Manipulatives

Our favorite purchased manipulatives are the Jumbo Cuisenaire Rods (got them on ebay). The rods are in 10 sizes, with the largest equalling 10 of the smallest. They are great for tons of different math concepts. There are also lots of activities that you can find on the web for them. (There are also regular sized rods, but I like the larger ones better for smaller hands, and they can be used as blocks as well)

I also like to use real world objects, depending on what dd's interested in. Right now the manipulatives we are using are Indian corn kernals (for sorting), gourds and apples (for sorting and nonstandard measurment).

i have a complete set of Kindergarten level math manipulatives from Newbridge Learning Company - they are nice, and dd likes to play with these as well. But I like the real world objects and cuisenaire rods better.

I truly dislike Cuisenaire rods. At first I thought I was some kind of freak, since everyone else seemed to think they were *the best*. Now I've figured out why I don't like them, and discovered others who feel the same. Isn't it funny how these things can strike different people different ways? What works for me and my family might not work for you! So, it's nice to also ponder "why" we like certain things.

Anyway, I like Montessori manipulatives because I think they nicely isolate the difficulty of the concepts on an incremental basis. Also, much attention is given to making the items pleasant to manipulate. My absolute favorites are the golden beads, which are used for (among other things) base 10 work. They are so pretty and so functional -- what a fantastic design! For buying Montessori manipulatives it would be a matter of browsing various Montessori vendor catalog (Neinhaus is sort of the gold standard, but their stuff is really expensive). You can also make many of the manipulatives yourself, using directions and inspiration from various books and websites.

Yeesh, a kid's calling -- gotta go!

I love Cuisenaire rods, too.. I'm curious, Gwen, about why you found out you didn't like them? We have 2 or 3 sets of the wooden ones, and they're great for building all sorts of things.... I'm sort of a sucker for anything blocks-ish, especially in good colors. I also like pattern blocks, and I think a bucket balance with various weights is a cool thing, too.

Rain spent 6 months at a Montessori kindie and loved the Trinomial cube, so I got her one at a yard sale. I'm not sre what math concepts she got from it - some spatial awareness, I guess - but it was a fun thing.

Yu can make base ten counters by using beans and then gluing sets of ten beans to popsicle sticks for "tens"... although I've read how understanding of place value is one of those developmental things that just comes, even kids who can talk about ones and tens and all often don't really "get it", they just parrot.

Dar

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Okay, here's way more than you wanted to know about what I think about Cuisenaire rods:

We, too, have the wooden rods rather than the plastic, as well as pattern blocks and enough wooden blocks to build a small city. The kids love playing with pattern blocks, building new doll houses with the wooden blocks. They never touch the rods.

The way the Cuisenaire rods were used in Miquon always seemed forced to me. This whole business of learning that certain rods that look certain ways represent certain values...it seems so artificial. We already learn that there is an oral utterance "seven" that corresponds with the written word "seven" and the symbol "7", as well as the quantity of seven whatevers (beans, bears, siblings). Why do we need to further introduce the idea of a rod of a certain length and color? Dd quickly memorized the color-number correlations, but I always wondered to what end -- does this ever come up in real life? It seemed like we were adding another, unnecessary step.

When I looked at Montessori manipulatives I noticed that they always isolate the concepts. The rods used in the 3-6 class aren't multi-colored, for example, because that introduces another factor for the child to deal with; when examining relative length one *only* examines relative length, not color patterns. (BTW, I'd love to come over and play with Rain's Trinomial cube, too, LOL.)

So, in the meantime, everyone in homeschool-land seemed to be raving about the wonders of Cuisenaire rods for teaching math. Why weren't they working for us? Were we homeschool math failures?

Then I got ALAbacus Right Start, and found this in Joan Cotter's discussion of the cultural differences of teaching math in US vs Asia:

"Still another difference is their criteria for manipulatives. Americans think the more the better. Asians prefer very few, but insist that they be imaginable, that is, visualizable. That is one reason they do not use colored rods. You can imagine the one and the three, but try imagining a brown eight -- the quantity eight, not the color. It can't be done without grouping." (The grouping she is referring to is what goes on in your head when you picture 8 of something -- you actually picture a group of 5 and 3, or 3 and 3 and 2, or somesuch.)

