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Cube Trains: Composing and Decomposing Numbers

“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.

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

    2. 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 😉


    3. 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. 🙂

  1. 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!

  2. 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.

    1. 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.

  3. 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…

  4. 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!

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

  6. 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:)

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