Who can resist this picture?

Yeah, I drew it.

YOU: The kids thought that was pretty funny. I gave them one minute to write any questions they have about the math they would be using in their INB's. I took the quote from Phil Daro, "Writing means silence." I told them if they couldn't think of anything to write, draw the picture...theirs' were way better than mine. (Pictures later)
I have a monster fire truck...

Then I had the students to choose a partner and gave them 2 minutes to talk about the problem.

WE then had a group discussion. One young man walked up to the board and measured the width of the basketball to the width of the rim. "Is the hoop height regulation?" (Yay! someone asked!) yup, 10ft. "How far is he from the hoop?" "Is it allowed to have a fire truck on the court?" "What does he win?" (Easy, $1,000 per basket...of course they wanted to re-enact the whole thing...ya...no)

Without much prompting, someone asked, "how long does it take him to make a shot?" I revised this a bit, to "How long does it take the basketball to reach the hoop?"

I showed them this picture from Dan Meyers, To boost interest.

I told them the basketball was released from 18ft in the air. We Googled the average initial velocity of a basketball...it was 10ft/sec. I told them, since we weren't in motion, let's use 8ft/sec. (Makes numbers nicer for Zero Product Property.)

YOU/WE: Same thing again: one minute to write, two minutes to discuss, a few minutes to debrief. Many students had already written h = -16t^2 - vt +s. Sweet, right?

I pointed out the ideas I saw and heard that were productive and pointed out the ones that were on track, but needed some tweaking (desired height is not zero), and even some that were not at all relevant...um, like the circumference of the basketball...

I let them fuss and struggle and figure. It was so much fun! And it was too much fun to talk about why they got one negative root. We followed the arc of the ball behind the fire truck...there were a lot of "ahhhs."

At the end I showed this shot also from Dan,

Then the real discussions began, "That is totally Photoshopped...Dude...it was never going to make it."

It's going in!

I get it and can put it on the board. 

My 14 year old daughter is an amazing test taker. She missed one week of school last April due to the flu, missing almost the entire unit on writing equations of lines in 8th grade Algebra. My trying to teach her the missing lessons went about as smoothly as my husband trying to teach our older daughter how to play the piano...the only instrument she plays now is the ukelele.

The 14-year old knew that if she wanted to get into Geometry in 9th grade she had to score well on the CST's. (California State Tests, also known as STAR). I  "helped" her study for the test by providing her with all the released questions. The "helping" I did was mostly to keep her company and stay the heck out of her way. She would read the question. If she knew the answer she would find it, then read the others to make sure she isn't missing something slightly deeper than she thought at first. If she had no clue, she looked for the answers that made no sense whatsoever, then try to work backwards with what was left. I was fascinated. We had never directly taught her these skills. When I asked her about where she learned how to do that...she just said, "Duh, it's logical Mom."

I know that we brought up our children playing SCAN and SET and MAYA MADNESS and all other sorts of puzzles and logic games. I see my own child find joy in figuring out stuff and I "hit" this "play" button in my classroom.

She scored Advanced on the Algebra STAR and is enjoying her year in Geometry.

I bring all this up because of the new situation I am in, being a veteran teacher in a new district. How humbling to be on the formal evaluation end of teaching again. I am appreciative of the opportunity to reflect on my craft and think more deeply about why I do what I do.

Recently I was "dinged" for moving away from "traditional lessons" and using a puzzle (the Tarisa puzzle I shared earlier) that involved "cutting" and "putting a puzzle" together. This type of lesson "distracted from my objective." Now, I will grant you that I did not have a "pre-meeting" to explain the objective I had, though had I been given the opportunity, I am not sure I would have had the insight I have now.

Why are puzzles important? First, the students had to know the properties of exponents to answer the questions on the "domino" pieces to know how they fit together. Academic objective. Check. A puzzle to motivate. Hook objective. Check. Cutting out the dominoes AFTER they figured out the solutions. Hmm...14 and 15 year olds. I am certainly not going to cut them out! Anticipation objective. Check. Working together, blowing off steam, socializing, and appealing to the kinestetic learn objective. Check. Critiquing the reasoning of others objective. Wow. Check. Constructing viable arguments objective. Wow. Check. And the bonus objective, the one most valuable to me really, is having the "four or three or six" pieces that don't match and what to do with them, and the organic math arguments that arise in the process of elimination. CHECK! 

And you know what else? Helping scaffold for ELL students. Learning language is...social.

I think I did my job. Do you? Why else do you like puzzles? I would love to hear from you. 

Friend and Master Teacher Shawn makes these very, very important points:

Puzzles are important because they are:
A. fun
B. interesting
C. infinitely changeable in that you can do whatever you want with them, not just what the author intended
D. help people understand that strategy is important and so is luck
E. help people determine that last time I did this it worked, so I should do that again OR maybe I'll try another strategy
F. Are opportunities to engage with many strategies leading to many answers and often asking necessary questions to unlock another potential strategy.
In other words: puzzles are artistic representations of static (boring) questions. Experience with puzzles allow for artistic (creative) solutions and process.
I love that Shawn reminds us that puzzles are fun! I love Shawn, I really do.

...engagement. That is what I am being asked for in regard to asking students questions.

