Buses

I just returned from taking my son (turns 3 in a month) to preschool. One of the many perks to Spring Break so far! On the way to preschool, my son spotted a city bus.

Son: Ohhhh! A bus!

Me: Right. What type of bus? 

Son: A city bus. 

A little background knowledge here: He loves trucks! Let me rephrase that. He loves anything larger than a car, has an engine, is big, makes a lot of noise, is big, does construction, is big, intakes diesel, etc. I've seen many kids share these interests, especially when the garbage man does his rounds in our neighborhood. You'd think the garbage man was passing out ice cream or something (and he doesn't need that silly Ice Cream truck music either). We have multiple truck books that get frequent use before nap and bedtime. We have a surplus of toy trucks and Legos, recently added to by the most generous, wonderful, and great Fawn. You're the best!

Back to our drive. We had just stopped at a red light and on the other side of the street he spots a school bus.

Son: Ohhh! A school bus!

Me: You're right!

Son: We've seen two buses!

Me: I know. Look what's coming up behind the school bus.

Son: Another bus.

Me: And what type of bus is that?

Son: A city bus.

Me: So how many buses have we seen?

Son: Three!

Me: That's right. We've seen 2 city buses and 1 school bus, so we've seen a total of...

I pause for him to fill in the blank.

Son: Three!

We're still stopped at the red light and have a little time before the green light. I turn around and illustrate this again with my fingers, because lately he's been doing really well identifying the numbers one through five on a single hand. Since we saw two different types of buses, I use two hands. I hold up on hand with two fingers up and say, "We've seen two city buses" and on the other hand I hold up one finger saying, "and we've seen one school bus. So we've seen a total of how many buses?"
I expect him to say "three" because it's fresh in his mind, but he pleasantly surprises me and I can see his eyes moving across my fingers and mentally counting the fingers to verify the word 'three' matches up with Dad's fingers. "Three." he says.

The light turns green and we're on our way. We have less than five minutes until we get to preschool. Of course, I'm keeping my eyes peeled for more buses. No buses. Shucks. However, we pull into the parking lot of the preschool and park. Before I exit the car to get him out, I turn around and want to try something. Simply for fun.

Me: So we saw two city buses [I'm holding up two fingers on one hand]. What if we saw two school buses [I hold up two fingers on my second hand]. How many buses would we have seen?

Son: Three.

Me: Are you sure? Count my fingers.

Son: One... two... three... four, five, six, seven, eight, nine, te...

Me: Okay, silly. [holding up two fingers on each hand again] If we saw two city buses and two school buses, how many total buses would we see?

Son: Three.

I left it at that. He's content with the concrete. It's not about future counting for him. It's about what he just experienced, what's relevant, what's applicable and what's associated with his interests. I made a small attempt at the abstract, just for fun. There's no need to push this any further. He's convinced we saw three buses and he's right. He doesn't care about a fourth bus that we didn't see. Plus, it's time for preschool. Man, I love vacation. I get to have conversations like this with my son. It doesn't get any better than that.

Buses,
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[UPDATE]
*Read what happened two days later in Buses [Day 2].

Not Drawn to Scale

I hope you'll allow me to vent for a bit. I have been encouraging my students to be in tune with the 8 Mathematical Practices by Standard of the CCSS for some time now. It's pretty safe to say that my students know I really favor Mathematical Practice Standard 6, Attend to Precision. However, some of the resources I occasionally use in class are beginning to play tricks with everyone's minds, including mine. Here's a resource I have, Cooperative Learning and Geometry by Becky Bride.

Don't get me wrong, I like this book. It has some great explorative exercises that have appropriately challenged my students. For example, look at this exercise to help students derive the 30-60-90 triangle relationships. Take an equilateral triangle, its altitude, and the Pythagorean Theorem to find out the special relationships between the shorter leg, longer leg, and hypotenuse. Great.

Here's where I start to beat my head against the wall. The book uses diagrams that simply shouldn't be used, especially in the context of 30-60-90 triangles. Look closely...

That's right, the 30 degree angle is opposite the longer (drawn) leg for questions 1, 3, and 4. My students get bothered by this contradiction. I do too. I have no problem admitting this to them. I'm honest with them saying, "I know guys. It goes against everything we strive to do in here. I encourage you guys to attend to precision and check for reasonableness. Yet, I give you this. I'm sorry. It says at the top 'not drawn to scale', but they should be drawn to scale. Right guys?!"

I think this about sums it up. Students will come up and ask about the dimensions they've solved for and whether or not they're reasonable. I'm proud of my students for making sense of their answers and checking for reasonableness.  I know something is a skew when my response to those students is,

"I never assume those things are drawn to scale." 

I feel rotten saying this to students. I feel like I've just provided them with a worthless and menial task. I've let them down. I feel dirty. Mr. Stadel's quality control group hasn't done their job. What message are we sending students? Do they think we're out to trick them? Do the directions read, "Find the mistakes?" They should. It's times like these that force me to (gladly) keep a closer eye on the content I provide my students with. Don't just throw some triangles at them with random angles and units. Make sure they're reasonable.

