Well. . . another day in the fraction trenches for the fourth graders in the Studio--that's for sure! We had a late start today for icy roads, so I thought to myself, "Let's do a quick warm up discussion then get back into those fractions of sets that we struggled with on Friday."
Mmmmhmmmm . . . quick. Riiiiiight.
Here's how today's discussion unfolded. Check out the prompt--see the square divided into pieces? The prompt simply asked them to explain what fraction is shaded--and to explain their thinking.
The good news--students immediately got to work and were confident in their answers.
The bad news--MORE MISCONCEPTIONS!
Here is one student's work . . . she added a dotted line and explained that if you draw a line through it you get 8 pieces--and one is shaded so you get 1/8. Smiles.
Then I moved to the next table and saw this one . . . 3 1/2. Three "whole" sticks and 1/2 of another one. Sigh. Deep breathing. So I finished my rounds and went to the easel (Smartboard on the fritz today) and wrote out the most common answers that I had seen--see photo below. I chose to NOT put the 3 1/2 up there . . . I was hoping the discussion would help this student see the error in her thinking--but I will be watching her closely--and also the person next to her who had the right answer and then CHANGED it to copy hers. Sigh. Two steps forward, one step back.
So I asked students to vote on which answers are correct. See the number of votes in the photo below. Interesting, wouldn't you say?
I thought this was intriguing (NOTE: I had 21 students present--so students DID vote for more than one in some instances--always allowed . . . and very "Smarter Balanced" friendly) so I wrote the following question underneath our information. I asked the students to turn and talk with one another to see what they thought. Lots of heated chatter and hand motions followed!
So we voted again. I asked how many of them thought that the number sentence was true. NOTE: I still had 21 students present. I got 100% agreement--that NEVER happens in my room!
So I called their attention back to the easel and said something like, "I notice that each and every one of you feel that 1/8 is the same as 1/2 of 1/4. Let's vote again about which of these answers you feel represent the shaded part of the square. Look. At. The. Results. Are you as puzzled as I am? I gave them some additional talking time, and a few more crossed over . . . but not everyone.
So I tried this approach. I drew a new picture with NO lines. I explained it was my son's birthday cake--and I asked how much he ate. After some brief discussion, they came up with the idea that it was 1/8 of the cake (except, mind you, of the ONE student who in the above photos refused to accept that we were talking fractions because the pieces were not equal--he refused to admit that this was 1/8 as well. Tenacious little bugger!)
So to make things interesting, I explained that I really precut the cake like this. . . and I asked if he ate the same amount or a different amount. I got some tentative "same" responses. Some said "No, this time he ate 2/16." Others weren't sure. Others said "So 1/8 is the same as 2/16?"
I think I see where things are headed next . . .So much for my easy warm up! I'll be putting this one on the back burner to get a little more confidence going with fractions of sets and number lines--then it will definitely be time to tackle equivalent fractions! It's time! Thanks for stopping by--hope everyone had a safe Monday!
This blog post is now a part of my comprehensive fraction unit available by clicking the image below. Hundreds of teachers have now used it to change the way they teach fractions!