→ Animated slides on the Lab Gear model for signed number arithmetic.

Note that for each operation, the model is based on what students already know. For addition, you put down the first number, then the second number, and finally count. For subtraction, you put down the first number, take away the second number, and count. For multiplication, you put down sets and count. Of course, to make all this work with negative numbers, you need more ammunition. The three "zero" rules suffice: start with zero, and it's OK to either add or remove zero in the form of opposites. (This approach need not replace what you already do for integer arithmetic. Like all models, it is limited in its applicability. Use it to complement what you already do.)

This is the eighth animated Lab Gear slide show. (Click here for links to the others.) When I'm done expanding that collection, I hope to create soundtracks for all of them, but this probably won't be very soon.

→ Tweaks to my Pythagorean theorem animations, to allow you to change the shape of the right triangle, and see that the theorem still holds. (Unfortunately, the first one doesn't work consistently for me in Safari. I'm not really sure why or if it will work for you. In Safari, it works on my laptop, but not my desktop. On Firefox and Chrome, it works on both machines.)

The Pythagorean applets are among several animated demonstrations accessible from the Proof page on my site.

As long as I'm talking about this, I should make clear I don't think that demonstrations alone are very effective. Just showing something to students guarantees neither understanding nor retention. Demonstrations are most effective if they are preceded and/or followed by other representations, by discussion, and/or by writing.

For example, if you plan on using the Lab Gear demos, first have the students actually do the corresponding activities from the Lab Gear books, then show the slides (or have students look at the slides on their own devices,) and finally have them write a short summary of the ideas and techniques.

Likewise, if you plan on using the Pythagorean demos, precede them with work on paper or geoboards (use the links I give there!), and follow them with formal proofs if appropriate for your class.

If you see no role at all for demonstrations, I have to disagree with you. They do add a useful trigger for reflection and discussion — just don't overestimate what they can do.

--Henri

PS: some of the applets I link to on my applets launch page are interactive, and go beyond mere demonstrations.

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