The Sounds of Imaging Numbers

One of the most difficult standards for 1st grade students to own is the idea of adding or subtracting multiples of tens OR a group of ones.  Without it…all other numbers fall apart. (1.NBT.4-6)

Karen is a phenomenal 1st grade teacher.  Being new to the district, I’m truly thankful for how welcoming her class has been all year long.  Karen’s students get really excited to see me when I walk in the room and that’s such an awesome feeling.  But to be completely honest, I think I get more excited to see them and listen to their thinking.  I guess we’ll say the love is mutual!

I needed to try an idea out, so without warning I showed up to Karen’s class carrying my weapon of choice.


Snap cubes…my weapon of choice.

The activity:

  • Students were asked to get a piece of paper and a pencil.
  • I was going to drop cubes into a basket and students were asked to write down the total number of cubes in the basket.
  • Students had to close their eyes and listen for the cubes dropping.
  • Students were not allowed to used tally marks, numbers, fingers or anything to keep count.  I wanted to see how they were able to image numbers.  We started out by keeping it simple.

  • Being that this was a 1st grade class, all but 3 students were able to get the correct count.
  • I was purposeful to make sure that the iteration between drops wasn’t consistent.  I wanted this to be more than rote counting through rhythm.

Then we moved to counting by tens and ones…

  • I was sure not to just add tens first, then ones.  I wanted to mix it up for an accurate reflection of who could image numbers.
  • This screams formative assessment and small group because of how easy I was able to identify student ability (I like easy).

Then we went for the gusto and did backwards counting by tens and ones…

My Takeaways:

  • The students absolutely loved this activity and so did their teacher.  I am always worried when new things pop in my head and I want to try them out.
  • I was really impressed with how students were able to image numbers.  That is a testament to how Karen has hammered home the idea of tens and ones to her students.
  • There was no way to know if students miscounted because they couldn’t identify the difference in the cubes dropping. Was it a 10?  Or was it a 1?
  • Nowadays I see lots of manipulatives embedded into teaching practice but there still needs to be an opportunity for students to image numbers as they transition through the Concrete-Representation-Abstract model.
  • In the C-R-A model, I seldom see or hear of teachers providing their students an opportunity to employ mental math.  Sure it happens during Number Talks but not beyond that 10 minute-a-day window.  I need to be sure to include the importance of imaging more often.
  • What I liked about this activity was that understanding wasn’t built around skip counting.  It was built around the idea of more and less which focused on quantities.
  • I often forget about an underpinning progression on the road to computational fluency. I’m glad Karen’s class reminded me of the importance in imaging.

    Screen Shot 2015-05-12 at 10.50.30 AM

    The NZ Maths Numeracy Project does a beautiful job focusing on all 3 and how they’re connected.

Stay thirsty my friends!

About gfletchy

K-8 math consumer trying to listen and learn each day. Stay thirsty my friends!
This entry was posted in counting, Strategy Development, Teacher Content and tagged , , , . Bookmark the permalink.

24 Responses to The Sounds of Imaging Numbers

  1. Katie Breedlove says:

    I love this idea! I can definitely see this introduced earlier in the year as well with students drawing the “rods” and “units” as well. What a great way to get kids thinking! Much more involved than your typical WORKsheet (and yet your students did a lot more work!).

    • gfletchy says:

      Thanks Katie! This activity definitely exceeded my expectations on numerous levels. It was awesome to see the wheels turning each time I dropped some cubes into the basket.

  2. What strikes me about this activity is not only how attentive the students need to be, but how attentive I imagine they WANT to be. It’s like you have a secret that they are listening for. I am wondering whether or not you told them the “right” answer. I get that this activity isn’t about the right answer, but I am wondering if students looked for that.

    • gfletchy says:

      It’s funny that you ask that question Paula because the very first time I revealed the answer all the students cheered and immediately I thought about the 3 students that were incorrect (gulp…I felt awful). I told the class it was a brand-spanking-new activity that no 1st grade class had ever done in the history of the world. Mistakes were going to happen and they were really receptive to that idea.

      Going forward I asked students to “kiss their brain” if they were right which was a silent way to indicate to their teacher and I that they were correct. I alternated between the exact answer and giving a range which was ridiculous at times.

      Example: if I dropped 42 tubes I’d say “if the number you have written down is between 18 and 75 you’re right”. I tried to catch every kid in the range I shared. I would always share the range after I walked around to ensure the range was inclusive.

      • Wow! What a great way to handle the “being right” issue! Of course students want to know if they’re right, to get that validation of their efforts, yet it can feel like a swift kick to students who don’t get it, which, probably, are the ones that you most don’t want to alienate.
        I’ll bet these students will ask you to do this activity with the again and again. This particular kind of listening, and internalizing what they’ve heard, seems very much outside of the classroom experience, especially the math experience. It also seems like a great way to corral in “busy” class. I’m going to be thinking about ways that I can use this kind of sound engagement with the classes that I teach.

