Let me just say, I love number bonds! They are invaluable tools that are underutilized and undervalued, in my opinion, in many elementary classrooms. No matter if you teach kindergarten or 5th grade, these math tools can help your students develop number sense. Of course, if you’re new to elementary math, you probably have questions. You may even be wondering, “What is a number bond?” I’ve got two words for you – game changer.
Why the Importance of Number Bonds?
First of all, they provide much needed structure for an abstract concept. They are graphic organizers used in math that allow students to show the different parts of a given number. Comparatively, ELA teachers use graphic organizers all the time to help students organize their thinking in writing. Number bonds do the same thing for numbers! They encourage learners to think flexibly about numbers. Not to mention, they support learning by providing structure and a visual representation.
By the same token, number bonds also serve an important purpose in facilitating students in understanding part-part-whole relationships. In truth, this is one of the most important of all the early numeracy skills. The part-part-whole understanding is undeniably critical because of its application across so many different math concepts. One powerful math tool that effectively demonstrates this understanding is the number bond. Without a doubt, they demonstrate to students not only how numbers join together to make a whole, but also how whole numbers can be decomposed into two or more parts.
Number Bonds in K-2
Number bonds are especially important in kindergarten, first, and second grade math. To be sure, early learners need a strong conceptual understanding of numbers. Of course, that begins with part-part-whole relationships. For this reason, hands-on manipulatives and visual aids are important for students who are working to understand abstract concepts of number. This is especially true with concepts like addition and subtraction!
It is not enough to simply tell students that 5 + 3 = 8. If you’ve ever taught missing addends at any age, then you know asking students to solve 5 + __ = 8 can be quite a challenge! Students certainly need to examine this for themselves with hands-on tools and visual representations. Rekenreks, ten frames, and number bonds are wonderfully useful math manipulatives.
In kindergarten, students work to understand numbers through ten. At this age, students need frequent opportunities physically to compose and decompose numbers. This is best done with manipulatives and visual models. Their use will expedite numeracy development and help students to see the relationships between parts and wholes. Undoubtedly, the more students work with numbers through 10 with these math tools, the more readily they will recognize the smaller quantities, or parts, that make up the whole.
In first grade, teachers can expand this beginning number sense to include making tens. Students are able to “make tens” because they know how to decompose and compose numbers. Likewise, they can easily break apart one number and rebuild the number into a nice friendly “ten and some more.” They may not know it as such, but they’re using either the commutative property (as shown below) or the associative property (depending on how the numbers are decomposed).
In second grade, students move into making groups of hundreds by breaking apart numbers to 1,000. It is important to realize that students are coming into a stronger understanding of computation. This occurs most notably with their flexible thinking about small quantities and the properties of operations. If students have had developmentally appropriate math lessons in K-2, then they’ll be more prepared to transfer their prior knowledge to these new values in 3-5. All of their work with rekenreks, ten frames, number bonds, place value charts, and the like, will help them mentally compose and decompose large numbers with ease!
A Word of Caution - Number Bonds are Necessary
Flexible thinking about numbers seems like such an inconsequential practice that many K-2 teachers fly through these lessons or omit them altogether. I feel this is chiefly done in an effort to satisfy school system or state-level pacing guides and curriculum maps. However, it seems to me that flexible thinking is severely underdeveloped in many elementary students. These students don’t get enough hands-on experience working with numbers. They need time actually composing and decomposing smaller quantities to develop the groundwork needed for flexible thinking about numbers.
We’re losing time on the back end of their elementary years with remediation, because they didn’t fully develop the concept in K-2. Take the time, K-2 teachers, to break out the manipulatives and put them into practice. The kids don’t need to watch you making and breaking with the manipulatives, they need to do it themselves.
Moreover, this is a critical underpinning in mathematics that aids students in performing quick mental math calculations in the upper grades. Similarly, it will free their mental workload for more challenging aspects of problem-solving. To put it differently, students won’t have subitized the small number relationships, so there will be no transfer to the larger values. Without this capability, your students will surely struggle later on.
And, now I’m stepping off of my soapbox.
Number Bonds in 3-5
In third grade, teachers can make connections to multiplication and the distributive property using number bonds. That is to say by using what they already know about decomposing a whole number into its parts, students can begin to multiply using this powerful math property. In the same fashion, students are set up for success in the fourth grade. After all, students will need to use the distributive property to multiply and divide multi-digit numbers with partial products and partial quotients.
