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Jennifer M. Tobias

When students have many tools, including context and common numerators, they are more apt to develop mathematical proficiency.

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Stephanie A. Casey and Jonathan D. Bostic

Implementing the practice of looking for and making use of structure differs when addressing statistics content standards compared with mathematics content standards. Read about suggestions for tuning out noise in data to teach SMP 7 in statistics.

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Francis (Skip) Fennell, Beth McCord Kobett and Jonathan A. Wray

Student understanding of fractions as numbers, a foundational element of fraction sense and a critical prerequisite of work with operations, is explored through real-world connections.

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Esther M. H. Billings, David C. Coffey, John Golden and Pamela J. Wells

A professional development workshop supports teachers' understanding of the Standards for Mathematical Practice and helps them transfer this knowledge to the middle school classroom.

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Maryl Gearhart and Geoffrey B. Saxe

Try these methods for integrating diverse learners.

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Imani M. Goffney

Edited by Naima F. Goffney

My name is Naima Goffney, and I am an eleven-year-old seventh grader at Julius West Middle School. I am taking algebra 1 this year. I wanted to write the Math for Real because in math class I do not always think that what we are learning is related to the real world. At home, my mom shows me all the different ways I am mathematically smart, which makes me want to try harder in school during the “rougher” days. We can use math to know more about how to improve our skills and find the math we learn in school more interesting and more related to our real world as middle schoolers.

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Natalya Vinogradova and Larry Blaine

The Maximum Chocolate Party game requires students to divide and compare fractions in a practical and concrete context.

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Kasandra Dickman and Laura Bofferding

This department explores a game used to help students learn about additive inverses, or “zero pairs.” Authors describe some common reasoning that students used while playing the game and provide activity sheets geared toward students in grades 5–7.

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison and James Hiebert

In our March editorial (Cai et al., 2018), we considered the problem of isolation in the work of teachers and researchers. In particular, we proposed ways to take advantage of emerging technological resources, such as online archives of student data linked to instructional activities and indexed by learning goals, to produce a professional knowledge base (Cai et al., 2017b, 2018). This proposal would refashion our conceptions of the nature and collection of data so that teachers, researchers, and teacher-researcher partnerships could benefit from the accumulated learning of ordinarily isolated groups. Although we have discussed the general parameters for such a system in previous editorials, in this editorial, we present a potential mechanism for accumulating learning into a professional knowledge base, a mechanism that involves collaboration between multiple teacher-researcher partnerships. To illustrate our ideas, we return once again to the collaboration between fourth-grade teacher Mr. Lovemath and mathematics education researcher Ms. Research, who are mentioned in our previous editorials(Cai et al., 2017a, 2017b).

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Laura Bofferding

First graders restructure their ideas about foundational number concepts when they encounter negative integers.