Pythagorean - Part 2

Part 1 with my new intro for this year is HERE.

Our finished right triangle pages looked like this...

 

I know that's kind of a crazy picture. I used my CamScanner app and sent it to a student that was in ISS so she could check her work before moving to the next activity. 

If you don't have CamScanner I highly recommend it! I can scan and save as a high quality pdf right from my classroom - huge time saver!

Anyway... next we completed this little booklet. 

It was all about the relationships between areas and side of the squares formed. Never once did my students plug into a formula while completing their book - I love this! The types of problems are from Christa Lemily here, I just made it into a little booklet for their INB. The students were all commenting about how easy it was and how much sense it made. When we completed our town map next, the students were breezing through. I had to show one example about how mathematicians organize their work because we hadn't been showing work before. But conceptually, they did great!

They completed the map with more ease than my students did last year, and these students are classified as "less advanced" than my students were last year. That, to me, says the intro and conceptual booklet worked!! YAY!

Next we calculated distance between points.

When you flip the flap down that says "Calculating Distance Between Two Points" it looks like this...

Yes, I know, the distance formula is not explicitly an 8th grade standard. But if I'm doing distance between points on a coordinate grid why wouldn't I mention it?! We talked about how they would see this formula later and it contains the same math as the Pythagorean Theorem. We color coded the same work in both methods so students could see the connections. Hopefully they'll remember this at least a little next year and go look it up. Fingers crossed!

So there it is, my week of Pythagorean Theorem and distance. Got any helpful critiques or suggestions?

Here are your files:

Pythagorean Theorem - A New Intro!

I've never started Pythagorean with an investigation like this before and so far I'm loving it!!

I got the awesome idea from Christa Lemily at BetterLesson.com. Here's her wonderful stuff.

I've always talked about the two leg lengths squared and we've even gotten blocks out before, but I've never had students determine if it's a right triangle on the first day using this method. We haven't named what we're doing as the "Pythagorean theorem" yet, but we're using it and it's converse.

We did this on the same day that students were finishing a retest opportunity so I had kiddos in all different places. I posted on the board that once they completed their retest they needed to go to bit.ly/righttriangle. From there they scrolled through the pictures and were self-guided.

Here's a fun desk picture from yesterday!! :)

Starting our pythagorean investigation today! Fun, fun stuff!!! #mtbos #mathchat @gowjhswildcats pic.twitter.com/VbKRImtQmY
— Jessie Hester (@MrsHestersMath) March 10, 2014

UPDATE:

Part 2 is here.

Pythagorean Thoerem

Pythagorean Theorem... around town!!

 Most of my kiddos were already fairly familiar with Pythagorean Theorem as it is a pre-algebra topic and we were in Algebra 1 class. We did it for a day to make sure everyone was a pro! And because I was doing all CCSS-7, CCSS-8, and CCSS-Alg 1 standards (yikes! remember from here?)

Anyway...

We reviewed some basics, talked about what the theorem was really telling us (equal areas), talked about the theorem's converse, and talked about triples. All of those notes quickly went on the front of the map foldable. You can see those ideas in the picture above.

Then we got to the fun part!

I used google maps to zoom in on an area of town, relatively close to our school, that had some straight-line streets. I used my google maps image to create this for students.

The premise is that AT&T is laying fiber optic lines for its U-Verse service and we're calculating the total amount used by the technician. The map was blank when I gave it to students and we drew in the thick black line as a class to represent where the cable was being laid. I think I will go ahead and include those lines on the document when I give it to students next year. It will speed up the process and no learning will be lost.

This is what the map looked like with just "fiber line" drawn in.

After drawing in our fiber line, I gave students the actual measurements, again from google maps, for a few of the street sections. I didn't give them every piece they thought they wanted, but enough so that all the others could be obtained. Gotta make 'em work for it!

I told students that the technician was starting at the northern most corner so that's where we started. We needed to find six different individual lengths to find the total, so we used six different colors in our notebook. We calculated the first length together to make sure everyone was doing okay. From that point on students wanted to work with their partners so I let them go for it, especially since most knew what they were doing. Students then checked their six individually lengths and total with me before receiving their homework assignment. I was able to make sure everyone was confident that way. I also roamed around the room while they calculated to give tips and encourage.

Overall this activity went very well; I'll definitely be doing it again. Students got invested and practiced Pythagorean theorem multiple times, without just grinding out a worksheet full of problems. YAY!

What are your tips and tricks for Pythagorean? Please share!!!