4th Grade Brain Train: Multiplication Mysteries
Contributed by LSA Lower School
Teaching mathematics often involves more than equations and formulas. It’s about nurturing a mindset that embraces challenges, values exploration, and sees mistakes as steps toward success. Recently, our teaching team designed a lesson to help 4th-grade students tackle two-digit multiplication problems in a way that built both their mathematical skills and their confidence to persist through struggles. The results revealed the transformative power of thoughtful planning and student-centered teaching.
The “Brain Train”: Framing the Lesson for Growth
The lesson opened with a question designed to set the tone: “What does it mean to board the Brain Train?” This concept was more than a metaphor; it was a classroom mantra selected by the students to embrace mental effort and view mistakes as learning opportunities. This idea, paired with the challenge of solving 42 × 30, positioned students to explore their thinking without fear of judgment.
To support their efforts, students received structured worksheets featuring multiple spaces for various approaches, place value blocks, and explicit encouragement to try different strategies. The stage was set for discovery.
Independent Work: Discovering Individual Strategies
During the first phase of the lesson, students worked independently to solve the problem. This allowed each student to approach the task at their own pace and in their own way. Observations of several different student pairs and their processes revealed the diversity in their strategies:
Pair #1 started by writing the problem vertically, as they had seen in past lessons. T hesitated initially, experimenting with arranging the numbers side by side, while H attempted mental math. He quickly wrote down multiple answers without showing his calculations, reflecting uncertainty despite his speed.
Pair #2 approached the task differently. K quietly experimented with drawing pictures to conceptualize the problem, while SG spent considerable time erasing and revising, narrating his thought process as he built confidence in his steps.
Pair #3 demonstrated contrasting patterns. SI dove into solving the problem confidently but struggled to transition from traditional methods to more creative approaches. Alana hesitated at first, often glancing at SI work, but grew more engaged as she discovered her own strategies.
This stage showcased the students’ foundational skills while highlighting their struggles and breakthroughs in adapting to new problem-solving methods.
Pair Work: Collaboration in Action
In the next phase, students partnered to compare strategies and refine their solutions. This stage brought new dynamics into play:
Pair #1 debated their differing answers while using place value blocks. Their discussion revealed gaps in their understanding but also showed how manipulatives helped them align their thinking.
Pair #2 worked methodically, with SG eagerly explaining his process. K’s quiet confidence grew as she integrated some of SG’s methods into her own work.
Pair #3 initially struggled to find common ground. However, by breaking the numbers into smaller parts and using blocks, they collaboratively developed a solution they were proud to share.
These collaborative efforts underscored the value of peer-to-peer learning, as students supported each other in navigating the complexities of the problem.
Sharing and Reflection: Learning Through Presentation
The lesson concluded with students presenting their solutions to the class. This step allowed them to articulate their thinking and learn from their peers’ diverse approaches. For example, SG’s detailed explanation of breaking numbers into place value blocks inspired H to revisit his earlier attempts. Meanwhile, SI confidently demonstrated her method, connecting it to techniques she had learned previously but also revealed that relying on algorithms to early can stifle exploration of other approaches. This phase emphasized the importance of process over correctness, reinforcing the idea that every attempt contributed to understanding.
Looking Ahead: Building on Success
This lesson reaffirmed the value of exploratory learning and collaboration in mathematics. Moving forward, we plan to:
Prioritize Time for Exploration and Struggle: A key feature in this lesson was prioritizing exploratory work as the main feature of the lesson rather than leaving it to the end if we have extra time. We can bring this idea into the initial intro for other key lessons. It’s a diagnostic for how well they understand the math and it can set students up for better success with an entire topic…paving the way for building connections and deeper understanding. They also have more fun!
Expand the “Brain Train” Concept: This metaphor resonated with students and will be used to introduce other challenging topics, reinforcing the idea that learning is a journey. The brain train is “training your brain!”
Support Multiple Attempts to Build Perseverance: Providing tools like the "idea sheet," which allowed students to try multiple times, helped them stay engaged and taught them that learning often requires several attempts. This approach encouraged perseverance and emphasized that mistakes are a natural part of learning.
Be Ready with the Right Questions: Having questions/ feedback ready beforehand helped to assist the varying needs of each student or group. Asking more open-ended questions empowered students to think independently. Planning these questions as a team was helpful.
Focus on Process over Perfection: Shifting our focus from emphasizing correct answers to guiding students to trust and understand the process made a big difference. By allowing them space to make mistakes, we helped them see the value in problem-solving and resilience, teaching them to invest in the process rather than just the outcome.
Build a Supportive Environment for Individual and Group Work: Creating a space where all ideas were welcomed enabled students to share without fear of being wrong. When they felt their ideas were valued, we saw them become more willing to take risks and try new approaches, knowing they were supported by their peers and us. Giving them time to work individually before sharing in groups led to richer discussions and deeper understanding. Identifying the “brain train” and helping students anticipate this “struggle time” helped them engage.
By centering our teaching on exploration, reflection, and perseverance, this lesson laid a foundation for deeper mathematical understanding and resilience. The students' progress demonstrated the impact of a safe and supportive environment, where curiosity is nurtured, and every approach is valued as part of the learning journey.