I remember the first time I saw a set of pam harris problem strings in action, and honestly, it felt like a lightbulb finally clicked for my students. If you've spent any time in a math classroom, you know that glazed-over look kids get when you start talking about "carrying the one" or "flipping and multiplying." It's that moment where they stop thinking and start trying to memorize a recipe they don't really understand. But when you switch things up and start using strings, that whole vibe changes.
The thing about math that many of us grew up with is that it felt like a series of disconnected rules. You did the long division, you got the answer, you moved on. But Pam Harris has this incredible philosophy that "Math is Figure-out-able," and her problem strings are the primary tool for proving that to kids every single day.
What's the Big Deal with a String?
At its simplest level, a problem string is just a sequence of math problems designed to highlight a specific strategy or mathematical relationship. But calling it "just a sequence" is like calling a Five-Star meal "just some food." There's a lot of intentionality behind the scenes.
When you use pam harris problem strings, you aren't just throwing random equations at the board. You're leading a journey. You start with something accessible—a "clue" problem—that everyone in the room can solve. Then, you move to a problem that's just a tiny bit harder, but it's directly related to the first one. By the time you get to the fourth or fifth problem, the kids are solving complex mental math that would have terrified them ten minutes earlier.
It's all about building "relational thinking." Instead of seeing 49 times 8 as a terrifying vertical calculation, a kid who has been through a few strings might think, "Well, I know 50 times 8 is 400, so I just need to take away one 8." That's not a trick; it's a deep understanding of how numbers actually work.
How the Magic Happens in the Classroom
Usually, when I'm running a string, I've got my marker ready and the kids are gathered around. There are no calculators, and often, there's no paper. We want the thinking to happen in their heads and out loud.
I'll put the first problem up—maybe something like 10 times 14. Everyone knows that one's 140. Easy. Then I'll write 5 times 14. I wait. I don't just call on the kid with their hand up first. I want them to see the relationship. How does 5 times 14 relate to 10 times 14? They realize it's just half.
Then we might do 2 times 14. Then 1 times 14. Finally, I'll drop the "challenge" problem: 18 times 14.
Now, if I had started the class with 18 times 14, half the kids would have pulled out a piece of paper and the other half would have checked out mentally. But because we built this "string" of logic, they can look at the board and realize they can just add the pieces they already figured out. They see that 10 + 5 + 2 + 1 is 18. So, 140 + 70 + 28 + 14 gets them the answer.
It's a massive confidence booster. They aren't just "doing math"; they are constructing math.
Why This Beats the Standard Algorithm
Don't get me wrong, I'm not saying the standard algorithm is evil. It's a tool. But it's a tool that often gets taught before kids have any "number sense." If you teach a kid to follow a procedure before they understand the relationship between the numbers, you've essentially taught them to be a low-functioning calculator.
The beauty of pam harris problem strings is that they force the brain to look for patterns. Our brains are literally hardwired to find patterns. When we teach math as a series of isolated steps, we're actually working against how the human brain wants to learn.
When kids use strings, they start to develop what Pam calls "sophisticated strategies." They move from counting by ones, to skip counting, to additive thinking, and eventually to multiplicative reasoning. They start to realize that they can manipulate numbers to make them "friendlier."
It's All About the Facilitation
One thing I had to learn the hard way is that you can't just write the string on the board and walk away. The teacher's role in this is huge. You have to be a bit of a facilitator and a bit of a detective.
When a student gives an answer, the question isn't "is that right?" The question is "how did you see it?"
I've had kids come up with ways of solving things that I hadn't even thought of. By modeling their thinking on the board—using number lines or ratio tables—I'm showing the rest of the class a visual representation of that student's brain. This helps the visual learners catch up to the abstract thinkers, and it creates this collaborative environment where everyone's strategy is valued.
Pam harris problem strings really shine here because they provide a safe space to fail. If a kid gets a wrong answer, we can usually trace the logic back through the string and find the exact spot where the relationship broke down. It's not "you're wrong"; it's "let's look at how this piece fits with the last one."
Moving Beyond Just Multiplication
While multiplication is a common place to start, you can use these strings for almost anything. Fractions are a big one. Most kids (and let's be honest, many adults) find fractions intimidating. But if you use a string to show how fractions relate to division or how they can be compared on a number line, the mystery starts to evaporate.
You can use strings for decimals, percentages, and even high school algebra. I've seen teachers use pam harris problem strings to help students understand the distributive property without ever having to chant "FOIL." They just see how the areas of rectangles can be broken down into smaller pieces. It makes the abstract suddenly very concrete.
Tips for Getting Started
If you're looking to try this out, my biggest piece of advice is to start small. You don't need to overhaul your entire curriculum on Monday. Just pick one string and try it out as a "warm-up" or a "number talk."
- Keep it brief. A good string should only take about 10 to 15 minutes. It's a sprint, not a marathon.
- Wait for the quiet. Don't jump to the first person who shouts out. Give the "slow and deep" thinkers time to process the relationship between the problems.
- Model the thinking. Use a document camera or a whiteboard to draw what the kids are saying. If they say "I doubled it," show that doubling on a number line.
- Stay curious. Ask "Who did it a different way?" as often as possible.
Final Thoughts
The real magic of using pam harris problem strings isn't actually about getting the right answer. It's about the shift in the classroom culture. It turns math from a performance where you're either "smart" or "not smart" into a puzzle that everyone is invited to solve.
I've seen kids who used to hate math—the ones who would literally hide under their desks or sharpen their pencils for twenty minutes to avoid a worksheet—suddenly leaning in and arguing (politely!) about which strategy is more efficient. That's the dream, right? We want kids who don't just know how to do math, but who actually believe they can do it. And honestly, these strings are one of the best ways I've found to make that happen.