I am very aware who is engaged and absorbing information, formulating a plan, or completely out in la-la land. If the person who is out in la-la land is is not being distracting...is just well, physically present, but mentally elsewhere, does he/she need to be asked a question and startled out of their stupor (a regular ed kid, not an ADD or other)? Does a shy student who I can see in their eyes or on his or her paper have to answer? If I ask a student to share out, and that student respectfully requests not to go up in front of the class, is okay if I let them pass?

I am not being rhetorical, I really am asking your opinion. And if you feel as though everyone should publicly participate, how do you achieve that without popsicle sticks? I couldn't keep track of who is in and who is out...really if you must go through 35 students before a student can answer again, what prevents that really verbal kid from causing trouble? (The student who is an A+ student who never wants to say a word in front of the class, will ALWAYS raise her hand and correct a number in the problem, the date, or the assignment number. I LOVE THAT!)

Anyone, anyone? Please let me know your thoughts.

On another note, here is an anticipatory lesson I used for Zero Product Property that I thought went really well:

(coming soon)
I could have asked this:

There are 54 countries (most of the time) in Africa. There are 196 (mas or menos) countries in the World. What percent of the World's countries are African?

Instead I asked this "What percent of the world's countries do you think are in Africa?"
We recorded the guesses...

Then we did this:
How many countries are in Africa?
And then we did this:

How many countries are in the world?
And THEN we framed the question and wrote an equation and solved it. So much more fun!

We were also revisiting a poorly written test question (by me!) on purpose. Well it had a purpose that didn't work on the test, yet I was still able to use it when we discussed the "correct" answer. (I purposefully made the question so that there wasn't any one correct answer, however, I neglected to have the students explain their answer.)

Marianna said, "I wrote California if you are talking about size, and New Mexico if you are talking about percent of land," (Yah, Baby!) (I won't mention the the kid who said, "New Mexico is a state?")

Then from some lovely blogger who gave me the idea, I threw out there: let's add another column,

Forest Acres per person? Would that change our opinion?

I just love those teachable moments when everyone is arguing about...numbers...

What was your most recent teachable moment?

PS Sorry about the horrible image insert job, I am learning! 

I wasn't in that great of shape Friday morning. An unsettled night sleep made for a potentially groggy day. Ever have one of those? And yet I managed quite well. Amazing what a brainstorm at 2am will do for a gal! (I did get home that afternoon to discover that I had my cami on backwards--ie--the skinny bra part in the back was in the front...good thing it was cold enough to wear my droopy scarf all day.)

I knew I needed a really good Hook to (re) teach percent problems. I looked through this really old POW book and found this problem for my warm up: 

So I did my happy dance because I felt like I had purpose. I let the kids wrestle with it for 3 or 4 minutes. Then I stopped them and told them this TRUE story: my brother is a Pilot for X airlines. Back in the late 80's, early 90's, his airline started to get into financial trouble. I asked the students, "who works for an airlines?" We brainstormed and came up with a list (good kiddos!) I erased all the low skill jobs from baggage handlers to air hostesses and hosts (yup, sorry you all, low skill). That left mechanics and pilots. Next question, who can work anywhere else and get a high paying job? No-brainer for most (yeah, there are some kids who think non-military pilots are in high demand), MECHANICS! Cars, Planes, Trains, and Automobiles. So when the company asked folks to make concessions, it was up to the pilots. Airline X asks the pilots to take a two year temporary pay cut of 25% of their annual salary, where at the end of the two years, the company would return the 25%. (you math folks know where this going!)
Boy were the kids mad and shaking their heads. "That's not fair." Of course not, had the lawyers and union reps had paid attention during ALGEBRA, this never would have happened. Then I asked them to do this:

Which is a better deal? Taking 25% off a $100 purchase then paying 10% tax, or paying the whole $100 including tax and then getting the discount? Go! Same, same...now go back and have another look at your Warm-up. Is there anything you want to change, add? You have 120 silent seconds to move your pencils across paper (and/or use your handy-dandy calculator).

I got "blah!" I got "blah-blah!" What is the answer Ms. Z.? Who's right? "I have no clue, I haven't done the problem and probably won't get to it for awhile." Go home and ask your parents. Ask your neighbors. Survey your whole block! Now put all that fun away, you have a Chapter test to take!

The most important part for me, was not giving the answer right away. I wanted them to hit it several times and rationalize/reason for themselves.

It is curious to me, that the most likely-to-not-do-their-homework, most squirrelly, students were the ones with the most insight into percent problems...could "suss" them out in their heads and had a high degree of accuracy.

It was a long day of directed teaching...of course there was another way to approach the whole enchilada, and sometimes the subject is just so much fun to go exactly the way you want it to go.

Next time I would put one of Dan Meyer's 101qs and ask what questions the students have, and sometimes you just gotta give them their Chapter tests with enough time to finish.

Do you have a favorite way to teach percent problems?
So when I apply for my dream job, I may have to change the title of this post. BTW, I dedicate this post to Fawn, I hope she is okay if I use Poopy in my post.

At our high school, the typical referral is for trash clean up during lunch or after school. Sunny California, say hi to your friends, plug in...not too bad...

So here is my alternative:

In a room you must sit. No head phones no electronics, no magazines...and a loop of the following greats from the 70's

Love Will Keep Us Together

Up, Up and Away

and the one that will assure the most engaged, self directed, helpful learner ever:

(This should be rated NR-17 or worse)

Bay City Rollers

What would you add?

(Fawn, I haven't had the pleasure of meeting you yet...and you have truly inspired me to give back...may the spray be worthy!)


I found this one too:

That's the way I like it! Uh, huh...