It was nice to find a quote from an authority figure that seemed to validate my opinion. As you can imagine, we switched to Right Start (gosh, that Joan Cotter must be smart -- she agreed with me! LOL). And we leave the Cuisenaire rods to others that enjoy them. Overall, it was a good learning experience for me that different materials will work for different families, and just because everyone else *loves* something doesn't mean we will.

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I do like the Cuisenaire rods, but I've wished before that they made blocks in just a natural wood color (with maybe slight grooves carved in to delineate "ones") for this very reason. When I use them with DD (and when I used them in class as a teacher) I find myself saying ones and twos, etc. rather than greens and yellows (or whatever - I don't have them memorized. )

As for the original poster's question, I also think having pattern blocks (as someone else mentioned) is a great math manipulative to have on hand. (Hexagons, trapezoids, equilateral triangles, squares...they sell them in buckets.)

You may think this is strange but what I hit on as my son's favorite manipulative for math is change.

We counted out 100 pennies. got out a 1$Bill to compare it to as one whole

We grouped the pennies in tens and compared them to a dime. It made counting by 10 a very understandable concept.

The same with nickles and counting by five.

4 Quarter as 4 parts of one whole dollar.

I know some people may frown on bringing children into the knowledge of money but it is a concept my 5yo ds really gets. Very concrete.

T

I wonder why?

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I plan on teaching my ds about money, earning money, spending money, saving money, budgeting donating money etc from as soon as possible.

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I'm not sure, I never have actually brought the subject up. Then again most of the kids my ds plays with are public school kids and church kids. They don't seem to have a concept of money at the same age as my ds.

We talk at home about saving money, what things cost etc...

Since I'm off topic can I tell a story?

Ds has been catching on to saving and counting money. he wanted to trade me 4 quarter for a paper dollar, so OK, then trade 10 dimes etc.. When he got $5.00 he wanted to trade them for a five dollar bill, I thought OK. (this is mostly money he saved from doing little jobs for Dad)
Well I didn't know he had a plan. He saw a toy at the dollar store that cost $5.00. He bugged us every five minutes for 3 days. We knew it was a piece of junk but finally decided to let him go buy it.
It broke one day later he cried and cried and cried, and then finally he said "It is already broken and my $5.00 is gone!!

I felt like it was a great lesson

In defence of cuisenaire rods, which I happen to think are brilliant...

The reason the colours are used is because the values are not fixed. This is also the reason they're not scored. Light green is usually a three, but when dark green (usually 6) is given the value of one, light green = 1/2. I think the mental act of ascribing a specific but not intrinsic (i.e. not fixed) value to something like a rod is excellent preparation for algebra. My kids have been doing linear algebra right from the start. "Let's say red is 4" is similar to "let's say y is 4."

Montessori manipulatives are very much base-ten oriented, and that's great if you simply want to explore fixed numerical values within a base-ten system. We also have a base-ten set that jives with our cuisenaires, and we're currently using it to work with long division using decimals.

But we've been able to do some awesome things with Cuisenaire rods that you can't do with other manipulatives, including using them in music for rhythmic notation (in simple metre a beat = purple, in compound metre a beat = dark green, sixteenth notes are whites, eighths are reds, and so on). We pair that with a Kodaly-style rhythmic narration ("ta, ti-ti, takataka, ta"). Once again we have colour, length, written symbol, value and word associated. The bridging between these various modalities creates, IMO, very strong and flexible conceptual understanding and appeals to a vast range of learning styles. We also used the rods for pitch notation of whole steps and half steps in a variety of scales (a friend of mine created 11, 12 and 13-cm rods to cover an octave which made this even more fun). We've also done extensive work with base-2 and base-8 numerical systems using the rods. And we've used them for metric measurement. My kids can all hold their fingers apart to show exactly 9, or 4, or 12 cm. Since we live in a metric country, this is very useful.

Miranda