What is 3/5 Follow Up

One great thing about blogs, you can reflect on what you have done in class, and remind you when you haven’t done a follow up you intended to do.


So, I needed to go back to What is 3/5.  My students had made some good connections during that week and I wanted to see how much of it was retained.  I went with a basic warmup today.


I decided on this because I really want students to expand their thinking past one basic shape for fraction representation.  As I expected however, the first two diagrams students drew were circles and rectangles.  I was pleasantly surprised when one student drew a pentagon.


At first I was worried when I was walking around the room, typical comments on why their figure was 3/5 included “3 out of 5 are shaded.”  I am thinking, WHAT? We covered that fully just a month ago, how could they backtrack again?  My worries were unfounded when for the last explanation students showed me they were indeed thinking of EQUAL parts, not just 3 parts out of 5.  In the first responses it is easier to “explain” that way without fully relating everything.  When I asked students to revise it so that I would know exactly what they were thinking, they came up with what a few students already had (as you can see in the student work photo):

3 out of 5 equal pieces are shaded

I am proud of them for remembering the concept and how to explain it so I could understand their thinking, and told them so.



How many options do I have?

Chris says the following problem has a limited number of solutions:

Directions: Fill in the empty spaces so that you create two distinct parallel lines.  You can use whole numbers 1 through 6, but can only use a number once.

___ x + ___ y = ___

___ x + ___ y = ___

How many solutions does it have?  Provide evidence for your answer.

Is there another way to represent the number of solutions for this problem?