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Let’s uncover what makes this tool such a game-changer for K–2 classrooms. More than a counting aid, the Rekenrek supports deep number sense, place value understanding, and flexible thinking about addition and subtraction, all while being incredibly easy to manage and implement.
We’ll talk about why the structure of the Rekenrek (based on fives and tens) is developmentally spot-on for young learners, how it helps students unitize and anchor their thinking. You’ll also hear what to look for as your students transition from counting all to more efficient strategies, and how a Rekenrek makes that thinking visible.
This episode offers strategies you can try right away, even if your students are just starting to build fluency. Plus we’ll look at ways to connect Rekenrek work to the CRA model for even greater impact. Let’s keep growing together!
Hello, Meaning Makers! Today we are so excited to share about one of our favorite math tools for students from kindergarten through third grade grade – the Rekenrek.
If you’re asking yourself, what the heck is a Rekenrek? Well, don’t worry. We’re going to tell you ALL about it, including where it comes from, how it supports students’ development of place value and number sense, and how you can get started using Rekenreks right away, even if you don’t own one. Let’s dive in!
Exploring the Rekenrek: A Powerful Math Tool for K-3
Originating in Holland, the Rekenrek was developed by mathematics curriculum researcher Adrian Reffers, who sought to create a tool to support children’s mathematical development. Translated to English, Rekenrek means “counting rack”.
Visualizing the Rekenrek and How It Works
Let’s paint a picture of what a standard Rekenrek looks like in case you have never seen one before… imagine two metal rods about the size of a straw, one above the other. Each rod has ten beads (a group of five red beads and a group of five white beads) that slide along the rod. The rods are held in place with a wooden frame.
All beads start on the right side of the Rekenrek with the white beads flush against the wooden frame. The beads are moved from right to the left to represent a total.
The Difference Between a Rekenrek and an Abacus
Many people confuse a Rekenrek with an abacus, but they are not one and the same. While they both have rods with beads, they serve very different purposes.
An abacus has ten rows of ten same-colored beads with each row of beads representing a different place value, from ones on the bottom row to billions on the top row. There’s so much more we could say about the abacus, but we’ll save that for another day! Just remember that the abacus is based on the number ten.
On the contrary, the Rekenrek is based on the number five, which is visible in the groupings of five beads. Students see five red beads and five white beads on top and the same on the bottom.
This mimics the structure of our hands and feet, with five fingers on each hand and five toes on each foot. Students are able to see that five red beads and five white beads make ten, just like five fingers on one hand and five fingers on the other hand make ten and five toes on one foot and five toes on the other foot make ten.
Building Understanding From the Benchmark of Five
Now, you might be wondering why a tool based on the number five would be beneficial when our number system is based on the number ten – it is called the base ten number system after all! Well, in order to understand ten, it is imperative for students to understand the benchmark of five.
Unitizing Five and Ten with a Rekenrek
The Rekenrek allows students to unitize five. This means that they first see five as being made up of five ones because they can see and touch the five individual beads.
This leads to students being able to see them as a group of five by seeing the color block of five red (or five white) beads and moving the group of five beads along the rod together as one group.
Students eventually use the Rekenrek to unitize ten in the same way. They can touch each individual bead and see them as ten ones, and they eventually see them as a group of ten and move them along the rod as one group.
Strategies on Numbers Within Twenty with a Rekenrek
Students’ understanding of the benchmark of five helps them with composing and decomposing, as well as adding and subtracting numbers within twenty. The strategies students use with these skills can later be applied to their work with larger numbers.
Additionally, as students count the beads on the Rekenrek, they develop one-to-one correspondence as they touch each bead and assign it a number. At the same time, students develop cardinality by recognizing that the last number they say when counting the beads refers to the total number of beads in the set.
These skills, along with unitizing and anchoring to the benchmarks of five and ten, all help develop students’ number sense.
