Summary:

Karen Bailey's first and second graders at the Borton Primary Magnet School in Tucson, Arizona are introduced to a lesson on fractions after listening to the children's book Gator Pie by Louise Mathews. Following the reading of the book, students are instructed on how to make fraction pieces from four different-colored fraction strips. The fractions pieces made are halves, fourths, and eights. The pieces are cut and labeled after students guess how many pieces will come from making folds. Ms. Bailey creates a chart recording the folds and pieces (e.g. 0 folds = 1 piece, 1 fold = 2 pieces; 2 folds = 4 pieces; 3 folds = 8 pieces, etc.) Students then are introduced to a game that uses the fraction pieces and a number cube (with fractions on its faces). In the game, they are required to reach one whole by rolling the cube and placing pieces on the whole strip until it is covered with pieces that add precisely to one whole. The lesson ends with Ms. Bailey facilitating the recording of combinations that equal one whole. She also has an opportunity to help children begin to reason why the expression "n/n" equals one whole. Students are challenged to use repeated reasoning about what they think the numbers 2/2, 4/4, 8/8, etc. represent.

Standard Connection:

(Practice Standard)—In this lesson, Common Core Standards Practice #6—Attend to precision—can be detected. In the game, children must attend to precision as they alternate taking turns and try to roll the precise fraction combinations that will allow their whole strip to be covered. If one whole is exceeded it escapes no one's notice because this results in a forfeited turn. During the game students add fractions informally. Aided by use of the fraction pieces, students create equations that represent fractions that add up to one whole. Students, again, attend to precision when they use precise written and oral language to communicate fractional sums that equal one unit.

(Content Standard)—The domain that captures the mathematics content is—Number and Operations—Fractions. Students are beginning to understand "a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts." They also are learning to think of "a fraction a/b is the quantity formed by a parts of size 1/b."

Questions to Consider:

Recording expressions that added up to one whole is important to this lesson. How did recording these combinations further the students' conceptual understandings of fractions? When and how would you teach a group of students that division by zero is an indeterminate or undefined? How would you use the "partitive" meaning of division to explain your answer? How would you use the "measurement" meaning of division to explain your answer?

6. Attend to precision

3.NF Number and Operations—Fractions