Unit B
Unit Fractions
Equally partition area, linear, and set models
When partitioning, students have informal understanding of sharing and proportionality as a result of early equal sharing experiences. Students build upon this when equally partitioning models to create unit fractions.
Background
A unit fraction is the base unit of any fraction and always has a numerator of 1; for example, 1⁄4, 1⁄15, 1⁄23 are all unit fractions. Every fraction can be decomposed into unit fractions. For example, 3⁄4 is 3 one-fourth units (so one-fourth is the unit fraction and we are thinking about 3 of them). Partitioning a model involves determining and creating a unit fraction.
Consider the fraction one and three-fourths. This number can be decomposed using a unit fraction.
One and three-fourths
Seven one-fourth units
One and two-fourths can be composed using a unit fraction.
A student may say, “One whole is the same as 4 one-fourth units. I added another 2 one-fourth units to the whole to obtain 6 one-fourth units. So I can see that 6 one-fourth units is equal to one and two-fourths.
Use of unit fractions supports a deeper understanding of quantity. Notice that in the student dialogue above, early understanding of equivalency is being developed, i.e., one and one-half is the same as six-fourths. Counting by naming the unit fractions helps students to see the parts of the fraction when composing and decomposing. Notice that both counting unit fractions and composing and decomposing fractions are pre-cursors to addition and subtraction. For example, composing 6 one-fourth units is the same as adding 6 one-fourth units together to make one and one-half.
Tasks
Brownie Sharing
Students use paper folding to partition a pan of brownies (a sheet of rectangular paper) into equal portions (first four, then eight, then ten) through a simple storyline told by the teacher.
Desktop Fractions
Students will estimate and mark fractional amounts using the edge of their desks as a linear measure and the top surface as an area measure. This task is best used after a solid understanding of number line has been established.
Additional Prompts
These tasks emerged out of the fraction research. Teachers may wish to use them as diagnostic or summative assessments, exit cards, number talk prompts, or additional practice questions. By considering both the specifics of the cell and student use of purposeful models, teachers can support students in acquiring a strong conceptual understanding.