CFC Day 22

LEARN – DAY 22
Construction Foundation Course

Week Five: Day 22 (Tuesday)
Content for the day
• Hour 1: Construction Math
• Hour 2: Blueprints
• Hour 3: Materials Handling
• Hour 4: Materials Handling

Materials for the day
• Wooden standard ruler, one per student.
• Calculators, one per student
• Wooden flat scale (1/4 and 1/8) architect’s ruler (1 per
student)
• A magnetic dartboard (e.g., Amazon.com, $12.00)
• Resource 5.9 - How to Read an Architect’s Scale
• Resource 5.9A - Architect’s Scale Wall Chart Triangular
architect’s ruler (1 to show)
• Resource 5.10 - Calculating Square Footage Practice
Sheet
• Resource 5.11 - Calculating Square Footage Floor Plan
Sketch

Materials for the day (cont.)
• Resource 5.12 – Calculating Square Footage Instructor
Answer Sheet
• Resource 5.13 – Student Worksheet – Cylindrical
Volume Problems
• Resource 5.14 – Instructor Resource – Cylindrical
Volume Problems
• Resource 5.15 – Basics of Material Handling
• Resource 5.16 - The Standards System Student Copy
and Resource
• Resource 5.17 - Meters, Liters, and Grams Student Copy
Blue, yellow, and green plastic strips
• Orange, red, and brown plastic strips
• Homework: Math and Measurement Raps

First and Second Hours (7:30 – 9:30) - 1
5 min. Tell students that they are developing math skills
necessary to complete their training and to perform well on the
job. Remind them that over the past five days construction math
has focused on basic math operations and measurement. The
next units will focus on important construction math skills like
using ratio and proportion and we’ll continue to work with lines,
shapes and angles.
Remind students to take notes and use blank vocabulary cards
to define terms as you use them. Explain that today we’ll
continue to calculate square footage. Ask students to recall the
definition of square footage [a measurement of area, and area is
the measurement of any two-dimensional space contained
within a set of lines]. Call on a student for the formula for
calculating the square footage of a square of a rectangle [A=l x
w].
Construction Math

Have students work in pair-shares to calculate problems
in Resource 5.10 - Calculating Square Footage Practice
Sheet. Call on pair-shares for answers.
Solutions: #1: wall = 516 ft2; opening = 12 ft2
#2: wall = 532 ft2; opening = 21 ft2
#3: wall = 600 ft2; opening = 35 ft
#4: wall = 630 ft2; openings = 27 ft2
Share answers as a group.
While students are performing the calculations, hand out
wooden standard rulers and calculators. Call on a student
for the answers to the Practice Sheet. Confirm correctness
with a second student.

10 min. Remind students that a square foot doesn't necessarily
have to be shaped like a square or a rectangle. The dance floor
above could be shaped like a triangle and cover the same
amount of area. If you were asked to determine the area of a
triangle the formula would be different, but the concept is the
same.
Ask students to use their rulers to draw a triangle on a ½ size
sheet of scratch paper. The base or bottom of the triangle is
4”and the height is 3”. Draw a 5” line segment to connect the
two legs to form the third and longest line of the triangle. Ask if
anyone can tell you what type of triangle you have formed. [right
triangle] Tell students to create a vocabulary card for right
triangle. A right triangle has one 900 angle.

Stretch Break. Have students stand and form a 900
angle with their arms. Wait until all students have
formed the angle with their arms. With arms still
extended, ask if anyone can tell you the name of the
longest line in a right triangle. [Hypotenuse] Ask
students to repeat the word two or three times and
then show them a memory device for the term. With
your arms extended to form a 900 angle wave the
hand that is extended upward several times while
saying “Hi, Hi, hypotenuse.” As you say
“hypotenuse,” lower the hand extended upward to
form the hypotenuse and touch the hand extended
outward. Ask students to repeat the words and
gesture several times.

When students are seated have them return to their drawing of
a right triangle. Ask them to imagine and then draw what would
happen if a duplicate copy of their drawn triangle was rotated so
that the two hypotenuses aligned perfectly. What shape would
be formed? [rectangle] Ask students what they think the formula
would be to find the area of a right triangle and write the
formula on the white board [Area of a triangle = ½ (Base x
Height)or A=½bh] noting the change in terms from length to
base and width to height. Ask students to create a vocabulary
card with Area of a Triangle on the front and the formula on the
back of the card.
Have students calculate the area of the 3”x4”x5” triangle that
they drew. [6”] Call on a student for the answer. Use wait time
and call on a second student to confirm the answer.

