After reading @ChrisHunter36’s post: http://reflectionsinthewhy.wordpress.com/2013/06/09/more-decimals-and-ten-frames/ I could not believe I had never thought to use 10 frames when working with decimals.
Today we began our unit on decimals and I decided to use the 10 frame (now called a “one frame” in my room) as a quick image to get a feel for how my reason about decimals as a part of a whole and the types of equations they could write to represent the way they viewed the frame.
I started with this frame:
I had to explain how we used this as a visual in K-2 to build combinations of ten and later use more than one frame for students to think about addition and subtraction strategies. One student then asked, “Um, how are we going to use them in 5th grade?” Perfect intro. We came to the conclusion that in the younger grades each box is equal to one making the whole frame equal to ten, hence the name.
Me, “Well, what if the whole frame was 1? What would each box be?
Student, “1 tenth.”
Me, “Great and how can we write that?”
Student, “1 over 10 or point 1.”
Me, “So what decimal does the frame on the board represent?”
Student, “Five tenths.” Everyone gave a quick shake of their hand in agreement. (The signal in our number talks)
Now that we had the basic understanding, I did a quick image flash of this frame:
I got thumbs up right away, agreed there were 9 tenths in the frame, and then students shared equations for how they viewed the frame. The said…
1 – 0.1 = 0.9
0.5 + 0.4 = 0.9
9 x 0.1 = 0.9
Then of course the comedian that just loves to make me write more than necessary… 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 = 0.9 He would laugh to think he now got me to type that out as well 🙂
We were moving fast through this so I thought I would throw out two frames to see how they reasoned about going over the whole. I know from past experience that some students will line .9 + .3 up vertically and add straight down to get an answer of .12, it is the most common mistake that I think using the one frames will be helpful in minimizing by providing students the concrete visual of a whole.
I flashed this quick image next and asked students to write what number is represented by the two frames and equations that represent how they “saw the dots.”
Here are some responses (right and wrong):
I saw 1.2 and 0.12 in journals as I walked around, but then a student shared out that he thought it was 12/20. I LOVE when a student does this…makes it so much more interesting. I wrote all three answers on the board. I asked them who believes their answer is correct, they all raised their hands (confident bunch), so I told them to choose one of the the other two answers and explain what the misunderstanding is that led to that answer. I got some great work that we shared out and agreed finally on 1.2.
Here is what they said…
So, thanks so much to Chris. I can see many One Frames in my future number talks!
Wow! Thanks for sharing this (and for the shout-out). “Why didn’t I think of that?” is a common reaction I get from the teachers I work with. Ten-frames and one-frames were introduced at the same time to me by my colleagues (as a secondary math teacher, I had no prior experience w/ either), so I didn’t have that same reaction. But I am surprised that one-frames are not more common in professional learning resources.
Also, I love your handling of this common math mistake. I’ll be sharing this with the teachers I work with as a general strategy. It’s so tempting to jump in at the beginning to address the misconception (“What does this represent, again?”) but allowing the student herself to realize her mistake while trying to disprove a classmate’s answer is much more powerful.
Thanks again, Kristin. (See you at NCTM NOLA?)
Thanks so much Chris. Yes, I will be at NCTM NOLA! Cannot wait to connect with all of my Twitter colleagues! I am actually presenting on Number Talks K-2 in which we do a TON of ten frame work, so it is amazing to see the connections in the upper grades.
See you in a couple weeks!
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Wow. I am having that same “Why didn’t I think of that?” reaction! I teach 5th grade, and this is so powerful that it will be introduced to my students immediately. Thank you so much for blogging and sharing your expertise.
Thank you so much Marian! Isn’t it crazy we don’t think of these things?? It makes SOO much sense! I have now moved into 100 grids for quick images to add into the hundredths, they love it!