Introducing Number Bonds with Hands-On Experiences

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.

Last week I blogged about number bonds and part/whole thinking, something I’ll be working with my Firsties on after the break. I’ve been thinking through how I want the lessons to go in my head. This is going to be my introductory lesson the first day back.

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Put linking cubes of two colors into a bag. There’s nothing magic, of course, about using linking cubes. You could use teddy bear counters or other manipulatives. What’s important is that you have two different colors. I will probably repeat this activity on several different days using different manipulatives each time. You might want to put more of one color in the bag, so you increase the chance that you’ll pull out only one color.

Display the number bond cards for the number three–there are only two as shown in the picture above. You want cards showing the whole and both parts. I’m starting with the number three just to introduce the idea of a number bond, explain how the cards represent the number bond, and show how to write the equations associated with a number bond. Ask students to look at the cards and make observations about what they see. Some ideas they might verbalize include:

  • There are numbers in boxes
  • There are three boxes on each card
  • Some boxes are bigger than others
  • One card shows 1, 2, and 3, and 1 + 2 =3
  • The boxes have words in them–part and whole
Show the students the bag containing the linking cubes. Let them look inside and explain that there are cubes of two different colors. Have one student draw out 3 cubes without looking (or choose 3 students to each draw out one cube), and place the cubes on the table with the cards. Ask the students how they would describe the cubes that were chosen (all green, two greens and one yellow, etc.). Have students turn and talk to a partner about which of the number bond cards they think matches the cubes that were drawn and why.

The conversation can now go something like this:

Which card do you think matches the cubes?  The one that has 3 as the whole and 1 and 2 as parts

Why do you think that one matches?  Because there is one yellow cube and two green cubes and it has a 1 and a 2

So the parts are the colors?  Yes

How about the 3 that’s on the card?  How does that match the cubes?  Because we pulled three cubes out of the bag…there are three cubes total

Oh, so the whole is the three cubes…one part of the whole is yellow and the other part is green!  Yes

Next, I would connect the cubes to the equations without, however, writing them yet.

So 1 (touching the yellow cube) plus 2 (pushing the two green cubes together with the yellow cube) equals 3.  Or 2 plus 1 equals 3. If I have 3 cubes, and I take away the yellow cube (push it away), how many cubes are left (2)? If I have 3 cubes and take away the 2 green cubes (push them away), how many cubes are left (1)? I

Finally, I would use the mat and ten frame to represent the same number bonds and write the equations. So I’d put one of the cards in the space and have the students tell me how to represent the number bond on the ten frame. I’d ask them to tell me the addition and subtraction equations while I model how to write them.

We will repeat this activity numerous times using different numbers for the whole. Once the students are comfortable with the process, the activity can be used in a workstation. Differentiate the activity by having students use the number they are working on. See this blog post for more information about identifying a student’s number using a hiding assessment.

The ten frame/equation mat is part of my Using Number Bonds to Develop Part/Whole Thinking unit, which you can grab here.

Check out this post for some next steps in teaching number bonds.


  1. Sarah Nicole

    This will be perfect for me to use with some of my 2nd graders who need math interventions! Thank you for sharing!

    • Donna Boucher

      My pleasure, Sarah! I love that you are filling in the gaps for your kiddos!

  2. lorena

    Nicely done. Thank you for posting this. 🙂

    • Donna Boucher

      You’re welcome, Lorena! Happy New Year! 🙂

  3. Anonymous

    Excellent, even as review for 3rd graders! Thank you.
    Lelhani Morris-Pouessel

    • Donna Boucher

      Many of our older kiddos have gaps, and these activities are perfect for them!

  4. marjana Helton

    And again, I will say the grouping needs to be done on top of the numbers and not next to the numbers. This in turn will help promote fractional number sense later in life for students.
    Why make such a great product and take any criticism on it.

    • Donna Boucher

      Marjana, I appreciate your comments, however, I feel that if our goal is to promote deep understanding and flexible thinking, students need to understand the meaning of the parts and whole regardless of the layout. My kiddos see number bonds with the whole on the side, on the top, and on the bottom!

  5. Leann

    Thank you so much for this Blog post. This is my first year as a math interventionist and I am finding your page very helpful in planning lessons for my first graders.


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