The Abacus

An abacus is an ancient counting tool that has been used all over the world, for centuries, primarily in Asia.  The frame is traditionally made of wood with wire or small wooden rods running through it.  On each of the rods there are beads that move from one side to the other. Children being using an abacus by moving the beads from one side to the other and counting them as they go.

abacusThe abacus pictured above is designed for an early childhood environment.  This one has 10 rows of 10 beads.  An abacus designed for older children or adults provides “decks” or separate areas to represent place value.

Since children take in information through their sense of touch (as well as their other senses), the abacus makes good sense.  It reinforces one-to-one correspondence and number sense.

Did you know that blind children all around the world learn mathematics with an abacus?

Inchworms or Centibugs – You Choose

One of our Math at Home readers requested the link to the Inchworms I wrote about recently.  I went to Google and put in the search terms inchworm and manipulative and the first thing that popped up was a site that sells the Inchworms I was looking for as well as Centibugs – a new manipulative I have never heard of.

They are essentially the same thing except they are a standard centimeter unit.

This got me thinking about how much easier it would be for children to understand units of measure if we taught and used the Metric System.  It is a Base 10 system which coincides much more closely with the way we teach counting and number.  There are no variances between liquid measures and solid measures in the Metric System (a liter is a liter is a liter, but an ounce is different if it is a fluid ounce or a solid ounce). There are many more reasons why adopting the metric system just makes plain sense, however it probably won’t happen in my lifetime.  This article explains why it won’t happen and why Americans don’t really want it to (or care enough to do anything about it).

Here’s to the Metric System.





On Friday, Math at Home presented at the Opening Minds conference in Chicago.  We spoke about the Math at Home site and our upcoming Professional Development series, soon to be available through the Gateways to Opportunity ilearning system.(More to come about that exciting project over the next couple of weeks). At the end of our talk, we presented the attendees with buckets of counting worms and walked through some possible learning activities that could be done with them.  Although the worms we had were a bit different, they reminded me of this post from 2013.

Have you seen these?  These are called Inchworms and they are actually one inch long.  That means they are standard units of measure (because an inch is an inch is an inch) while looking like a non standard unit of measure.  When children use these to measure, they might say, “It is 3 inchworms long,” which also means that it is actually 3 inches long. This is an important step in children’s understandings of measurement, which can be reinforced by laying these inchworms out next to a ruler to show that they really are one inch each.

It might be fun to introduce the “Inchworm Song” as well.  If you don’t know/remember it, it goes like this.

“Inchworm, inchworm, measuring the marigolds
You and your arithmetic, you’ll probably go far.
Inchworm, inchworm, measuring the marigolds
Seems to me you’d stop and see how beautiful they are.

2 and 2 are 4, 4 and 4 are 8, 8 and 8 are 16, 16 and 16 are 32.”

Weighing with a Bucket Balance

Balances and scales are rich with opportunities for children to consider weight and size.  The Bucket Balance, pictured below is made for the classroom and it encourages children to weigh objects “relatively” to a standard weight or “relatively” to another object.  Through trial and error, they can see if an object is lighter or heavier than another object and then adjust the balance until they make it the same.

Remember, young children may be fooled by appearances, so they may think that something that is “bigger” may weigh more, while that might not be true at all.

Learning Resources says of the Bucket Balance that it is “Perfect for exploring basic measurement concepts.” Children can measure, explore volume and compare solids and liquids.

Bucket Balance


This coming Thursday, I am going to write about a gross motor game that uses the bucket balance.  I think you are going to like it.


Numbered Gloves

IMG_0020-2I saw these in a gift store. You can’t really tell from the picture, but they are really little, sized for a two or three-year old’s hands.  They got me thinking about using every opportunity we have to encourage numeral recognition and mathematical thinking even labeling a child’s body with letters and numbers.

Now, I can’t imagine that teachers can run out and buy these adorable little gloves, but I know that my dollar store sells the exact same gloves in solid colors for a dollar apiece.  Wouldn’t it be nice to go and get enough pairs for the children in your room, ideally in white or yellow (or another very light color) and make your own numbered gloves?  The benefits of making your own are really plentiful.

1.  Begin with the numbers 1,2, and 3 and only mark those numbers on the right glove.

2.  Have the children only wear that glove and use them while singing songs like Three Little Ducks Went Out One Day or Three Little Monkeys Jumping on the Bed, and then encourage children to not only sing the songs, but to use the appropriate finger to represent the numbers of ducks or monkeys.

3.  Provide another visual cue on each finger; i.e., dots (pip) to represent the number.

4.  Add one more clue perhaps by color coding the numbers as well; 1= red, 2= blue, etc.

Once your kids have mastered the use of 1,2, and 3, add the next numerals up to 5 and continue to include the other visual clues (pips and colors).

I might even write a large R on the right-handed glove, and an L on the left-handed glove.  This seems like a really nice and fairly easy way to provide more avenues for children to travel down as they explore early math.

If you give this a try, take some pictures and send them to me, I will put them on the blog.



Cuisenaire® Rods

There are few manipulatives out there that are as interesting and beautiful as a wooden set of Cuisenaire® Rods.  Developed 75 years ago by Belgian teacher Georges Cuisenaire these “rods” come in beautiful colors in varying lengths.

The units are color-coded which provides additional visual cues for children. If you look carefully at the above photo, you can see that the units of 1 are white and the units of 2 are red, units 3 are green and so on.  When using them with children, you can refer to the lengths by their unit number as well as their color.

Unlike Unifix cubes, traditional Cuisenaire ® Rods do not attach to one another (although there are sets that do attach).  This provides a different set of possibilities for children as their uses may be less obvious and may require a bit more ingenuity.

