Build basic fraction concepts from students’ informal understandings of sharing and proportion.

Children have an intuitive understanding of basic fraction concepts, such as dividing a whole object into equal pieces or sharing a set of objects among a group of people, by as early as preschool. Teachers can structure activities that create connections between this informal knowledge of sharing and the formal fraction concepts of ordering and equivalence relationships. Informal sharing can be presented in terms of division (e.g., partitioning objects into groups of the same size) or ratio (e.g., the number of objects in relation to the number of people sharing).

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Learning Together About Building on Informal Understandings of Fractions

Math coaches and specialists can use this professional development sequence to help primary grade teachers learn about the importance of working with even very young children on informal fraction...

Tool
Document
03/12/2014
932 views

Discussion Prompts: Initial Fraction Concepts

Teachers can use these prompts to help children extend their thinking during informal encounters with fractions. The question and strategy prompts remind teachers how they can take advantage of...

Tool
Document
03/12/2014
983 views

Creating Story Problems: Initial Fraction Concepts

Use this planning tool to create problems that build on children’s informal understanding of fractions. The planner outlines the components necessary to construct a progression of...

Tool
Document
03/12/2014
901 views

Same Parts, Different Whole: Lesson Plan and Worksheet

A fourth-grade teacher’s lesson on finding fractional parts of rectangular arrays and a group of objects requires students to compare the same fractional parts of different-size wholes. Related...

Sample Material
Document
03/12/2014
1082 views

Sharing Cookies Worksheet

As seen in Equal Sharing in Grade 1, a teacher uses the progressively more difficult sharing challenges on this worksheet to differentiate instruction. Related Files: Equal Sharing in...

Sample Material
Document
03/12/2014
1287 views
Equal Sharing in Grade 1

Equal Sharing in Grade 1

Watch a teacher guide students through a problem set requiring fair sharing of objects and sets of objects. Using Sharing Cookies Worksheets, she provides differentiated challenges based on...

School Example
Video
03/12/2014
1301 views
Teaching Fractions in Grade 2

Teaching Fractions in Grade 2

Watch a second-grade teacher describe a review lesson designed to check understanding of fractions, decimals, and percents. This classroom presentation was shown in the topic National Mathematics...

School Example
Video
03/12/2014
459 views

Fractions With Cuisinaire Rods

Students use the worksheet to record their explorations of equivalent fractions using Cuisenaire Rods. Their work is shown in Representations of Part-Whole Relationships. Related Media and...

Sample Material
Document
03/12/2014
977 views
Representations of Part-Whole Relationships

Representations of Part-Whole Relationships

Listen to how a math coach works with second graders on fair sharing and fraction equivalence challenges. The lesson culminates with students exploring parts of a whole and equivalencies,...

School Example
Video
03/12/2014
851 views
Building on Intuitive Understanding

Building on Intuitive Understanding

Dr. Thomas P. Carpenter discusses the importance of building children’s conceptual understanding of fractions based on intuitive ideas about sharing and apportioning objects. He demonstrates...

Expert Interview
Video
03/12/2014
1192 views
The Conceptual Basis for Fractions

The Conceptual Basis for Fractions

This multimedia overview introduces how children’s intuitive understandings of sharing and proportion can serve as a foundation on which to build formal instruction of fraction concepts. This...

Overview
Video
03/12/2014
1302 views
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