Teaching Number Bonds - Math Coach's Corner

Teaching Number Bonds

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 think if you asked people to tell you what they know about Singapore Math, many would say, Oh, that’s model drawing. And while that’s one part of it, it really starts much earlier than that with their incredible routines for building number sense. Enter number bonds, a cornerstone of Singapore Math.

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In her book Why Before How: Singapore Math Computation StrategiesJana Hazekamp explains number bonds this way:

Number bonds help students see that numbers can be “broken” into pieces to make computation easier. With number bonds, students recognize the relationships between numbers through a written model that shows how the numbers are related.

A number bond for the numbers 2, 3, and 5 might look like the model below. I have also seen the whole on top with the parts branching down.

You might notice a similarity to fact families, and you’d be right. There are a couple of differences, however. First, we often teach fact families through rote memorization only. Kids can rattle off 2 + 3 = 5, 3 + 2 = 5, 5 – 2 = 3, and 5 – 3 = 2, but they often don’t really  understand how the addition and subtraction sentences are related. Second, we don’t usually focus on all the fact families for a given number, for example, 5. Through working with number bonds, children learn that 2 and 3 make 5, but so do 4 and 1. In other words, they experience multiple ways to decompose the same number. Start out working with smaller numbers and gradually work toward larger ones, and of course, the kiddos will need LOTS of concrete practice. The part/part/whole mat pictured below is a great tool.

To explore combinations for 5, start with 5 counters in the WHOLE area of the mat. Ask kiddos to move their counters into the two parts. Avoid saying, “Move 2 counters to one part and 3 to the other.” Let them explore and come up with their own combinations. Record the combinations as number bonds on an anchor chart. Keep asking the kiddos to ‘show you another way’ until all combinations have been recorded.

An easy game that provides concrete practice for number bonds is Shake and Spill. Working with a target number, for example, 6, children shake and spill that many counters onto the playing board. In the picture below, the central graphic is a duck. Some of the jacks fell on the duck and some off. The combination would be recorded 6 = 3 + 3 or 3 and 3 make 6 or some other variation. Then they pick up the 6 counters and shake and spill again. Notice that I put the playing board inside the workstation box to contain the jacks!

You can grab your free Quack Attack Shake and Spill by clicking here.

Once kiddos have had lots of practice creating and recording number bonds, you can move to missing part activities. The flashcards shown below are based on a Van de Walle activity. Notice how this one activity combines concrete (clothespins or counters), representational (dots), and abstract (numeral) learning. A perfect extension would be to have students write the number bond for each card they use.

The right side of each flashcard folds over to hide one of the parts. Students can use manipulatives, like the clothespins shown here or the counters shown below, to ‘act out’ the number bond and find the missing part.

You can pick up your own set of missing part flashcards here.

After the kiddos have had lots of concrete practice with the missing part flashcards, you can use them as actual flashcards, asking the kiddos to tell you the missing part.

This is such a critical skill, and there’s no such thing as too much practice for your Kinders and Firsties!  You’ll want to have many different ways for them to experience number bonds without getting bored.  Pictured below you see another missing part activity using number bond cards. Use together with the part/part/whole mat for concrete practice when you first introduce them.

BTW, have you read my post on number bracelets?  Do you now recognize that as just another number bond activity? 🙂

Finally, if you want to check out where a number bond goes after Kindergarten, check out this post.

42 Comments

  1. Shel

    Love these ideas! Would you suggest using ten frames or base ten blocks for the missing part flashcards, for working on number bonds up to 20?

    Reply
    • Donna Boucher

      Ten frames or unifix cubes. According to Van de Walle, base ten blocks are still quite abstract to kiddos because they can’t break them apart.

      Reply
  2. Mary Lirette

    This is an excellent post. Thanks for the refresher on Singapore Math Strategies and the adorable freebie game! 🙂

    Mary
    Mrs. Lirette’s Learning Detectives

    Reply
    • Donna Boucher

      Thanks for the kind comment, Mary! I loved the conference and the chance to delve deeper into Singapore strategies.

