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Tips for Using Project-Based Learning to Teach Math Standards

Andrew Miller

Instructional Coach at Shanghai American School
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Editor's Note: Andrew Miller is a consultant for the Buck Institute for Education, an organization that specializes in project-based curriculum. He also creates curriculum and instruction at Giant Campus, which seeks to create 21st century learners using PBL in an online environment.

Let's be honest. Designing PBL for Math can be a different beast. With the pressure of high-stakes testing and a packed curriculum, I often coach teachers who are nervous about giving time to a robust PBL project. In addition, because of the plethora of math standards, it can be difficult to choose the right learning target(s) for the project. Here are some tips for teachers designing individual Math PBL projects.

Reframe the term "Real Life" Math

Many standards include the idea of applying math to real life. We all want this as teachers. We want our students to not only see the connection in math to real life, but also to explore them. Below is an example from the Math Common Core Standards.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions and decimals) using tools strategically. Apply properties of operations to calculate with numbers in any form; fonvert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

4. Use variables to represent quantities in a real-world or mathematical proble, and construct simple equations and inequalities to solve problems by reasoning about the quantities

There are many more standards like this throughout the Common Core that related to "real life" math. This is a great place to start, but we can do better.  I think the real potential lies in the redefining the word "problem." I think this term has been sampled over the years. When you say "math problem" we often envision an equation, whether that be word or simple calculation to solve. Couldn't it be more? What if the problem was that we need to find the most cost effective design for a classroom, given materials and certain parameters? What if the problem were to predict what would happen if the oil spill in the Gulf had not been stopped, and using this information to convince policy makers to make changes in environmental protections? What if the problem was to create a salary schedule for the student store to reward hard workers while still keeping a profit? These are the types of ideas teachers need to be having when thinking about the word "problem" in math. The old definition of the word "problem" is not rigorous. Redefining the word "problem" within the frame of Project-Based Learning is rigorous, and still demands real world connections in an authentic way.

Pick or Make the Appropriate Time

I know the structures in place for Math teachers. Sometimes there is not enough time for a project. Sometimes, it's just not the best use of time. If a standard needs to be covered in a short week unit, then it isn't the best place for a project. However, if there is a 3-week unit coming up around a specific math learning target, this would be a great opportunity to create a project. There is time and space for you the teacher to get your "feet wet" in implementing the project. In addition, you might be able to combine the learning targets in a project that seem to fit together. Your allow time increases and you can have students create products that demonstrate learning of both targets or standards. As a teacher, be creative with the time you have, either in looking for the best opportunity or creating an opportunity.

Pick a Standard with Easy Real-Life Application

"Don't try to fit a square peg through a round hole." Sometimes you can try too hard to make a PBL project align to a math standard. Some are easier than others to align. Pick standards that you know or have seen used in real life. If you are unsure, ask you colleagues. I like to say, "The Wisdom is in the room." I'm sure your colleagues, whether it be math teachers or CTE teachers have some great ideas. Pick standards that clearly can have a practical purpose in analyzing a problem and/or design a solution to that problem. It is much easier to teach Right angle triangles, number sense, or graphing in a PBL project that it is factoring. (PS: I would love to hear from any teachers who have managed to create a PBL project from a seemingly difficult math standard. You rock!)

As teachers, we always have structure and forces as work, from the federal to the school level. Curriculum and Instruction can be a challenging place to navigate in these structures, especially where the curriculum and pedagogy is counter-paradigm to the traditional. I encourage teachers Math teachers specifically to give PBL a shot, regardless of the structures. Hopefully, these tips give you some strategies and comfort you enough to implement Math PBL projects in their classroom. Feel free to steal ideas from the Buck Institute for Education's Project Search, but make it your own. Remember, if we want our students to really wrestle with rigorous math concepts, then we must create space and environment for this work to happen.

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Matthew Sears's picture
Matthew Sears
Program Director at NC New Schools Project


I'm a HUGE PBL advocate, taught wall-to-wall math PBL for 3+ years, and want all math teachers to read this post and take your advice. However, I'm afraid that your remark...

  • "Pick standards that you know or have seen used in real life. If you are unsure, ask you colleagues. I like to say, "The Wisdom is in the room." I'm sure your colleagues, whether it be math teachers or CTE teachers have some great ideas. Pick standards that clearly can have a practical purpose in analyzing a problem and/or design a solution to that problem."

...doesn't necessarily leave teachers with enough information to get started if they are feeling lost or their colleagues aren't able to help. And I don't want to make the case here, but there is evidence that many teachers don't necessarily have the content knowledge or real-world experience to draw upon for project creation.

I'd like to propose a strategy that I used when I found it difficult to find connections in designing math PBL experiences: Dust off that old technology, the TEXTBOOK, and look at those "Challenge Problems" that have all of the stars next to them at the end of problem sets. Some very smart people have put a lot of time into those little nuggets and they can serve as seeds for quality projects.

Case in point: In fall 2007, as a rookie PBL teacher, I was looking to design a project that taught exponential equations in Algebra 2. I came across a problem in the back of section that was asking student to calculate the "Apparent Magnitude" (A.M.) of different objects in the night's sky (A.M. is how bright objects seem to us from a distance). Not understanding the topic myself, I dove deep to learn that A.M. works with distance and luminosity (actual brightness) in an exponential fashion (see and That exploration, and a conversation with a physics teacher friend (your recommendation), led to a project where students designed space goggles, using two polarized lenses that could adjust to different brightnesses, for astronauts to use when visiting other (and far brighter) solar systems. A video of that project presentations can be seen here:

I like this strategy paired with your advice for several reasons:

  1. Textbooks are already in the hands of teachers and bring the thoughts of many scholars who authored the books
  2. Looking in depth at one example will often present logical connections to other topics we must teach--in this case I had to also bring in logarithms to help students solve the exponential equations. Talk about a great feeling...students asking ME to show them how logarithms could be useful in their work.
  3. There are these "challenge problems" in nearly every section of a course (granted they are of varying quality)

Just thought I'd share what has worked for me. Thanks for the great post, Andrew. I agree whole-heartedly that, "Designing PBL for Math can be a different beast." And while so many teachers/schools are hungry for math PBL, there are too few resources available.

Best regards,


Michael Paul Goldenberg's picture
Michael Paul Goldenberg
mathematics coach

Is it REALLY necessary to kow-tow to bad ideas like the Common Core and its many bastard off-spring (coming soon to a nation near you)? You've got some nice points to make about PBL. Why sully them with the "standardista" stuff?

Andrew Miller's picture
Andrew Miller
Instructional Coach at Shanghai American School

Matthew, thank you for your help in pointing teachers to specific places to look for those learning targets that will work for them. You suggestions are insightful and useful! I appreciate it. As I'm sure you know, my focus is on multiple tips, so I appreciate that you could go in depth on ones I articulated.

Michael, I share your hesitancy about Standards Based Instruction. It does have its pitfalls. In fact, one of my favorite books is Beyond Standards, by Carol Jago, current NCTE president. She goes in depth on many of these pitfalls I'm sure you have experienced. I believe in Standards Based Instruction, as long as those pitfalls are avoided.
However, my audience is teachers. Standards, both state and common core, are part of the teacher world and reality. Teachers are addressing and targeting specific standards in order to increase student performance. PBL can be challenging when it comes to aligning standards, but it can be done. I want teachers to feel confident that what they are designing to targeted standards and that PBL can help students learn them. PBL is standards based, and thus their needs to be support for teachers around this.

Thanks for the feedback and comments!

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