Build a Plan to Support Student Understanding of Fractions Using Number Lines

Build a Plan to Support Student Understanding of Fractions Using Number Lines
Made by Friday Institute @ NC State
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About this Micro-credential

Key Method

Educator creates a fractions lesson plan that anticipates multiple student strategies and possible misconceptions. The lesson uses number lines as the primary representation tool and shows evidence of questioning designed to elicit students’ thinking.

Method Components

How do I develop a fractions lesson plan using number lines, applying what I learned in the student interview?

A fractions lesson plan that applies what you have learned in a student interview can be on any lesson-planning template as needed to meet local requirements. All plans should include the objectives for the lesson, use number lines as the primary representational tool, and focus on a fractions concept.

Components of what you learned in the student interview might include:

  • revised student prompt(s)
  • anticipated student strategies
  • possible student conceptions, considering the following:
    • anticipated prior knowledge
    • anticipated challenges
    • anticipated understandings
  • planned questioning to elicit and/or develop student thinking

Example of possible components for a lesson focusing on building an understanding of the magnitude of numbers:

Prompt: is open-ended and does not lead students to a specific strategy, but does encourage the use of number lines as the primary representation.

“If the only mark on a number line is 58, can you specify where 34, 16, and 76 are located?”

(See downloadable PDF for images)

Anticipated challenges and/or understandings:

  • Students may look at only the numerator or only the denominator of the fraction (treating the fraction as two independent whole numbers).
  • Students may understand the relationship between 4ths and 8ths but not know how to approach a denominator that is not a multiple of four.
  • Students may believe that there “are not 6ths” on this number line.
  • Some students may fold the paper into 6ths, understanding that they can ignore the 5/8ths.

Research & Resources

Supporting Research

  • Carpenter, Thomas, Fennell, Francis, Geary, David, Lewis, James, Okamoto, Yukari, Siegler, Robert, Thompson, Laurie, Wray, Jonathan. “Developing Effective Fractions Instruction for Kindergarten through 8th Grade. IES Practice Guide. NCEE 2010-4039”. What Works Clearinghouse, Institute of Education Sciences, September 2010,
  • http://ies.ed.gov/ncee/wwc/PracticeGuide.aspx?sid=15

Resources

  • Illustrative Mathematics Fractions Progression Videos

    Unit 2: Equivalent Fractions, Unit 3: Comparing Fractions, and Unit 4: Addition of Fractions. This website, created by a community of mathematics educators, provides a series of eight videos (ranging from four to seven minutes) explaining the fractions learning progressions used within the Common Core State Standards. The same concepts and skills will be included in other standards, although they may be organized differently. The videos present the mathematics content in the context of teaching suggestions and examples of students’ strategies and misconceptions. These videos can help you review your own knowledge of fractions while gaining suggestions for effective teaching.
    https://www.illustrativemathematics.org/progressions

  • Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning Mathematics

    Based on a meta-analysis of teaching mathematics to students with learning disabilities, this report offers seven research-based instructional practices that have been shown to be effective with this group of learners. Each of the seven recommendations is explained, shown in practice, and offers a summary of its supporting evidence.
    http://www.centeroninstruction.org/files/Mathematics Instruction LD Guide for Teachers.pdf

  • Fractions on a Number Line
  • Author: Eliza Hart Spalding School of Math and Tech (ID)
    Source: Doing What Works Library at WestEd

    A fourth-grade teacher describes students’ challenges in moving from a part-whole interpretation of fractions to seeing them as numbers. Students work on locating fractions, decimals, and percent equivalents on a number line. A summary and transcript with time markers is available.
    http://dwwlibrary.wested.org/media/fractions-on-a-number-line

Submission Requirements

Submission Guidelines & Evaluation Criteria

Following are the items you must submit to earn this micro-credential and the criteria by which they will be evaluated. To earn the micro-credential, you must receive a “Yes” for Parts 1, 2, and 3. Through any of a variety of methods (written, scanned, audio, video, and/or multimedia), you must demonstrate an ability to describe and implement a fair-sharing lesson that supports student understanding of fractions. You must also reflect upon effectiveness of the strategy and how to adjust moving forward.

Part 1. Overview questions

(200-word limit for each response)

How did student interview(s) inform how and where you included the instruction of number lines in your lesson planning? How did you know this would be effective?


Part 2. Evidence/artifacts

Please provide a lesson plan that you designed that was informed by a student interview and includes a prompt using number lines as the primary representational tool.

(Your artifact submission will be assessed based on the following rubric. You must earn a “Yes” score on this portion of the total submission in order to earn the micro-credential.)

Part 3. Reflection

How did the student strategies and conceptions from the student interview impact your lesson planning in this context and more generally?

Except where otherwise noted, this work is licensed under:
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
http://creativecommons.org/licenses/by-nc-nd/4.0/

Requirements

Download to access the requirements and scoring guide for this micro-credential.
How to prepare for and earn this micro-credential - in a downloadable PDF document

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