Classroom Benefits of Rekenreks: Easy Setup and High Engagement
One of the things we love most about Rekenreks from a classroom management standpoint is how easy they are to manage. A Rekenrek is only one item but it has twenty counters built in. There are no individual counters to organize, keep track of, or clean up. When students take out a Rekenrek, they are taking out twenty counters all at once. It’s so simple!
Now, at first, students will likely be fascinated with the way the beads move along the rods. In fact, your classroom might sound a bit like a percussion rehearsal. But just like with any math tool, we must establish and maintain expectations for how they will be used in the classroom. The initial noise created by the beads is worth it – we promise!
Keep in mind, instead of using Rekenreks with all students together as a whole group, you can always use them with students when they meet with you in a small group. Companies also make large teacher demonstration Rekenreks, which would be ideal for a whole group lesson.
DIY and Virtual Rekenrek Alternatives
If you don’t have any Rekenreks, consdier asking your administration if they are able to purchase some for you to use with your students. You don’t need an entire class set. Just enough for a small group will do!
But if purchasing Rekenreks isn’t possible, there are lots of tutorials online that show you how to make them using pipe cleaners, pony beads, and cardboard. Essentially, the pipe cleaners act as the rods and they attach to cardboard, which acts as the wooden frame.
There are also lots of free virtual Rekenreks available on virtual math manipulative websites. You can project the Rekenrek onto the screen for the whole class to see. Similarly, if your students have access to iPads, they can use the virtual Rekenreks on a virtual math manipulatives website or app.
Rekenrek Variations
When you search for Rekenreks online, you might see some variations other than the standard Rekenrek I’ve been talking about thus far.
There are Rekenreks that only have ten beads, five white and five red. These are sometimes used in the first part of Kindergarten or for students who are only working within ten who might be overwhelmed with two rows of beads. Alternatively, you can always take an index card and temporarily cover the bottom row of a standard Rekenrek.
You might also see a Rekenrek with one hundred beads, set up the same way as the standard Rekenrek with each row containing ten beads, five white and five red. While this has the same number of beads as an abacus, the alternating groups of five white and five red maintain the focus of the benchmark of five. This Rekenrek can be used in the same way as the standard one, but with larger numbers through one hundred.
Getting Started with Rekenreks in Your Classroom
One of our favorite ways to introduce Rekenreks by allowing students to observe and/or explore them freely. Then, ask, “What do you notice? What do you wonder?” Have students share their observations and questions with the class. There’s no need to explain the benchmarks of five and ten initially – students will pick up on that over time.
Next, say a number and ask students to build that number. Have them tell how they made that number. Ask if there are other ways they could make that number. For example, I can make 7 by sliding 7 beads on the top. Or I can do 5 beads on the top and 2 on the bottom, 1 on the top and 6 on the bottom, etc.
Alternatively, show students a Rekenrek with beads already moved and ask them what number it shows and how they know.
When you think about it, Rekenreks are like counters and a number line all in one! Each bead acts as an individual counter, but together, I have a number line of ten on the top and another number line of ten on the bottom. How cool is that?
We just mentioned that the Rekenrek is based on the number five because of the groupings of five beads, which mimics the structure of our hands and feet, with five fingers on each hand and five toes on each foot.
Can you think of another math tool that utilizes the benchmark of five? If you guessed a ten frame, you’re right!
When students work with ten frames, they are able to see that when all the squares are filled in on the top row, that makes five. And when all the squares are filled in on the bottom row, that makes another five. And five and five make ten.
As students use these tools to unitize and understand the structure of numbers, they are developing Math Practice 7 as they “look for and make use of structure”.
Supporting Subitizing with Rekenreks
Rekenreks, fingers, and ten frames all help students subitize quantities, particularly the benchmarks of five and ten.
Benchmarks of Five and Ten with Rekenreks
Let’s take a closer look at five. On the Rekenrek, students learn that when all the red beads on the top are pushed over, that equals five. Just like how when all my fingers on one hand are up, that equals five. And when all the squares are filled in on the top row of a ten frame, that equals five. When students “just know” that all the red beads on the top of the Rekenrek equal five, they do not have to count each one. In other words, they are able to subitize it.
