Number and Operations—Fractions

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

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This webpage contains sample items and performance tasks from the Smarter Balanced assessment system in mathematics as well as English LA/Literacy. They are intended to help teachers, administrators, and policymakers implementing the Common Core State Standards (CCSS) prepare for next-generation assessments and plan the required shifts in instruction. Sample items and tasks can be viewed by grade band (grades 3-5, 6-8, and high school) or content focus. They showcase the variety of item types, including technology-enhanced items and performance tasks, that will be included in the assessment system. A drop-down tab provides information on each item, including grade level, CCSS alignment, and a scoring rubric for performance tasks. | Assessment, Interactive Media, Problem Set Grade Level: 3, 4, 5, 6+ | |

This 88-page document addresses the meaning of the Common Core State Standards for teaching fractions in grades 3-7. For each grade level the specific standards that are addressed are listed, followed by a detailed explanation of what the standards mean, including visual models, and any misconceptions teachers or students might have about how specific standards apply to fractions in the CCSS. | Instructional Strategy, Reference Materials, Article Grade Level: 3, 4, 5, 6+ | |

In this 7-minute video Dr. David C. Geary describes how to build students' understanding of the concepts behind the operations with fractions. He identifies the reasoning behind several student misconceptions and urges teachers to use these misconceptions to build conceptual understanding. A transcript of the video is available in PDF format. | Video Grade Level: 4, 5 | |

Thinking Blocks is an interactive Flash tool for modeling and solving math problems visually. Students represent quantities and relationships by placing blocks and braces on a work space and using the tools to resize and label them accordingly. Users can change the color of blocks, move them, copy them, divide them into equal parts, and separate them. A pencil tool and keyboard are also available. The site includes video tutorials demonstrating how to use the tool and how to model a wide variety of problem types. It also contains a bank of hundreds of word problems. | Activity, Interactive Media, Problem Set, Tools, Video Grade Level: 1, 2, 3, 4, 5, 6+ | |

This iOS app gives students an opportunity to visually model and calculate six different types of fraction applications, all in the context of solving word problems. Types of problems include finding a fraction of a number, using a known part to find the whole or another part, and problems using the four operations. Teachers can track a student's progress throughout the problem sets. An online version of this application is cataloged separately as a related resource. | Interactive Media, Mobile App, Problem Set, Video Grade Level: 4, 5, 6+ | |

This interactive Flash activity gives students an opportunity to visually model and calculate six different types of fraction applications, all in the context of solving word problems. Types of problems include finding a fraction of a number, using a known part to find the whole or other part, and problems using the four operations. A video demonstration introduces the method, and then students work on problems. Teachers can track a student's progress throughout the problem sets. | Activity, Interactive Media, Problem Set, Video Grade Level: 4, 5, 6+ Resource is part of a PD collection | |

In this lesson plan, students use recipes to practice three ways of doubling fractions using representations, addition, and multiplication. To complete this lesson, students learn to convert between improper fractions and mixed numbers. Included is a three and a half minute video called "The Right Amount of Cupcake Mix" and student worksheet. | Activity, Lesson Plans, Video Grade Level: 4, 5, 6+ |