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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In this 9-minute video, Amy Spies shows her 4th grade class working through a problem multiplying a fraction by a whole number. During the lesson Amy realized that the students were not pulling out the knowledge that she had intended. She then revised the lesson and gave them examples and non-examples and through discussion had them make the connection between repeated addition and multiplying a fraction by a whole number. Students also gained a deeper understanding of the meaning of the numerator and denominator in these repeated addition problems. | Lesson Plans, Video Grade Level: 4, 5 | |

In these pattern block activities, students explore geometric models of fractions to discover relations among them, reinforcing their concepts of fractions and providing a visual model for fraction operations. Lessons can be worked on paper or using a pattern block applet. Teacher notes are included. | Activity, Problem Set Grade Level: 3, 4, 5, 6+ | |

This interactive Java applet allows users to explore rotations and composing shapes by selecting various shapes to place on the drawing board, then moving and rotating them. There are many other possibilities for instruction including fractions, patterns, ratios, tessellations, symmetry, patterns, and perimeter. Shapes which can be placed on the board include equilateral triangles, isosceles trapezoids, regular hexagons, rhombuses, and squares. Pieces and groups can be cloned, and the colors can be changed. Their dimensions allow them to tessellate easily. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5 | |

This progressions document from the Common Core Standards Writing team explains how fractions are incorporated in the standards from third grade through fifth grade. Each grade level includes an explanation, important vocabulary, and illustrations. | Instructional Strategy, Reference Materials Grade Level: 3, 4, 5 | |

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 | |

This collection of lessons, interactive Flash exercises and teacher utilities supports the learning of fraction concepts using side-by-side symbolic and pictorial representations. The lessons cover identifying, comparing, renaming and operating with fractions using circle and number line models. The Fraction Maker feature allows a teacher to create visual models to illustrate those same topics with fractions chosen by the user. The site includes student games and worksheets as well as suggestions and resources for the teacher. | Activity, Game, Interactive Media, Tutorial Grade Level: 3, 4, 5, 6+ |