A key challenge in education is effectively engaging children in learning activities. We investigated how a narrative story impacts engagement and learning, as well as how feedback can provide further benefits. To do so, we created an interactive, tablet-based learning platform with a multi-step math task designed using Common Core State Standards. Subjects completed a pretest and then were assigned to a condition, either one of three variations of the system (narratives, narratives with hints, and narratives with a tutoring chatbot using wizard-of-oz techniques) or a control system that has children complete the same learning task without narratives nor feedback, before the subjects completed a post test. 72 children in U.S. grades 3--5 participated. Our results showed that embedding learning activities into narratives boosted children's engagement as evaluated by coding video responses and surveys, and the integration of a tutoring chatbot improved learning outcomes on the assessment. These results provide evidence that a narrative-based tutoring system with chatbot-mediated help may support effective learning experiences for children.