5 min. So what if that dance floor isn’t shaped as a rectangle or
a right triangle but is, in fact a circle? If you were asked to
determine the area of a circle the formula would be different, but
the concept is the same.
Draw a circle on the white board with a dot in the center of the
circle. Ask students to create a vocabulary card for the term
radius. As you draw a line from the dot to the inside edge of the
circle, use and define the term radius. Remind students that the
radius is half of the diameter.

Write the formula A = πr2 on the white board. Ask
students to create a second vocabulary card with
Area of a Circle on the front and the formula on the
back. Note that π (pi) is a special number whose
value is the ratio of any circle's circumference to its
diameter. Explain that we find the area of a circle by
multiplying 3.l4 (the value of π) times the radius
squared. Ask students to determine the value of the
radius squared if the radius of circle on the board is
5 inches. [25 sq. in.] Multiply 3.14 x 25 sq. in. = 78.5
sq. in.

5 min. Have students work in pair-shares to
determine the area for circles with the
following radii: 4 ft.; 6 in.; 3 ft. While students
are performing calculations, hand out
Resource 5.11 - Calculating Square Footage
Floor Plan Sketch. Call on pair-shares

5 min. Have students work in pair-shares to
determine the area for circles with the
following radii: 4 ft.; 6 in.; 3 ft. While students
are performing calculations, hand out
Resource 5.11 - Calculating Square Footage
Floor Plan Sketch. Call on pair-shares for
answers. Use wait-time and confirm correct
answer with other pair shares.

25 min. Have pair-shares calculate the square
footage of each room in the sketch of a floor
plan and the total square footage of all rooms.
Tell students to use a calculator and to round
up even if the remainder is less than a half.
Pair-shares who finish early should be ready to
share strategies for checking their work to
ensure that it is accurate. Call on pair shares
for answers and examples of how they arrived
at their answers. Use wait time and confirm
answers with other pair shares.

15 min. Remind students that Square footage is a
measurement of area, and area is the measurement of
any two-dimensional space contained within a set of
lines. Ask what happens when you need to work in
three-dimensional space, for example the length, width
and depth of an object? Draw a cube on the board and
wait.
Explain that three-dimensional space is measured in
volume. So if we need to know the volume of a board,
like when we need to calculate board feet, we multiply
the width of the board x the length of the board x the
thickness of the board.

Have students turn to p. 63 and look at Figure 2-26 to
see how different shapes of wood can have the same
measure in board feet. Explain that a significant
amount of lumber is sold by the board foot rather than
the linear foot. Have students create a vocabulary card
for board foot as you define the term. The board-foot is
a specialized unit of measure for the volume of lumber
in the United States and Canada. It is the volume of a
one-foot length of a board one foot wide and one inch
thick.

Draw the following illustration on the white board.
The volume of one board foot is calculated as 12” x 12” x 1” =
144cubic inches (in3). To determine the number of board feet in
one or more pieces of lumber use the following formula:
Number of Pieces x Thickness (in.)
X Width (in.) x Length (ft.)
12

10 min: Write the formula for calculating board feet on
the white board and have students add it to their
vocabulary card for board foot. Walk students through
this practical application: You have one “2 x 4” that is
10 feet long, and you need to figure the number of
board feet. You know that the formula for determining
board feet is L (in feet) x W (in inches) x H (in inches) =
board feet. You can’t just multiply the numbers you
have as L x W x H because 2 of the measurements are
in inches and 1 is in feet. That’s apples and
gooseberries. So you need to convert the units of
measure so they are all the same.

Convert the 10’ length to inches
10’ x 12 inches/ft. = 120 inches
Then calculate the cubic inches of the board by
multiplying L x W x H:
120” x 4” x 2” = 960 cubic inches
There are 144 cubic inches in a board foot. How do we
determine the number of board feet? Wait time. Call on
one; get second opinion. Divide. So…960 cubic inches
divided by 144 cubic inches = 6.67 board feet.

