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“Knowledge without experience is
just information.” –Mark Twain
Construction Related Math 3/4
Written and Adapted by Shannon Sims
Adult Basic Skills Department
Rogue Community College
Table of Contents
Conversion Bingo…………………………………………………… 3
(Adapted from YouthBuild USA Working Hands, Working Minds Curriculum)
Angels in Construction……………………………………………… 11
Ratios and Proportions………………………………................... 15
Congruent Triangles………………………………………………… 20
Getting Things “Right”………………………………………………. 24
(Adapted from YouthBuild USA Working Hands, Working Minds Curriculum)
Pythagorean Theorem………………………………………………. 29
Perimeter in Construction…………………………………….…….. 33
Area in Construction…………………………..…………………….. 37
Construction Word Problems………………………………………. 44
Bringing it all together………………………………………………. 45
(Adapted from YouthBuild USA Working Hands, Working Minds Curriculum)
2
Conversion Bingo
(Adapted from YouthBuild USA’s Working Hands, Working Minds Curriculum)
Learning Objective:
Students will play BINGO in order to review standard measurement units and practice
measurement conversion from inches to feet to yards.
Time: 1 hour
Materials:
Three pieces of Flipchart paper labeled: Inches, Feet, Yards
Markers
Tape Measures
Rulers
Yardsticks
Handout: Converting Inches, Feet, and Yards
Photocopies of Bingo cards (2 per student)
Conversion Bingo Checklist
Small Prizes if desired
Warm Up: 10-15 minutes
Separate class into three groups. Have each group stand around a piece of flipchart paper
labeled either: inches, feet, or yards. Give each group a marker. Explain that they will have 2
minutes to write down everything they know about the topic on their paper. Answer any
questions and let the students begin.
Be sure to monitor time. Have the group switch after 2 minutes have passed. The students at
the Inches paper go to Feet, Feet go to Yards, and Yards go to Inches. Have them read what
the previous group has listed and add anything that group might have missed.
After 2 minutes, have the groups switch for one third and final time. Like before, the
groups should read what the previous groups have written. When finished, they should
summarize what is on the flip chart and give a brief one minute report out to the class.
Use this time to address any learning gaps. Be sure to discuss that 12 inches = 1 foot, 3
feet= 1 yard, 36 inches= 1 yard, etcetera.
New Information: 10 minutes
Pass out the handout: Converting Inches, Feet, and Yards
Allow the students to complete this worksheet and discuss as a class.
3
Experience! 30 minutes
Have students standup and create a spectrum based on their comfort level with conversion.
Fold the line of students in half, creating pairs of students where the most comfortable
student is paired with the least comfortable student, and the second most comfortable
student with paired with the second least comfortable student and so on.
Give each student two BINGO cards.
As you read off word problems from the Conversion BINGO checklist, the students should
try to find the answers on their cards. If they find the correct conversion, they should cross
it off their card. The first student with 5 in a row vertically, horizontally, or diagonally wins.
Check for Understanding: ongoing
As students BINGO, make sure they read their answers so you know if they are converting
their answers correctly.
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity?
Generalize- How do we use conversion in our daily lives?
Independent Practice: Homework
Have students create 3 conversion problems for future BINGO games. Check them as a
class for accuracy and add them to your collection to use later.
Handouts: See following pages for handouts and bingo cards
4
Converting Inches, Feet, and Yards
In your life, and especially on a construction site, you will need to know how to quickly convert
measurements.
Think back to the classroom discussion…
What math do you need to do to make the following conversions?
Feet to inches?
________________________
Inches to feet?
________________________
Yards to feet?
________________________
Feet to yards?
________________________
Bonus! Yards to Inches?
________________________
Complete the following
conversions:
7 feet equals ______ Inches 48” equals ______ft 2 yards equals _____ ft 33’ equals ______ yards
3 feet equals ______ Inches 36” equals ______ft 36 yards equals _____ ft 24’ equals ______ yards
19 feet equals ______ Inches 12” equals ______ft 15 yards equals _____ ft 3’ equals ______ yards
24 feet equals ______ Inches 63” equals ___ft ____in 5 yards equals _____ ft 93’ equals ______ yards
47 feet equals ______ Inches 32” equals ___ft ____in 42 yards equals _____ ft 15’ equals ______ yards
Bonus!
