Grades: 3‒4

Students make area models of fractions whose denominators are 1 larger than their numerators. They examine these fractions to determine which one is closest to 1. Students also explore a visual representation of the fraction ^{n}/_{n+1}, where *n* begins with a value of 1, and repeatedly increase *n* by 1 to discover that as *n* gets larger and larger, the value of the fraction becomes ever closer to 1.

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 of fractions and their symbolic forms.
- Students will determine which fraction in a list of fractions is closest to 1.
- Students will examine fractions of the form
^{n}/_{n+1 }and determine that as*n*increases, the value of the fraction becomes increasingly close to 1.

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

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