This brief article defines "low threshold high ceiling" mathematical tasks (LTHC) and explains how they allow all students to develop mathematically. They provide a simple entry point so that struggling students can succeed, and at the same time involve rich mathematical concepts that challenge high achieving students. The article cites examples of LTHC problems from all levels of the NRICH archives. Several are cataloged separately: Magic Vs, Noah, Incey Wincey, Square It.