2 yards equals _____ Inches 36 yards equals _____ ft 15 yards equals _____ ft 42 yards equals _____ ft
5
Conversion BINGO Checklist
_____ Inches in 1 foot
_____ Inches in 2 feet
_____ Inches in 2.5 feet
_____ Inches in 3.5 feet
_____ Inches in 4 feet
_____ Inches in 5 feet
_____ Inches in 5.5 feet
_____ Inches in 7 feet
_____ Inches in 11 feet
_____ Inches in 12 feet
_____ Inches in 1 yard
_____ Inches in 2 yards
_____ Feet in 48 inches
_____ Feet in 1 yard
_____ Feet in 60 inches
_____ Feet in 6 yards
_____ Feet in 84 inches _____ Feet in 21 yards
_____ Feet in 96 inches _____ Yards in 36 inches
_____ Feet in 108 inches _____ Yards in 216 inches
_____ Inches in 3 yards _____ Inches in 6 yards _____ Feet in 24 inches
6
BINGO Cards
B I N G O B I N G O
66 8 2 36 72 66 8 24 3 12
216 3 60 18 7 18 132 30 5 72
24 9 Free 4 132 60 1 Free 48 4
108 12 144 30 5 42 84 2 216 63
42 84 63 48 1 7 144 108 9 36
B I N G O B I N G O
36 18 7 132 63 66 8 144 63 60
48 30 144 8 24 132 18 7 84 36
108 4 Free 9 1 1 216 Free 5 4
60 3 72 216 84 12 3 108 9 48
66 42 12 5 2 42 72 24 2 30
B I N G O B I N G O
7 84 72 24 36 60 72 18 48 36
5 3 108 48 63 4 144 108 132 63
8 144 Free 132 216 84 3 Free 30 24
4 12 1 2 18 42 5 8 1 2
66 30 9 42 60 66 12 216 7 9
7
B I N G O B I N G O
36 18 12 48 5 84 216 5 1 108
108 144 132 72 7 7 2 12 72 4
30 216 Free 1 4 63 36 Free 144 42
63 2 6 8 3 30 48 8 60 3
9 42 84 24 66 9 18 132 24 66
B I N G O B I N G O
144 24 1 216 84 4 108 9 63 7
63 3 8 5 108 30 72 5 1 12
4 30 Free 132 7 216 36 Free 132 18
9 72 12 1 66 144 8 3 2 42
42 60 18 36 48 24 84 60 66 48
B I N G O B I N G O
63 216 12 108 48 48 30 5 144 18
23 2 8 36 84 63 36 108 132 84
3 72 Free 18 132 1 216 Free 2 7
4 144 1 5 7 24 72 3 8 9
9 42 60 30 66 12 60 4 42 66
8
Independent Practice
Create 3 of your own conversions and BINGO cards to go with them:
B I N G O Conversion Problems:
1.
Free
2.
B I N G O
Free
3.
B I N G O
Free
9
Angles in Construction
Learning Objective:
Students will identify how angles and triangles relate to construction.
Students will identify the origins of angles
Students will define different types of angles
Students create their own reference page that identifies different types of angles.
Students will use protractors correctly.
Time: 1 hour
Materials:
Old home decorating magazines
Colored paper
Glue
Scissors
Protractors
Pencils
Handout: Types of Angles
Pictures of the following different types of angles from construction
o Acute
o Obtuse
o Straight
o Right
o Reflex
Warm Up: 10-15 minutes
Have students collect a home decorating magazine, piece of colored paper, scissor, and a
glue stick from the front of the room. Let them get up and move! You don’t need to pass it
out.
Explain that today you will be exploring the use of angles in construction. Give students ten
minutes to look through the magazines to find as many different angles as they can. Have
the students cut the angles out and keep them to the side.
New Information: 15 minutes
As a class, define the five different types of angles. Show pictures of these angles used in
construction.
Demonstrate how to use a protractor with the class.
10
Pass out the handout: Types of Angles
Allow five minutes for the students to complete this worksheet.
Experience! 25 minutes
Have students use the colored paper to create a personal reference page to remember the 5
different types of angles.
They should define the angle, show a picture of it, and name the angle.
When completed, they can stick this page in their binders to refer to it throughout the rest of
the term.
Check for Understanding: ongoing
As students create their reference page, go around and make sure they have found the right
construction examples in their magazine. Be prepared to assist them with ideas of where
they might find these angles in the world of construction- base boards, stair cases, cabinetry,
roofing…
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity?
Generalize- Why are angles important in construction? (professionalism, poor angles weaken
structures, correct fit)
Independent Practice: Homework
Have students draw angles of different degrees to demonstrate proficiency in use of a
protractor.
11
Types of Angles:
Using the pictures provided, create a definition for each type of angle:
Acute Angle
Obtuse Angle Straight Angle
Reflex Angle Right Angle
12
Independent Practice
Go to www.worksheets.com to generate a nice, easy to use pdf worksheet that will give students
practice using their protractors. This is a fantastic FREE resource!
13
Pictures of Angles in Construction
Acute angle
An arched doorway is a common
Obtuse angle found in construction.
There are many angles on this
cabinet… Can you find a right angle?
Is there a reflex angle here?
Floor joists make what type of angle?
I see two!
14
Ratios and Proportions
Learning Objective:
Students will measure classroom dimensions with tape measure.
Students will construct a scaled model of the classroom.
Students will read construction blueprint plans.
Students will use proportions to translate life size dimensions into blueprint plans.
Time: 1 hour
Materials:
Measuring tape (one for each student group)
Cardstock
Scissors
Glue
Markers
Tape
Rulers
Calculators
Handout: Let’s get familiar with Blueprints
Graph paper
Warm Up: 10-15 minutes
Students should work in pairs for this activity. Pass out measuring tapes to each student
group, and ask them to measure the dimensions of our classroom. (Length, width, height)
also have students record any identifying features such as windows and doors. They will
need to measure these things as well as their placement in the room. Encourage students to
get as detailed as possible in the 10 minute time frame.
Explain that today you will be exploring the use of ratios and proportions in construction.
Ask the class about their measurements. Be sure everyone knows the dimensions of the
room.
New Information: 15 minutes
Explain how you can draw something to scale. If our classroom measures 10 feet wide and
our scale is 1 inch equals 1 foot, how many inches would our wall be? Students should
understand that we would draw a line that is 10 inches long to represent the width of our
room.
Ask the students to convert the measurements they came up with in class to our new scale.
Allow adequate time for the students to complete this task.
15
Experience! 25 minutes
Ask each pair of students to join another pair of students so the class is working in groups of
four.
Have students use the cardstock paper, tape, rulers, and glue to create a model of the
classroom.
They should include: length, width, height, windows, doors, white boards
They can include tables, desks, chairs… the models can be as detailed as needed
When finished, create a space for the students to display their models.
Check for Understanding: ongoing
As students create their models, go around and make sure are grasping the task at hand. Be
prepared to assist them with ideas of how they might use the materials to create their
models.…
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity?
