## Common Core State Standards for Mathematics

Grade(s) 4 resources related to the following standard:
Number and Operations—Fractions
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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Teachers can use this interactive tool to help students build a conceptual understanding of subtracting fractions with common denominators by linking visual models to procedures. The page includes a video demonstration of the tool. Free registration is required to use the tool. A paid subscription is necessary to access curriculum materials and allow full student use.
Demonstration, Interactive Media, Video
These videos focus on specific standards and include examples/illustrations geared to clarify the meaning of the individual standard rather than to be a guide on how to teach it. There is an introductory video for the collection; the videos are organized by grade level and can be downloaded as well as viewed online.
Instructional Strategy, Reference Materials, Video
Grade Level: K, 1, 2, 3, 4, 5
This lesson activity from NCTM's Mathematics Teaching in the Middle School presents a fraction activity in which comparing fractions is explored through the use of sharing chocolate bars. In the lesson students present their reasoning, keep a table, and discover patterns. The PDF lesson/article contains many variations for challenge and extension.
Activity, Reference Materials, Article
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+
This library from the classic Annenberg Learner series contains 6 videos (15-20 minutes each) demonstrating how to incorporate the National Council of Teachers of Mathematics (NCTM) standards in grade 5-8 math classrooms. Using minimal technology resources, middle school teachers model effective techniques for guiding and assessing student understanding and offer strategies for keeping students motivated and engaged. Grade 5 videos feature work with equivalent fractions and geometry. The featured techniques also support integration of the CCSS Mathematical Practices. Support pages provide further elaboration and questions to focus viewer reflection and discussion.
Demonstration, Instructional Strategy, Video
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
This collection of 21 videos (2 - 12 min each) details the 3-part lesson structure used in Ontario math classrooms. Lessons involve open-ended problems and teaching practices that build self-efficacy, independence, collaboration, and communication. The videos follow a team of teachers and support staff as they plan and co-teach a lesson on fractions based on the 3-part structure: activation of prior knowledge, work on the problem, and consolidation and practice. The series includes clips offering related perspectives from Lucy West, Deborah Ball, Marian Small, and Steven Katz. Videos may be streamed or downloaded (.mov or .wmv). A downloadable (pdf) Viewer's Guide summarizes and elaborates on the videos and provides reflection questions.
Instructional Strategy, Lesson Plans, Video