Students in grades K-8 learn mathematics based upon Singapore’s framework for mathematics. Problem solving is at the heart of this approach, which also embeds skills, concepts, and processes. Throughout the grade levels, concepts are taught moving through a sequence of concrete to pictorial to abstract. Concrete learning happens through hands-on activities with manipulatives such as number lines, counters, or coins. Pictorial learning utilizes pictures, drawings, or other forms that illustrate the concept. Finally, the abstract algorithms are explored and learned to help solve problems. While manipulatives are used throughout levels, they are used much more frequently in younger levels. Through this approach to mathematics, students begin to think algebraically in the early grades. Building perseverance while encouraging students to take risks become key components of the math environment. The approach also strives to build ...productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy towards mathematics. -CCSS Equally important are the Standards for Mathematical Practices, which teachers are continually working to foster in their students.