Concrete to Abstract. It is widely acknowledged that students need strong conceptual understanding in many mathematics topics, fractions included, in order to fully understand or apply procedural skills. Many researchers, along with Singapore Math experts, recommend that instruction follow a concrete to representational to abstract sequence. We use manipulative models that support classroom, hands-on experiences, and our lessons progress from pictorial representations to numbers.
The following screens describe one exemplary lesson. Note how this lesson carefully scaffolds from pictorial models to numbers only in sets of 6 problems each. The Skills Check at the end has numeric procedures only, with no visual model support.
Step 1:
Models Only

Step 2:
Students manipulate the models further.

Step 3:
Student enters values to reflect the models.

Step 4:
Student writes the fractions and creates the models.

Step 5:
Student works with numbers only.
