Using Cuisenaire Rods To Move Students Forward in Conceptual Understanding

  • by Kelly Harmon
  • Oct. 20, 2020, 3:11 p.m.

By Ann Elise Record

Whenever we explore math concepts with students, having students see representations concretely, pictorially, and abstractly is so important for their brains. I have many math manipulatives that I love, but I think one in particular has the power to move our students forward on their math journeys from counting reasoning into additive reasoning and then, in grades 3-5, into multiplicative reasoning: CuisenaireⓇ Rods (The name Cuisenaire Rods and the color sequence of the rods are registered trademarks of hand2mind).

When I first saw them, I didn’t like them because the colors weren’t in rainbow order. It turns out, though, that there is a color coding system that will allow our brains to learn the colors and the corresponding number of units they are. In this post, I’d like to share with you how Cuisenaire rods can help us solve a common problem: fluency with subtraction math facts. Since the quantities exist as a group, we can help students focus on the number relationships and move beyond counting with addition and subtraction (and beyond skip counting with multiplication and division, but that’s a post for another day).

Don't Let Subtraction Take Students Down!

Over the past 20 years of working with many students in many different schools, one thing I see all the time is that subtraction takes the students out! For the younger students, I witness them counting back on their fingers to determine a fact like 15 - 8 (it’s hard not to when you are counting back a large amount like an 8). For the upper elementary students, I witness them doing the exact same thing except the subtraction facts are embedded within the subtraction in a division problem. There are two keys for developing fluency with subtraction:

  1. Understanding of decomposing numbers; and

  2. Knowing that subtraction has two meanings-removing objects and the distance between two numbers.

Cuisenaire rods can play a powerful role in developing their flexibility with subtraction while also developing their number sense.

Subtraction Fluency within 10

The first context we use when we explore subtraction with our youngest students involves the action of removing items so objects get eaten, broken, or given away. Because this action is in the story problem, it becomes natural that students act out the problem and count the objects as they remove them and then count the ones that are left.

As our students are introduced to working with larger numbers in grades 1 and 2, we want to help them move past the counting phase of reasoning and into additive thinking. The first step on this journey is to explore the second meaning of subtraction: finding the distance between the two numbers. A context such as Kylynn has 8 cookies and Delia has 6. How many more cookies does Delia need to have the same as Kylynn? This story situation encourages using addition to solve subtraction. So, rather than counting back 6, we can start at the 6 and count up to the 8. This is a tell-tale expression I use when I interview students on their basic facts using Dr. Nicki Newton’s Math Running Records ( At the same time, we can be exploring the decomposition pairs of all the numbers up to 10 so that if I ask a student 8 - 6, they will know it is 2 because 6 + 2 = 8.

Here is a Cuisenaire rod wall of all the pairs of addends that compose a 5. We can build these for all the numbers up to 10 and have students notice and wonder about all the number relationships.

Subtraction Fluency within 20

As we move into subtraction facts within 20, we want students to use strategies that make sense for their brains. Some prefer the removal thought process, while others prefer to think addition. We never want to dictate which strategies students use, but we can show that some strategies are more efficient with certain numbers than others. This is particularly true with subtraction.

Rather than counting back or counting up, students can think in chunks using 10 as a bridge. Here are two examples using Cuisenaire rods and notice the difference in the thinking to arrive at the same difference of 7.

If you are interested in learning more about how you can use Cuisenaire rods to explore fluency, word problem types, and the content standards for K-5, check out my on-demand workshops on the Power and Versatility of Cuisenaire rods. I have a class for K-2 content and another class for grades 3-5 accessible from my website:

Ann Elise Record has been an educator for twenty years in the roles of classroom teacher, K-5 Math Coach, adjunct faculty member for Plymouth State University, and currently Bureau of Education and Research presenter, contributing author of Fluency Doesn't Just Happen, and independent elementary math consultant. Her passion is working with educators to help them implement best practices within the three basic pillars of classroom math instruction that encourage growth mindset messages: math fact fluency, word problem structures, and understanding progressions of the content standards.

Kelly Harmon and Randi Anderson

About The Authors

Kelly Harmon & Associates began in 2001 with a mission of instructional coaching and providing rich literacy resources for educators and parents. Our work incorporates research-based best practices for teaching and learning.

Learn More »