Generalize- have a short discussion about architecture. How much school does it require?
How much does an architect earn?
Independent Practice: Homework
Handout: Let’s get familiar with Blueprints; students should read this article.
Have students use graph paper to draw a blueprint of the classroom model they created in
class.
16
Let’s Get Familiar with Blueprints
Information retrieved from:
http://www.thehousedesigners.com/understanding_blueprints.asp
Understanding Blueprints
Blueprints are much more detailed drawings than simple Floor Plans. Blueprints are exact detailed
scaled drawings of plans of a home, building, or structure which include many more details than a basic
floor plan.
Your blueprint plans and specifications are the documents used by your builder and contractors to
instruct them on how to build your new home. Each set of blueprints should include floor plans; plans
for the foundation and information on footings and framing; front, side and rear elevations; roof plan;
electrical layout and kitchen cabinet layout; and construction details.
Each set of blueprints include detailed documentation which fully describe the quality and specifications
of the materials needed to complete the building of your home. You can use your detailed blueprints to
get precise estimates of the total cost to build your home.
Blueprints are used to provide the builder with a complete set of two-dimensional instructions on
exactly how to construct the home. The most common sizes of blueprints for the construction of a new
home are 18" x 24" or 24" x 36"
Before the advent of computers, blueprints were drawn by hand on vellum (a semi-transparent film
which was specially processed and treated with ammonia), however, with the advances in computer
software the process of designing a floor plan have greatly improved and floor plans have now become
easier to create and duplicate. Now complete floor plans can be stored and printed just as easy as
printing this document from your computer.
We offer a wide selection of comprehensive and detailed blueprints in a wide assortment of house
styles, home plans and designs to fit any life style whether you are looking to remodel or build a new
17
home.
How to Read Blueprints
Scale:
Blueprint floor plans are typically drawn to a ¼" scale of the actual size of the home. This way the
builder will be able to scale the drawing of the home and come up with the correct measurement. As a
general accepted rule a ¼" scale means that for every ¼" on the plan will account for 1' of actual length.
Some details, like framing layouts or built-in details may be drawn at a scale of 1/8" or even ¾".
Any builder will know to look at the key provided on the house plan to determine the scale of the home.
Since the blueprints are drawn to scale if any portion needs to be changed or the contractor can scale the
drawing to determine the right measurements to make the adjustments. The scale of each drawing is
usually next to the title; however there are times when it is called out beneath the drawing or some other
place on the page.
Elevations:
Blueprints also generally include four elevation drawings of a home, the front, the rear and each side.
The purposes of these drawings are so that measurements can be taken for any necessary aspect and are
drawn to scale and also indicate what the home will look like upon completion. Elevation blueprints
also include ridge heights, exterior finishes, roof pitches and other design aspects to give a general idea
of the finished home. These exterior specifications can also provide details about the home's exterior
architectural styling.
Basement Floor Plan:
Basement floor plans (if provided) show how foundation and the structural integrity should be built.
These plans give further details about the location of footings, load bearing walls, steel rebar concrete
reinforcements, and other structural elements the home requires to support the walls and roof.
18
Electrical layouts:
Electrical diagrams (if provided) can often be difficult to read which is why the drawings of the
electrical layout of a home are often on a separate drawing. By keeping the electrical layout on it's own
drawing the electrician can begin wiring the home without reading through the entire building floor
plan. Electrical diagrams usually include legend or Key on the page which explains what each symbols
represents. From this diagram the electrician can determine the location of electrical outlets, fans,
fixtures, light fixtures etc. Electrical diagrams may also include legends for heating systems, door
swings and sizes, or even to specify certain finishes.
Framing Drawings:
Like every other drawings, the framing drawings (if provided) are also drawn to scale. Framing plans
include the basic skeletal structure of the home. Floor joist locations, walls, and roof trusses are the
overall detail of these plans. Generally locations of each stud are not included, due to a recognized
universal building code. However, in some cases there are instructions for particular wall construction
methods.
Plumbing and mechanical systems:
Since stock house plan blueprints are sold throughout the 50 states, regional preferences and climatic
variances dictate different mechanical systems and, as such, this information must be obtained locally.
Typically only plumbing fixture locations are provided, but this information is ample for the contractor
to install a plumbing system. However you may want to have the heating subcontractor provide a duct
and register layout for your review prior to construction. Your local utility company also may offer
various services to you in sizing a system for your new home.
Cross sections and details:
Overhead views or floor plan views of the structure provide detailed information about wall lengths and
room dimensions to do not fully provide enough information for successful construction of the home.
19
Therefore in most cases, a cross section of the home is included in a set of house plans. A cross section
of a home is drawing of the completed home as if it were sliced in half. This part of a home plan
provides the builder with an even better understanding the relativity of floor heights, rafter lengths
among other structural elements of the home.
Plot Plan:
A plot plans are comprehensive drawings of the site location or lot on which a new home is to be built.
Plot Plans are drawn to determine the placement of the home on the chosen building lot in reference to
the property boundaries, topography and house layout. Plot dimensions are normally recorded by a
surveyor, and are used to determine the exact location and positioning of the selected home in
relationship to the chosen lot. Plot plans will typically include the location of utility services, set back
requirements, easements; locations drive ways and walk ways. In some cases a topographical map may
be included that will supply the architect or builder with critical data on the slope and terrain of the lot
he or she is design a home for.
Since plot plans are prepared based on the exact size and dimensions of the house to be built and how it
will fit into a selected lot location they are not normally included in the purchase of stock floor plans,
however, plot plans can be drawn by a local professional draftsman, architect or engineer once a lot is
chosen.
