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Another Look at 2-Digit Numbers

A couple of weeks ago, I blogged about working with my firsties on 2-digit numbers.  This is a follow-up to that post.

Let me reiterate that the idea of tens and ones is not an easy one for young children to understand. It is incredibly abstract. As I said in my previous post, students need lots of experience with 2-digit numbers before they can fully understand the concept of tens and ones. And as with any new experience, students need concrete and representational experiences to support the abstract understanding. My students had previously worked with linking cubes (building trains of ten) and ten frames and counters. These are both concrete methods of instruction. With both, however, I recorded equations corresponding to their models to connect the concrete experience with the abstract (symbolic) representation.  That connection between concrete and abstract is often left out of instruction, but it’s so very important.

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Since the students had had a variety of concrete experiences, I decided to move on to representational instruction, so we used our individual student ten frame kits.  I love these!!  They are small plastic tiles that students can use to build numbers.  Each student gets his own little ‘wallet’ with tiles.  It’s a little faster than ten frames and counters.  Now, you might think this is concrete instruction because students are manipulating the tiles, but it’s not, it’s representational.  The dots on the tiles represent real counters on ten frames.  You definitely don’t want to start your instruction with the tiles.

I gave students a place value mat labeled tens and ones so they could more clearly see that the filled ten frames represent tens, while the partially filled ten frame represents the ones. You can download your own copy of the mat here.  Once again I gave students 2-digit numbers to build.  As we discussed what they had built, I recorded each number in two different ways, again trying to promote the idea that two tens equals 20.
If the ten frame kits are cost-prohibitive, you can create your own student kits using this file.  I also uploaded a B&W version, in case you want your kiddos to color their own.
Stay tuned after the winter break for more adventures in place value!

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  1. Hi Donna,
    Yeah, I guess the kits are cost prohibitive–and they’re more expensive from Am. Ed. Products than they are from Amazon! So I opted for the kits you provided. I was wondering if you could make a page of frames with black outlines of circles so they could be printed b&w and colored in (I’d like my students to color their own, using a single color of their choice). As I’m sure you realize, some of us need to print in b/w.

    1. Hey, Terri. I just added a B&W version. That was a great idea! Look for the link in the blog post. 🙂

  2. Thank you!! We already have your last post ready to use whe we come back from break. We will need to bookmark this one as well.

  3. Love your post! I use the ten frame wallets with many of my kids for place value at the beginning of the year. We also use them with addition strategies. A tip–if making your own sets, use a file folder and library pockets affixed on the inside. Then label to 10. This makes the “home-made” ones easy to access like the wallets. Also–“tucking them all in bed” is a term we use to help with management so they do not slip out of wallets. Courtney and I shared your blog when we presented at a conference in early December–you are such a wonderful resource!

    All the best–

    1. That’s a great idea!!! I was trying to think of a way to make the wallets and then I read this!!! Perfect! Thank you!

  4. I love all of your products. I especially love using the number bracelets packs. ( I have never made a comment before, so not really sure if this will work.) Thanks for all your excellent math packs. I use them down here in South Australia.

  5. Love your blog! My second grade team is using Cognitively Guided Instruction this year to guide our Math instruction. Your teaching ideas complement our philosophy and teaching! Thank you so much!


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