The board foot formula gives us a faster way to complete these
conversions:
1 piece of wood x 2” thick x 4” wide x 10 feet long = 80/12 = 6.67
board feet
Ask students to work in pair shares to solve the following
problems.
In his inventory, your boss has the following:
- 4, 2-by-10s, each 8 ft. long
How many board feet of lumber does he have?
Your boss needs 100 board feet of lumber in 2-by-10s. How many 8 ft.
2-by-10s should he buy?
Compare answers as a group.

10 min. Explain that in construction trades we must also know
how to find the volume of a cylinder. For example, many
foundations require “piles” which are cylindrical tubes and of
various lengths which are filled with concrete. Write the formula v
= πr2h on the white board and explain that in order to calculate the
volume of any cylinder the formula is π (pi) times radius squared
times the height or the cylinder. An example would be a cylinder
with a radius of 1’ and a height (length) of 5’. Therefore volume
equals 3.14 x 1 x 1 x 5 = 15.70 cubic feet. If there are 28 piles to be
poured for the foundation, 15.7 x 28 = 493.6 cubic feet.
Explain that there are 27 cubic feet in 1 cubic yard. To convert
cubic feet to cubic yards, we must divide 439.6 cubic feet by 27 (3
x 3 x 3) to get 18.28 cubic yards of concrete. Round up and add a
waste factor to make the order.

Calculating the formula would be less difficult if we were always
given the radius. But that's not how pipe for example is measured.
It is common to have the diameter so one must divide by 2 to get
the radius. Remember, the radius is any straight line that connects
a point on the circle with it's center. The radius is half of the
diameter. The diameter is a line segment that connects two points
on a circle through the center of the circle.

Also there is an inside diameter (ID) and an outside
diameter (OD) if pipe and such are used. So if you want
volume of a cylindrical container it needs to be
calculated using the ID for the interior space
calculation not OD (otherwise you are including the
volume of the pipe thickness as well as the capacity).
Walk students through one of the problems in Resource
5.13 – Student Worksheet – Cylindrical Volume
Problems. Have them work in pair-shares to solve the
remaining three problems. Share answers as a group.
Stretch Break

5 min: Do Resource 5.1 - Minute Measure PPT, slide #2, and
have students trade papers, correct, and enter their data on
their Personal Best chart. Ask them to use a ruler to connect the
first dot from yesterday to today’s dot. The name for this type of
graph is line graph; it clearly shows the direction and rate of
progress.
5 min. Read the first 2 paragraphs of Understanding scale, p.
44. Go through the entire Table 2.1 translating the 1’ to 12” and
asking the question, “How many 6” segments are there in 12”?”
2, so the ratio is 2:1. How many 3” segments are there in 12”?”
4, so the ratio is 4:1, Etc., gradually letting the class fill in the
numbers without your help.
Blueprints

25min: [The following materials will need to be prepared prior to
instruction.]
• Colored markers as described in the lesson that follows. Use thin
plastic material like Avery polypropylene plastic dividers or
Pendaflex colored folders. Measure and cut strips ½” wide and of
six different lengths. The strips should begin at 0” on the
architect’s scale and end on a marker line (though not
necessarily a numbered marker line but not between marked
lines.) Each color should be cut to the same length (e.g., 10 red
strips for a class of twenty each ½” wide by 14’ on the ¼” scale).
• Cut a piece of poster board approximately 6” wide by
approximately 18” long. Cut it so that when one end is aligned
with the 0 line of the Architect’s scale wall-graphic, the opposite
end aligns with a marked line, not in between lines. This prevents
the student from having to interpolate a measurement.

Read the second 2 paragraphs of Understanding scale,
pp. 44-45. Put up Resource 5.9A - Architect’s Scale
Wall Chart Triangular architect’s ruler (1 to show). Note
that it is NTS. Show students how to read the scale
using Resource 5.9 - How to Read an Architect’s Scale.
Give Work Teams assignments of 6 measurements to
find on their architect’s scale rulers. They will draw
lines of the designated length on scratch paper and
label them appropriately:
1/8”: 41’, 12’, 53’ and ¼”: 15’, 27’, and 30”
Have one Work Team explain their thinking and show
their results. Ask for a second opinion.

