Thursday, July 25, 2013

Teaching Number Bonds


I recently returned from the National Conference on Singapore Math Strategies in Vegas, and it was a fabulous week of learning!  Any conference that kicks off with a keynote speech by Ron Clark has got to be great, right?  If you have not heard of him or don't know about his Ron Clark Academy, you need to check it out!

A big takeaway for me from the conference is how misunderstood "Singapore Math" really is.  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.

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.
Here, two color counters are used.
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 part of the missing part flashcard set.  I used a ten-frame for the combinations for ten instead of  the random dot patterns.
You can pick up your own set of missing part flashcards here.

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, did you read my post on number bracelets a few days ago?  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.



34 comments :

  1. 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?

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    1. 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.

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

    Mary
    Mrs. Lirette's Learning Detectives

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

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  3. 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!

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    1. Thanks for bringing up the Print Friendly button, Jane! I love that feature! :)

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  4. 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!

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

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  5. Thank you so much for these great ideas! What a wonderful post!
    Sarah
    Sarah's First Grade Snippets

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  6. 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!

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    1. 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.

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  7. 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.

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    1. 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! :)

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

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

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  10. 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 kathytps@aol.com

    Thanks!

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

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  11. 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

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    1. 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!!

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  12. 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!!

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    1. 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!

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  13. 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

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    1. Hey, Nicole! Thanks for the invite. I just followed your Pinterest board. :)

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  14. 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

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    1. 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! :)

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  15. 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???

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  16. 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!

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  17. Great ideas! Great blog! This made me excited to create the kinder curriculum in our school here in the Philippines! :D

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

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Comments make me smile! :)

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