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}/_{2 }but as close to^{1}/_{2 }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

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