Use the 6” x 18” poster board to show students how to
use the colored strips. Hand out the blue, yellow and
green strips. Have Work Teams measure the markers on
the ¼” and 1/8” scales. Have one Work Team explain
their thinking and produce their outcomes. Get a
second opinion.
Hand out the red, orange, and brown strips. Follow the
same process with pair-shares.
Snack Break (9:30-9:40)

Third and Fourth Hours (9:40 –11:30) - 1
5 min. Mini-lecture on the basics of materials handling. Provide the
information in Resource 5.15 – Basics of Material Handling while
students take notes.
15 min. Proper lifting procedures. Show the video on proper lifting
procedures at http://www.youtube.com/watch?v=_YoOL3HipvA. Then
show the preview version of a fun video that shows the 5 steps to lifting
heavy loads:
http://www.youtube.com/watch?v=MhGUkWAA9WM&feature=relmf
Point out to students the heavy boxes you’ve brought in. Review the
steps in lifting as you demonstrate. Stress the importance of following
the steps. Not following the steps is not macho; it’s stupid.
Call on a mature student to demonstrate the steps again as you
narrate. Have students critically analyze his/her completion of each
step.
Have Teams practice having individuals lift the box. Have the student
who is lifting narrate each step.
Materials Handling or Manual Handling

15 min. Continue the mini-lecture with the
information on lowering loads from overhead and
stacking boxes. Remind students to take notes.
Demonstrate by putting one of the heavy boxes on
the top of a classroom shelf or cabinet, removing it,
and placing it on another to make a stack.
Have Teams practice having individuals lift the box
from overhead and stack it. Have the student who is
lifting narrate each step, as before.

• 10 min. Continue the mini-lecture with the information on off-
set stacking for other types of materials. Have students make
up vocabulary cards for the following:
• Off-set lumber stacking
• Off-set pipe stacking
• Off-set bag stacking
• Off-set brick stacking
• Off-set cement block stacking
• Chocking
• Spotter
5 min. Continue the mini-lecture with the information about
working from heights while students take notes.
Stretch Break

10 min. Have students study materials handling
notes (as study sheets) and new vocabulary cards to
mastery.
5 min. Introduce materials handling equipment by
asking students what equipment they know of that
helps workers move or lift material. Summarize by
saying that materials-handling equipment comes in
two varieties: non-motorized and motorized.
.
Materials Handling (cont.)

10 min. Distribute vocabulary cards for materials-handling
equipment:
Non-motorized (usually): Motorized
* Wheelbarrows * Powered wheelbarrow
* Hand trucks * Concrete mule
* Material carts * Industrial forklift
* Roller skids * Rough terrain forklift
* Jacks * Freight elevator
* Pallet jacks
* Pipe mules
* Pipe transports

Assign each Team 2 or 3 terms to teach and allow 8
minutes to prepare for presenting at about 1.5
minutes per term. Information for card back should
include
20 min. Have Teams present terms.
Name Care/safety
Purpose How to remember

15 min. Give Work Teams 5 minutes to study all
vocabulary cards to date. Use the balance of the
period to play Darts. Put up the magnetic dart board.
Line the class up in Work Teams. Give a definition
from the vocabulary cards. The first team member at
the very front of the line to respond correctly with the
term defined may throw a dart for points. Teams get
one point for the correct answer and additional points
based on where the dart lands on the dartboard.
Team members at the front of the line move to the
back of the line.
Reflection

Remind non-residential students that they can check out a tape
measure.
5 min. Homework review. Divide the class into five teams numbered
Team 1 through Team 5. Tell the teams that they may adopt their own
team name but to remember the number designation for performance
purposes. Hand out Resource 5.16 - The Standards System Student
Copy and Resource 5.17 - Meters, Liters, and Grams Student Copy.
Explain that each team will develop a rap for both of these sets of
lyrics. Note that some of the lyrics are missing and that their notes and
study sheets on Metric and Standard measure will likely help them fill
in the words. Tell students that two Teams will each perform one rap of
their choosing tomorrow. Remind them that class members will be
listening closely to their fine performances and to make sure that all of
the lyrics are correct.
Out the door:Model Notes,Reflection, binders on the shelf, shake
hands.

END
If you continue to click forward, you will see links to
presentations of similar content available through
slideshare.com
Content prepared for the National Office of Job Corps through Contract No. DOLJ111A21695
Job Corps Professional Development Support - KUCRL

CFC Day 22

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