A few weeks ago, I wrote about the “trading game” that is played with the family bear counters. Well, a more developed “trading game” can be played with the rods since each of the rods has a specific value.  White is worth 1 and red is worth 2 and green is worth 3.  In order to get a green rod, children must trade 3 whites, or 1 white and 1 red.  Give this a try and tell us what you think.

Dice are Cool

I know I am dating myself here, but back in the day, the really cool boys hung big, old fuzzy dice from their rear view mirror. You just knew that anyone who was cool enough to hang giant, pink or yellow fuzzy dice in their cars for everyone to see, must be someone really special. Fast forward 25 years, and now I think dice are cool because they provide endless opportunities for young children to explore mathematical concepts.

Below is a picture of a traditional “Shut the Door” game which asks children to roll the dice, count the pips (the dots on the dice) and then “shut” the numbered door shown on the dice.  When all of the doors are shut, the game is over.  There are ways to play this game individually or with others.  I especially like this one because it is a noncompetitive game that asks children to work together in order to meet the desired goal (all of the doors shut).k2-_56cc6d28-d584-4a5c-be62-777fd3f66344.v2

This version is played by as many as 4 children at once.  When children engage in this together, the play moves from being cooperative to competitive which is a natural progression as children get older.51xnDuuJ-KL._SX300_


Sumthing Wonderful – Sumblox

FullSizeRender-2Sometimes the greatest gems are found when you aren’t even looking for them. Two weeks ago, I attended the ISTE (International Society for Technology in Education) Conference in Philadelphia, PA.   I spent each day agog at the sheer quantity of amazing people, services, products, systems, and ideas designed for educators. As an early childhood person, it was equally mind-blowing to be around educational systems that have money, and are investing money in education. Oh, how I wish we could have an early childhood conference like that!

So, imagine my sheer delight when I found the least techie product imaginable, designed for young children.

The product is called Sumblox. These are handmade, wooden math manipulatives that harken back to the Froebel gifts and Montessori materials. The premise is quite simple; wooden blocks shaped like numerals that are sized to represent the quantity of the numeral.

Below, you can see that two “3” blocks are equal in size to one “6” block and three “2” blocks. Brilliant!


And here you can see that the “3” and “5” block are the same as the “8” block. So logical.

FullSizeRenderWe have seen similar products in the past (think Cuisinaire© Rods). Ten units of “1” are sized   to match one unit of “10”. However, these are so much better because they provide an additional logical dimension to the design. With Unifix Cubes or Cuisinaire Rods, children have to make the connection that each block represents “1”. With Sumbox, the number is there already.

I also appreciate that Sumbox is also a set of finely made wooden blocks. I could see putting these out on the manipulatives table for children to simply play with and build. I think it is important to remember that the greater goal of manipulatives is for children to play with them, handle them, and discover their attributes. The fact that they can also be used to compose and decompose number is an eventual use, but may not be the initial way young children use them. With exposure, children will begin to discover that they can build towers that are the same size, that the blocks are shaped like numbers, and there is greater mathematical purpose to them.

Sumbox comes in classroom packs and family packs. I have already sent this link out to my friends with young children since I think this would be a very good investment for a family. If I was still a child care director, I would purchase one set for each of my classrooms. That is how good I think this product is.


Sorting Boxes

Sorting Boxes for ToddlersChildren will sort naturally.  They really don’t need a lot of special equipment, toys, or materials because they separate, combine, recombine, and organize their “stuff” all of the time. When you simply observe them at play, you will often see them moving their toys around, seemingly in senseless ways.  But if you watch and listen closely, you might hear them describe what they are thinking about as they manipulate their objects.  It may not be readily evident to you, the observer and adult, that the child is sorting the Legos into piles of “Legos I can use to build this thing I am thinking about,” and “Legos that I don’t want to use to build my thing.”  To the child, these 2 descriptions are real categories and provide enough definition for his sorting purposes.

So, do they make good sorting materials for toddlers.  Yes – in fact, they do.  I like the sorting box pictured above because it has multiple ways of instructing and informing the child’s efforts.

1.  The boxes themselves are sized so that only the correct number of objects will fit inside each one.  That makes them somewhat self-correcting.

2.  They are color-coded – the number on the side of the box appears in the same color as the objects that belong inside. This provides another message about what belongs in each box.

3.  The boxes themselves are soft, so there are no sharp edges or corners to bump little heads.

4.  The sorting materials are the perfect size for toddler-sized hands.

5.  The boxes close and can be stacked, much like nesting boxes (almost like 2 toys in one).

All in all – this is a nice choice for toddlers.


Nesting Blocks

Last week I wrote about traditional Nesting Dolls as a great math manipulative, so today I thought we could explore Nesting Blocks as an extension that post. Nesting blocks provide all of the good fun of sequencing as the dolls do, but they have the added benefit of being square with flat sides.  This means that in addition to nesting them, children can build with them.

Regardless of the math potential, the fun of piling up the nesting blocks into tall towers and knocking them over is too good to pass up.

When my kids were little we had a set that had 12 blocks of sequential sizes.  They had animals on one side, numbers on the top, and were color coded.  This offered my kids several ways to put them in order, using the images on the sides as clues.  The littlest animal was on the littlest block (I think it was a mouse) and the biggest animal was on the biggest block (clearly a whale or an elephant).  The number 1 was on the littlest block, and so on.

Many hours were spent building them up and knocking them down.  In order to make the tallest tower, children have to put them in order from largest to smallest, so there is a payoff in getting it right and trying many times.  I tried to find a picture of the boys playing with these, as I am sure I have seen one somewhere, but my pictures are too disorganized to put my hands on them now.  I did, however, find this picture with this beautiful set of wooden nesting blocks.  See how they have clues on the sides.