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Grades: 3‒4

Students construct area models of fractions equivalent to 1/2, 1/3, 1/4, and 2/3. These equivalent fractions will include relatively small numerators and denominators, such as 2/4, as well as those with relatively large numerators and denominators, like 50/100. Students learn that equivalent fractions name the same quantity using different-sized fractional parts. The activity concludes with students discussing their various strategies for building equivalent fractions.

Note: This activity is available in two versions—an area model that represents fractions as parts of a circle and an area model that represents fractions as parts of a rectangle. 

  • Students will use an area model of fractions to explore part-whole relationships.
  • Students will understand the relationship between visual representations of fractions and their symbolic forms.
  • Students will make fractions equivalent to 1/21/31/4, and 2/3 using a given selection of numerator and denominator values.
  • Students will describe strategies for finding equivalent fractions.

Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (5) Use appropriate tools strategically; (7) Look for and make use of structure.

Content Standards

3.NF3; 4.NF1

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This activity is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: If you adapt and/or share this activity, you must attribute it to "KCP Technologies, a McGraw-Hill Education Company." You may distribute it only non-commercially under the same or similar license.

This material is based upon work supported by the National Science Foundation under KCP Technologies Award ID 0918733, with grant period September 1, 2009 through August 31, 2013. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.