20
Congruent Triangles
Learning Objective:
Students will determine that triangles are often used in the construction of bridges,
windmills, and other structures
Students will discover that triangles make for a strong base for constructions through
experimentation.
Students will analyze photographs of a bridge and a windmill and a plan for a flying machine,
identifying all congruent and similar triangles in each structure.
Students will design and build a bridge using congruent triangles
Time: 2 hours (to be broken into two class periods)
Materials:
Black and white pictures of windmill and bridge constructed out of triangles
Colored pencils, markers
Ruler
Protractor
Magnets- ball and rod type for each group (or straws)
Straws
Tape
Random items to test weight that the bridge can hold.
Warm Up: 10-15 minutes
Pass out pictures of the windmill and the bridge.
Using a ruler and protractor, have each student identify triangles by coloring in congruent
triangles and outlining similar triangles. They might want to use two different colors for this.
Go over all of the triangles they found in a class discussion.
New Information: 25 minutes
Separate students into pairs or small groups (2-3). Give each group a set of ball and rod
magnets with instructions to play around with constructions that are based on triangles and
some that do not have any triangles in their structure and to judge the strength of each
constructed figure based on how easy it is to crush/flatten/tilt the figure.
If magnets are not available, students could use straws to make constructions that use
triangles and polygons by tucking ends into ends and compare the strengths of the shapes by
trying to tilt and crush them.
21
Have a discussion on the experiment with the ball and rod magnets (or straws), in which the
strength of triangles should be the focus. Ask the class to identify where they may have
noticed triangles in construction before.
Experience! 15 minutes; 45 minutes
Day one- Have the students work in small groups to design the strongest bridge using only
straws and tape. They can draw plans, discuss building methods, and experiment with
shapes.
Day two- students will construct their bridge using only straws and tape. At the end of class,
each bridge will test its strength by seeing how much weight it can hold.
Allow time at the end of day 2 to test the weight capacity of the bridges. Bring a small prize
or privilege for the winning group, and display all of the bridges in the classroom for a week
or so.
Check for Understanding: ongoing
As students create their bridges, go around and make sure are grasping the task at hand. Be
prepared to assist them with ideas of how they might use the materials to create their
models.…
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity?
Generalize- have a short discussion about architecture. How much school does it require?
How much does an architect earn?
Independent Practice: Homework
Ask each student to research the use of triangles in construction. Have them bring in an
example of a triangle used in construction in their community. They could draw it, take a
picture of it with their cell phone, or write about it. This will connect what is learned in the
classroom to real life.
22
Windmill
Obtained from:
http://memory.loc.gov/cgibin/displayPhoto.pl?path=/award/nbhips/lca/145&topImages=14572r.jpg&topLinks=14572v.jpg&displayProfile=0&title=Livestock%20on%20the%20J
ames%20Gates%20ranch%20at%20Gates,%20Nebraska,%20%20showing%20Gates%20bridge%20on%20the%20Middle%20Loup%20River%20and%20T.J.%20Butcher's%20hom
e%20in%20the%20distance%20to%20the%20right.&m856s=$dnbhips$f14572&dir=ammem&itemLink=r?ammem/psbib:@field(DOCID+@lit(p14572))
23
Bridge
Obtained from:
http://memory.loc.gov/cgi-bin/query/I?cdn:1:./temp/~ammem_WhKg::displayType=1:m856sd=ichicdn:m856sf=n056530:@@@cd
24
Getting things “Right”
(Adapted from YouthBuild USA Working Hands, Working Minds Curriculum)
Learning Objective:
Students will be able to identify carpentry tools that create right angles.
Students will practice determining the squareness of a corner.
Students will practice making right angles with carpentry tools.
Time: 1 hour
Materials:
Sticky notes
Try Squares (1 for every 3-4 students)
Adjustable Squares (1 for every 3-4 students)
Rafter squares (1 for every 3-4 students)
T bevels (1 for every 3-4 students)
Rulers, yard sticks, measuring tape
Tape
Larger wood scraps
Handout: Getting Things Square
Handout: Determining the Squareness of a Corner
Warm Up: 10-15 minutes
Write on the board: ANGLE
Give students 5 minutes to write everything they know about angles on the sticky notes and
place them on the board around the word ANGLE.
Have a class discussion about what the students wrote- ensuring that you discuss important
concepts such as: what is a right angle, what does one look like, where are they in
construction? Why are right angles important in construction? What is a degree? How many
degrees are in a circle?
New Information: 15 minutes
Separate students into pairs or small groups (3-4). Give each group a set of tools that
measure right angles. If you don’t have the actual tools, print pictures of the tools you can’t
find. Ask the group to correctly identify the tools and determine their use on the worksite.
Hand out the worksheet: Getting Things Square” ask the students to complete the activities
in their groups. As a facilitator, ensure that everyone has an opportunity to handle each of
the tools.
Ask each group to report out on their experience. Revisit the questions asked previously:
identify the tools and determine the uses.
25
Experience! 20 minutes
Explain that while these tools are helpful, they are not necessary to determining the
squareness of something.
Pass out the handout: Determining the Squareness of a Corner”
Give each students group a variety of measuring devices, tape, and string. Assign each team a
corner in the classroom and ask them to use these materials to determine if these items are
square.
Make sure students record the process they choose and allow enough time for students to
share their process and their findings before the class is over.
Check for Understanding: ongoing
As students complete the activities, go around and make sure are grasping the task at hand.
Be prepared to assist them with ideas of how they might use the materials to accomplish
their tasks.…
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity?