        • gfletchy says:

          Trying to keep struggling students motivated is difficult. We want to empower them but not create a false sense of accomplishment. Its a fine line which I frequently struggle to balance.
          As you come up with more ways, please be sure to check back in and share. I was really surprised by the level of the engagement so I’m looking for more ways to integrate this idea. Thanks for chiming in Paula!

  3. Jana says:

    I want to try this activity. I’ve done something similar, but did not use 10s and am having a little bit of difficulty understanding how you did that. Can you please explain further?

    • Jana says:

      Nevermind! I found the videos. For some reason they didn’t show on my computer at first. I’m so on this, TODAY with 1st Graders in Alabama! Thanks!

      • gfletchy says:

        Great…Can’t wait to hear how it goes!

        • Jana says:

          I wish I could post pictures of the kids to show you how well it went! Total engagement and we’re in the last full week of school. One teacher said the kids were having a hard time listening, but they did! They loved it and the teacher was all over it! She and I had great conversation about the importance of providing opportunities for kids to develop the ability to image number. I asked students what they liked about this activity. Among the responses: it’s fun, I need to learn, it made me think hard, I had to count by 1’s AND 10’s, it was tricky (meaning it was challenging), etc. Your blog is my official favorite…keep pouring the Kool-Aid! I’m drinking it up and most importantly, sharing it. That’s what it’s all about.

  4. Damian Watson says:

    This sounds awesome, as a Secondary practioner I am trying to think of adapting the activity. What about another version where you play a digital sound eg chime for 10, bell for 1. It could be used for loads of different multiples as well. Thanks for sharing #inspired.

    • gfletchy says:

      That would be awesome to try out as well! You could also incorporate decimals in there as well (1, 0.1, 0.01). As a brain chewer you could throw in a horn as a power of 10.

      I was toying with the idea of returning and making it more abstract. A favorite book of mine is “One is a Snail, Ten is a Crab” which refers to the number of feet each animal has and is an excellent introduction to algebraic thinking. 3 crabs and 2 snails would have 32 feet. This activity definitely has a high ceiling. Keep me posted how high you take it.

      All the best!

  5. Joe Schwartz says:

    Love this Graham, especially going backwards at the end. I am also appreciative of the way you are tying things to the NZ Maths Numeracy Project. Seeing concrete examples of the progressions is really helpful.
    The video may not accurately capture the sound. Was their a noticeable difference between the sound of the single cube and the stack of 10?

    • gfletchy says:

      Thanks Joe. There was quit a difference in sound between the 10 and 1 dropping. I was also sure to drop the 10 rod from a much higher level than the 1. I think most students were able to distinguish the difference. For the students that were wrong more than 40% of the time, I’d want to see them in small group to see if it was the sound or the math.

      The Numeracy Project is amazing. Super pumped and looking forward to the TMC and NCTM NJ to collaborate in person!

  6. Simon Gregg says:

    How great to switch to sound for a while!

    Like Joe, I wondered about the difference between the sound of the tens and ones. I wondered if it could be accentuated by dropping them lightly on something more resonant, like some kind of big drum? I wondered if it would work with ones, tens and hundreds?

    Also, would it work dropping something more sonorous (some kind of tube cut to one and ten lengths)?

    It has reminded me, I want to do a lesson soon using boomwhackers, you know the things – like this:
    There’s, famously, a mathematical relationship between their length and their pitch. I want to try exploring that one day.

    The other thing I wondered is whether there’s a place for letting the kids get into pairs and dropping tens and ones for each other? Would that be too noisy? Perhaps if the pairs could get far enough away from each other…

    • gfletchy says:

      The acoustics weren’t that much of an issue but I love the idea of using different sounds. I think it just increases the abstraction and the level of flexible thinking. Why should one sound only be a 10? I know you’re always game for taking what students know and changing it:-)

      I have never seen the boomwhackers before but you have me wanting to know more. I am wondering all kinds of things about the pitch to length relation.

      And FWIW…I’m all for letting kids taking charge of this activity. Some are really good at selective listening so we’ll see.

  7. Joe Schwartz says:

    So I tried this Friday, with myself in the position of the student. I had trouble identifying the difference between the tens and ones dropping. Then I tried it with stacks of 10 snap cubes (like you used) and for ones I used little cm cubes. What do you think about the mix? Do you think it matters?

  8. mathkaveli says:

    This is such an interesting idea, I have got to try a variation for 2nd grade on Thursday. Thanks for sharing this just made me go, oh snap!

  9. Marian Dingle says:

    I simply love this activity. I will be sure to try it with my students next year, since I am always on the hunt for great Number Talks with 5th graders. And I will also be sure to share this post with those at the Summer Math Academy. Thanks for keeping all of our brains constantly thinking 🙂

  10. Tina C. says:

    Hello! This post was recommended for MTBoS 2015: a collection of people’s favorite blog posts of the year. We would like to publish an edited volume of the posts and use the money raised toward a scholarship for TMC. Please let us know by responding via email to whether or not you grant us permission to include your post. Thank you, Tina and Lani.

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