ALGEBRA IN ACTION
BY: THE WHIZ KIDS
Joel Bradshaw
Tracey Guida
Nina Mun
Nancy Scott
Steve Weitlich
WHY ALGEBRA IN ACTION?
How we see math word problems:
If you have 4 pencils and I have 7 apples,
how many pancakes will fit on the roof?
Purple, because aliens don’t wear hats.
BRIDGE DESIGN PROBLEM
1. Design a truss bridge (Warren, Howe, or Pratt) with the following
specifications:
Span = 102 cm
Width = 11.5 cm (# 3)
Vertical and Horizontal Beams = 17 cm (# 4)
Diagonal Beams = 24 cm (#5)
2. How many joints, vertical and horizontal beams, and diagonal beams will
be used in your design?
3. Sketch your design.
4. Build your bridge.
BRIDGE DESIGN: PRATT
Externally Applied Force, F
A
B
D
F
H
J
C
E
G
I
K
Using PASCO Bridge Set:
L = 17 cm = 0.17 m
h = 17 cm = 0.17 m
a = 24 cm = 0.24 m
L
a
h
L
FREE-BODY DIAGRAM (FBD)
Externally Applied Force, F
A
RA
B
D
F
H
J
C
E
G
I
K
L
RL
Find the reaction forces at A and L, RA and RL, respectively by
applying the equilibrium equations:
 F = 0 and  M = 0
METHOD OF JOINTS
Use the Method of Joints to analyze
each beam in terms of:
The magnitude of internal force
Whether the force is in compression or tension
Use symmetry and analyze only ½ of
the truss.
ANALYSIS OF JOINT A
y
FBD of Joint A
x
A
FAB
 Fy = 0
RA – FAC
h
a
FAC = RA
a
h
=0
a
h
L
RA
FAC
For the internal force in member AC
resolved into rectangular component forces:
 Fx = 0
- FAB + FAC
FAB = RA
L
a
=0
METHOD OF JOINTS: ANALYSIS RESULTS
Externally Applied Force, F
A
C
B
D
C
T
T
RA
C
C
C
F
C
T
E
C
H
C
T
G
C
J
C
C
T
I
L
T
K
Tension: T
Compression: C
RL
BUCKLING FORCE, FBUCKLING
FEF = RA
=
a
h
Fbuckling
4
Fbuckling
=
=
F
4
=
0.01016 m
a
h
a
h
4h FEF
a
4h 2EI
0.01016 m
=
4h
a3
Fbuckling = 769 N
(2EI)
a (a2)
0.006756 m
0.00254 m
E = 2.29 x 109 N/m2
I = 6.92 x 10-10 m4
Taking a safety factor of 2, the resulting
maximum load is 384.5 N or a load mass of
39 kg.
TESTING THE BRIDGE
5. Place your load in the middle of the
bridge. Analyze the joint at the support.
 Why should you begin your analysis with
this joint?
 Analyze the load distribution throughout
the truss including the magnitude of an
internal force and whether it is in tension
or compression.
6. Now, change the location of your load.
What happens to the load distribution?
Does it change?
HOW CAN WE USE THIS IN OUR
CLASSROOMS?
 Discussion Questions on Bridges
 Intro: The following diagram is a picture of a Warren Truss Bridge. The
bridge is comprised of horizontal, vertical, and diagonal beams. Each of
the beams are connected using a joint. Note: the horizontal and vertical
beams are the same length.
CLASSROOM USE CONTINUED.
 1. Use the picture above:
 A. How many horizontal deck beams on the bottom chord are there?
 2. Determine how many horizontal beams will be required to
construct the bottom chord of the bridge in the following
situations.
 A. Span of the bridge is 170 cm. The length of the beam is 17 cm.
 B. Span of the bridge is 24 m. The length of the beam is 4 m.
 C. Span of the bridge is 4km. The length of the beam is 5m.
 D. How are your answers in problems 1a and 2a related?
 E. Span of the bridge is S. The length of the horizontal beam is L.
RESEARCH BASED APPROACH
• Based on the idea of “Pattern
Tasks” by Margaret Smith
• Develops students’ algebraic
reasoning
• Begins with observing a pattern
from a picture
• The pattern is used for concrete
problems
• Students connect patterns to
algebraic equations
• Allows multiple representations
MAZE DESIGN PROBLEM
Design a shipping terminal with the following specifications. Your goal is to
maximize the number of storage containers in the container storage area.
 Total Area for the Shipping





Terminal: 20,000 ft2
Container Storage Area: 75% of
the total terminal area.
Loading and Unloading Area:
10% of the total terminal area.
Administration Area: equivalent
to 50% of the loading and unloading
area.
Rail and Trucking Space: 7% of
the terminal area.
Repair and Maintenance Area:
(to be determined by you!)
Specifications for the Container Storage Area:
The container storage area is comprised of containers
and pathways around the container.
The dimensions of a standard storage container are
8 ft x 20 ft.
Each container must have a pathway on at least 2 sides.
Pathways must be 8 ft wide.
THE MATH
Total Area for the Shipping Terminal: 20,000 ft2
Container Storage Area: 15,000 ft2
Loading and Unloading Area: 2,000 ft2
Administration Area: 1,000 ft2
Rail and Trucking Space: 1,400 ft2
Repair and Maintenance Area: 600 ft2
Maximum Capacity: 33.48 storage units.
Interpret this and incorporate it into design.
Pertinent Variables: Amount of pathway around container,
design, and layout
HOW CAN WE USE THIS IN OUR
CLASSROOMS?
 Apply system analysis method of problem solving
 Introduce in early education
 Generic approach to setting up problems by
 Define system
 Draw a picture
 Identify variables
 Identify independent equations
 Identify given information
 Solve literal equations
 Plug in numbers
HOW CAN WE USE THIS IN OUR
CLASSROOMS?
You are going to design a rectangular garden. The area of the
garden is 100 ft2. The perimeter of the garden is 80ft. The length of
the garden 2 times more than the width. Find the dimensions of
the garden.
 System: Rectangular Garden
 Variables: Area (A), Perimeter (P), Length (l), Width (w)
 Independent Equations: A = l*w
P = 2l + 2w
 Given Information: A = 100 ft2, P = 80 ft.
l = 2w
 Solve Literal Equations: l2 – (lp)/2 + A = 0
 Plug in your numbers!
CONCLUSION
 Problems are easily adaptable for any age
 More scaffolding for lower levels
 More variables and difficult math for higher levels
 If we introduce system analysis at a young age, they will
be better prepared for their STEM careers in the
future