Developing Part/Whole Thinking

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.

I’ve been working with my firsties on composing and decomposing the numbers 3, 4, and 5.  Last week, I used number bond cards and manipulatives–linking cubes and ten-frames–to introduce the idea of number bonds. Read more about that here. Over the weekend, I finished up a set of cards showing pictorial representations for number bonds, and this week we’re using those cards to further develop the idea of the relationships between the numbers in number bonds.  I wanted to give you an idea of how I plan to develop the concept throughout the week.


I showed the students a number bond card and we went over the meaning of the whole and parts. I reminded them they had built number bonds using ten-frames and linking cubes last week. I then showed the students a picture card that matched the number bond card and asked them to explain why the picture card matched the number bond card (There are 4 cubes.  Three are purple and one is red.). I handed out the mats we will be using the rest of the week. I have them laminated, and the students use wipe-off markers to show their work.

Working together, I modeled how they will use the mat to describe the picture cards. It took a LOT of modeling, and word choice is very important. I constantly repeated, and had the kiddos repeat, the meaning of each part of the number bond. My whole is four, because I have four cubes. Part of the cubes are purple and part of the cubes are red. The purple part is 3 cubes and the red part is 1 cube. Together, the parts make 4 cubes.

Then we wrote the equations. We wrote equations last week, but I can tell this is something the students will need lots of practice with. We discussed that for the addition equations, we are joining the parts together to make the whole (One red cube plus 3 purple cubes equals 4 cubes). As we wrote the subtraction equations, I referred to the picture card, covering the part we were taking away (If I have 4 cubes and I take away the red cube, I have 3 purple cubes left…4 minus 1 equals 3). We practiced several of these together.


We’re going back to concrete learning on Tuesday, but this time the students will use cards that show the parts, but not the whole, and they will use teddy bear counters to find the whole. They will still use the mats to show the equations.


Today’s activity will be similar to Tuesday’s, but students will use ten-frames and counters instead of teddy bear counters. It’s good for them to see a variety of representations.


Thursday I will introduce the missing part number bond cards. After discussing the card, I will show students three pictorial cards, only one of which matches the number bond card. Their job will be to decide which picture card matches the number bond card and explain why. They will also find the missing part.


To finish out the week, I want to do a little assessment to see what direction I need to take next week. I’m going to use the recording sheet shown below and have the students work independently to describe four different pictorial cards.

You can grab the number bond cards here and the pictorial cards here. I’d love to read your comments about how you develop part/whole thinking in your classroom!


  1. Positively Learning

    Thank you so much for this 🙂 We switched to teaching like this a couple years ago and it has made such a difference for our students’ understanding. I love the color-coded snap cubes, too! Thanks again, Jen

    • Donna Boucher

      My pleasure, Jen! Glad it validates what you’re doing!

  2. sherri webber

    Love these! Thanks for the ‘plan’ you used in how you are using them too…I will also follow that next week!

    • Donna Boucher

      It’s just so important, Sherri, to think through the progression of skills and understanding. Glad it was helpful to you!

  3. Mrs. Leeby

    I just want you to know that we were required to read this in a math cohort today, filled with K/1 teachers. You rock!

    • Donna Boucher

      Well that’s pretty cool! Hope it stimulated lots of great conversation!

  4. Mrs. Carlson's 2nd Grade Class

    I love this for my struggling 2nd graders. I bought both of your resources today and I can’t wait to use them!

  5. Jackie Barrett

    Hi there, I’m having trouble downloading the recording sheet. Google says no longer available?

    • Donna Boucher

      Huh, I just checked the link, Jackie, and it works for me. Try this link.

  6. marjana Helton

    Please change the orientation of your parts to wholes. the parts should be Above the Whole to reinforce fractional thinking that will be taught later in life. Branching numbers out to either side will only cause confusion later in mathematical thinking. Love the card idea but really have issue with the orientation of your comparisons. JMHO

    • Donna Boucher

      The emphasis of these activities is understanding part/whole thinking. I think students should have a good understanding of the concept regardless of the orientation. We are, after all, hoping to develop mathematicians who can think and work flexibly!

  7. Emily Hutchison

    Love this post! It is such a great reminder of the number sense understanding I want each of my students to have. I have learned a great deal from you and am grateful each day. Thank you.
    Curious Firsties

  8. Diane McMullen

    Thanks…as an interventionist I am always looking for simple ideas to help with number sense. Do you have any book suggestions to help teach number sense to Kindergarten’s who are ELL?

    • Donna Boucher

      Not specifically for ELL, no, I’m sorry.


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