I am preparing for my presentation at the annual US Math Recovery conferenceand thought it would be a great time to post about one of my favorite math manipulatives for PreK through 2nd grade; the Rekenrek…which just so happens to be the focus of my presentation at the conference next week. To start, here are my favorite resources for the rekenrek. If you don’t know what the heck a rekenrek is, read on past these and then come back.
When you want more detailed lessons that connect to the Common Core Standards and the big ideas in PreK-2 math, check out the book I wrote, Mastering the MathRack.
The Math Learning Center also has a free app, called the Number Rack.
I recommend if you want to purchase some for your class go to www.MathRack.com. (full disclosure, I do consulting work for the MathRack company. But the reason I do is because they make the best rekenreks on the market.)
Check out this video by Graham Fletcher for a very detailed explanation of how the rekenrek helps address many big mathematical ideas as well as the Common Core Content and Practice Standards.
The rekenrek is a tool that was created in the Netherlands and has been translated to be called an arithmetic rack or calculating frame. I personally call them MathRacks because I work with the MathRack company, but more people know them as Rekenreks. So in this post I will call them rekenreks. At first glance many people think it looks like an abacus. There is a slight but powerful difference, the color change. The color of the beads changes after 5 beads so that kids can subitize easier and relate quantities to the benchmarks of 5 and 10.
Kids can tell that the bottom row shows 4 because one of the 5 red beads was not pushed over.
The rekenrek is a unique tool that allows children to develop number sense at their own pace. With the built-in 5 & 10 structure, rekenreks help children build number relationships that lead to more advanced strategies. In every classroom, there are students of various mathematical abilities, yet as teachers, it is our job to get them all to proficiency. You might have some children who automatically know that 7 + 8 = 15 and others who have to count out seven objects, count out eight objects, and then count them all to determine it makes fifteen. Most manipulatives we use in K-2 classrooms do not help children get past the one-by-one counting and into more efficient strategies.
“In the United States, the manipulatives most commonly used with young children are single objects that can be counted – Unifix cubes, bottle caps, chips, or buttons. While these manipulatives have great benefits in the very early stages of counting and modeling problems, they do little to support the development of the important strategies needed for automaticity. In fact at a certain point they begin to reinforce low-level counting strategies. For example, to solve 6 + 7 with Unifix cubes, children need to count out six, then seven, and then either ‘count on’ as they combine or (as is most common) count three times – first the two sets, then the total” (Fosnot & Dolk, 2001, p. 103).
With the rekenrek, children can model and solve problems the same as they would with Unifix cubes, but the built-in structure of the rekenrek allows children the flexibility to develop more advanced strategies as well. Here are some examples for how kids might solve 7 + 8 using a rekenrek:
“I put 7 on top and 8 on the bottom. I see two groups of five red beads and I put those together to make 10. Then I have 2 white beads on top and 3 white beads on bottom to make 15. 7+8 = 2+(5 + 5)+3”
“I pushed over the 7 beads and saw I needed 3 more to fill the row. So I added the 3 beads and knew I needed to add 5 more (to add 8 total). I had 10 on top and 5 on bottom to make 15. 7+8 = (7 + 3) + 5”
Rekenreks help children develop these more advanced strategies by building number sense. Number sense develops as children have experiences with numbers and they build relationships about numbers. John Van de Walle (2006) describes four relationships that need to be developed for children to gain number sense with numbers up to 20 so they can use those numbers but also understand them:
Spatial relationships – having a visual picture of an amount, also recognizing how many without counting by seeing a visual pattern (subitizing). One and two more, one and two less – this is not the ability to count on two or count back two, but instead knowing which numbers are one and two less or more than any given number by understanding the pattern of numbers. Benchmarks of 5 and 10 – because ten plays such an important role in our number system, and two fives make up ten, students must know how numbers relate to five and ten. Part-Part-Whole – seeing a number as being made up of two or more parts.
Traditional textbooks tend to focus on skills associated with numbers; count to 8, recognize the numeral 8, write the numeral 8, and then operate using the numerals. The relationship building is limited, and sometimes completely missing. If you are looking for a way to build number sense, let them play around with a rekenrek. If you need resources, don’t forget the ones I shared at the top of this page.
