Math-in-CTE Lesson Plan Template
Lesson Title: Surface Area, Area, and Volume
Author(s):
Phone Number(s):
Lesson # 5
E-mail Address(es):
Occupational Area: Ag Construction
CTE Concept(s): AGPD02.01#2 Introduction to Power, Structural and Technical Systems
Math Concepts: Geometry – the student uses geometric concepts and procedures in a variety of situations. The
student solves real world problems by finding the area of squares and rectangles. The student solves real-world
problems by finding the surface area of rectangular solids. 10.3.2.1.b,c.
Lesson Objective:
The learner will construct a cube.
Supplies Needed:
Sheet metal, oxyacetylene torch, chalk, tape measure, proper safety equipment, brazing
tip, pencil
THE "7 ELEMENTS"
TEACHER NOTES
(and answer key)
1. Introduce the CTE lesson.
What do you think the area of the football field is?
What do you think the area of the basketball court is?
Discuss student comments. Some may know the area or
at least dimensions of the fields.
Encourage students to offer reasons to find area. Some
Why would we need to know the area of the football field and
examples may include, resurfacing the basketball courts,
basketball court?
seeding or resodding the football field. Encourage
discussion to other areas. For example area of the parking
lot to resurface it, area of metal needed in a project, area
of board needed to build a project, etc.
2. Assess students’ math awareness as it relates to the CTE
lesson.
Formula to find area of a rectangle or square is length
times width measured in units squared.
How could we find the area of the football field or basketball court?
Discuss conversion factors to change different types of
measurements.
To find the area of the football field, basketball court, or any other
rectangular object; multiply the length times the width.
To convert inches to feet, divide the number inches by 12
because there are 12 inches in a foot.
What if you have measured a rectangular object in inches, but your
materials is sold by feet?
To convert feet to inches, multiply the number of feet by 12
because there are 12 inches in a foot.
To convert inches to feet, divide the number inches by 12 because
there are 12 inches in a foot.
To convert feet to yards, divide the number of feet by 3
because there are 3 feet in a yard.
To convert feet to inches, multiply the number of feet by 12 because
there are 12 inches in a foot.
To convert yards to feet, multiply the number of yards by 3
because there are 3 feet in a yard.
To convert feet to yards, divide the number of feet by 3 because there
are 3 feet in a yard.
To find surface area of a figure, you would simply find the
area of each side of the figure using formula to find area of
To convert yards to feet, multiply the number of yards by 3 because
a square or rectangle, and then add.
there are 3 feet in a yard.
Optional activity to do here if time permits: take the
What is it called when we find the area of more than one side of
students out and have them measure the dimensions of
something; for example how much wood on each side of a chest?
the basketball court and football field to find the area of
To find surface area of a figure, you would simply find the area of both.
each side of the figure using formula to find area of a square or
rectangle, and then add.
For example: A cube has 6 sides, so we would find the area of 6
sides then add those together.
3. Work through the math example embedded in the CTE lesson.
Handout #1
In the next few lessons we will construct an object that will look Answer key included.
similar to a cube, but without a top. Another example of what your
Discuss handout: processes and answers.
project should look like would be a box without a lid. How many sides
will our projects have?
Our project will have 5 sides.
In order to build our project correctly we need to find the area of all
five sides.
Let’s do so on this handout.
To find area as we discussed earlier, take the length of the object
times the width of the object.
4. Work through related, contextual math-in-CTE examples.
Handout 2:
Your job now is to practice what we have learned. Complete the Question #1 Find the area of the steel plate. Multiply 66 x
questions on this handout. We will do first one together.
31 = 2046 square inches.
Question #1
Find the area of the following steel plate:
66 in
31 in
Give students time to complete the handout and then go
over the answers. Answer key is included.
66 length x 31 width = 2046 square inches.
5. Work through traditional math examples.
Handout 3:
You may have also had to figure area in different situations. Let’s try Answer #1: 1 times 1 ½ = 1 ½ equals the amount of yards
to solve these next examples on handout #2.
of material you have to start with. Multiply 1 ½ by 3
because there are 3 feet in a yard and you have 4 ½
1. You have a piece of material that is 1yd by 1 ½ yds. You cut a
square feet of material. 1 times 3 = 3 equals the amount of
piece of rectangular material out to make a scarf that is 1 ft by 3ft.
feet of material you are using for the scarf. 4 ½ subtract 3
How much material is left over in feet after you are finished with the
= 1 ½ feet of material left over.
scarf?
Answer #2: 5 times 2 = 10 square feet
2. Find the area of the figure:
Answer #3: There are a couple of different ways to do this
5 in.
2 in.
problem. One way is to take 5 times 7 = 35 and 4 times 3
= 12 then 35 + 12 = 47 square feet.
