Saturday, August 23, 2008

Algebra 1: Intro to square roots

Students often have trouble seeing a square root as a number when the radicand is not a perfect square. The point of this activity is to help students develop this understanding by using a geometric metaphor.


square root intro.doc

4 comments:

Jackie Ballarini said...

Very nice Dan! I like that it also develops estimation skills (the between what two numbers part).

Dan Greene said...

Thanks Jackie. In the next lesson, students will be asked to plot the length of the side on a number line, given a picture of a square and then given a radical expression. This should further sharpen their estimation skills, as they will be expected to plot the point closer to one of the two integer values. Also, it should help reinforce the idea that a radical is a number even if you can't evaluate it exactly in your head.

I'll post that handout once it, you know, gets created!

jd2718 said...

Nice. I like refining the "between which two numbers" part, to allow for "close to"

sqr(98) is a bit less than 10, sqr(38) is a bit more than 6, sqr(55) is between 7 and 8...

At some point, the idea that
sqr(91) > sqr(90)
might be of use, and it's not that far a stretch.

Are you using a text? I don't know any that have square roots up front.

Dan Greene said...

Yeah, that's what we'll be doing. Plus, I might have them use 4 function calculators to try to get the "best" estimate they can of, say, sqr(28). As they work their way closer and closer, I think it helps them not just understand square roots more, but it's also a good place value exercise.

We have the McDougal Littel book, but I don't think we are going to use it this year. Our first unit is "Evaluating Expressions"; we'll learn square roots, basic powers (it's just repeated multiplication! j/k :), order of operations, and substituting values into variables.

The second unit will be "Simplifying Expressions" where we deal with combining like terms, the distributive property, and understanding the difference between evaluating and simplifying.

I'm actually not the lead teacher on Algebra 1 this year, so I won't be posting about it as much, but I will put in my box.com as much stuff as I can as it becomes available.