Number Bonds and 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 on place value with my firsties, but when we get back after the winter break, I want to do some work on composing and decomposing numbers to 10.  This is technically a Kindergarten skill, but remember that I work with RTI kiddos.  Understanding how to compose and decompose numbers to 10 is the basis for developing addition fact fluency, so it’s super important.

A great way to start with number bonds is with a little activity called Shake and Spill.  Working with a target number, students can explore the different combinations that make that number.  This is a very concrete way to see that numbers can be decomposed into different parts.  Remember, however, that we want to overlap concrete learning with abstract representation.  Enter the number bond.  It’s a graphical representation of the combinations for a number.  So, after students have had a chance to explore Shake and Spill without recording the combinations, introduce how to record the combinations using a number bond.  The next step would be to have students write the four corresponding equations.  But remember, baby steps…not all at one time!

After students have worked with Shake and Spill and have had practice recording the number bonds and equations, you can move to a different representation–ten frames.  Students can now work with number bond cards and represent the number bonds using a ten frame.

I recently updated my number bond flashcard product and renamed it Using Number Bonds to Develop Part/Whole Thinking. It’s already a best-seller, but I love the changes I made to it. The cards all used to be missing part, but that’s really difficult for kiddos (especially my struggling babies). I wanted to change the cards to allow the students to truly develop an understanding of number bonds over time, so I created three different sets of cards.

  1. Both parts and the whole known This will allow the students to work with the relationship among the numbers in a number bond at the simplest level.  They can build the number bond and write the equations without having to find an unknown.
  2. Both parts known, the whole unknown  At the next level, students will combine the two parts to find the unknown whole.
  3. Whole known, one part missing  This is the most difficult skill. Students need to have had lots of practice with the other structures or they will try to simply add the two numbers they see on the cards.

Finally, I’ve got a couple of freebies for you (and me!  ha ha).  Click here to grab the Winter Owl Shake and Spill and here for the Number Bond Recording Sheet.

Happy holidays!!  🙂

Update: Check out this blog post for more on introducing number bonds.

12 Comments

  1. Kerry

    Thank you for this resource! I have been struggling with how to start teaching these! Do I do part-part-whole? Fact families? Number bonds? My district uses a part-part-whole organizer where the whole is on top and the parts are at the bottom.

    Reply
    • Kerry

      THANK YOU! I am just so used to teaching “fact families” that is in engrained in me! lol Do you think it is confusing if I switch around the orientation of the boxes?

      Reply
    • Donna Boucher

      Hopefully this post gives you an idea where to start, Kerry! The phrase “fact family” is no longer used in either Common Core or our Texas TEKS. Instead, it’s all about the relationship between addition and subtraction, which number bonds address perfectly!

      Reply
    • Donna Boucher

      Not at all! I think it will help them think flexibly. The true understanding is ‘part’ and ‘whole’.

      Reply
  2. Lauren

    I teach first grade. Most of my children easily understood fact families, because we’ve spent so much time composing and decomposing this year. There are a couple that are still having difficulties– especially with finding the missing part. I’m going to give this a try in my small group with them. Thanks for the great idea!

    Reply
    • Donna Boucher

      Missing part is so tricky, Lauren! I think the ten frames and counters really help with the understanding, especially if your kiddos already have a good understanding of parts and whole.

      Reply
  3. Helena Jones

    I teach second grade and we use the part-part-whole with the whole on the top and the parts underneath. We also rotate the sheet so that it looks a lot like this one. I think it helps the children to be more flexible in their thinking if they see the same ideas in different formats. This has to be one my students’ favorite strategies for solving problems.

    Reply
    • Donna Boucher

      I like the idea of rotating the page, Helena. Love hearing that number bonds are helping your students be more successful! It’s a powerful way of thinking.

      Reply
  4. Dalia Mireles

    Now that I’m a math recovery specialist I know the importance of using bonds and 10 frames, and other manipulatives and I’m also a curriculum specialist and encourage the teachers to use things like this

    Reply
    • Donna Boucher

      It’s absolutely essential, Dalia! I think that often time kiddos with gaps in math were rushed through the concrete stage of learning. Teachers need to be very careful to not make their instruction too abstract, especially in the primary grades. Worksheets are easy, but hands-on is the way children learn!

      Reply
  5. Erica

    I didn’t like that the cover sheet to this is not in the package I paid for.

    Reply
    • Donna Boucher

      Erica, I am so sorry that you were disappointed! I honestly didn’t realize that the cover sheet is important to some folks. That was the original cover sheet and when I reformatted to a square cover, I took the original out of the packet.

      Reply

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