Most educators know the familiar benchmark about 3rd grade as a critical year for learning how to read, but what’s overlooked is how important it is for laying the foundation of a K-12 math experience. I’ve taught 4th grade for most of my three decades in the classroom, but this last school year I taught 3rd graders due to staffing changes. Unfortunately, I saw signs that the foundation is shaky.
At the start of the year, I led an activity in which students had to complete problems to learn about me. First, I asked them to subtract 16 from 20 to find the month I was born. Only two out of 18 students could do that. Next, they had to use mental math and peer conversations to find the day I was born; I was surprised when many students had to use their fingers to add.
These were indicators that students are lacking number sense and a solid understanding of math concepts, which may be contributing to low math scores nationwide. In past years, I encountered 4th grade students who lacked fundamental skills, but I assumed they lost ground in the summer or were not working at higher levels in 3rd grade. I see now that the problem starts earlier—students are entering 3rd grade without skills they should have. In the same way educators are looking closely at early literacy, we have to examine what’s happening in early elementary grades in math—from the moment kids enter school.
Going Beyond the Surface
My 3rd and 4th grade colleagues had their own evidence that the way we teach math is still far too surface-level. Worksheets dominate, and kids don't have enough thinking time in class. Students can mimic teachers but aren’t always processing math for themselves to make learning stick. For example, by 3rd grade, students should have skills for simple problem solving and basic number sense, including using base ten for mental math when adding and subtracting. Students need to understand a problem’s situation. My colleagues and I agreed that we needed to prepare students to explain their thinking when solving problems and to find and correct their own mistakes.
To address this, I made changes in my classroom to help students think and express themselves in mathematical ways. I attended a training on Building a Thinking Classroom, centered around education expert Peter Liljedahl's work and organized by the North Carolina Center for the Advancement of Teachers. I also studied our state standards and, as a member of the National Assessment Governing Board, worked on an initiative to create a new math framework for the National Assessment of Educational Progress, also known as the Nation’s Report Card. The latest framework emphasizes procedural skills and conceptual understanding of math.
Interim data indicates that the changes are making my teaching more effective. Our 3rd grade students completed math benchmark testing, known as NC Check-Ins 2.0, and my students did significantly better on the 3rd grade test than my 4th graders did on their assessment last year: 76 percent met proficiency in 2025-26 compared to 64 percent of my class in 2024-25. After sharing results with my colleagues and at the North Carolina Council of Mathematics conference, I believe that the approaches I’ve tried are replicable across other classrooms.
Make math collaborative.
Research shows students benefit from discussing their reasoning and working together. One activity I introduced involved finding perimeters of polygons. In a typical lesson, a teacher might pass out polygons cutouts and model how to measure each side, then add them all together. Instead, I tried a small-group thinking activity using white boards:
I’m building a garden, and I need to know how many feet of wood should go around my garden bed. How many feet of wood should I buy if the bed is 5 feet by 6 feet?
One group drew the rectangle and labeled its dimensions. Then, they labeled all sides but only added two sides (the length and width). One student said, “We need wood around the whole thing.” They problem-solved to add all four sides. When I asked the class what they noticed about this group’s work, one student said, “If you want wood around the entire thing, you have to know how much is on each side.” They understood the lesson because they had time to collaborate with their peers and sketch to visualize a familiar object, which created context.
Another way to make math collaborative is to routinely ask students to explain their answers. For example, I recently noticed two students during a Number Talk activity having a disagreement about the correct answer. They were supposed to read a problem and solve it mentally, then discuss their answers in small groups.
When one of the students proudly explained her answer with the class, students showed their “respectfully disagree” hand signal. The student was asked to defend her answer and talk through her process, which helped her realize where she made an error. Rather than an overbearing correction, she came to true understanding by retracing her steps with peer guidance.
Ditch the old tricks.
When teaching fractions, we might fall back on out-of-date tricks like the “butterfly method,” also known as the “cross multiply” method; students multiply the denominator of one fraction to the numerator of the other. It is a shortcut to find common denominators, but it doesn’t build concrete understanding.
Instead, try strategies that teach foundational concepts and build number sense with hands-on activities. For comparing fractions, I ask students to use paper fraction strips, which represent fractions of a whole folded into different sizes. Students can see how the sizes of each part get smaller when the number of pieces in the whole gets bigger. We start with those that have the same denominator and then move to different denominators. Because the pieces are color-coded, students can visualize that the yellow 1/2 fraction strip is the same size as two of the green 1/4 pieces. Students discover that “all we are doing is doubling,” which builds understanding for later finding common denominators.
Another common “trick” is telling a story when multiplying two-digit numbers. For example, if we were multiplying 32 x 24, there was a time when I would model the traditional algorithm and share a story that starts: “32 is visiting 24. The four has to visit the 2 first so 4 x 2 = 8 … “ and continue until we solved the problem. Now, to build understanding of double-digit multiplication, we use base-ten blocks and build arrays of 32 rows of 24; students can hold and picture the concept so that by the time they practice the algorithm, they don’t need a story trick.
Make problem solving relate to the real world.
As most of us are aware, there is so much value in assigning real-world problems to help students see the math in their everyday lives. One example involves estimating and subtracting decimals using relative measurements with an activity called “Three Acts.” In Act 1, I show students a video of someone drinking from a water bottle and ask, “How much water is left?” Students come up with an estimate. In Act 2, I show them a picture of the label, which reveals the amount in a full bottle. Students determine what was left in the bottle after it was partially consumed. We close with Act 3 with a video of the leftover water being poured into a measuring cup. As I walked around the room listening to students’ discussions, I couldn’t help but smile when I heard, “Wow, I thought there would be a lot more left!”
Having a real problem with topics students enjoy or problems useful to solve makes them eager to talk to each other to figure it out. These kinds of problems get students thinking about the practical math they encounter in daily experiences.
A Fresh Outlook
Though I didn’t ask to move grades this year, I’m grateful that it allowed me to look at math instruction differently and start conversations with colleagues to rethink our practices. A chance to look critically at your methods and see where you might want to make changes can get you—as well as the students—seeing with fresh eyes. It’s my hope that, with these strategies, more 3rd grade students move into the next year with a strong foundation that 4th grade teachers can build on.