Generalize- have a short discussion about architecture. How much school does it require?
How much does an architect earn?
Independent Practice: Homework
Ask each student to use what they learned today to determine if the angles in their homes are
square. Have them write a one page journal explaining their process, their discoveries, and
what they learned overall.
26
Getting Things Square
It is essential to get things square in construction. Getting something square means to form a right
angle. Pieces don’t fit correctly unless the angles are correct and pieces that don’t fit right weaken
the building’s structure.
A Square is a tool that carpenters use every day. They measure angles and check for right angles. To
use a square, simply lay it against a joint you are making to see if it is a true right angle, or lay one leg
of the square against an edge and the other leg of the square will give you the perpendicular to that
edge, allowing you to make square cuts, ect.
Try Square
A steel blade 6” to 12” long attached to a thick, squared off wooden or metal handle.
Adjustable Square
A Try Square with a 12” sliding blade that marks right angles on one side of the handle and 45
degrees on the other.
Rafter Square
A flat steel square. One leg is called a blade and it is 24” long and the other is called a tongue and is
16’ long.
T Bevel
This tool has an adjustable angle. The blade pivots on the handle and can be locked in any position.
It can be used to transfer any angle from one place to another. This can be used to line up repeat
angles and cuts. You can set an angle and copy it. This tool is used for rafters and cross braces.
Draw each tool in the boxes below:
Try Square Adjustable Square Rafter Square T Bevel
Try These:
Test the square of the edges of your wood scraps and other surfaces in the classroom
Draw lines perpendicular to the edge of a piece of wood for cutting
Use it to place a wood scrap perpendicular to another piece of wood
Check the squareness of a bookcase in your classroom to see if the weight of the books has
changed the angle of the shelves.
With a T Bevel, check the angle by lining it up with an existing angle of a piece of scrap
wood you’ve just set to mark another piece of wood to match the angle of the first piece.
27
Determining the Squareness of a Corner
We know this to be true:
In any true rectangle, the diagonal cuts the rectangle into 2 right triangles.
In any true rectangle, the two diagonals are equal in length.
If you lay out lines AB and BC perpendicular to the walls, and you find that AC and BD are
not equal, you’ll know that at least two of the corners are NOT square. Either you laid out
the lines wrong, or the room is not square.
Another way to check if two lines are perpendicular is to set a 3-4-5 triangle on them. Any
triangle with sides in that proportion (3-4-5) is a right triangle, with the 3 and 4 side
perpendicular.
Try this:
For each corner of the classroom, measure 4’ along the base of the floor.
Mark that point.
Measure 3’ up the wall along the inside corner.
Mark that point.
Now check to see if the distance between your first measurement and your second
measurement equals 5. If it is, then a right angle is formed by the juncture of the wall and the
floor.
Corner One Square Not Square
Corner Two Square Not Square
Corner Three Square Not Square
Corner Four Square Not Square
28
Pythagorean Theorem
Learning Objective:
Students will be able to use the Pythagorean Theorem to determine the squareness of a
corner
Students will identify how angles are used in construction.
Students will develop vocabulary with respect to geometric terms used in construction.
Time: 1 hour
Materials:
Handout: Geometric Terms in Construction
Paper, pencils, markers
Rulers, yard sticks, measuring tape
Framing square
Tape
String
Cork tiles
Thumbtacks/ pushpins
Scissors
Warm Up: 10 minutes
Distribute the worksheet: Geometric Terms in Construction
Allow time for students to work on this independently or in pairs.
Have a class discussion about terms- definitions, where are they in construction? Have you
heard these before?
New Information: 15 minutes
Separate students into pairs. Assign a term from the crossword puzzle to each of the groups.
Each group will create a reference handout that defines their assign geometric term that is
used in Construction.
Ask each group to report out on their experience. How was it to try to create a teaching tool
for someone else?
Collect the documents, bundle them together to create a reference packet. Use a copy
machine to create a copy for each student so they can use this as a reference later.
Experience! 20 minutes
Have students work in small groups of 3-4 students.
29
Give each group a set of materials. (measuring tape, ruler, yardstick, string, scissors,
pushpins)
Give the students the following instructions:
o Mark a long, straight line by stretching a piece of string between two pushpins
secured in the corkboard. This piece of string will not move; call this string the base.
o Attach an equal length of string to each pin, ensuring that these stings are a little
more than half as long as the first string. Call the strings the arc strings.
o Keeping the arc strings stretched tight, move the ends to draw arcs. The arcs will
touch each other at two points.
o Place a pushpin at each of the points where the arcs touch and connect the pins with
another piece of string. This string should create a right angle with the base string;
check this with your framing square.
o Make a sketch of what was created.
Make sure students record the process they choose and allow enough time for students to
share their process and their findings before the class is over.
Check for Understanding: ongoing
As students complete the activities, go around and make sure are grasping the task at hand.
Be prepared to assist them with ideas of how they might use the materials to accomplish
their tasks.…
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity? Did this help you see the
importance of right angles in construction?
Generalize- When would you use this technique in construction?
Independent Practice: Homework
Ask each student to create a GED type question with respect to the Pythagorean Theorem.
Show an example practice test GED question-
Oscar's dog house is shaped like a tent. The slanted
sides are both 5 feet long and the bottom of the house
is 6 feet across. What is the height of his dog house, in
feet, at its tallest point?
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Geometric terms used in Construction
1
2 3
4
5
6 7
8
9
10
ACROSS DOWN
1 Two lines that are the same distance 1 Describe two lines that meet to form a
apart at all times. right angle.