      Reply
  3. TheElementary MathManiac

    Another great post!

    Tara
    The Math Maniac

    Reply
    • Donna Boucher

      Thanks, Tara! 🙂

      Reply
  4. Jane

    Thanks for the great ideas to help kiddos understand this concept. I also love the fact that your posts can be made into PDF files that can printed and/or saved to my math files on my computer. I will always know where they are (hopefully) & won’t be researching through all the blogs I follow to try & find the info again!

    Reply
    • Donna Boucher

      Thanks for bringing up the Print Friendly button, Jane! I love that feature! 🙂

      Reply
  5. ilovetotchkinder

    Wonderful post! I am so excited to “amp up” my math instruction this year. Our district is rolling out Common Core, and I have been feverishly reading, making, collecting, etc. everything I can get my hands on for math…
    You are definitely one of my “go to” blogs for information, tips, and great ideas! Thank you!

    Reply
    • Donna Boucher

      What a neat compliment! Glad to hear you’re going into the new school year with such enthusiasm!

      Reply
    • Donna Boucher

      My pleasure, Sarah! 🙂

      Reply
  6. Meghan Z

    Thank you so much for sharing this! I have wanted to try number bonds in my room, but wasn’t sure where exactly to start. I’m going to look into getting the book you mentioned too.
    As I was reading through the comments, I notices you said base ten blocks are still considered abstract. I agree, my first graders struggle with this each year. What do you suggest starting them off with? I’ve tried Lima beans before, and then glued them to Popsicle sticks, but I’m afraid that’s just as abstract if they can’t take them apart.

    Thanks so much!

    Reply
    • Donna Boucher

      Hey, Meghan! Van de Walle suggests “groupable” objects, such as putting beans in small cups or using linking cubes, which can be grouped and then broken apart. I’ve seen the bean sticks, but agree that it’s a disadvantage early on that they can be taken apart.

      Reply
  7. Sandi MacDougall

    I am enjoying your blog so much I thought I needed to write and tell you. Your posts are thorough with solid, practical information. It’s refreshing to read a blog focused on Math. In early childhood classrooms in particular, I feel there is more emphasis on Literacy. This year I am introducing a guided math style format with math workshop. I’m excited to get started.

    Reply
    • Donna Boucher

      Thanks so much for taking the time to comment, Sandi! It’s always nice to hear that my blog is meeting the needs of teachers! 🙂

      Reply
  8. Shuna Patterson

    This post is great! Thanks so much for the useful information

    Reply
    • Donna Boucher

      You’re so welcome, Shuna! 🙂

      Reply
  9. Patty

    Oh my goodness…Love these ideas. Thanks so much for sharing!

    Reply
    • Donna Boucher

      Glad it was useful to you, Patty! 🙂

      Reply
  10. Kathy Griffin

    Hi Donna,

    We met at the Vegas Blogger Meet Up on July 16. I was trying to get in touch with you. Could you email me at [email protected]

    Thanks!

    Reply
    • Donna Boucher

      Hey, Kathy! The Meet Up was a blast! So much fun meeting other bloggers. I just emailed you. 🙂

      Reply
  11. Katania

    Hi Donna,
    I know you posted this a while ago and I read it right away since it is sent to my email, however, I was on vacation and was unable to write a comment. Yes, you read that right, I was on vacation and I was reading your blog!!! Let me just say how much I love reading your blog. I have used many of your book recommendations and they never disappoint. I especially loved this post as well as the number bond post. I actually printed this post out to reference later for my students. Everything you post about makes me either shake my head in agreement or shake my head saying why didn’t I think of that. Thank you for sharing your amazing math talent with the rest of us.
    Thank you,
    Katania

    Reply
    • Donna Boucher

      Hey, Katania! Just getting around to catching up on all the comments!! It is absolutely my pleasure sharing about math, but it’s really nice to hear that you feel it’s having a positive impact on your teaching. That’s why I love blogging–one big, happy learning family!!

