Welcome back to Part 2 of Abacus Fun!
If you missed part one, be sure to go back and find out more about the functionality of an abacus, how to use it for subitizing and simple addition and subtraction, and directions for you to learn how to make your own simple abacus! Today, we hope to show you that an abacus is so much more than just a “simple device” for counting or adding, with applications that extend into much higher level operations and concepts.
Multiplication with the Abacus.
By learning multiplication on the abacus, the kids really learn to skip count and actually read the beads. I’ll never forget learning about the abacus at a workshop and the instructor giving me the task of skip counting by 7s to 70, forward and backward. The catch was that I couldn’t count the beads, I had to just read them the way they were. So I started off pushing 7 (which I knew because I saw 5 red and 2 white, completing every row before going on to the next one. Next, I needed 3 white and 4 red. This is an excellent exercise to help make sure kids know how to decompose in many ways to be able to do this exercise!
In our multiplication journals, the activity for the extension day is to grab an abacus and count by the number they were learning that week. For example, if we were learning the patterns of 4, we can skip count by that number to it’s decade (40 in this case) forward and backward. If we were learning the patterns of 4, they’d be skip counting by 4s to 40 forward and backward – but be sure to remind your students: they can only read the beads!
Example: Show me 40, push 4, read the beads (36), push 4 beads, read the beads (32), push 4 beads, read the beads (28), etc.
Division on the Abacus.
Kids can visually see how a number can be divided into groups by demonstrating division on the abacus. If I start with 12, and ask how many groups of 3 are in 12. Kids can start to pull the beads into groups of 3. We can start by pulling the 2 individual beads and 1 from the 10 to show 1 group of 3, pull another 3 to make 2 groups, pull another 3 to make 3 groups, and then we have 3 left, which makes 4 groups in all.
As they pull across the beads in the desired quantity, kids can count how many groups they have to understand that For division, I would say, how many groups of 6 are in the number 30. Kids can visually see the conceptual part of division using the abacus.
Yes, we can even use the abacus for fractions! If we start with 12 on the abacus, what is ⅓ of that number. Kids would have to look at the 12 being the total that we want to take out ⅓ of, so how do we take a quantity like that and break it into a fractional part? What happens if we took the number 9 and I wanted you to break it into 4ths? Could you do that? What would happen or what problems would you run into? You can do a lot of those types of fractions.
What?? Sure! The idea here is that whole row of the abacus and each bead would be 1/10th of a whole. Depending on how you use that, you can help kids to look at it differently.
Addition/Subtraction of Decimals
Let’s start with 0.6, which we can represent by pushing 6 beads across. Then, I want to add 0.8 but I can’t just push over 8 beads on the next row. I have to complete the whole. The new number would take up multiple rows, similar to the addition problem we did with whole numbers. So we would build .8 by pushing 8 beads across, and then look to see how it could bond to the next whole number. I look at 0.6 and realize that we only need .4 to get to the next whole number, so I decompose .8 into .4 and .4, take .4 and put it with 0.6 to get a whole 3, and then add the .4 back to get 1.4.
If I asked you to take 7 away from 2.6. Kids could see, looking at place value, that they have to take away the whole row, break it into 10ths and look at how they could actually subtract that quantity.
Remember D.C. and the advanced side of our Addition Strategies poster? That poster shows how your students kids can learn the idea of decomposing, The concept of D.C. can apply to decimals in the same way).
The abacus has many many functions. I think it’s important to have an abacus for every child in a classroom to be able to do the different activities. If we can’t have one for every child, at least having one for every child to share. But it doesn’t have to be the big, cluncky, loud abacus. They can make their own! We used to make them out of tongue depressors, bamboo sticks, and hot glue, but over time, the beads would slide on their own and weren’t very conducive to the “show me’’” part of development. Making an abacus with a mesh backing provides a bit of grip so that students can build a number or problem and actually hold it up to show you what they’ve done.
You can also differentiate for kids that might find the abacus as a bit too much, such as special education students or those that need math intervention, by making their abacus go to 50, and then add the other rows on later when the child is ready to build on that concept.
Number Rack form the Math Learning Center. (web, iOS, Google Chrome) This app can be used on the Google Chromebook or it can be downloaded onto an iPad or iPhone. I remember using this with my son Connor in 1st grade while we waited for his sister at dance. He just couldn’t grasp the concept of making 10. If he had 8+5, he could always be counting on his fingers! He’d get 8 in his head, and then start counting up.
As soon as I pulled out the Number Rack, he could see conceptually what I wanted him to do and he was able to grasp the concept much more quickly when I said to make a 10. This app lets you customize the number of rows in your abacus, which you could do based on your sum so it mightbe a little less overwhelming for the kids. It also has the capability for kids to write on it, so kids could write their problem on it, and then answer the question and show you in the abstract, or show you pictorially how they arrived at their answer.