Another way is to take 3 times 9 = 27 and 4 times 5 = 20
then 20 + 27 = 47 square feet.
Answer key included.
3. Find the area of the figure:
3ft
4ft
4ft
5 ft
6. Students demonstrate their understanding.
Handout 4: Directions to construct cube.
Now that we can all find area, let’s get started on our projects. Students will construct a cube without a top.
Handout #4 is the directions to your project. Read and follow the
directions very carefully. Remember to follow all proper safety
procedures previously learned.
7. Formal assessment.
Handout 5: Quiz
Quiz
Answer Key included
Additional area problems were developed for your quiz. Complete
your quiz making sure to show all of your work.
NOTES:
Handout #1
To find area: multiply length times width and the answer will be in units squared.
Find the total area of metal needed for a 4 inch by 4 inch by 4 inch box or cube without a lid.
Find how much metal will be needed total for everyone’s project.
Metal comes in 4 foot by 8 foot sheets. How many sheets of metal will we need to purchase for everyone’s project?
Find the total area of metal needed for a 4 inch by 4 inch by 4 inch box or cube without a lid.
Your procedures could be done in a few different ways.
One way:
4 x 4 = 16 square inches
4x 4 = 16 square inches
4 x 4 = 16 square inches
4 x 4 = 16 square inches
4 x 4 = 16 square inches
16 + 16 + 16 + 16 + 16 = 80 square inches
Another way:
4 inches x 4 inches x 5 pieces of metal = 80 square inches
Find how much metal will be needed total for everyone’s project.
This answer will vary because of the number of students in the class.
For 20 students you would:
80 square inches of metal for each student x 20 students in the class = 1600 square inches of material total
Metal comes in 4 foot by 8 foot sheets. How many sheets of metal will we need to purchase for everyone’s project?
Convert feet to inches: 4 x 12 = 48 and 8 x 12 = 96 then 48 x 96 = 4308. 4308 – 1600 = 2708 square inches left. So one sheet of metal will be
enough.
Handout #2
Show all of your work.
1. Find the area of the following steel plate:
66 in
31 in
2. Find the area of the following countertop:
3 ft
6ft
5ft
4ft
3. Find the surface area of the following box: Each edge measures 6 inches.
Answer Key
1. 66 x 31 = 2046 square inches
2. 5 x 4 = 20 and 10 x 3 = 30 then 30 + 20 = 50 square feet. OR 3 x 6 = 18 and 4 x 8 = 32 then 32 + 18 = 50 square feet.
3. 6 in x 6 in (area of one side) x 6 number of sides = 216 square inches
Handout #3
1. You have a piece of material that is 1yd by 1 ½ yds. You cut a piece of rectangular material out to make a scarf that is 1 ft by 3ft. How
much material is left over in feet after you are finished with the scarf?
2. Find the area of the figure:
5 in.
2 in.
3. Find the area of the figure:
3ft
4ft
4ft
5 ft
Answer Key
Answer #1: 1 times 1 ½ = 1 ½ equals the amount of yards of material you have to start with. Multiply 1 ½ by 3 because there are 3 feet in a yard
and you have 4 ½ square feet of material. 1 times 3 = 3 equals the amount of feet of material you are using for the scarf. 4 ½ subtract 3 = 1 ½ feet
of material left over.
Answer #2: 5 times 2 = 10 square feet
Answer #3: There are a couple of different ways to do this problem. One way is to take 5 times 7 = 35 and 4 times 3 = 12 then 35 + 12 = 47 square
feet.
Another way is to take 3 times 9 = 27 and 4 times 5 = 20 then 20 + 27 = 47 square feet.
Handout #3 (extension)
1. You have a piece of material that is 1yd by 1 ½ yds. You cut a piece of rectangular material out to make a scarf that is 1 ft by 3ft. How
much material is left over in feet after you are finished with the scarf?
2. Find the area of the figure:
5 in.
2 in.
a. What would happen to the area if you doubled each side?
b. What would happen to the area of the figure if each side is ½ it’s original length?
3. Find the area of the figure:
3ft
4ft
4ft
5 ft
Answer Key
Answer #1: 1 times 1 ½ = 1 ½ equals the amount of yards of material you have to start with. Multiply 1 ½ by 3 because there are 3 feet in a yard
and you have 4 ½ square feet of material. 1 times 3 = 3 equals the amount of feet of material you are using for the scarf. 4 ½ subtract 3 = 1 ½ feet
of material left over.
