Tuesday, May 29, 2012

Ten-Frames and Number Sense

For young children, developing number sense is critical, and manipulatives play an important part that process. 
But are all manipulatives created equal?  When we consider that true number sense involves understanding of quantity as it relates to place-value, then the answer may surprise you.
Look at the two different representations of the quantity eight:


Though it is important to give children experiences with a wide range of tools, which model would be a more useful tool for building understanding of number?

For many students, the first representation would be much too abstract.  In order to verify the quantity, they would have to count each tile or cube one by one.  However, when they see eight on a ten-frame, they are able to identify the quantity of eight as it relates to ten.  This visual may be more helpful in developing and retaining the sense of ten. 
Seeing quantities as instantly recognizable without having to recount from one is an important step in the stages of counting.  Students develop cardinality when they can understand that the final number they counted represents the quantity of objects in a set.   The ability to subitize comes later when students can instantly recognize a quantity of objects.
The use of a ten-frame helps children build mental images, develop the ability to subitize, and foster understanding of part/whole relationships, all important in strengthening a foundation for later work with place-value.  The use of manipulatives such as cube-trains, though helpful in early states of counting, does not provide an instantly recognizable and distinct picture of the wholeness of ten.
The use of the ten-frame also aids in assessing a student’s ability to reason abstractly, construct viable arguments about mathematics, and look for and make use of structure – three of the Mathematical Practice Standards within the Common Core. 
Consider these student’s responses to the following mathematical models of eight:
Ten-frames easily show the order and organization of our base-ten number system.  They provide students with the flexibility of counting each dot individually, or seeing a quantity of dots as combinations of smaller groups of dots.  Students can also see a particular quantity and it's relation to ten.  More importantly, a student is able to develop multiple strategies for counting quantities and understand the connections between them. 
If you have not made use of the ten-frame in your classroom, I encourage you to try it!  You can download a free set here.  Happy counting!! 
Thanks for reading along.  Be sure to visit my blog and say hello!  You can find it here.


www.teachthemath.comDr. Penny Messick is an Instructional Specialist with the Alabama Math, Science, and Technology Initiative (AMSTI).  She spent 25 years teaching K-2 and is a strong supporter of inquiry based learning.  She spends most of her days providing resources and professional development for elementary teachers across south Alabama.  Penny blogs at www.teachthemath.com.  She can also be found on Facebook, Twitter and Pinterest


  1. I love the ten frames but I also love 'Numicon' and I use both with my preschoolers. In fact I constructed the ten frames with my students using the Numicon pieces by coloring the wholes and using the number ten Numicon piece to outline the card. Then I laminated the cards. Mine do not have the lines though and after reading this post I am considering doing sets with lines. It will then be a more effective tool. The lines give a dimension, which now I'm thinking is essential.
    What I like about the Numicon pieces is that you can combine them with play dough, use with water, in the sand box, print it using paint and many other ways to explore number sense. I have yet to blog about it.
    What is your opinion about Numicon Dr. Penny?

  2. Hi Amelia, thanks so much for your insightful comment. I have no experience using Numicon but I am always in search of great tools to use with students. I will have to do some research or perhaps you could send me some information or links where I might investigate this tool. Thanks!

  3. Hello Penny!
    Great blog...simple and powerful. I work a lot with preschool and Kinder kids. You're spot on!

  4. Thank you for the great *freebie*! Are you familiar with Rekenreks?

    Heather's Heart

  5. Yes, Heather, Rekenreks are another great tool useful for developing number sense early on! I don't think their use is as widespread as it should be in the classroom. :-)

  6. Thanks for sharing your great free printable, Penny! I always loved using manipulatives for math. Of course, I typically used the Montessori golden bead materials, but the ten-frame is a great concept, too! I pinned it to the collaborative Math and Geometry Pinterest board at http://pinterest.com/kristi_cck/math-geometry-global-ideas/ Deb @ LivingMontessoriNow.com

    1. Thanks for pinning the ten-frames Deb! I appreciate it!

  7. Thanks for this. I have been hearing alot about ten frame and how to use it in the classroom. Now I have somewhere to start!

    P.S. I am your newest follower!
    stop by visit me sometime at my prek blog, Teaching Munchkins

    Teaching Munchkins


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