## MAKE YOUR OWN FRACTIONS—COMPARISONS TO ONE HALF

Grades: 3‒4

Students make area models of fractions and compare the fractions to 1/2 . They make fractions less than 1/2 , greater than 1/2 , and as close to 1/2 as possible. Students investigate the relationship between the numerator and denominator in fractions of each category. They develop the understanding that if a fraction’s numerator is less than half its denominator, the fraction is less than 1/2 , and if the numerator is greater than half the denominator, the fraction is greater than 1/2.

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.

OBJECTIVES
• Students will use an area model of fractions to explore part-whole relationships.
• Students will understand the relationship between visual representations and symbolic forms.
• Students will compare fractions to 1/2 .
• Students will recognize that the relationship between the numerator and the denominator determines whether the fraction is less than or greater than 1/2.
• Students will identify a fraction less than 1/but as close to 1/as possible for a given selection of numerator and denominator values.
COMMON CORE CONNECTIONS
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.NF1; 3.NF3d

This activity is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: http://creativecommons.org/licenses/by-nc-sa/3.0/. 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.
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