Answer #2: 5 times 2 = 10 square feet
a. 10 times 4 = forty square feet (the new area is four times larger than the original area)
b. 2.5 times 1 = 2.5 or 2 ½ square feet (the new area is ¼ of the original area)
Answer #3: There are a couple of different ways to do this problem. One way is to take 5 times 7 = 35 and 4 times 3 = 12 then 35 + 12 = 47 square
feet.
Another way is to take 3 times 9 = 27 and 4 times 5 = 20 then 20 + 27 = 47 square feet.
Handout #4
Directions to construct cube.
Step 1: Obtain metal from storage.
Step 2: Measure and mark 5 squares of metal that are 4 inches by 4 inches with chalk.
Step 3: Cut out your squares using the cutting torch or plasma cutter. Number the squares 1 through 5.
Hint: Be absolutely sure of your measurements and dimensions before you cut.
Step 4: Tack squares 1 and 2 at 90 degree angles perpendicular to each other using the speed square. Remember to tack at the corners only.
Square 2
Square 1
Step 5: Tack square 3 to square 1 at the corners.
Square 3
Square 2
Square 1
Step 6: Tack square 4 to squares 1, 2, and 3 at the corners.
Square 3
Square 2
Square 4
Square 1
Step 7: Tack square 5 to squares 1, 2, and 3 at the corners.
Square 5
Square 3
Square 2
Square 4
Square 1
Step 8: Weld all edges of the cube with an oxyacetylene welder using a brazing tip.
Handout #5 Quiz
Show all of your work. Partial credit may be awarded for correct procedures.
1. Find the area of a garden with dimensions 6 ft by 21 ft. How many square yards is the garden?
2. Find the area of the following sheet of steel:
6 ft
4 ft
3. Find the area of the excess metal in the following sheet of steel: The metal comes in 8 ft by 4 ft. sheets. The piece of metal that is being cut out to
be used is 3 ft by 3ft.
4. Find the surface area of the following figure:
12 in
2 in
12 in.
5. What is the surface area of the following figure? Each side of the cube measures 4 inches long.
Answer Key
1. 6 ÷ 3 = 2 and 21 ÷ 3 = 7 because there are 3 feet in a yard. Then 7 x 2 = 14 square yards.
2. 4 x 6 = 24 square feet.
3. 8 x 4 = 32 square feet and 3 x 3 = 9 square feet. 32 – 9 = 23 square feet left over.
4. 12 x 12 = 144 are of side x 2 number of sides the same = 288 square feet
2 x 12 = 24 x 4 number of sides the same = 96 square feet
96 + 288 = 384 square feet total surface area
5. 4 in x 4 in = 16 square inches area of one side x 6 number of sides = 96 square inches total surface area.
Handout #5 Quiz (extended)
Show all of your work. Partial credit may be awarded for correct procedures.
1. Find the area of a garden with dimensions 6 ft by 21 ft. How many square yards is the garden?
a. What happens to the area (in feet) of the garden if you tripled the length of the sides?
b. What happens to the area (in feet) of the garden if you reduce the each side of the garden to a third of its original length?
2. Find the area of the following sheet of steel:
6 ft
4 ft
3. Find the area of the excess metal in the following sheet of steel: The metal comes in 8 ft by 4 ft. sheets. The piece of metal that is being cut out to
be used is 3 ft by 3ft.
4. Find the surface area of the following figure:
12 in
2 in
12 in.
5. What is the surface area of the following figure? Each side of the cube measures 4 inches long.
a. What happens to the surface area of the cube if you double the length of each side?
b. What happens to the surface area of the cube if you half the length of each side?
Answer Key
1. 6 ÷ 3 = 2 and 21 ÷ 3 = 7 because there are 3 feet in a yard. Then 7 x 2 = 14 square yards.
a. first figure in feet: 6 x 21 = 126 square feet. New figure 18 x 63 = 1134 square feet. The new area is nine times larger than the original.
b. first figure in feet 6 x 21 = 126 square feet. New figure 2 x 7 = 14 square feet. The new area is one ninth the original.
2. 4 x 6 = 24 square feet.
3. 8 x 4 = 32 square feet and 3 x 3 = 9 square feet. 32 – 9 = 23 square feet left over.
4. 12 x 12 = 144 are of side x 2 number of sides the same = 288 square feet
2 x 12 = 24 x 4 number of sides the same = 96 square feet
96 + 288 = 384 square feet total surface area
5. 4 in x 4 in = 16 square inches area of one side x 6 number of sides = 96 square inches total surface area.
a. 8 in x 8 in = 64 sq in area of one side x 6 number of sides = 384 square inches
original surface area was 96 sq inches – the new surface area is four times larger than the original.
b. 2 in x 2 in = 4 sq in area of one side x 6 number of sides = 24 square inches original surface area was 96 sq inches total surface – new
surface area is ¼ the original.