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.
A unit fraction is the base unit of any fraction and always has a numerator of 1; for example,
1 / 4
1 / 5
1 / 23
3 / 4
Consider the fraction one and three-fourths. This number can be decomposed using a unit fraction.
one and three fourths
seven one-fourths 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.
Students use paper folding to partition a pan of brownies (a sheet of rectangular paper) into 4, then 8, then 10 equal portions through a simple storyline the teacher tells.
Using their desks or tables, students will estimate and mark fractional amounts along the edge as a linear measure and on the top surface as an area measure. This task is best used after a solid understanding of number line has been established.