I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

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Tag Archives: discovery toys

Playing with Algebra Concepts

I’ve been itching to get into some basic abstract algebra goodies. With the help of the Cuisenaire Rods, Simply Fun Sumology number tiles and the Discovery Toys Busy Bugs, I’m able to do that.

Start with wrap around addition.

This type of math is officially called “modular arithmetic.”  We are only going to use the numbers 0, 1 and 2.

It begins as regular addition. And since we are only using those three numbers, all our answers have to be either 0, 1 or 2. So when we add 1+2, we wrap around.

If we were to count in our system, we’d say: “0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, …”

The addition table looks like this:

(Notice you could do this with numbers from 1- 12 and it would be clock addition!)

Now things get buggy.

Switch out all the number tiles with some pretty color Cuisenaire Rods. They don’t have to be the “right” rods. We’re only looking at the colors. Here’s the progression I did:

The end result is a very abstract chart!

You can “bug” two things together.

Like this:

(I know – a spider isn’t a bug. But run with me on this, okay?)

Notice that each of these are directly from the “spider table” above.

You can read this as, “Purple spider green equals green,” just like you would say, “Zero plus one equals one.”

And then turn your child loose!

First make a chart, or download the this one.

You can, but don’t have to, start out with numbers. The rules are this:

  • You can only use three colors.
  • All three colors must go across the top.
  • All three colors must go down the left.
  • Fill in the 9 spaces however you want, as long as it’s only those three colors.
I did this one with the blue beetle as the “addition” piece:

So what can you do with a goofy “blue beetle table”?

Let your child play, for one. And experiment.

You can also talk about commutativity and associativity, identities, inverses… but I’ll leave that for another article!

What do you think? Does your child want to play like this? What else can you do? Share your thoughts in the comments.

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One Response to Counting Isn’t an Inherent Concept

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6 Responses to Teaching Subtraction Using a Balance

  1. I like your idea of using of the balance – it’s beautifully visual, but I would hesitate to call what you’ve done subtraction. Of course, it’s formally equivalent to subtraction, but this to me looks more like the “missing number”, or complementary addition flavour of the operation, which is not necessarily understood as the same thing by a young learner. i.e. To me, you’ve demonstrated the formal equation 5 + ? = 12, rather than the concept of 12 – 5 = ?.

    • Thank you for your thoughts, Stacey.

      As you’ve pointed out, 5 + ? = 12 is the same thing as 12 – 5 = ?. If we tell a young learner that they can’t understand this, then they will believe us.

      They can understand this. Actually, they are much better at understanding this than we are. They have not been socialized out of understanding what is inherent to them.

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4 Responses to Using Toys as Curriculum Tools to Teach Arithmetic

  1. Bon,

    I think it’s a good opportunity to introduce fraction ideas and names from the get-go. For example, 9 divided by 6 is one and one-half rather than one and three left over.
    The 3 left over need to be seen, IMO, in relation to the unit container of 6.

    • I agree, Gary. The trouble I’m having is with the words “divided by” and “goes into.” When you pour sand from one cup to the other, there is another “go into” idea there.

      I’m going to need to think on that one some more.

      But you are right – the language here would be good to include. Thanks for the comment!

    • Buy them online at http://www.tinyurl.com/dtedtoys2 – that’s an official site of mine through Discovery Toys (they don’t have an affiliate program so I became a “dealer”). Totally legit – company’s been around for >30 years.

      I hope you enjoy them, Makenna – and remember, they are guaranteed for LIFE! (that’s really the best part about them)

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