Have you ever felt this way? Have you ever been caught in this situation? What did you do? How do we avoid these situations again? How do we demand better quality content from publishers? How do we make sure we provide our students with content that matches the CCSS and Mathematical Practices? Maybe you're okay with these types of diagrams, so please explain why. I want to hear from you all on this.

nOt tO sCAlE,
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Race Car Math

If you've looked at any of Dan Meyer's Algebra or Geometry curricula on his blog, you'll notice he has "Race Car Math" throughout many of his Keynote slides. Since I couldn't put two and two together on this one nor find anything on his blog explaining it, I simply asked him.

My loving wife bought my son and me an RC Ferrari car for Christmas 2011 (featured in the 3 Act lesson Ferrari Ride), but I figured I'd invest a few bucks in a classroom RC car for Mr. Stadel's room. I made my way over to Toys "R" Us and spent less than $15 on this bad boy. The remote is about the size of a crayon box and the car is about the size of a cantaloupe. It doesn't go crazy fast. It's just the right size and speed for a middle school student, boy or girl. This might be one of the best $15 I've ever spent.

This week, we spent Wednesday reviewing linear systems in algebra and quadrilaterals in geometry. We have reviewed with Math Basketball numerous times this year and the ground rules are very similar. Check out Dan's Math Basketball directions if you need some guidance. Here's how I roll in my class. I toss a slide up with the following information. *The slide for my students is less text-heavy.

1. Work individually in your notebook (unless I announce "GROUP ANSWER" meaning students work with their group/table on their giant whiteboard).
2. Show all work.
3. Talking = DQ  (*talking during "group answer" is allowed)
4. One person stands with answer (all members of a group must stand before standing again).
5. 10 seconds with car:
1. Big box = 1 point
2. Medium box = 2 points
3. Small box = 3 points

When students are done solving a question you've thrown up on the board and most (if not all) groups have a representative standing, I usually call on the last person that stands up. They explain and/or give their answer. If any other person agrees with the answer, they sit down. I've already been circulating the room checking student work, so mentally I have a decent idea who has the correct work (answer) or not. If anyone is still standing, that means they disagree and have a different answer. I repeat this until every student sits down. If all groups have the same correct answer, I announce that. If there's one different answer, I (for time reasons) will demonstrate the correct solution while students watch in suspense to see who's correct.

Whoever stood and got the answer correct comes to the front of the room to represent their group in driving the car. If a person got it wrong, they are to stay at their desk and study the board so they can write down the correct solution or talk with someone around them for the correct solution. Since students must drive the car along an L-shaped path, they can follow it to the finish line. Here's what's at the finish line.

Students can drive the car into the largest box worth 1 point, or two other boxes with narrower openings worth two and three points. The 3-point box is the narrowest. In order for the team to get their points, they must enter the box (cross the plane) with the two FRONT tires before the end of 10 seconds. I count down. Ready. Set. GO!

We had a couple of groups somehow get two tires on the same side of the car in the box, but it didn't count. Set up your own rules. Whatever they are, stick to them. Many kids said they liked this better than math basketball. I can't blame them. You should see some of their shooting form. On second thought, you might not want to see their basketball form when shooting a nerf basketball. Scary!

My favorite exchange came from Chase in geometry who scored three points for his team with ease.

Student 1: "Chase, you're really good at that."

Chase: "Yea, I'm part of an RC car club."

Student 2: "Really?"

Chase: (sarcastically) "Yes, after school I practice driving RC cars."

Student 3: "Really Chase? Wow! Do you really?"

Chase: "Yes, I'm part of an RC car club." and sat down.

Chase remained straight-faced the entire exchange. Hilarious! I'm not sure if some students were still convinced he was part of an RC club, but he's not. Since this was my first time with Race Car Math, I'm happy how I kept fine-tuning it throughout the day to make it more efficient and student-friendly. For instance, with larger classes I said we would solve two questions first before racing the car. If they got both questions correct, their team would simply double the points of the box their car entered. If a team only got one question correct, they would get the box's points at face-value. This also allowed students to send up who they thought could best drive the RC car. For round two, that person could not drive again.

I found that the classroom dynamic and energy to be better when I did more "group answer" questions and students collaborated on their giant whiteboards. It's a win-win. They get to stand up, talk to each other, and collaborate just like any other day in class. Plus, I get to listen to them problem-solve, argue, agree, and cheer each other on.

*[Update] Here's an idea for the to-do list: Another way to play is have students accumulate correct answers for a sequence of approximately three questions. Each group earns 10 seconds with the car for every correct answer. Set the boxes up like goals on a soccer field, maybe 15 feet apart. If the group got three questions correct, they have 30 seconds to drive the car between boxes to score as many points as possible. If you test this one out before me, let me know how it goes.

Ready-Set-Go!
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