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    Default The A to Z's of Hands on Math

    The A to Z's of Hands on Math
    I remember the first time I encountered Cuisenaire rods in a graduate workshop. “Be sure you allow time for kids to play with them,” began the instructor, looking around at a room full of educators turning the tiny blocks into towers and patterns of stripes. As we knocked over towers and tried to pay attention to the instructions on how to use these colorful little things with students, we laughed. Even the adults were drawn to playing with their math.


    I've since learned that there are a million ways to play with your math and hold it in your hands. It'snot a necessary step for absolutely every student, but for most, it makes math more fun, more tactile, and easier to understand. Math manipulatives can be a lifeline for some math strugglers, a shortcut to understanding for some thinkers, and a means to get to a deeper understanding for others. There are dozens of different products out there for both arithmetic and geometry and even an array of products for algebra. There are also ways to make math hands on by bringing itinto the real world in other ways.


    The simplest math manipulatives are probably counters. Nearly all of us were born with a nice set of ten of them attached directly to our hands. You can get fancy, of course,and buy a set or you can use what you have around the house. For the smallest math learners, going from the symbolic abstraction of numbers to the reality of a quantity of things sitting in front of you is a big step in early learning. In fact, it was a big step inour development as a species to be able to do this. If you and your kids ever want to think about just how big a step, the Terry Jones documentary The Story of 1 is a fun look at the history of how numbers became numbers. We're so used to being able to think of four chairs or four apples or four fingers as just “4” that it's easy to underestimate how hard it is for the brand new learner.


    Next comes the even harder in counting up past your fingers. Going beyond ten means beginning to see a pattern in the way we structure our numbers and understanding place value. This is where counters can be useful to start, but can quickly become tedious. Different possibilities begin to really open up. Kids can place numbers on a hundred board or put manipulatives together to see bigger numbers. Some materials, like Unifix cubes, take the counter and turn it into a piece in the puzzle. Join them together and you have a rod that represents a larger number. (Note that Legos are a good substitute for these.) Other manipulatives, like Montessori beads, Cuisenaire rods, or base ten blocks let kids seethe patterns in the numbers by putting them together to make staircases, squares, and other patterns.


    One of the oldest and best known math manipulatives is the abacus. There are lots of different versions of the abacus out there. The most popular one for homeschoolers is some version of the abacus used by the Right Start curriculum where each line has ten beads that are two colors to help students see the halfway point and each level represents another place value. Moving the beads means adding or subtracting numbers. If you become fluent with an abacus, it can calculate large numbers extremely quickly. In Japan, some people practice the mental abacus whereby they use the image of the abacus in their minds to do the calculations in competitions, moving the beads back and forth mentally rather than physically.


    There are also lots of great tools specific to various hands on tasks. Many people have clocks for learning to tell time or play money for learning to count. You don't need play money though. Real coins are great tools for place value as well once a child understands that the penny is ones, the dime is tens and the dollar is hundreds. Fraction wheels are especially useful for younger students first learning about fractions. Spinners and dice from games help kids learn about probability. There are algebra tiles are a great way to introduce the abstract ideas behind algebra. The Hands on Equations program helps explain basic concepts in algebra, including integers and variables using a scale, pegs, and number cubes.


    My favorite tool for arithmetic is still the Cuisenaire rods, simply because I believe they're the most versatile single manipulative you can have. Cuisenaire rods don't have markings to allow kids to count up to their value the way that most other manipulative blocks do. Instead, students are encouraged to see the rod as a whole, which helps take the symbolic representation a step further. After playing with them for a few days, most kids will internalize their values. More importantly, the“six” rod or the “three” rod can be used to represent something more than 6 or 3. They can show fractions, ratios, negative numbers, or help kids see why certain triangle measurements won't work. They are an incredibly flexible tool. Every time I think we'refinished with Cuisenaire rods in our math journey, they seem to come out again for a lesson. I suspect I won't feel really comfortable passing our set on until both my kids are past high school level geometry.


    Geometry has special manipulatives, as well. While there are some which are mostly just practical, most of these particularly invite play. Like a box of Cuisenaire rods, a bucket of pattern tiles is almost impossible not to play with. Even older kids tend to get draw into making patterns and exploring shapes by tessellating them out onto a table. Pentominoes and tangram tiles are made for doing puzzles. However, some of the best hands on activities with geometry involve making your own discoveries or building things yourselves. What better way to learn that all the angles in a triangle add up to 180 degrees than to make and cut up triangles to show the angles form a line? Or what better way to show how shapes look flattened into nets than to actually make shapes?


    In general, that's the step beyond manipulatives and into the real world. We start by helping young kids learn about the abstraction of numbers. Manipulatives help guide students through these abstractions, but by the time kids are in upper elementary and middle school, we've often moved so far away from those counters that it's important to remember to dip back into the real world with math labs and projects or simply using tools to explore math in the real world so it doesn't become only a conceptual abstraction. Of course, word problems can do this too, but just like for younger kids who are holding their first Cuisenaire rods or moving their first beads across an abacus, there is something special about physical interaction for most students. Some ways we've taken concepts to the real world has been building models with ratio,playing with origami, making hexaflexagons, playing store, and making Incan counting ropes.




