## Apply Fair Sharing - Demonstrating Understanding and Application of the Fair-Sharing Context

Educator understands what fair sharing is, as well as when and how to apply it in fraction instruction.
Made by Friday Institute @ NC State
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### Key Method

Educator articulates instances when fair sharing was incorporated into previous fraction instruction, and leverages this knowledge to appropriately describe how they incorporate the use of fair sharing into future fraction instruction.

### Method Components

#### What is fair sharing?

Fair-sharing activities have been shown to be effective in generating student understanding of fractions for a number of reasons. Fair sharing leverages the intuitive understanding that young students have about dividing items into equal (fair) parts when sharing with others when explaining fractions concepts for all age groups.

#### How can using fair sharing improve instructional practice?

Students’ intuitive understanding of fair sharing can be leveraged to offer multiple entry points to fraction concepts. The context affords the use of multiple student strategies which educators can use to connect concepts to life experience, build student intuition around specific concepts, and to foster deeper understanding of concepts through probing questions and classroom discourse that digs into what reasoning supports different strategies.

#### Strategies for applying fair sharing into instruction:

Introduce fair sharing in the context of whole numbers and progressing into prompts that require positive rational numbers to share fairly.

• “Two students sharing four apples fairly -> six more students arrive, how can the four apples be shared fairly?”

Build intuition and understanding of the concept of the whole.

• Fair-sharing tasks can be presented without a clearly defined whole. This allows students to consider what decisions need to be made in order to appropriately name the fractional response.
• - “If three equal-size cakes are shared fairly among nine people, how much cake does each person get?”

• Correct responses include (and many more):
• 1/3 of a single cake
• 1/9 of the three cakes

## Research & Resources

### Supporting Research

• Empson, Susan B., and Linda Levi. Extending Children’s Mathematics: Fractions and Decimals. Portsmouth: Heinemann, 2011. Print.
• 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

• Lamon, Susan J. Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. 2nd Edition. Mahaw: Lawrence Erlbaum Associates, 2005. Print.
• Mack, Nancy K. "Learning fractions with understanding: Building on informal knowledge." Journal for research in mathematics education (1990): 16-32.

### Resources

• Developing Effective Fractions Instruction for Kindergarten Through 8th Grade, Recommendation 1
This writing is an excerpt taken from the IES Guide, Developing Effective Fractions Instruction for Kindergarten Through 8th Grade. This excerpt covers the first recommendation, pages 12-18.
http://bit.ly/1OUs5mZ
• The Conceptual Basis for Fractions
• This video introduces how children’s intuitive understandings of sharing and proportion can serve as a foundation on which to build formal instruction of fraction concepts and skills, including naming, equivalence, comparing, and adding.
http://dwwlibrary.wested.org/media/the-conceptual-basis-for-fractions

• Building on Intuitive Understanding
One of the authors of the IES Practice Guide on Developing Effective Fractions Instruction discusses the importance of building children’s conceptual understanding of fractions based on intuitive ideas about sharing objects. He demonstrates examples of children’s responses to challenging problems that help them expand and articulate their thinking. There is also a summary and a transcript with time markers available.
http://dwwlibrary.wested.org/media/building-on-intuitive-understanding

## 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 and 2. Through any of a variety of methods (written, scanned, audio, video, and/or multimedia) you must demonstrate an understanding of what fair sharing is and how fair sharing can be used to support fraction instruction and student understanding. You must also effectively reflect on how fair sharing applies to your instruction.

#### Part 1. Overview questions

(200-word limit for each response)

• What is fair sharing and how might you use it within the context of your instruction?
• How does fair sharing support student understanding of fractions?

#### Part 2. Evidence/Artifacts

Reflect on a time when you taught fractions in the past and how fair sharing would have been a useful context for supporting your students’ understanding. Provide an insightful reflection that demonstrates your understanding of the potential for fair sharing in improving your instructional practice, using the rubric below as a guide. Please submit one or more artifacts (such as writing, scanned documents, images, video, audio, etc.) for your reflection.

(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.)