What is the Proper Way to Show Numbers in a Ten Frame?
Ten Frames are amazing! But after I presented today at my State’s Math Academy, I was thinking more about how you fill a ten frame and what reasoning each builds for kids. For instance here are four different ways to show the amount 7 using ten frames:
So, how you represent numbers in ten frames builds different mathematical ideas…none are WRONG, but I do feel that some are more important than others. I guess I am having a hard time with the ‘random placement’ of objects in ten frames. I don’t see it building anything for kids except their own development of a personal grouping system instead of reliance upon using the structure of the ten frame…however, the power of using the ten frame is ITS STRUCTURE, so why place them randomly???? I believe it probably has a place later down the line of work with ten frames, but I am questioning even that??
This question has been plaguing me for a long time, mainly because of all the darn ten frame apps out there that place the objects randomly within the app and in today’s workshop I did some Quick Images to highlight how different placements make it harder for kids to subitize. What are your thoughts? Does it bug you to see ten frames filled randomly or am I the only one?????
UPDATE!!!
Ok, it didn’t take long for this blog community and my Twitter friends to help me realize this is another case for why I call myself a RECOVERING Traditionalist. Randomly placed Ten Frames have bugged me for years, but you guys were quick to let me know it was just the Traditionalist side of me that was bugged. We should allow the kids to fill the frame whatever way they want instead of us dictating how they fill it…that way they make sense of the tool for themselves. I am totally slapping my head this morning, because I just recently posted about how I hate when teachers tell students how to use Base 10 Blocks for subtraction and we need to just let the kids decide how to use them, and here I am saying the complete opposite for Ten Frames…just shoot me. I want to give special thanks to Tracy Johnston Zager aka @TracyZager . If you are on Twitter, go follow her…and if you aren’t on Twitter, come join us! I’ve learned so much in these few months that I have been active on Twitter. The hard part is you can only type 140 characters. I’d like to share with all of you what Tracy shared with me and my Twitter response to her, but it is separated into multiple messages due to the character limitations of Twitter:
So, thank you for helping me realize that filling the frames sequentially has a purpose when subitizing after kids have had time to play with the tool and see the usefulness of the structure. The structure is apparent to us adults, but we need to let kids play around and help them make sense for themselves. Also, note the change to the caption on the random Ten Frame…it used to say “forces kids…” but now reflects more of my Recovering viewpoint. 🙂
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It does bug me a bit but mainly because of my subitizing experience. I don’t easily see items like that and know what they are but if a child can quickly see 7 and verbalize it I’m ok with it. I think it’s my own issue with the randomness that bothers me.
Except thier own development of personal grouping! Just a thought but don’t kids need thier own development of personal grouping to have a full understanding of the quantity of 7? Not that we as teachers should model that randomness (hopefully we have more specific goals for our model), but kids should be allowed & even encouraged to think those ways on thier own. Then the students themselves realize the efficiency is building for “10” or doubles. Plus if working w number bonds it further reinforces the power of using 10.
I wonder if we don’t allow randomness we take away some of the students learning?????
Good point!!! You are so right! Thank you for your quick reply. I love how this has bugged me for years and all I had to do was put it out there and got feedback instantly to help clarify my thinking and helped me realize it was just that darn traditionalist inside me. I have updated the post with my clarified thinking.
I would have a hard time using random 10 frames in first grade. I feel that it only increases the reliance of counting single objects. You might as well just throw 7 counters down. I wouldn’t even use groups of 3 and 4 (for the example) until they were familiar with math facts.
But wouldn’t using the ten frames with different groups (like the 3 & 4) help kids learn their math facts? They see a group of 3 and a group of 4 and work to discover that it makes 7. I would do this only with the small sets because kids have the ability to subitize the 3 and 4 instead of having to count them individually. Plus if you do them in a string, like show a 3 and 3 first, then the 3 and 4, it gives you the opportunity to discuss the relationship between the two.
The proper way to show numbers in a ten frame is all of the above! By seeing all of the models for showing numbers in a ten frame, kids get to see lots of ways to take apart the number. For example when you show 7 and have 5 in the top and 2 in the bottom, many kids will get that 7 is 5 and 2. (this is called 5 wise) When you have 4 on the top and 3 on the bottom they get to see this composition of 7. (this is called pair wise). When they are randomly thrown down and you show a kid that, they might see it as 3+4 or as 3+1+3 or some other combination. I like to flash all kinds of ten frames at kids and listen to their responses about what the number is and how they know they are right. In fact, right now on Facebook my fan freebie is a set of 30 different ten frames that I use with K-2 students all the time! There are examples of pair wise, five wise and random ones. Use them all!
Thank you for sharing the resource!
Wow! I learned a new word today. I had to look it up on google.
If a child can verbalize his thought and explain/justify his way of solving it then there is nothing wrong with random.
Dalia,
Thank you, I agree. I think my problem was I used ten frames A LOT for subitizing activities and when they are randomly placed it makes it more difficult to subitize. But the random placement does build other important concepts that sequentially placed ten frames don’t.