    * I've said what my favorite manipulatives for math are. What are yours?


    * Do you use manipulatives? Why or why not?


    * Do you agree that most kids need manipulatives?


    * What else do you do to help kids move between the abstract and the concrete in math?
    Last edited by farrarwilliams; 06-29-2015 at 03:48 PM. Reason: strange formatting issues
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    Senior Member Arrived Elly's Avatar
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    It's so good to see you here again! This post is very timely for me, as we've both been struggling with his math for the past few years and I want to go back to basics to try and help him develop better number sense. I bought the Right Start games a few months ago and I wish I'd got their abacus years ago, for the support of grouping and visualising numbers. We haven't used it a whole lot, but it's something I would tell people to get early on after my experience!

    Elly
    4th year of homeschooling DS, now 9!

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    Right Start's abacus is cool. I've seen that some other places have started selling knockoffs with the same place value marks on both sides. They sell a neat book - Activities for the AL Abacus that is super useful. We loved those Right Start games - I also waited on getting them and finally gave in toward the end of first grade or the start of second. But they were completely worth it.
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    Senior Member Arrived Elly's Avatar
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    I was looking for a book about things to do with the abacus, but I missed that. I'll have to check for it again. (Are you back to stay?)

    Elly
    4th year of homeschooling DS, now 9!

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    Maybe. I missed you and some other people.

    Do you have a favorite Right Start game yet. We played Corners like mad for about two years. It was the game we took to Africa with us because it was so tiny but also now I have sweet memories of playing it sitting outside at picnic tables by our campsites.
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    Senior Member Arrived Elly's Avatar
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    I love the look of corners, but DS isn't quite there yet. We've dipped in so far, but when we get back from Tahoe next week I want to start doing more regular choices. He's also enjoyed other math games like Sum Swamp and an arithmetic lotto game I had as a kid.

    Elly
    4th year of homeschooling DS, now 9!

  8. #7

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    We use the Cuisenaire rods sometimes...if something is not clicking, it's great to get them out and have her 'play' with them so she can see the process and get a better sense of the why. I remember when we first got them out a little over a year ago and it was great seeing something click while she used them - made us both happy! Haven't seen the need for an abacus, but it does sound intriguing. And I second Elly, it's good to see you back ; your reviews have helped tremendously over the last 2 years!
    Living in OR for now, mom to DD, 8, and married to DH for 16 years. We also have 2 dogs and 4 chickens that are near and dear to our hearts!

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    Yay, Farrar's back! I've missed your posts!!

    We used Saxon math's manipulatives - my DD loved them. I just sold the kit, however, because DD doesn't really need/want to work with them any more. I have tried to get more math games into the mix, but so far none have stuck. I always heard great things about Cuisenaire rods, but just never went down that path since I had the Saxon.

    I'm interested to know how many of you use manipulatives past 3rd/4th grade math. My DD is doing 4th grade now, and I just haven't found a need for them, despite our early success with them.
    Working mom homeschooling DD (10) who is working on a 4th-6th grade level and keeps me hopping! SimpleMoney is my new venture. www.simplemoneypro.com

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    Welcome back!

    I do use manipulative with math. I have used Legos, the single Legos worked especially well for a short while.

    We used Mammoth Math and it was working for a while, but we are now moving towards a more unschoolly way for math. To make it more tangible/tactile, we are now playing more games. We have money games, dice, and card games. Some games with the explicit goal to learn math and others just need math to successfully complete the game. But also we are using science experiments to learn math.

    In a sense, we are using manipulatives through game playing and the science experiments. Using the dice, money, as well as measuring items (thermometer, scales, rulers, etc) are different ways of viewing numbers and make the math more integrated into what he wants to learn. I think it helps kids to use tangible items to understand math, there are just different ways to get there.

    Also, videos have been very effective in learning and understanding math. Much more than I would have expected.
    A mama who teaches college writing, as well as help her 11-year-old in
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    Quote Originally Posted by Starkspack View Post
    I'm interested to know how many of you use manipulatives past 3rd/4th grade math. My DD is doing 4th grade now, and I just haven't found a need for them, despite our early success with them.
    I've been surprised how many times I come back to them. I pulled out the Cuisenaire rods the other day for building triangle lengths for BalletBoy, who is doing fifth grade math. In general, I'm finding that middle school math needs plenty of geometry manipulatives. The amount of geometry that kids are expected to know in middle school has really changed since I was last teaching middle school math. But having things like geometric solids and other visual aids has been nice. And then there's algebra. I'm so glad we did Hands on Equations, which was so good for visualizing algebra.
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The A to Z's of Hands on Math