Cube Trains: Composing and Decomposing Numbers

cube trains

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

“More learning time in Kindergarten should be devoted to number than to other topics.” 

That statement is from the introduction to the Kindergarten Common Core State Standards for Mathematics. In other words, all standards are not created equal. There are two distinct types of skills related to numeracy—those related to counting and cardinality (CCSM K.CC) and those related to operations and algebraic thinking (CCSM K.OA).

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Counting and cardinality refers to knowing and writing number names and the counting sequence. It’s also understanding one-to-one correspondence. In other words, knowing the 5 represents 5 objects. Finally, comparing numbers is included in counting and cardinality.

Operations and algebraic thinking, on the other hand, requires that students understand that numbers are made up of smaller numbers—that smaller numbers can be composed to make larger numbers and larger numbers can be decomposed into smaller numbers. For example, the number 5 can be made with 0 and 5, 1 and 4, or 2 and 3. This aspect of number is the foundation for understanding basic addition and subtraction facts, which are required to perform multi-digit computations.

The entire Kindergarten year should be filled with activities and routines devoted to developing fluency with combinations for the numbers to ten, regardless if that is the current “unit”.  Dot cards, number bracelets, and rekenreks are all excellent daily activities.

Activities that develop an understanding of number combinations are the same regardless of the target number. You can use the same activity to learn combinations for 5 as you can for 6, 7, 8, 9, and 10. For that reason, you want to build your arsenal of composing/decomposing activities or the kids will quickly tire of them. A terrific resource for quick and easy activities for composing and decomposing numbers is Building Number Sense, by Catherine Jones Kuhns. The book is literally nothing but activities for learning combinations for the numbers to ten. It’s a bonus that they all require very little prep or materials.

One of the activities in the book is Cube Trains. Students use linking cubes to make cube trains showing all the combinations for the target number. I thought it would be helpful to create some little mats for the kiddos to use.

cube trains

The sheets for the numbers 3 through 6 are sized so students can actually create their cube trains and put them in the spaces. After they build the cube trains, they can color the recording sheet with two different colors. Linking cubes won’t fit on the sheets for the numbers 7 through 10, but I would suggest that students still build the trains.

You can grab your freebie by clicking on this link.

36 Comments

  1. Anonymous

    Great blog. I enjoy reading your blogs and I share your knowledge with my staff. Thank you for sharing!

    Reply
    • Donna Boucher

      My pleasure! Thanks for sharing. 🙂

      Reply
    • Donna Boucher

      Easy and effective! The best kind of activity, right Tanya? 🙂

      Reply
  2. Karen

    Thanks so much! These will make a great center for my kinders.

    Reply
    • Donna Boucher

      You’re welcome, Karen! 🙂

      Reply
  3. lorena

    This is great! Thank you SO much for sharing, Donna! 🙂

    Reply
    • Donna Boucher

      Glad it’s useful, Lorena! 🙂

      Reply
  4. Anonymous

    Thanks for sharing. This is perfect for my class!

    Reply
    • Donna Boucher

      So glad! Thanks for leaving a comment. 🙂

      Reply
  5. Tammy

    And if kids don’t come into first with this information, it’s appropriate for first grade to take it on?
    ❀ Tammy
    Forever in First

    Reply
    • Donna Boucher

      Absolutely, Tammy!!

      Reply
  6. Mrs. Clancy

    Great post! This book looks great…thanks for sharing! Melissa

    Reply
    • Donna Boucher

      It’s a very usable book! It should be dog-eared and worn. 🙂

      Reply
  7. Sandi MacDougall

    Thanks, Donna. Another book to investigate.

    Reply
    • Donna Boucher

      It’s an excellent one for K-1 teachers, Sandi!

      Reply
  8. Miss VerSteeg

    Love this activity! It will be perfect for my 2nd graders to do during their ‘teaching’ time with their kindergarten buddies. Thanks for the idea and freebie, Donna! 🙂

    Cathy
    [email protected]
    http://www.missversteeg.com

    Reply
    • Donna Boucher

      Oh, that does sound perfect, Cathy! BTW, I ordered that other Catherine Jones Kuhns book you recommended. Should get it later this week!

      Reply
    • Miss VerSteeg

      Oh, yay! I hope you find it useful! It’s an honor to finally be able to share something with YOU, rather than just taking all your ideas to my classroom! LOL 😉

      Cathy

      Reply
    • Donna Boucher

      Got my book today, Cathy! I’ve only glanced through it, but I like the way it organized and how easy the activities seem to be! Thanks for the hot tip. 🙂

      Reply
  9. Kim McCoy-Parker

    Cathy I have followed your blog for the last 5 months and want to thank you for the wealth of information I gain from your blog on a weekly basis. Thank you so much for sharing!

    Reply
    • Donna Boucher

      Thanks for the sweet comment, Kim! It’s something I enjoy, so I’m glad it’s helpful to others. 🙂

      Reply
  10. Lisa V

    Just tried the link to do this for Today’s math lesson, and the link is bad. Can you reload it and see if it is me, or if it is a server problem? Thanks! It is Monday at 8am in Ohio.

    Reply
    • Donna Boucher

      Were you able to get it, Lisa? Sorry I didn’t respond this morning, but I had already left for school when you posted this.

      Reply
    • Lisa

      No, I just tried again and it said the pdf was not available.

      Reply
    • Donna Boucher

      I’m really sorry, Lisa! I think everything is working okay on my end. Are you trying to access it from school computer? Maybe it’s being blocked. Email me at [email protected]!

      Reply
  11. TheElementary MathManiac

    Another great product! I have been using your number bracelets with great success this past week.

    Tara
    The Math Maniac

    Reply
    • Donna Boucher

      Thanks, Tara!! I love hearing that the number bracelets are working so well. 🙂

      Reply
  12. Amy B

    WOW-never heard of these~ LOVE the idea!!! And, another math book I’ll be getting 🙂
    Thanks so much as always!
    Amy Burton

    Reply
    • Donna Boucher

      Nice to know I can still introduce you to new stuff, Amy!! 🙂

      Reply
  13. sol5

    I use a similar activity with wine corks painted with blue and red on each half and lined in an eggs box… but the vertical disposition seems better than the horizontal one I use… Thank you for helping me to improve my activities…
    I enjoyed the explanation you wrote to introduce the train activity… It looks like that of two french math teaching theoricians…

    Reply
  14. Kissa Clark

    I am so glad that I stumbled across your blog! Thank you for sharing your ideas. We are beginning this skill and your activities will help me tremendously!

    Reply
  15. Terri Brown

    I subscribe to your blog but found this oldy-but-goody on Pinterest. Thanks for the freebie–love your stuff!

    Reply
  16. Cathy Lukesh

    I printed the cube train pages. However, I’m not sure what the children write on the 3 and 4 page across from where they color in the cubes. You have a horizontal and vertical line there. Please let me know. I looked for a picture of what you did but didn’t find any:)

    Reply
    • Donna Boucher

      They write the combinations. There’s a picture in the blog post!

      Reply
      • Cathy Lukesh

        Thanks so much!!!

        Reply

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