Fraction Fest, Day 2

Today, we wanted to explore the question, "Do equal parts have to be the exact same shape?"  In yesterday's activity, several kids thought the actual shape didn't matter, as long as they took up the same space.  Some kids thought that it mattered very much.  Today's activity was meant to challenge that thinking and have kids come up with an answer on their own.

I gave the class this problem.

I asked them to prove if they thought this rectangle was broken into fourths.  The students not only had to decide if it was true or false, but also had to convince their classmates that they were right.  We took a few minutes to see what we thought.

Students felt very strongly when they had made their decision.

This is our "No, the shape is not in equal parts, so it cannot be true" group.

This is our small "Yes, the shape is divided into 4ths....the shapes don't have to be the same"  group.

Our first student came up to prove her side....she felt that the statement was true.  Her thinking was that the rectangle was divided into halves first.....then each half was divided again into halves....so yes, it was divided into 4ths.  She even re-drew some lines to illustrate her point.  This convinced some kids, but not all.

 Then the no side presented their argument.  At first, they said that the triangle sections were larger than the smaller rectangle sections.  They had different PERIMETERS......as a class, we agreed that perimeter was probably not important and that area was what we were looking for.  That got this group to thinking that the triangles had a different overall area than the smaller rectangles.  To prove this point, they decided to cut out the triangles and show that.

 Sorry it is so blurry, but once they cut the triangles, they realized that the triangles could actually be cut again to make the shape of a square.  And that in fact the area (or footprint) of the triangles was the same as the rectangle sections.  This was enough for most of the False group to change their mind.

Not all the students were convinced, but more are starting to understand that looks can be deceiving when thinking about fractions.  It is very important to understand the WHOLE.....and how you can break it into fractions.  Tomorrow, we will explore the HALF!