet
3. Change a fraction to a
1.
2.
3.
4.
5.
P x T x W x L divided by 12 if one is in feet 75 bd. Ft.
P X T X W X L divided by 144 if all are inches. 8.67 bd.ft.
3 divided by 4 = .75
Cost per board foot alder $ 12.57 oak cost is $23.84
Stiles =8.67 x .20 = 1.73 +8.67 = 10.40 bd.ft.
decimal ¾’’
4. Cost of lumber for
alder $1.45 and the cost
of lumber from
oak
$2.75
All for the stiles for the
kitchen cabinet.
5. 20% is added to total
board feet for waste.
4. Work through related, 1. PX TX W X L X.007 another formula for calculating board feet.
contextual
math-in2. 1.008 bd. Ft.
CTE examples.
1. 2 pieces 1 x 6’’ x 12’’
rails for kitchen cabinet
2. Cost of lumber for
alder $ 1.46 the price
from oak $ 2.77
5.
Work
traditional
examples.
through
math
ANSWERS are on the second page of the Math Practice Sheet
See Math Practice Sheet
6. Students demonstrate WORK SHEET BELOW
their understanding.
ATTACHED.
Work sheet with 5
problems that include p
x t x w x l divided by 12
or 144
Along with another 5
questions with the type
of wood and the cost of
the wood per board feet.
7. Formal assessment
Do the board feet for the
following Corner hutch.
picture of hutch
*The
base
kitchen
cabinet will be done at a
later date.
Kitchen cabinet to be done at a later date
Key to hutch
6 shelves= 5.06
2 sides=9.44
1 top piece= .89
2 upper rails= .32
1 mid rail = .17
2 lower rails= .35
1 bottom piece = .25
1 door = 2.15
TOTAL = 18.63 X.20 = 3.73 +18.63 = 22.36 TOTAL BD.FT. Multiple by the cost of wood per board feet. Example
ash $2.75. 2.75 x 22.36 = $61.45 total cost for wood
NOTES:
BOARD FEET WORK SHEET
P
X T
X
W
X
NAME_____________________________
L
TOTAL BD.FT.
WOOD TYPE
COST BD.FT.
3
1
7 3/8
2’
PINE
$1.48
15
1
6’’
48’’
ASH
$2.75
2
1
6’’
1’
RED OAK
$2.78
12
1 ½’’
7 7/8’’
26 3/8’’
HICKORY
$3.86
22
½
4 5/8’’
16 .75
WALNUT
$ 5.28
P
X T
X
W
X
L
3
1
7 3/8
2’
15
1
6’’
48’’
2
1
6’’
1’
12
1 ½’’
7 7/8’’
26 3/8’’
22
½
4 5/8’’
16 .75
TOTAL BD.FT.
WOOD TYPE
COST BD.FT.
WALNUT
$5.28
PINE
$1.48
HICKORY
$3.86
ASH
$2.75
RED OAK
$ 2.78
TOTAL COST
TOTAL COST
BOARD FEET WORK SHEET
P
X T
X
W
X
ANSWER
L
NAME__KEY___________________________
TOTAL BD.FT.
WOOD TYPE
3
1
7 3/8
2’
3.69
PINE
15
1
6’’
48’’
30
ASH
2
1
6’’
1’
1
RED OAK
12
1 ½’’
7 7/8’’
26 3/8’’
25.97
HICKORY
22
½
4 5/8’’
16 .75
P
X T
X
W
X
L
3
1
7 3/8
2’
15
1
6’’
48’’
2
1
6’’
1’
12
1 ½’’
7 7/8’’
22
½
4 5/8’’
5.92
TOTAL BD.FT.
WALNUT
WOOD TYPE
3.69
WALNUT
30
PINE
COST BD.FT.
$1.48
TOTAL COST
$5.46
$2.75
$2.78
$3.86
$82.50
$ 2.78
$100.25
$ 5.28
COST BD.FT.
$5.28
$31.25
TOTAL COST
$19.48
$1.48
$ 44.40
1
HICKORY
$3.86
$3.86
26 3/8’’
25.97
ASH
$2.75
$71.42
16 .75
5.92
RED OAK
$ 2.78
$16.46
Name ______________________
Boardfeet Math Practice Sheet
Calculate:
a) 3 + 4 x 2
b) 6 + 8 ÷ 2 – 3
c)(4 + 2) x (5 + 2)
d) 4 + 2 x 5 + 2
Calculate but watch the units
a) If you were driving on I-15 for 3 hours at an average of 70 mph, how far would you have driven?
b) If Elmer Fudd knows that he will average 80 bu/acre in a good year, how much grain can he expect if he plants 120 acres in
that grain?
c) If Sheeszo Smart travelled 500 miles in 7 hours, including rest stops, what was her average speed?
Change the following percents to decimals.
a) 25%
b) 30%
c) 100%
Percent increase is anything over 100%. So, a 10% increase is really 110% of the original number.
The new number can be found if you multiply the original by the decimal for 110% (1.10)
So, the new amount after a 10% increase is really 1.10 times the original number.
EXAMPLE: The cost of paint increased 10%, if the old price was $28 a gallon, what is the new price?
$28 x 1.10 = $30.80
a) You calculated that you would need 30 sheets of plywood for a job, your boss tells you to add 5% for wastage. How many full
sheets should you order?
1) 29 sheets
2) 30 sheets
3) 31 sheets
4) 32 sheets
b) A foreman told a worker to increase their output by 20%. If the worker averaged 50 finished parts a day, what would their new
quota be?
1) 44 parts
2) 48 parts
3) 52 parts
4) 56 parts
Name ______________________
Boardfeet Math Practice Sheet ANSWERS
Calculate:
a) 11
b) 7
c) 42
d) 16
Calculate but watch the units
d) If you were driving on I-15 for 3 hours at an average of 70 mph, how far would you have driven? 210 miles
e) If Elmer Fudd knows that he will average 80 bu/acre in a good year, how much grain can he expect if he plants 120 acres in
that grain? 9600 bushels
f)
If Sheeszo Smart travelled 500 miles in 7 hours, including rest stops, what was her average speed? 71+ mph
Change the following percents to decimals.
b) 25% 0.25
b) 30% 0.3
c) 100% 1
Percent increase is anything over 100%. So, a 10% increase is really 110% of the original number.
The new number can be found if you multiply the original by the decimal for 110% (1.10)
So, the new amount after a 10% increase is really 1.10 times the original number.
EXAMPLE: The cost of paint increased 10%, if the old price was $28 a gallon, what is the new price?
$28 x 1.10 = $30.80
b) You calculated that you would need 30 sheets of plywood for a job, your boss tells you to add 5% for wastage. How many
full sheets should you order?
2) 29 sheets
2) 30 sheets
3) 31 sheets
4) 32 sheets
c) A foreman told a worker to increase their output by 20%. If the worker averaged 50 finished parts a day, what would their new
quota be?
2) 44 parts
2) 48 parts
3) 52 parts
4) 56 parts