Although educators agree that making connections with the real world, as advocated by "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), is important, making such connections while addressing important mathematics is elusive. The authors have found that math content coupled with the instructional strategy of "predict, check, explain" can bridge such real-world contexts. In so doing, this procedure supports the research-informed teaching practices of using evidence of student thinking and aiding meaningful mathematical discussion. In contrast to the common symbols-first approach, in which students manipulate symbols and memorize the mathematics, we have found that allowing students to investigate motion phenomena through the use of technology-based representations can foster students' deep understanding of mathematics. As an example, the authors describe a high-cognitive-demand task that connects a real-world context with mathematics while supporting seventh-grade students' understanding of rate and proportionality.