Redesigning 18.01 (Calculus) around authentic problems and downstream connections

18.01 (Calculus) is a GIR taken every fall by about 150--200 students – the first-year students with the least math background. It has an important role in educational equity, making mathematically intensive work in science and engineering available to all students. With support from ACF, we have been restructuring the course around real-world problems that teach mathematical skills important in downstream science and engineering. We are applying for a renewal to consolidate this work and to include a new topic: vectors. Vectors are used throughout 8.01, the Mechanics GIR usually taken alongside 18.01. However, most students have not studied vectors in high school, so 18.01 students currently don't study vectors until 18.02 in the spring. The 8.01 teaching team describes vectors as the main mathematical difficulty students have and strongly supports our introducing vectors in 18.01.