What is a Rekenrek?
Have you seen a math rack or rekenrek before? The rekenrek is a math tool that was created by Adruan Treffers of the Freudenthal Institute in the Netherlands and has been translated to be called an arithmetic rack or calculating frame. A rekenrek, number rack, bead rack, has two rods
, with 10 beads each, five red and five white. Similar to a 10 Frame, it helps students see numbers as groups that can be recognized, manipulated,
and used to find multiple solutions for problems while developing their number sense.
How to Introduce a Rekenrek
I usually wait a bit before introducing Rekenreks in Kindergarten, giving the students time to become comfortable with their one-to-one correspondence and number sequence. When introducing a new math tool, I like to give my students time to play with it and get it all out before we use them for instruction. Start by asking your students what they notice about the rekenrek. (20 beads, 2 rows, 10 red, 10 white, 5 of each color on each row etc.) Before asking them to use it as a tool but after explaining how to care for it like not using excessive force or leaning on it. (I have one rekenrek we had to superglue back together after a student had it underhand and accidentally broke it ), I gave them the chance to explore it, feel the beads and give it a good shake! When showing how it works, I try to model thinking about sliding the beads as a unit vs one by one and encourage the students to try the same, but not all of them are ready for that and that’s fine too. To begin, you may want to start with just one row and you can cover the bottom row with a folded paper or index card.
Page 7 of this resource by the Math Learning Center has a great step-by-step introduction lesson I use along with other lesson ideas using rekenreks with grades Kindergarten, First, and Second!
How to Use a Rekenrek Counting Frame
To set up a rekenrek, or to set it at “0” slide all the
beads to one side, I often remember it but a little rhyme, white on the right. You tip it to the right so all the beads are on the right side with none on the left. When using students can move the beads one by one, working up to being able to move them with fewer swipes.
If you're ready to dive into using rekenreks you can get some free printable resources here!
What to look for
As your students continue to use their rekenrek, the way they use it can tell you a lot about where they are in developing their number sense and anchors to five and ten. Are they moving beads one at a time or can they slide a unit? If they can unitize their numbers can they move their beads all at once or are they using five or 10 to build from. For example, if they are asked to show 7 beads, are they moving the 5 red beads and two more or can they move 7 all at once?
Begin to encourage them to move their beads to make numbers with one push, if they don’t on their own
How will a rekenrek help students? Benefits of a rekrekrek
Subitizing
A lot of manipulatives used in kindergarten like cubes, links etc. help students develop one-to-one correspondence, which is a crucial skill young mathematicians need, but don’t often lend themselves to moving beyond counting one object at a time. Since a rekenrek is contained, visually organized, and easy to reset it can help students move beyond counting by ones when they are ready. When used often, students begin to remember what different numbers look like on a rekenrek without counting, thus subitizing.
Supports Anchors to 5 and 10 and Moving Beyond Counting by Ones
A Rekenrek is perfect for building number sense in kindergarten, first, or even second grade students, supporting anchors to 5 and 10 with the two colors of beads. With continued use and support they can develop more sophisticated counting strategies and begin grouping or unitizing numbers rather than moving one bead at a time. Having an “anchor” to a number in my mind means that numbers that they are familiar with, know how many it is without counting, picture it in their head, can then relate their mental picture to other numbers and manipulate that model in their head.
Composing and Decomposing Numbers
Decomposing numbers is essentially understanding that numbers can be made up of other numbers. Since rekenreks have 10 beads on the top and bottom they lend themselves well to having two groups of counters you can partition and manipulate to begin to see part-part whole relationships in numbers. You could have your students show you a 5 for example and prompt them to show you using both rows. They can then make 5 with 3 on top and 2 on the bottom, 4 and 1, etc all equaling 5.
Another great tool to teach decomposing numbers is a 10 frame or part part whole mat. If you’d like to know more about those, check out this blog post about teaching decomposing numbers or video.
Double and Near Doubles, The 10 Within
A rekenrek provides an organizational scaffold that supports students' learning and doubles and near doubles. For example, if the problem was 8 + 8 once 8 is shown on both rods, it becomes easier to see that 8+8 is the same as 10 + 6 because of the two colors of bead. Which again helps kids anchor to 10 as they work on teen numbers and beyond.
Addition and Subtraction
Once your students are familiar with the way single digit numbers look on a rekenrek, they can use that knowledge to model various addition and subtraction problems using numbers as units vs need to construct each number before solving the problem. For example if I have the problem of 9+6 they may use a variety of known information to solve the problem. They may know to compensate for the 9 and make it a 10 and 5 more by putting 10 on top and 5 on the bottom, or move over all the reds, and then 4 to the top and 1 to the bottom to get their answer, the might slide 5 then 4 to make a 9, then 5 and 1 to make a six if an anchor to 5 most familiar to them, there are so many possibilities!
Rekenrek Activities
Full Group
Quick Images
Quick Images is a great way to start or end your math block. To play you show the students an image of a rekenrek for 3-5 seconds and your students have to either figure out how many beads are shown on the rekenrek or recreate that image on their rekenrek, whiteboard or rekenrek recording sheet. (The recording sheet is included in this Rekenrek Free Download)
You can use these ready-to-use Google Slides or Printable Multipurpose Rekenrek Cards for this activity.
Small or Full Group
One Push, Two Pushes
For this game you either give the students a number or pick a number for them to make. Have them think of how many beads there are and how they can show that number with one push of the beads if it's a number 1-10 or two pushes if it's a number 11-20. The idea is that they are thinking about unitizing the number instead and making it in the fewest number of pushes instead of moving the beads one by one. This game could be done in a center, but they may revert to a counting-by-one strategy instead of groups.
Centers or Stations
Pick, Build and Cover with Mini Version or Multipurpose Flash Cards
To play, your students will pick a rekenrek card, build it on their rekenrek and then find the number on their game mat and cover it. You can easily differentiate this game by using only numbers 1-10, 1-20 or 11-12.
Spin and Slide
To play spin and slide, you will have your students either spin a spinner with rekenreks on it or numerals. Then your students will slide the beads in place to match the number they spun and show the numbers spun on their recording sheet . Try to encourage them to slide all the beads at once if they are ready for it!
⭐Save on the Rekenrek Centers Activity Bundle!⭐
Spin and Cover
For this game you will need a paperclip and pencil as a spinner or spinner, I like these from amazon (not an affiliate link). Spin a number using the spinner and find that number on the chart. After the number has been found, the students will cover that rekenrek with a counter and continue until all numbers have been spun. Black and White and Color versions of 1-10 and 11-20 are included in the free download!
How Many Combinations Can You Find?
To play How Many Combinations Can You Find, give your students the number they will be decomposing if you are working on one number at a time or have them spin, roll a dice, or pick a number card and have them try to find different combinations for the number they are focusing on, draw the combinations they found on their recording sheet, and write the numbers in the combinations they found. They can play on their own or with a partner, with one student moving beads on the top and the other on the bottom and together they can check to see if they found the target number and show the combinations they found on their recording sheet.
Free Online Rekenreks
If you are looking to use a rekenrek online, my favorite interactive bead rack is available here on Didax.com. They have a 20 Bead Rack and a 100 Bead Rack.
Or look for some free Rekenrek Activities and Lessons from the Math Learning Center and activities from K-5 Math Teaching Resources.