Fourth & Fifth Grades
As a fourth grade math teacher, I used number bonds all the time to help my students make connections to part-part-whole relationships with large quantities. Some of my favorite memories from teaching are from when I was fortunate enough to teach the same children in first and fourth grades. I knew what we had accomplished together in our first grade classroom, so I definitely used that shared experience to make connections to my students’ prior learning.
Even if you don’t have the opportunity to teach your learners twice, it’s still so important to make those connections! Tell your students, “I know that in third grade you learned how to break apart a single factor to multiply. Now, we’re going to learn how to decompose both factors to find partial products when multiplying.” Or even better, your school may provide you with opportunities to plan vertically with the grade level above and below you! If that’s the case, then Lucky You! Just make connections based on the conversations you’ve had with the teachers in the other grade levels about the instruction that takes place.
Numbers Less than One
Furthermore, number bonds are also very helpful when working with numbers less than one. Fractions get tricky for many students. There may be a misconception that needs to be addressed. Albeit unintentional, somewhere along the way, we elementary teachers have helped this misconception take root.
We have taught “the” whole and not “a” whole. To undo this misconception some students will have, you will need to do a bit more explanation. Students need to expand their schema of “whole” to understand that “a” whole is no longer just “the whole thing,” as in “all” or “total,” but a whole can also be known as a value of one. Number bonds can help with this as you decompose a whole into its fractional parts. Upper elementary math teachers can also use number bonds to help students understand that a whole can be decomposed into fractions when computing with fractions or even when computing with mixed numbers.
The Many Uses of Number Bonds
There are many engaging ways that you can practice number bonds with your students. Make them as fun and entertaining as you desire! Turn a number bond activity into a center-based game using dice where students roll the whole part. You could even use dominoes for the parts of a whole. This is perfect for small group teacher led instruction as well!
During class instruction or whole group, mix up number bond models by placing them in dry-erase sheets. Students could race to solve multiple problems. The best part about the dry-erase sheets is that you don’t have to waste copies or spend a lot of time on prep. You can use them again and again! Besides, what student doesn’t love the opportunity to get out the dry-erase markers?! Mix it up even more by using manipulatives to represent the quantities for students who still need that level of support.
Another fun idea would be to use divided plates as the number bonds! You can get a stack of a hundred for a couple of bucks from the Dollar Store. Gather beads, counting chips, counting cubes, seasonal erasers, or other hands-on learning tools for students to experiment with. You could have number cards, dice, etc… There are so many ways that you can engage your students with hands-on, minds-on activities using number bonds!
Understanding part-part-whole relationships is critical to building a strong foundation in mathematics. To help with this, I’ve created a Number Bond Worksheet that will allow students to grow and strengthen their number sense through repeated, differentiated practice. This is a great way to practice missing addends! They are perfect for your differentiated math workstations and allow students to practice for part-part-whole relationships of numbers 5 -10! Each practice page has three levels of practice, making it suitable for each type of learner. Activity sheets for below-level and on-level students contain visual supports to scaffold and support learning.
Digital Practice for Number Bonds
This past school year has presented unique challenges for educators across the globe. Some of you may have been teaching from home with virtual learning or distance learning, and some have even used hybrid models of teaching with in-person instruction in the classroom and distance learners signing in on Google Meets or Zoom. So, I want to provide you with the resources you need even if you aren’t in the classroom.
I created a Digital Number Bonds Activity for Google Slides to help students build their number sense with numbers to 20. This activity includes 34 slides with moveable pieces, making it interactive and engaging! Students will drag and drop numbers, along with other moveable items to complete number bonds. Use this activity for whole groups, RTI or MTSS, or even virtual math stations! Now, this isn’t just limited to distance learning. This is a great way to incorporate technology into your in-person math instructional routine.
More Number Bonds Resources
So, we’ve discussed several important aspects about why number bonds are needed, and I’ve even shared about how amazing they are. Now l’d like to share a few more resources that you may find helpful in teaching with these math must-haves in your classroom.
Scroll through these awesome resources. Did I mention that they are all FREE?
The Mighty Number Bond
In conclusion, number bonds are simple, but also very powerful tools, for helping children build a strong understanding of number relationships. They help kids break down numbers into smaller parts that make up a whole, and they are a wonderful introduction to teaching addition and subtraction. Although they are more commonly thought of with small addition and subtraction under 20, the math models are also great for developing understanding of larger numbers. Number bonds are especially helpful for upper grades teachers when working with fractions. Finally, if you are in need of a digital activity, you may love my Number Bonds Activity for Google Classroom! This provides students with a great visual representation for teaching the parts of numbers and especially missing parts of numbers, aka missing addends, in the early elementary grades.
How do you use number bonds in your classroom? There are so many options to choose from!