Hands-on manipulatives help kids turn the idea of math into concrete concepts, and an abacus is one of our favorite manipulatives. We just use a simple 100 bead abacus. It has ten rows with ten beads on each row. The beads are grouped in fives by color. This just helps kids to begin to see groups without always having to count every single individual bead. Ours also has the beads reverse color after 50 so kids can see the groups of fifties as well.

Here are a few simple ways to use an abacus with kids:

- Learning Numbers – start by just practicing numbers and counting. Make it a game where you say a number and the kids sees how fast he or she can show that number. Each bead on the abacus represents 1, so they start at the top and slide that number of beads over. If it’s a number bigger than 10, they can learn to immediately slide the first row of 1o over, and then continue. Once they are doing lots of double digits, they can learn that the first digit (the groups of ten) is shown by sliding over whole rows, then the extra ones are added by sliding single beads. Below you can see the number 15 shown.

- Adding — Next kids can use it to learn to add numbers. It’s especially useful for regrouping. For example, to add 7+8 they slide 7 beads over on the first line, and then another 8 over on the second line. Without even moving anything, they can see the group of 10 yellow beads and then 5 more blue beads.

- Regrouping — Teaching addition with regrouping can go even further when they are using multi-digit numbers. Have them experiment with making trades for groups of tens using sums like 39+8, 57+23, or 44+18. As they begin to move and manipulate the beads they will gain a greater understanding of what carrying means as they create groups of tens. Sometimes to regroup you’ll actually make trades. For example, if you add 7+8 you probably slid 7 beads over on the top wire, then 8 on the bottom. You can also show how you can trade the 3 blue beads on the bottom for the 3 blue beads on the top, making a group of ten (essentially, putting them in a group for the tens column)

- Skip Counting — Practice counting by 10’s, 5’s, 4’s, 3’s, 2’s and so on. Slide the appropriate beads along as you count.
- Patterns — Point out patterns you see. For example:

10-5=

20-5=

30-5=

40-5=

- Multiply — Multiplication involves adding groups of numbers. It is just repeated addition. This can be easily shown on the abacus by sliding 6 beads on each of 4 wires (4×6, or 4 groups of 6). You can also show how multiplication is commutative (6×4 is the same as 4×6). Addition is also commutative and can be shown as well.
- Divide — You can show division problems pretty easily in two different ways. Think of twenty divided by 4. Show twenty beads on the abacus, then begin putting them into 4 groups, one by one. You’ll end up with 5 in each group. You can also do the same problem by showing twenty beads and putting 4 beads into each group. This time you’ll end up with 5 groups.

If you use an abacus from RightStart Math (that’s the one we chose), you will also be able to turn it on its side to use for more instruction in making trades, carrying, and place value concepts. My kids all seemed to pick up these concepts quickly with the abacus basics I showed up above, but if you want to see more of that you can check out RightStart’s suggestions. We use Saxon Math for our curriculum, but I really love RightStart’s abacus as a companion to it. My kids always pull it out when they are starting on their Saxon Math facts worksheets. They’ve all developed great number sense by using manipulatives. I have to admit, working with an abacus has given me better number sense too. Mental math has become easier as I’ve learned to visualize the groups.

I love a good math toy that actually teaches something and isn’t JUST a toy.

## More From Layers of Learning

Here are some more fun lessons from Layers of Learning. Hope you check a few of them out. Beach ball math is the way I get my kids excited when practicing math facts flashcards is too boring to stomach anymore. And everyone loves it when M&M’s make an appearance in our math session.