Part/Whole Relationships

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.

It seems that lately we hear more and more about the importance of number bonds, part-whole relationships, and composing and decomposing numbers. As I spend more time in primary classrooms, I am noticing more and more part/whole connections and realizing what an essential understanding it is.

The obvious part/whole connection is to addition and subtraction. Kids learn fact families, but do they really understand the relationships? If a student doesn’t realize he or she can use subtraction to find a missing addend, then I would say, no, they don’t understand.

But how about these other, more subtle, connections to parts and wholes.

  • Money  Coin equivalencies rely on decomposing and composing numbers. Understanding that 2 dimes and a nickel is the same amount as a quarter requires students to decompose 25 cents into its parts. Twenty-five is the whole, and 10, 10, and 5 are the parts.

You can grab some missing coin puzzles in this blog post.

  • Fractions Classic parts and whole! If students know and routinely use the language of part/whole, then fractions are a logical extension to them and the meaning of the numerator and denominator make more sense to them. The denominator is the whole and the numerator names a part.

  • Time  Understanding parts and wholes can help kiddos better understand the benchmark minutes on a clock. If the whole is 60 minutes and it’s 3:15, it’s easy to see that there are 45 minutes until 4:00. Sixty is the whole, 15 and 45 are the parts.

I’m sure there are more connections, and I hope you’ll post some in the comments. The thing about connections is that once you start to see them, you almost can’t stop! But remember, it’s all in the language you use with the kiddos! Be sure to engage your students in great mathematical conversations about parts and wholes.


  1. Beegirl

    You have to try this number bond game at You can choose from 1 or 2 beadstrings. It is an excellant tool for part whole connections. We are focusing on Using Addition To Solve Subtraction right now in my grade 2 class.I would really appreciate it if anyone who uses this tool would share their experiences.

  2. Jen Sykes (Hello Mrs. Sykes)

    Love this! Thanks for sharing. I am your newest follower. Come visit my blog sometime! 🙂
    Hello Mrs Sykes

    • Donna Boucher

      Just did, Jen, and I’m a new follower. Link up on my Blog Hop page!

  3. Lori

    Our school is looking at having our math goal for the year being Number sense. There are so many components of Number sense. Do you have somewhere the important components for the various grade levels? I teach first grade. As a former kindergarten teacher I feel I know what assessments I would do for K but I’m unsure about 1st. I appreciate your input. I love all of your posts. I’ve read books you’ve suggested. With the above post, I love it. I just recently started having my students decompose money in this way and I can see so much value in it. Thank you.

    • Donna Boucher

      Kathy Richardson’s Assessing Math Concepts are a great resource. They are not necessarily grade banded, but they follow a continuum of stages in number sense development.


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