This document compares and contrasts project-based learning (PBL) and problem-based learning (PrBL). It provides examples of how each could be used to address common core math standards involving geometry, modeling, and three-dimensional shapes. For a final project, PBL could involve designing a new high school building within constraints, while PrBL could involve determining the most economical packaging system for cans. Both approaches incorporate 21st century skills like communication, collaboration, critical thinking, and creativity.

1. Active
learning
A Closer Look at the Two PBL’s
By Carolyn Fisher
September 8, 2013
Project - Based
Learning (PBL)
Problem Based
Learning (PrBL)

2. Comparison provided by Emergent Math, 2012 (see reference list at end of presentation for full citation).

3. ACTIVE
LEARNING
Comparison provided by Emergent Math, 2012 (see reference list at end of presentation for full citation).

4. Consider an emphasis in the NEW common core math
standards: “Extending to Three Dimensions”
G.GMD.3 Use volume formulas for cylinders,
pyramids, cones, and spheres to solve problems.
G.GMD.4 Identify the shapes of two-dimensional
cross-sections of three-dimensional objects . . .
real-life
An example for a high school geometry class

5. An example for a high school geometry class
Another huge emphasis in the NEW common core
standards: MATHEMATICAL MODELING
G.MG.3 Apply geometric methods to solve design
problems (e.g., designing an object or structure to
satisfy physical constraints or minimize cost; working
with typographic grid systems based on ratios).

6. How could a teacher address these standards?
Have students design a new high
school for the year 2015 that
maximizes learning spaces and
opportunities within given physical
and monetary constraints (ie: consider
both land and money available in
terms of layout and design).
Project - Based
Learning (PBL)
Using . . .
Reference:
Elizabeth, 2013

7. How could a teacher address these standards?
Problem Based
Learning (PrBL)
Have students determine the best
packaging system for 12 cans of pop so
as to minimize wasted space (volume)
and minimize amount of cardboard
needed (surface area). Is the system
currently used the most economical?
Why or why not?
U
sing
Reference:
Piccini, 2012

8. What might a FINAL PROJECT look like?
Project - Based
Learning (PBL)
Using . . .
ave students design a new high school
the year 2015 that maximizes learning
aces and opportunities within given
ysical and monetary constraints (ie:
nsider both land and money available
terms of layout and design).
• Detailed blueprint and site-map
• Scale model of at least 1 room
- student choice of building materials
• Total cost estimation of project
- student research required
• Presentation of proposal to a panel of
architects in the community

9. What might a FINAL PROJECT look like?
Problem Based
Learning (PrBL)
Have students determine the best
packaging system for 12 cans of pop so as to
minimize wasted space (volume) and
minimize amount of cardboard needed
(surface area). Is the system currently
used the most economical? Why or why
not?
• Presentation of solution to class with
mathematical explanation
- OR -
• Letter to a pop company either
supporting or disagreeing with their
current method of packaging pop complete
with a mathematical explanation for
their reasoning
U
sing

10. Project - Based
Learning (PBL)
Using . . .
ave students design a new high school
the year 2015 that maximizes learning
aces and opportunities within given
ysical and monetary constraints (ie:
nsider both land and money available
terms of layout and design).
• Detailed blueprint and site-map
• Scale model of at least 1 room
- student choice of building materials
• Total cost estimation of project
- student research required
• Presentation of proposal to a panel of
architects in the community
What 21st century skills are included when . . .
Communication
(plan & present)
Critical Thinking (design)
Creativity (create)
Collaboration
(research & analysis)

11. What might a FINAL PROJECT look like?
Problem Based
Learning (PrBL)
Have students determine the best
packaging system for 12 cans of pop so as to
minimize wasted space (volume) and
minimize amount of cardboard needed
(surface area). Is the system currently
used the most economical? Why or why
not?
• Presentation of solution to class with
mathematical explanation
- OR -
• Letter to a pop company either
supporting or disagreeing with their
current method of packaging pop complete
with a mathematical explanation for
their reasoning
U
sing
Collaboration
(compare with peers)
Communication (plan
& present)
Creativity (build it or draw it)
Critical Thinking (explore all solutions)
What 21st century skills are included when . . .

12. What 21st century skills are included when . . .
Problem Based
Learning (PrBL)
U
sing
Project - Based
Learning (PBL)
Using . . . - OR -
The 4 C’s of
21st Century Learning
Communicaton
Collbaboration
Critical thinking
Creativity
f
Problem solving

13. References used in this presentation
Elizabeth, C. (2013, Jan. 28). Example of PBL in the geometry classroom:
Architecture & geometry. [Video file]. Retrieved from
http://zlockmath.blogspot.com/2013/01/example-of-pbl-in-geometry-classroom.html
Emergent math. (2012, May 24). “Isn’t Problem Based Learning easier than Project
Based Learning?” and 10 other myths about PrBL. (“Real or not real”). [Web log
comment]. Retrieved from http://emergentmath.co
m/2012/05/24/isnt-problem-based-learning-easier-than-project-based-learning-and-10-
other-myths-about-prbl-real-or-not-real/
Piccini, T. (2012, Feb. 4). 3 Acts - Pop box design. [Web log comment]. Retrieved
from http://mrpiccmath.weebly.com/1/post/2012/02/3-acts-pop-box-design.html