"There is no one way"

Monday, January 23, 2017

Algebra Manipulatives

 A middle school teacher writes:
Just a little note and question about Lab Gear. I have been having so much fun with my students using Lab Gear again this year. The 3D-ness of it totally blows the other (cheaper) algebra tiles that I used last year out of the water!
I have heard this often from people who have used both tiles and Lab Gear. For one thing, the 3D-ness allows the blocks to represent monomials such as x^3, xy^2, and so on.


But besides the mathematical arguments, the blocks are easier to use, and more fun than the tiles.

Not related to the 3D-ness is another design feature that makes the Lab Gear work remarkably well: the 5, 25, 5x, and 5y blocks make it possible to quickly build relatively large products such as (x+5)^2 or (y+7)^2. Such problems with tiles take a lot of tiles and a lot of time. Moreover, the corner piece helps separate the length and width from the area:


(Readers who are not familiar with the Lab Gear can get information on my Web site. For a full comparison of all the algebra manipulatives, see this page.)
I gave the 7th graders an assignment to build their own Lab Gear Perimeter puzzle for homework and the results were incredible - it was so cool to see how deeply they understood the idea of length and perimeter.
I love that you asked your students to create their own puzzles!

Perimeter puzzles are a genre I pioneered im the Lab Gear books. They make a nice algebra-geometry connection, as they motivate combining like terms in a context where it makes sense, and where students have a need for that simplification. The 3D-ness of the blocks makes it possible to extend this to surface area problems and puzzles.
Although the 3D-ness also means kids try to make elaborate structures which topple to the ground! My threats to make them find the surface area of anything they build are met with "yay! we will!"
:) A good problem to have.
I noticed in the book published by Didax that you (they?) put the chapter on minus after the chapters on multiplying with Lab Gear. Is there a reason why? I have always done distributing the minus sign right after combining like terms.
That was my choice for the Algebra Lab Gear: Algebra 1 book. In the middle school book (Basic Algebra) I deal with minus at length, and early on, as it's a big middle school topic. That's probably what would make sense with your 7th graders.

In the Algebra 1 book, I use what I think is the best sequence for high school. Dwelling on minus early in a high school algebra class is not a good idea -- boring for some kids, confusing for others. Better get into topics such as factoring and distributing as early as possible, and save minus for later, at least in the context of manipulatives. Minus in the corner piece is complicated and not a good idea early on. Also, as far as I'm concerned, using the Lab Gear for equation solving is definitely not the main or first use of the blocks in Algebra 1.

That said, I realize that lots of people do Algebra 1 in middle school, which is why I recommend having both books and deciding on your own priorities and sequencing. You'll also have more examples for the most important topics, as those appear in both books.

Thanks for writing!

--Henri

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