## MAKE YOUR OWN FRACTIONS—COMPARISONS TO ONE HALF

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