## Fractions at a Conceptual Level

An understanding of fraction concepts is foundational for student success in mathematics as called for in the Common Core. Both the CCSS and the Practice Guide, *Developing Effective Fractions Instruction for Kindergarten Through 8th Grade*, recognize the importance of using tools such as number lines to build student fluency in interpreting and representing fractions. This collection of videos explores a variety of techniques, tools, and student and teacher explanations, which teachers can use to guide their presentation and clarification of fractions on a conceptual level.

In the first video, a fourth-grade teacher uses a number line to emphasize fraction/decimal/percent equivalence and that a fraction is a number. She continually asks her students “How do you know?” to elicit explanations of their placement of the fractional numbers on the diagram. Next, Jonathan Brendefur, a professor at Boise State University, talks about using number lines to model the different interpretation of fractions in a variety of contexts. In *Solving a Real-World Fraction Division Problem*, a fifth-grade teacher presents a real context for exploring division with fractions, purposefully selecting multiple representations and modeling good questioning.

## Fractions on a Number Line

A fourth-grade teacher describes students’ challenges in moving from a part-whole interpretation of fractions to seeing them as numbers. Student pairs work on locating fractions and decimal and percent equivalents on a number line.

## Multiple Interpretations of Fractions

Jonathan Brendefur describes how he helps teachers understand and teach different interpretations of fractions.

## Solving a Real-World Fraction Division Problem

A fifth-grade teacher poses a fraction division problem and challenges students to find different approaches to a solution.