4 A true vertical. 2 Top.
6 Even with the surface. 3 On the other side.
8 Straight up and down; the opposite of 5 Forming a right angle.
horizontal. 7 Even with the Earth's surface.
9 A true horizontal.
10 Another word for a 90 degree angle.
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Geometric terms used in Construction
(Solution)
P A R A L L E L
E
R S O
P L U M B P
E R P S
N F L U S H O Q
D A O S U
I C V E R T I C A L
C E I T R
U Z E E
L E V E L O
A N
R I G H T T
A
L
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Perimeter in Construction
(Adapted from YouthBuild USA Working Hands, Working Minds Curriculum)
Learning Objective:
Students will develop a formula for finding perimeter.
Students will find the perimeter of a rectangle and different figures.
Students will solve problems using perimeter.
Time: 1 hour
Materials:
Tape measures
Several balls of yarn (one color for each group)
Masking tape
Scissors
Optional: Candy or small prize for the winning team
Handout: Finding perimeter: Real Objects
Handout: Finding perimeter: Problems
Warm Up: 10 minutes
Challenge! Suppose you were asked to install new baseboard around the base of the walls of
this classroom. How would you know how much baseboard to buy?
Have students THINK-PAIR-SHARE and record the best strategies on the board.
Have a class discussion about the strategies. Make sure to work in a discussion about
doorways, heating structures, and cabinets, or anywhere you might need to subtract length.
New Information: 20 minutes
Separate students into groups of 3.
Distribute paper, pencils, and tape measures.
Have the students sketch a quick blueprint of the room. They can use the tape measures to
find the measurements of baseboard they would need.
Have the students record their measurements on their drawing.
Experience! 20 minutes
Have students calculate the total amount of baseboard needed, and have them write the total
on the back of their blueprint.
Once the students have finished this, give them the EXACT amount of “baseboard” they
calculated they would need. The baseboard for this activity will be yarn. Use a different color
for each group.
Give each group a pair of scissors and masking tape.
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Have each group carefully tape their yarn around the room. When they come to a doorway
or other obstruction, they should cut their yarn and continue on the other side.
The team who comes closest to the perimeter wins.
Make sure students record the process they choose and allow enough time for students to
share their process and their findings before the class is over.
o Answers might include:
we measured each side (S+S+S+S)
We measured the length first and then the width (L+L+W+W)
We multiplied the length and the width by 2 and added them together
(2L+2W)
Distribute handouts Finding Perimeter: Real Objects and Finding Perimeter: Problems
Have the students work individually toward completing these worksheets.
Check for Understanding: ongoing
As students complete the worksheets, go around and make sure are grasping the task at
hand. Be prepared to assist them with ideas of how they might use the materials to
accomplish their tasks.…
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity? Did this help you see the
importance of right angles in construction?
Generalize- When would you use this technique in construction?
Independent Practice: Homework
Ask each student to create a practice question with respect to the Perimeter. Solve them as a
class.
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Finding Perimeter: Real Objects
Find the perimeter of 7 different objects in our classroom. First measure the length, then the width.
Then use the following formula to write an equation. Solve the equation.
For Rectangles: 2(L) + 2(W) = perimeter
For non-rectangles: S+S+S+S= perimeter
1. Object A is: This page
Its length is: 11 inches. Its width is: 8 ½ inches.
Equation: 2(11) + 2(8 ½) = 22 + 17 = 39 inches
2. Object B is:
Its length is: Its width is:
Equation:
3. Object C is:
Its length is: Its width is:
Equation:
4. Object D is:
Its length is: Its width is:
Equation:
5. Object E is:
Its length is: Its width is:
Equation:
6. Object F is:
Its length is: Its width is:
Equation:
7. Object G is:
Its length is: Its width is:
Equation:
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Finding Perimeter: Problems
1. How much fence material must a landscaper use to surround an area that is in the shape of a
square 18 yards on each side?
2. Allowing three feet for door space, how much baseboard would a carpenter need to enclose
a square room that measures 12 feet on each wall?
3. Subtracting 2’11” for a door space, how much baseboard would be needed to go around a
rectangular room that measures 11’5” X 11’7”?
4. A store has windows in the shape of triangles. How much molding is needed to enclose four
windows is a window measures 1’9” on each side?
5. A triangle has sides which measure 10 inches. Allowing three extra inches for each corner,
figure how much molding would be needed to enclose it.
6. How much fencing would be needed to enclose a garden that is shaped like a trapezoid if the
sides measures 40 feet, 38 feet, 35 feet, and 31 feet?
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Area in Construction
(Adapted from YouthBuild USA Working Hands, Working Minds Curriculum)
Learning Objective:
Students will define and develop a formula for finding Area.
Students will find area through discovery.
Students will define square root.
Students will solve problems using area.
Time: 1 hour
Materials:
Square foot tiles
One inch graph paper
Sidewalk chalk
Measuring tapes
Handout: Finding Area
Handout: Practice with Area
Handout series You are the Contractor I, II, III
Warm Up: 10 minutes
Challenge! Hold up a square foot tile. Ask the students: If you needed to cover the floor in
tile, how would you figure out how many tiles to buy?
Have students THINK-PAIR-SHARE and record the best strategies on the board.
Have a class discussion about the strategies. Make sure to work in a discussion about any
obstructions where you might need to consider subtracting or adding length.
New Information: 10 minutes
Have the students figure out the answer by laying out tiles or by measuring with a tape.
Ask:
o How many rows of square foot tiles would be needed to cover the floor?
As a class, draw a picture on the graph paper of a room with the measurements of the
classroom. Have them draw with you. Ask questions such as:
o How many tiles should be represented as the length of the room?
o How many rows are there?
