What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for negative numbers and use creative reasoning with negative integers (Bishop et al., 2011). Building on that knowledge, the author describes a unique task, The Tree Problem, that supports children in the messy process of extending their number system from whole numbers to including negative integers. The Tree Problem facilitates opportunities for imagining negative integers. The task also supports children in creating their own ways of making sense of integers. After describing the task, the author illustrates how a fifth-grade student, without prior instruction with negative integers, used imagination and perseverance to build a number system with flexible representations of negative numbers.