Manipulatives

So, manipulatives are a crucial part of early math education. They are a "hands-on" kind of learning. I have seen that my kids can make mental leaps when they actually SEE or MOVE the numbers.

So, here is the primer I wish I had when I started Saxon, when all the books, catalogs, and moms were throwing around these vocabulary words I didn't know.


I start out with the most important one of all, "Counting Bears." These bears can stand in for numbers when kids are learning counting and skip counting and all sorts of maneuvers. Indispensable. I got the weighted ones which are counting bears AND weighted for the balance scale (below).
Dad = 12 grams, Mom = 8 grams, Baby = 4 grams.
1 Dad = 1 Mom + 2 Babies etc. Also workcards are available for younger kids to practice patterns and such. Lots of products that use these.


Fake money because we all don't have tons of bucks lying around to be practiced with! (maybe I have a little sense. Ha! Ha! sorry.) This way the practice money doesn't disappear when we want to go to the dollar theatre.





"Pattern blocks." Definitely spring the extra few bucks for the wooden ones. The kids use these in math but also they are just plain fun to make patterns with (think stained-glass window). Used a lot with Saxon 1-3. Lots of workbooks and idea books are out there that use pattern blocks. If your kids loves them they can surely find things to do with them.







Did I buy this for my kids, really? I don't know. I know I wanted to turn the gears myself. I think I remember the big Judy clock from grade school, and not being able to manipulate it for as long as I wanted to. So when I saw this, child-sized geared clock I immediately ordered it. (My kids like it too.) And as the teacher this time around, I like that it has the 5, 10, 15... labels on it, and that the gear-shaped individual minutes are marked.


These are leftovers from my months with Miquon. They're called "Cuisinaire Rods."They are good for visually explaining 'one-more' or showing the relationship between 2+3=5, 3+2=5, 5-3=2, 5-2=3 etc. I keep thinking that I'll label all the red ones as "2" and so on to make it simpler to just pick one up and know what it represented, opposed to comparing to another. Hey... I paid for them, they're mine... I can!


These are also used a lot in Saxon 1-3. They are called "linking cubes." They lock together and are useful for showing numbers when you don't want to slide 7 bears across the table and recount them... they are good for many things.





These are called "Tangrams." They are a favorite of my Lego-loving son. You try to see how the shapes fit together to make the dark shape, then you can flip the card over and see if you are right. Very inexpensive. I definitely prefer the hard plastic ones. These are one manipulative that has a cottage market of additional products that build on it. Lots of options that are based on using these, primarily various images to figure out.


This is a simple thing to make yourself, but sometimes you get free or hand-me-down cardstock shapes like these. When you are illustrating the properties of a certain shape, its good to let the kids handle one or trace it or press it into playdoh while you talk, instead of staring at a sketched shape on scratch paper.







Same thing here- these are just flashcards. They are included in the Saxon workbook pack. They're just numbers on cards. Good to see if your kid can identify each number, put them in order or reverse order or whatever. Also makes younger kids feel "big" if they mess around with them just like the bigger sister or brother.







There are so many "Base 10" sets out there- transparent ones for overhead projectors, colored ones, foam ones... all sorts. I make do with these stiff cardstock ones my MIL handed down to me. They are useful for showing the kids how ones roll into tens, and how tens are a standard grouping. You can easily laminate a mat with "100" printed on the left, "10" printed in the middle, and "1" on the right, and show how whatever number you pull out of the air fits into their "place value."

A balance scale. Reading about pan scales vs balance scales vs this and that can be confusing. This is not a scale, but a balancing tool that is able to determine if given items or collections of items weigh more or less (or the same) as each other. For comparing and estimating. Then, of course, if you have an item of a know weight, such as the bears (above), you would be able to determine their weight. This one can hold water too.


A "geoboard." Lots of fun. Its meant to be used to show congruent shapes. You use rubber bands of varying color and size to make patterns or shapes by looping them around the pegs. You choose a geoboard based on the amount of pegs. Some offer pegs that show a pie shape (ie, slices). Also a huge amount of fun for smaller kids to feel busy and important while the big kids work.



Not really a math manipulative, but an early learning math-prep/ fine motor skills "toy," "lacing beads" are great for little kids to practice using both hands in tandem and pushing the shoelace through the hole in the bead. I tied a knot on the end the first day, and let 'em at it. The beads can make patterns by color or by shape, so they can do a little venn diagramming later.



"A Hundred Number Chart" is absolutely indispensible. I send my kids to the wall to walk their fingers from one number to another. Ours is color shaded- all the 5's are pale green, all the 10's are pale blue, and the rest are yellow. Great for showing patterns. There is a 8 1/2 by 11 inch number chart in the back of each "Morning Meeting" book that comes with the Saxon homeschool packages. I have another one in a plastic sleeve that we use at the table.

What I want but don't need are 3x3 post-it style 100 number charts!





These are some inexpensive dice to toss around instead of flashcards. You have to have tricks like this up your sleeve-

"No, Mom, I don't waaa-na do flashcards!"
"Ok, then I guess we can throw dice instead..."
"Can we? Oh, Thank you Mom! You're the best!"




These are some counting discs that I inherited from my MIL last year. We haven't used them alot for math, but they're in all the catalogs, so some people must love them. We do use them for bingo as chips. Here's some mom math for you:

old play-doh can + discs = baby busy for 5 minutes.



mama4x MANIPULATIVE WANT LIST
not needed, but wanted



A nice set of gram weights. How luxurious. Delta Math and Science has a huge variety of weight sets.










A beautiful, accurate, expensive scale. Maybe in High School?










We'll get this later, I'm sure. Its only a few dollars. Mirror to show symmetry. Cool.









Geo-solids. Very neat. Of course, I just hand them an orange or point to the globe for sphere; a can of olives for cylinder; remind them of the pyramids for... what's it called? Oh! Pyramid.




This is the three-dimensional base ten set. Exactly the same as my flat cardstock ones but you can hold them and stand them up.


I'm so pleased you are utilizing Classical Curriculum!
Teresa (Tracy) Dear



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