Once you have made the drawing with measurements drawn to scale, each one inch box
depicting a square foot, ask students to figure out how many squares there are in the picture.
If they don’t suggest this themselves, ask them to count the number of squares.
After they have finished counting, ask if there might be another way to find how many
squares are in the picture. Show them you can add the number in each row as many times as
there are rows; write the number next to each row to show how this might be done.
Continue asking until you arrive to the following formula as a class:
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o Length X Width = Area
Experience! 30 minutes
Have students complete the worksheets “Finding Area” and “Practice with Area” (needs to
be completed outside).
When finished, have a class discussion and go over answers together.
Check for Understanding: ongoing
As students complete the worksheets, go around and make sure are grasping the task at
hand. Be prepared to assist them with ideas of how they might use the materials to
accomplish their tasks.…
Debrief: 10 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity? Did this help you see the
importance of area in construction? Could you teach someone else this concept?
Generalize- When would you use this technique in construction?
Independent Practice: Homework
Have each student complete the “You are the Contractor Series I II III”
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Finding Area
Find the Area of 7 different objects in our classroom. First measure the length, then the width. Then
use the following formula to write an equation. Solve the equation.
For Rectangles: (L) X (W) = area
For non-rectangles: varies
1. Object A is: This page
Its length is: 11 inches. Its width is: 8 ½ inches.
Equation: 11 x 8.5= 93.5 square inches
2. Object B is:
Its length is: Its width is:
Equation:
3. Object C is:
Its length is: Its width is:
Equation:
4. Object D is:
Its length is: Its width is:
Equation:
5. Object E is:
Its length is: Its width is:
Equation:
6. Object F is:
Its length is: Its width is:
Equation:
7. Object G is:
Its length is: Its width is:
Equation:
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Practice with Area
Use sidewalk chalk to draw the following:
1. Draw a rectangle (not to scale) with an area of 30 sq ft, and a length of 10 feet. Label the sides.
2. Draw a square with an area of 36 feet. Label the sides.
3. Draw a square with an area of 25 feet. Label the sides.
4. Draw two different rectangles, both with areas of 36 sq ft, but with different lengths and widths.
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YOU be the Contractor I
You are contracted to install carpet in a living room.
The room is 12 feet wide and 15 feet long.
A closet in the room is three feet wide and three feet deep.
How many square yards of carpet are needed to cover the floor and closet? (1 sq yd = 9 sq ft)
Carpet costs $7.59 per square yard.
You charge your client $11.00 an hour for labor and delivery.
You estimate the job will take four hours
What are your total costs for this job?
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YOU be the Contractor II
You are contracted to install tiles on a basement floor.
The floor is 55 feet long and 22 feet wide
Tiles cost $2.00 a dozen
Glue costs $8.95 a gallon; you estimate that you will need two gallons
Your charge your client $9.00 an hour for labor and delivery.
You estimate the job will take six hours.
How many square foot tiles will be needed to cover the floor?
What will be your total costs for this job?
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YOU be the Contractor III
You are contracted to lay a plywood subflooring in two rooms in a new house.
The living room measures 16’ x 12’
The dining room measures 12’ x 12’
Plywood is in 4 x 8 sheets
Plywood costs $12.00 a sheet
You charge your client $11.00 an hour for labor.
You estimate the job will take four hours.
How many sheets of plywood will you need?
What will be your total costs for this job?
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Word Problems in Construction
Learning Objective:
Students will use the skills they have developed to answer construction related word
problems through a Jeopardy style game via power point. (included in packet)
Time: 1 hour
Materials:
Jeopardy Game (On CD)
Computers
Projector
Buzzers for each group.
Warm Up: 5 minutes
Challenge! What have we learned so far?
Have students write everything they have covered so far on one of the board. When
finished, review their answers, fill in anything they might have missed, and celebrate your
accomplishments so far.
Experience! 45 minutes
Have students separate into groups.
One group will begin by selecting a category and a dollar amount.
Click on the dollar amount.
A question will appear on the screen.
The first group to buzz may answer the question.
If the question is answered correctly, they earn the dollar amount on the screen
If the question is answered incorrectly, they lose that dollar amount and another team can
steal.
The team that earns the most money wins the game.
Debrief: 5 minutes
Report- What happened?
Analyze- Was it enjoyable? What was difficult about this activity? Did this help you see the
importance of word problems?
Generalize- When would you use word problems in construction?
44
Bringing it all Together
(Adapted from YouthBuild USA Working Hands, Working Minds Curriculum)
Learning Objective:
Students will collaboratively design a functional piece of furniture
Students will draw their designs to scale
Students will estimate and authenticate expenses
Students will draft a budget
Students will present their final product
Time: 2-3 hours/class periods
Materials:
Rulers
Graph paper
Beginning Carpentry books/ Computer access for research
Furniture ads from news paper
Building material ads from newspaper
White paper
Phone books and telephones
Handout: Budgeting costs/ Estimating Expenses
Handout: Budget Reflection
Warm Up: 10 minutes
Tell the students that today they will work in teams to design an entertainment center. They
will use all of the skills they have been building over the course of the term.
Challenge! Ask the students to think about all the belongings they have at home and to
brainstorm a list of these together. They might include items such as: television, DVD
player, books, pictures, trophies, stereo equipment, game consoles, ect..
Have the students take a few minutes to create a quick sketch of a design that might best
hold all of these things.
Allow volunteers to share their designs.
New Information: 40+ minutes
Arrange students in groups of three or four. Be creative when making groups. Make sure the
student’s skills are complementary, but different. It would be a shame to have all of the
strong drawers in one group, right?