      Reply
  12. lindsay

    Thank you SO much for writing this post! I am a first grade teacher and introduced number bonds last Monday. We need lots more practice and my fellow teachers and I are all racking our brains as to how to help our kiddos understand this better. I can’t wait to use these activities this week and share them with my teacher friends!!

    Reply
    • Donna Boucher

      Hats off to you and your teammates, Lindsay, for understanding the importance of and embracing number bonds! That is a HUGE part of first grade learning. Be sure to search using the labels on the side bar of my blog for “composing” or “decomposing” for more ideas!

      Reply
  13. Mrs. Lovelace

    Hello!

    I love your number bond ideas and see that you use Singapore math. I was wondering if you’d like to join my collaborative board on Pinterest that’s all about Singapore math. If you’d like to just go ahead and go to the board and follow. Once you’re following I will add you as a collaborator and you can start pinning your resources from your blog or TpT. The only requirement is that the items be about Singapore math/number bonds/bar models/etc.

    Pinterest Board: http://www.pinterest.com/nlovelace/singapore-math-in-the-classroom-all-grades/

    My blog: http://onetwothreemathtime.blogspot.com

    Thanks!
    Nicole

    Reply
    • Donna Boucher

      Hey, Nicole! Thanks for the invite. I just followed your Pinterest board. 🙂

      Reply
  14. Sara Franza

    Donna, I am so thankful you post some of these older blog posts to facebook where I can be reminded of good teaching practices. Love how you always challenge, encourage, and help me build solid a mathematical foundation in my kiddos. Thanks so much!!!!
    Sara

    Reply
    • Donna Boucher

      Sara, I am so proud of the way you are building not only your mathematical teaching practices, but also those of other teachers on your campus! I love your growth mindset! 🙂

      Reply
  15. kvvira

    Lovely…. was always wondering how to introduce number combinations to my darling daughter,
    What would be the pre-requisite level for this???? Should my child be able to recognize numerals and number value before i introduce the bonds to her???

    Reply
  16. Anonymous

    Thank you so much for this post, and blog in general! As a newly qualified teacher I worried maths would always be my Achilles heel. However, I found your blog extremely helpful, and am gradually starting to feel excited as opposed to intimidated about teaching maths! Thank you for the inspiration!

    Reply
  17. Myn Tinio

    Great ideas! Great blog! This made me excited to create the kinder curriculum in our school here in the Philippines! 😀

    Reply
  18. Cathy Lien

    I. Love. Your. Blog. It’s amazing!!! Thank you for everything!

    Reply
  19. Janelle

    Hello there! I am a big fan of your blog and find that working to break apart and put together numbers is essential for my kindergarteners’ understanding of addition and subtraction. My question for you is this- what are some good picture books to help reinforce the idea of decomposing and composing numbers? I am searching and coming up empty handed. Any ideas?

    Reply
  20. Amanda Brenner

    Hi Donna!

    I a math interventionist as well, in my second year of teaching. I have found your blog extremely helpful! I have learned how to use so many strategies with my kiddos! I use number bonds all the time with my younger students, but I have some still struggling with the decomposing of numbers! I saw some more strategies in this post on how to represent the numbers that I cannot wait to begin using! Thank you for your amazing posts!

    Reply
    • Donna Boucher

      Always glad to hear that something I’ve posted has helped a teacher in the classroom, Amanda! 🙂

      Reply
  21. Ibrahim

    Dear Donna,

    Thank you for sharing.

    Reply
  22. volunteer

    Εxcellent write-up. I definitely appгeciаte this ԝebsіte.
    Continue the good work!

    Reply
  23. Ronna

    This is so awesome. Thank you!!

    Reply
  24. Alla

    Hi Donna!
    Great ideas! Great blog!
    This game is good too – Number Bonds Memorizer – iPad App
    Thank you!!

    Reply
  25. Peter

    I’m very much inspired when I’ve visited your blog. Your blog is really informative relevant to topics. Hope you will continue with new article.

    Reply

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