The shift began the moment students saw the task. Because it was framed around the real-world context of a summer camp, they were instantly engaged. Many started by sharing their own camp stories or experiences with group activities, which made the mathematics feel connected to their lives. I asked them to imagine they were camp directors planning cabin groups and supplies, using factors and multiples to make decisions. This simple framing helped them see how abstract math concepts could solve everyday problems.
Using Exemplars to Build Mathematical Thinking and Discourse
Written by: Meghan McLain, M.Ed., Sixth-Grade Teacher, NH
Using Exemplars has been a powerful tool for shifting my classroom culture toward thinking, reasoning, and perseverance. The open-ended nature of the tasks encourages students to take risks, make mistakes, and learn from them. It also gives me rich opportunities to assess understanding beyond basic computation. Through their work, I can see how students are reasoning, the models they choose, and how clearly they communicate their thinking.
Engaging Students With Real-World Math
This fall, my sixth graders worked on the “Summer Camp” task from Exemplars, which focuses on using factors and multiples to find the greatest common factor and least common multiple. This was our first experience using an Exemplars problem, and it immediately set a tone for the kind of mathematical community I wanted to build—one centered on reasoning, discussion, and persistence.
"The shift began the moment students saw the task. Because it was framed around the real-world context of a summer camp, they were instantly engaged."
Shifting the Focus From Answers to Understanding
As students dove in, I encouraged them not to rush to an answer but to show their thinking. This focus on process over product helped establish the classroom norm that the goal of math is understanding, not just getting it “right.”
Students worked in pairs, which sparked rich conversation and reasoning. I heard exchanges like, “Let’s check if that number works for both soccer balls and baseballs.” When one student realized her solution didn’t fit both conditions, she said, “I guess I need to rethink it,” instead of giving up. Those moments—when students revised, questioned, and justified—showed that a true culture of perseverance was taking root.
One of the most impactful aspects of the lesson was the built-in differentiation. The “Summer Camp” task offered three levels of challenge, which allowed me to support all learners. Some students started with the more accessible version to build confidence and understanding, while others tackled the more challenging version. This structure helped every student feel successful and capable of contributing.
Reflecting on Mathematical Strategies Together
At the end of the lesson, we gathered for a debrief. Students shared their strategies on the board, explaining how they used factors and multiples in different ways. Together, we discussed the effectiveness of each approach and what it revealed about mathematical relationships. For some, it was the first time they realized that there could be multiple correct strategies in math—and that communication and reasoning mattered just as much as computation.
"I enjoyed using Exemplars tasks throughout the year to deepen mathematical thinking, promote authentic problem-solving, and nurture a growth mindset across our classroom community." "
Thinking Like Mathematicians
By the end of this single task, the shift in our classroom culture was visible. Students began to approach new problems with curiosity rather than hesitation. They asked more “why” questions, challenged one another respectfully, and celebrated creative approaches. Overall, the “Summer Camp” task was a tremendous success. It not only reinforced key content about greatest common factors and least common multiples but also helped students develop the habits of mind of real mathematicians—exploring, reasoning, and justifying. I enjoyed using Exemplars tasks throughout the year to deepen mathematical thinking, promote authentic problem-solving, and nurture a growth mindset across our classroom community.