Did you know there are many different types of abacus??
Sometimes we see videos from places overseas where kids are very accurately calculating things and flipping through beads very quickly. There are actually many different types of abacus that are available – Chinese, Japanese, Russian, Polish, German, Roman – to name a few, and they are based on different number systems.
An abacus has many names as well. It can be called a number rack, a 100 rekenrek, math rack, abacus, 100 bead rack – people have come up with a million different names for the same tool!
The abacus that we use in the United States is called a Danish abacus, and it is in line with our base-10 number system where each row of the abacus has 10 beads, and it has 10 rows to equal 100. At one point, I thought an abacus was something you’d see at IKEA or in a childrens’ nursery or playroom as a decoration. But an abacus can actually help students learn and practice many mathematical concepts in a very developmentally appropriate way for students in elementary school. Students can practice subitizing, conservation to a number, addition, subtraction, place value, multiplication, division, fractions, and even decimals!
While we are about to discover the incredible versatility of the abacus, please note that an abacus it can be overwhelming for our youngest students. The rekenrek (demo size or a homemade version) or a Counting Buddy is a more appropriate tool in a preschool or Kindergarten classroom. They actually have a very similar functionality, but they only go up to 10 or 20. Once students get about halfway through 1st grade, we need to transfer them to an abacus. The abacus can be used in 1st grade all the way through 5th.
In your math curriculum or district-purchased book, it will most likely give the abstract means or potentially the pictorial, but remember: we need kids to have CPA – Concrete, Pictorial, and Abstract. Kids in 5th grade are not too old to use an abacus! The abacus can be a great vehicle for kids to conceptually see what’s going on. There’s a large demo abacus that’s great for kids in a small guided group as well!
Once kids have that full understanding of how the abacus is operated and they’re able to do different activities, that’s really when you can go deeper into concepts.
The abacus is “cleared” and ready to use when all the beads are pushed to the right with the red beads in the lead. It might feel odd, but as we build numbers and quantities, we push the desired number of beads to the left and then we read the abacus from left to right.
Many of our schools put a smiley face in the upper right-hand corner of the abacus to help kids remember how it should be cleared because many students have trouble with directionality. If I were to say “push all your beads to the smiley face,” the abacus would be happy or cleared. If the abacus was upside down, it would be a sad face.
Make your Own!
A typical abacus costs about $12, so having 30 in a classroom can add up quickly. Not mention the fact that 30 abacus would be incredibly bulky and can be very loud (just shake one – you’ll see!) with all the beads going. For just under $2/kid, we can actually make an abacus using a mesh backing from the cross-stich section a craft store (some Walmarts also sell it). I usually get a “7 mesh” backing. The sheet you can get is quite large – about the size of a large piece of construction paper – for under a buck! You can make 3 different abacus out of one sheet! Use 10 black pipe cleaners (this is important – we prefer black or maybe dark brown because multicolor pipe cleaners can be distracting as kids are learning).
On most of the abacus, they have 5 of one color bead and 5 of another bead, most other websites or apps use white and red, so we keep that the same with the design of our abacus.
Use red and white beads, 5 red and 5 white on each row. Yes, other colors are more exciting, but you really want to capture the idea of the number system and provide consistency for your students, so stick red and white. Some of the online manipulatives will switch the lead color of the beads once they get to 50, halfway through the abacus. This would help indicate a benchmark number of 50. So if I showed you 62 on the abacus, you’d see the lead beads change colors and immediately be able to subitize and know that the first section is 50, that there is a row of 10, which makes 60, and then 2 more to make 62. There’s not really a right or wrong way. A lot of abacus apps and websites are set up that way, so if you have students make their own abacus, you could certainly switch the lead color halfway through to help them recognize numbers that are higher than 50.
Subitizing with the Abacus
This is really the first step developmentally for students. We do a lot with 10-frames, we do a lot with the counting buddies or scatter plates, but we don’t often take it to the next level. The next level should be that, by the end of 1st grade, the student can subitize all the way through 100 without counting. A great website for practicing this skill is http://www.dreambox.com/teachertools. If you scroll down to the 1st grade section, and you’ll see an abacus (they call it a MathRack). This tool will flash up an amount on the abacus and the kids have to quickly tell you the quantity.
