When we look at fractions as adults, they seem easy. But they’re not so simple when you’re eight or nine! Up until now in class, we’ve been learning about fractions that are parts of a single whole, such as one brownie or one pizza. If you divide a brownie among 3 people, it means to make 3 equal, or at least equivalent, pieces. Each piece is 1 out of 3 equal pieces: 1/3. If the brownie is cut up into 6 equal pieces, you each get 2 of those pieces: 2/6, which is equivalent to 1/3.
Today, however, we began exploring how the idea of fractions applies when your whole is a group, such as a batch of 12 cookies or a collection of 36 marbles. When you have to split a batch of 12 cookies evenly between 2 people, suddenly 1/2 is 6 cookies. “1/2 = 6”??? Most sensible third graders will realize that that doesn’t look right! The concept that a group of objects can be described as both 6 (cookies) and one-half (of the whole that is a batch of 12 cookies) is one of the challenges of fractions.
As the week goes on, Ms Marcy and I will be guiding the children in discovering the relationship between division and fractions, as they continue to explore fractions that are part of a group.