Inform students that they must work together to incorporate their individual ideas into one
design for an entertainment center.
Students must initially complete the following (there will :
o A sketch of their group’s design along with measurements
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o A rationale that explains the design features
o A brief presentation to share with the class.
Allow the students at least 20 minutes to look through carpentry books, newspaper article,
or use the internet to research ideas.
Check for Understanding 30 minutes
Have each team share their final design with the large group.
Ask each group presents, ask the students questions such as:
o How well did your group work together?
o Was everyone able to share their perspective?
o Was it difficult to let go of a design feature the group didn’t agree to? How did you
deal with that?
o What do you think is the best feature of the design?
o Do you think it will be difficult to actually construct your entertainment center?
o What techniques would you need to use?
o What math skills did you use?
Experience! 30 minutes
Have students individually create a scale drawing of their design using graph paper and rulers
Talk about scale and ask each student to select the scale they are drawing in and create a key
on their drawing. (1 inch= I foot)
Present drawings to the large group.
Have a discussion about the importance of measuring accurately. Poor measurement can
lead to:
o Unsafe structures
o Pieces that don’t fit together
o Waste of product
o Loss of money
o Slow process- work needs to be checked often
Experience! 40 minutes
Have students rejoin their teams again. Pass out builder supply ads and the Estimating Costs
handouts to each group.
Lead a group discussion with students about estimating the cost of building their
entertainment center.
Ask students:
o How much do you think it will cost to build your entertainment center?
o What type of wood will you use? How much wood will it take?
o What other materials will you need? How much of each?
o What type of finish will your entertainment center have? (paint, stain, varnish) How
much will you need?
Have students use the Estimating Costs worksheet and work in their teams to brainstorm a
list of materials they will need to build their entertainment center.
46
Pass out Budget Worksheet to each group. Have them use the worksheet and phone books
to contact three building supply stores to get quotes for their materials.
Have a group discussion about phone etiquette.
o Where in the phonebook can you find building supply stores?
o How should you introduce yourself?
o What questions should you ask?
o How can we ensure we are not all calling the same place?
Have students complete the budget reflection worksheet and convert findings into fractions
and percentages. Discuss the students’ answers.
o What centers did you find to be the cheapest? What deals did different groups find?
o Were your costs close to your findings? Were you surprised by the actual costs?
o Why were there differences?
o What changes could you make to your design to bring down the cost of your
project?
Debrief: 30 minutes
Report- Have groups present their individual findings to the group.
Analyze- Have students reflect on the activity. Was it enjoyable? What was difficult about
this activity? Who has the most reasonably priced entertainment center? Who had a center
that is easiest to build?
Generalize- You did a lot in this activity: designing, estimating, budgeting, converting
measurements and numbers, gathering and presenting information, and participating on a
team. Is there one skill that you enjoyed using more than others? What jobs exist that
employ this skill?
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Estimating Costs
Material Needed Size needed Number needed Estimated Cost Per Item Estimated total cost
Total
48
Budgeting Costs
Material Needed Number Store #1 Store #1 Store #2 Store #2 Store #3 Store #3
needed Price per item Total costs Price per item Total costs Price per item Total costs
Totals:
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Budget Reflection
1. List your three total bids here:
a. __________________________________
b. __________________________________
c. __________________________________
2. What is the difference between the highest bid and the lowest bid?
3. Your lowest bid is what percentage less than your highest bid?
4. If the manager of the store with the highest bid offers you a 10% discount on all
materials, would the discount make that store the most economical for this project?
With the 10% discount, what would your new total be?
5. If the manager of the store with the highest bid were to cut your cost by 1/5, how
much would you save? Would this discount make this store the most economical for
your project?
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6. There is a sales tax of 7% on the materials you want to purchase. Add this cost to
each of your bids. What are your total costs at each of the stores with the sales tax
added on?
Bid total #1____________________+ 7% sales tax________________=____________
Bid total #2____________________+ 7% sales tax________________=____________
Bid total #3____________________+ 7% sales tax________________=____________
7.
a. What item on your materials list costs the most? What percentage of your
total cost is this item?
b. Estimate the fraction of your total costs is spent on this item.
c. What could you do to lower the cost of this item?
8. Draw a pie chart of the breakdown of costs for each material.
9. If you were to travel to all three supply centers or stores, purchasing the lowest priced
materials at each store, would you save money on your total cost? How much?
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Budget Reflection: facilitator resource
1. List your three total bids here:
a. __________________________________
b. __________________________________
c. __________________________________
2. What is the difference between the highest bid and the lowest bid?
The difference = highest bid – lowest bid
3. Your lowest bid is what percentage less than your highest bid?
Since the highest total less 10% is equivalent to 0.9 times the highest bid, you can
give your students the following formula: (0.9 x highest bid)- lowest bid. If the
resulting number is greater than zero, the discount did not make the store the most
economical. If the resulting number is less than zero, then this did make it the
cheapest. If the resulting number is zero, then the discount made it equal to the
lower amount.
4. If the manager of the store with the highest bid offers you a 10% discount on all
materials, would the discount make that store the most economical for this project?
With the 10% discount, what would your new total be?
Amount saved= 1/5 x highest bid.
At this point, if desired, you can review multiplying fractions. Will this discount
make this store the cheapest? Since the bid with a 1/5 discount is 4/5 x highest bid,
to answer this question you may use the formula: (4/5 x highest bid)-lowest bid.
5. If the manager of the store with the highest bid were to cut your cost by 1/5, how
much would you save? Would this discount make this store the most economical for
your project?
Percentage of total costs = cost of (most expensive) item divided by total cost.
This number can then be converted into a percentage.
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