Once the students can subitize pretty easily, they can start building numbers as you call them out. The “Show Me” activity is all about having kids show you a certain amount and having conversations about how they knew the number they were showing you was what you asked for. It’s amazing to hear kids’ number sense even after only a few times of using the abacus!
“Show me 3. Clear. Show me 5. Clear. Show me 7. Clear. Show me 9. Clear.” Observe. As the child is building the numbers, after they clear the beads every time, do they continue to one-to-one count when building their next number?
Many times, well-meaning teachers observe this and begin to tell their students things like, “Here! You can just push over 5 – you don’t have to count!” But you really want the kids to discover that strategy on their own! Usually, by the time I get to “Show me 9,” the student will usually push over the 5 red beads and then finish with the 4 white ones. I’ll say “Wait a minute! How do you know that’s 9? You didn’t count them!” Kids will say, “Well, I already know that there are 5 red ones and then I have to add 4 more.” Or, they might say, “I know the whole row equals 10, and you wanted me to show 9, so I just left 1.” Just observing a student working with one row of the abacus and evaluating their actual understanding of conservation to a number is incredible! We want students to be able to anchor to that 5 so they don’t have to recount every time, which is why we do a lot of our subitizing activities. Students must know that the abacus doesn’t have the capability of adding more red beads to the row, so there will ALWAYS going to be 5 red beads. The kids who lack the concept of conservation will continuously go back and count the red beads.
In the 1st grade classrooms, teachers sometimes get frustrated during whole group instruction as the students got to higher numbers on the abacus. The teacher says, “Show me 23.” On the one hand, you’ve got a child who is one-to-one counting trying to get her 23 and, on the other hand, you have another child who is moving over 2 rows of 10 and then 3 individual beads and telling you, “I have 23 because it’s 7 less than 30.” The key is to really get kids communicating their thinking and developing a depth of understanding about our number system.
Unfortunately, in today’s world, we have so many kids who are so confused by place value. If you ask a child to show you the number 56 on the number chart (which is actually a more abstract tool because it’s just full of numbers). The teacher wants the child to just look at the chart and point 56, then go immediately to 66. However, the child counts one-to-one. We’re pushing 1st graders to understand a pattern that they don’t really get. The number grid is going to be highest abstract tool, where the abacus is going to be the most conceptual tool for a child. If they were to build 56 on an abacus and then move 10 additional beads over, they’re going to see quickly by reading and understanding the number system of it that 10 more is 66. Many kids today can find the missing number on a 100s chart because they’re just plugging in numbers, but they don’t really understand the place value system. The reality is that we need to spend more time with the abacus.
Adding with the Abacus
A lot of kids have a conceptual understanding of D.C. and the idea of composing and decomposing, but we can visually represent that strategy with an abacus or Counting Buddy.
Let’s take 8 + 5. On a Counting Buddy Sr., I can push 8 beads over, then move 5 more over, but not push them all together yet. This helps the kids easily see how they should decompose those 5 beads into 2 and 3 because of their color. Then, D.C. is happy because he can make a 10, and we can see the answer to the problem is 13. The same concept can happen on the abacus, but with larger numbers. If I were to build 26 on the abacus and then build the number 8. We know that D.C. wants to find the decade, so after we build the 26, they go to the next line and build 8. We ask how many more they need to get the first line to the decade. It’s very clear on the abacus that we only need 4 more to reach the decade. Therefore I can decompose my 8 into 4 and 4, put 4 up with the 26 to get an even 30, and then I know the answer is 34.
Subtraction with the Abacus
You can see if kids really understand what’s happening when we talk about subtracting and represent the problem with the abacus. Let’s take 62 minus 12. We can break 12 into 10 and 2, and then the kids really have to look at the quantities and think about how they’re taking away one 10 and 2 ones.
Abacus Fun Activity Cards
We are so excited to introduce our brand new Abacus Fun activity cards that show the addition and subtraction activities that kids can complete with their abacus! These cards can be used starting when the abacus is introduced in 1st grade all the way through 5th grade! See a preview by visiting our store!
Available as a digital download for $4, you can print them in color, on cardstock, and laminate, if desired. Cut the activities apart and put them on a ring so you can flip through the cards as a reminder of the variety of uses of this wonderful tool!
Get your download today!