In order to help students subitize quantities on the Rekenrek, they need support seeing those benchmarks of five. Try asking students to show a given amount of beads in one push (or as few pushes as possible).
Let’s say that I ask a student to show me 7 beads on their Rekenrek. If a student pushes each bead over individually, one at a time, they aren’t recognizing that benchmark of five. A student who pushes over five beads and then two more beads sees that seven is made up of five and two more. A student who pushes all seven beads over at one time also sees that seven is made up of five and two more but was able to execute it in one action, which is even more efficient.
If you ask students to show a certain number of beads on the Rekenrek and they need several pushes, honor what they did and then ask, “Can you try showing that same number of beads but in one push?” Discuss which way is more efficient and why it might be beneficial to use the more efficient way.
From Counting All to Counting On
This same idea helps students progress from “counting all” to “counting on” when adding. Let’s examine how students might use the Rekenrek with both of these strategies with the problem 5 + 3.
- The first student pushes five red beads across the top bar, one at a time, counting “1, 2, 3, 4, 5”. He then moves two white beads across the top bar and counts “1, 2”. He then goes back to the first red bead and counts all the beads he has pushed over, touching them one at a time as he counts, “1, 2, 3, 4, 5, 6, 7… 5 + 2 = 7.”
- Another student pushes all five red beads across the top bar in one push and says, “5”, and then she pushes two white beads over, one at a time and says “6, 7… 5 + 2 = 7.”
- A third student pushes all five red beads across the top bar in one push and says “5”. Then she pushes two white beads over in one push and says “6, 7… 5 + 2 = 7.”
The first student used the “counting all” strategy. He counted out the number of beads for each addend, then recounted them all as one group to get the total number of beads.
The second student showed she was able to utilize the benchmark of five to count on because she pushed all five red beads over in one push and counted on the remaining two beads.
The last student was also able to count on but in the most sophisticated way by pushing the benchmark of five over in one push, and then the two white beads in one push.
Exploring Number Conservation with Rekenreks
Rekenreks also help students develop the idea of number conservation, which means that while a number can be broken up in a variety of ways, the total amount doesn’t change. In other words, numbers can be decomposed, but the total amount, that whole that we started with before breaking it up into parts, is unchanged.
Rekenreks particularly help students develop number conservation with five and ten. As they utilize different combinations of beads to make these quantities, they see that the total amount is always the same.
For example, let’s take the number five. Here are some of the ways a student might show five on the Rekenrek:
- 5 red on top, 0 red on the bottom (5 + 0 = 5)
- 3 red on top, 2 red on the bottom (3 + 2 = 5)
- 1 red on top, 4 red on the bottom (1 + 4 = 5)
- 0 red on top, 5 red on the bottom (0 + 5 = 5)
Connecting to Concrete, Representational, Abstract Thinking
As we mentioned earlier, one great way to begin using Rekenreks with your students is to ask them to build a given number. In the example we just mentioned with building the number five, there are many different ways to show this number on the Rekenrek.
Ask students to explain how they knew it was that many. Ask if there are other ways they could make that number. To enrich this task even further, have students draw a picture of the beads they pushed over on their Rekenrek. A simple template of two lines acting as the rods gives students the space to draw the beads they pushed over. They can do this for all the ways they were able to show that number.
Having students write the number 5 would complete the trifecta for, you guessed it, CRA – concrete, representational, abstract. The Rekenrek is the concrete, hands-on experience. The drawing is the representational, and the written numeral is the abstract. The combination of these three elements provides a rich, meaningful experience for our students.
Meaning Makers, we hope you enjoyed our deep dive into Rekenreks. What new ideas might you try with them? What questions do you still have? Be sure to let us know!
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Until next time Meaning-Makers, have a great one!
