Introduce unit fractions through partitioning a single object among sharers¶

Strategy · All strategies
Evidence · 2 claims (2 for) · 2 studies (1 causal, 1 theoretical), q1–q2 · 0 of 2 report an effect size · 2 claims rest on one study

Description¶

After students are comfortable dividing sets equally, teachers introduce the new challenge of partitioning one object so each sharer receives an equal share. The presentation states: "she introduces the new challenge of unit fractions" via a problem where "there is only one apple and three children want to share it," with problems growing gradually more complex, such as three children sharing four apples. Fraction names such as one-third are introduced while working through these problems.

Design Implications¶

Context¶

Requirements¶

• Students should first show comfort with dividing sets equally

Constraints¶

Target Learners¶

• primary-grade students

Target Learning Goals¶

• unit fractions
• fraction names
• partitioning a single object

Claims¶

• Learning is effective when it builds on children's existing knowledge in real-world contexts, and early fraction foundations matter because many older children struggle with rational numbers [+W]
• Primary four students taught with a variation-theory-designed lesson were far more likely to give a correct, properly explained answer about 'equal shares' in fractions than comparison-group students [+M]

Related Strategies¶

• Begin fraction instruction with activities that involve dividing groups of objects equally
• Use varied equal-partitioning problems to develop fraction comparison and equivalence
• Build on children's informal proportional understandings to prepare for ratio and proportion

Examples¶

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Key Sources¶

• The Conceptual Basis for Fractions. (2011). Developed at least in part with Federal funds from the U.S. Department of Education under contract number ED-PEP-11-C-0068. https://creativecommons.org/licenses/by-nc-nd/4.0/