Math-in-CTE Lesson Plan Template
Lesson Title: Let’s Excavate!
Author(s):
Bruce Barta
Lesson #
Phone Number(s):
(406)-268-6210
Amanda Kohut
E-mail Address(es):
[email protected]
(406)-268-6155
[email protected]
Occupational Area: Construction
CTE Concept(s): Excavation
Math Concepts: area, volume, units
Common Core State Standards – MT: N-Q, A-REI-3, G-GMD
Lesson Objective:
Supplies Needed:
Students will be able to calculate the amount of material that will need to be removed based on a given
plot plan.
Students will be able to comprehend concept of volume.
Students will know units of volume for excavating.
Students will be able to apply formulas to solve a variety of volume and excavation problems.
Pencil, calculator
Optional: soil density chart
TEACHER NOTES
(and answer key)
THE "7 ELEMENTS"
1. Introduce the CTE lesson.
Today we’re going to talk about how to calculate the amount of earth to
remove from the job site.
•
Volume (cubic), measured in feet and translated to cubic
yards.
•
Calculate cost and determine type and amount of equipment
to have at the site.
ASK: What unit of measurement will we use to calculate the amount of
earth being moved?
ASK: Why is it important to know how much earth needs to be
removed?
ASK: What measurement information will we need to plan an
excavation?
ASK: Who is responsible for calculating earth removal on a jobsite?
•
•
Volume being removed, size of bucket, truck capacity, job
site storage space, work space available / restrictions
Foreman / Superintendent / Site Supervisor / Project
Engineers / Laborers / Equipment Operators
2. Assess students’ math awareness as it relates to the CTE
lesson.
Bring up pictures/ power point of various sizes of excavating
equipment.
•
Have very small and very large options to emphasize the
importance of reasonable equipment.
•
Volume
•
Area / in construction we call this the footprint
•
Speaker box, lumber(brd ft), refrigerator, camping tent,
concrete, soil, fertilizer, gasoline, swimming pool
•
V = Bh (area of the base x height)
ASK: Which of these is reasonable to use on our jobsite?
Where might you use the others?
ASK: What do we call a 3 dimensional measurement?
ASK: What do we call a 2 dimensional measurement?
ASK: What are some examples of other items that are measured in
volume?
ASK: How would we calculate the volume of earth we need to remove
to build a house?
V = lwh (length x width x height)
-
This will be measured in feet, and will need to be
converted to yards. 𝑉 𝑓𝑡 3 ×
1 𝑦𝑑 3
27 𝑓𝑡 3
= 𝑉 𝑦𝑑3
3. Work through the math example embedded in the CTE lesson.
EX: On a basic term, let’s find out how much earth we need to remove
if we want to build a house that measures 36 ft wide, 28 ft long, and
needs to be 7 ft deep.
•
•
Show plans in power point.
Talk about finding benchmark; calculate depth using
benchmark as baseline. For this example we will assume
slope of property is zero. Talk about over dig, work area, etc.
ASK: What type of unit will be used to give the total amount of earth
that needs to be removed?
•
Cubic yards (volume)
ASK: What type of units are given on our plans?
•
Feet (linear)
ASK: How do we start to find the volume of earth we need to remove?
•
Use the formula for the volume of a rectangular prism.
V = Bh = lwh
V = 28 x 36 x 7 = 7056 ft3
ASK: Is this in the units we need? How do we convert?
•
7056 𝑓𝑡 3 ×
ASK: What excavation equipment would be appropriate for this job?
•
Reasonable would be a backhoe with a 1 yd3 bucket. Discuss
how long it takes based on bucket size and what would fit in
a normal lot.
ASK: What happens to the soil when you excavate?
•
When soil is disturbed during excavation, the volume is
increased. Soil Data Tables in power point and on hand out.
Expansion rates are usually 20-30%. We will use 25% for our
work today. 261.3 yd3 x 1.25 = 326.7 yd3
ASK: How many truck loads will it take to remove all the earth?
•
A truck can haul approximately 10 yd3 based on size and
weight. We will need 33 trucks.
1 𝑦𝑑
3 𝑓𝑡
×
1 𝑦𝑑
3 𝑓𝑡
×
1 𝑦𝑑
3 𝑓𝑡
= 7056 𝑓𝑡 3 ×
1 𝑦𝑑 3
27 𝑓𝑡 3
= 261.3 𝑦𝑑3
4. Work through related, contextual math-in-CTE examples.
1. Find the volume in yd3 that a backhoe bucket can hold if it is 24 in.
wide, 36 in. deep, and 30 in. tall.
•
Write the given dimensions in feet by dividing each by 12.
24
36
30
𝑉=
×
×
= 2 × 3 × 2.5 = 15 𝑓𝑡 3
12
12 3 12
1 𝑦𝑑
Convert: 15 𝑓𝑡 3 × 27 𝑓𝑡 3 = 0.55 𝑦𝑑3
- This would probably be a ½ yd3 bucket since they are not
actually rectangular prisms.
2. Find the amount of earth in yd3 that will be removed if you are laying
a slab for a garage with extra parking pad. The dimensions are shown
below, and the depth needs to be 18 in.
•
(picture in power point)
The footprint will need to be separated into 2 rectangles.
14 x 18 and 24 x 30 or 38 x 18 and 24 x 12
18
The area of the base will be 972 ft2 times the depth ( = 1.5)
12
V = 972 x 1.5 = 1458 ft3
Convert: 1458 𝑓𝑡 3 ×
5. Work through traditional math examples.
3. Find the amount of earth in yd3 that will be removed if you are
installing a square swimming pool that’s sides are 21 ft. and has a
depth of 5 ft. Assume the slope of the property is zero. Also give the
number of truck loads needed to haul the soil away assuming 25%
expansion.
•
4. Find the volume of a rectangular prism that is 16 ft. by 18 ft. by 6 ft.
•
5. The area of a L shaped playground is 370 ft2. Find the volume in yd3
of pavement if it is 6 in. deep.
•
1 𝑦𝑑 3
27 𝑓𝑡 3
= 54 𝑦𝑑3
V = 21 x 21 x 5 = 2205 ft3
Convert: 2205 𝑓𝑡 3 ×
1 𝑦𝑑 3
27 𝑓𝑡 3
= 81.7 𝑦𝑑3
Expansion: 81.7 yd3 x 1.25 = 102.1 yd3
Trucks: 102.1 ÷ 10 = 11 trucks
V = 16 x 18 x 6 = 1728 ft3
Reminder 6” = what decimal? = 0.5
6
V = Bh = 370 x = 370 x 0.5 = 185 ft3
12
3
Convert: 185 𝑓𝑡 ×
1 𝑦𝑑 3
27 𝑓𝑡 3
= 6.9 𝑦𝑑3
6. Students demonstrate their understanding.
ASK: If you were a hotel clerk and a customer called and asked you for
the size of the hotel room, describe how and what you would tell the
customer.
•
Common will be floor dimensions,
encourage square footage (area).
ASK: You are buying a cargo type van for your construction company.
Dealer A has a van with a box that is 10 ft long, 6 ft wide, and 5 ft high,
while Dealer B’s van measures 9 ft long, 7 ft wide, and 6 ft high. What
is the cargo space for Van A and Van B. Which van will you buy and
why?
•
•
•
Van A: V = 10 x 6 x 5 = 300 ft3
Van B: V = 9 x 7 x 6 = 378 ft3
Talk about factors that would make you buy each van. Size
or space requirements.
7. Formal assessment.
Test: 5 questions, attached document
NOTES:
Key: attached