Students make area models of fractions greater than 1 expressed as improper fractions. Starting with fractions less than 1, students observe what happens to the fractions as their numerators increase, eventually becoming greater than their denominators. Students recognize that any fraction whose numerator is greater than its denominator is greater than 1. They also are able to describe the visual and symbolic representations of fractions greater than 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.
(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.