### Basic abacus as a manipulative

I don't want to leave out one of the best manipulatives there is for first and second graders: a simple "school" abacus that has 10 wires and 10 beads on each wire.

I don't mean a Chinese or Japanese abacus with a special counting system. I am talking about using a simple 100-bead abacus for counting, and treating each bead as 1. You don't have to learn any of these sophisticated systems that have been in use with various abacuses. Just consider each bead being 1, period.

Then you have 10 tens, or a hundred, in your abacus, and that goes a long way explaining tens and ones or 2-digit place value to first graders.

It is best if the abacus has the first five beads colored differently from the next five, in each row, like on the right.

Then the child will easily recognize 6, 7, and 8 beads without counting. Also, let's say you choose 6 beads on one wire and 8 on the next one. You can show how the five and five on those two wires makes ten, and some are left over.

To help a child learn the numbers up to 100, you can play a simple game with the abacus. When it's your turn, you say a number, and the child "makes" it or shows it on the abacus. Then your child says a number for you to show on the abacus.

You can also show the child other things, such as how the subtractions

10 − 5

20 − 5

60 − 5

are similar, or let the student find sums of 2-digit numbers, such as 23 + 45. He can move 2 tens and 4 tens, then 3 and 5 individual pieces — you can show how to add the tens and ones separately.

You can let the child explore what happens with 28 + 9.

You can also model multiplication: move 4 beads on each of the 5 neighboring wires, and there you have 5 times 4!

Browse Amazon's abacus selection here.

So this is not rocket science; it is very easy. You don't need to learn any special abacus systems.

## Comments

I totally agree about using a more simple abacus.

There is also something called an "abax" (for-runner of the abacus). I have a post about it at http://mathmojo.com/abacus/abax/abax1.html, using speed-math methods to add and subtract with it.

The thing about manipulatives like abacii and abaxii is that the were actually used for hundreds (if not thousands) of years. The are time-tested and proven by societies all over the globe.

That beats the plastic-junk mentality of a lot of the trendy "manipulative" manufacturers.

Thanks for your insightful blog postings!

Brian

Lori

-Ed

very grateful

Can you explain more what you meant by

10 − 5

20 − 5

60 − 5

and how that would appear visually, please?

And does anyone have a lesson plan for place value? I'd love to take a look at it.

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Then take away 5.

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It's nothing fancy.

Place value -- abacus with 100 beads can only be used to teach place value with tens and ones. Simply ask a child to make 24 or 67 or 82 etc. on the abacus. Or, ask a child to make 7 tens 4 or 3 tens 5 etc. Or ask the child make 65 and then add a ten more. That kind of play practices the concept of "tens and ones".