Should We Use the Term "pace" More?

I'm preparing to be one of the presenters at a 3-day NCTM Deep Dive Institute in July. Hope you can make it. Fawn will be presenting too.

I've come across some great tasks from NCTM, thanks to Peg Cagle (that's C-A-G-L-E everyone) that I've adapted to have a much lower entry point for teachers and students. However, I'm also looking to mix in some favorite Estimation 180 challenges and 3 Acts like Fast Clapper from Nathan.

Fast Clapper Act 1 from Nathan Kraft on Vimeo.

I really dig this task. At first glance though, it looks pretty straightforward. Act 2 could look as simple as showing students a screenshot like this:

Then tell students to use this ratio to predict how many claps this dude will complete in a minute. We could call it a day, but what fun would that be?

Here's what I think should precede any screenshot from the Act 1 video. Have students get out their cell phones and partner up. Record their partner clapping for various increments that are less than 30 seconds. For example: 0, 5, 6, 10, 12, 15, 20, etc. Keep track of it in a table...
Then see who is the fastest clapper in the class and if they can break the record. Talk about what might prevent the students or dude in the video from breaking the record.

Here's an additional place I'd like to take Act 2. Talk about the term "pace". I really like this question I'll be using from now on with students and teachers:

How often should we check to see if he is on pace to break the record?

I think this question opens up the mathematics, especially for a table of equivalent ratios and double number lines. Forget equations (proportions) here. Furthermore, it reminds me of the pace timers that you sometimes see on television during the Olympics.

Talking about the word pace, is this the same thing as rate...?
I'd really love to hear from you about the term "pace".

• How often do you use the word pace in math class?
• What context do you use the word pace?
• Are terms like rate or slope synonyms to pace?
• Tell me everything you know about pace or how you use pace in your class?

Seriously, I want to know. Teach me!

Pace yourself,

312

Questioning Strategies from the #MTBoS

This past week, a fellow asked me about questioning strategies.

Okay #mtbos, unleash your favorite book/blog/video/source on effective questioning strategies. GO!

— Andrew Stadel (@mr_stadel) May 22, 2015

I'm not sure where your brain goes when someone asks about questioning, but there's at least a few places my brain goes:

1. What questioning strategies can we use to unstick students when they're stuck?
2. What questioning strategies can we use to explore student (mis)understanding?
3. What questions can we ask when designing lessons/activities/tasks?
4. What questions can we ask when launching lessons/activities/tasks? 
5. What questions can we ask...

Thanks to Twitter and the amazing #MTBoS, here's the list you all gave me. Hope this is helpful. If I missed any resources, please add them in the comments.

Questioning,
327

P.S. Here's the list.

Ketchup (Guess vs. Estimate)

I had breakfast at a restaurant this weekend and noticed the ketchup bottle on the table. You know, the bottles that are red plastic? That are supposed to appear full? I always get a kick out of these bottles. Here's why..

I immediately wonder how much ketchup is in the bottle?

Take a second to think how almost any answer is pure GUESS.

WHAT information would you want to know here to make an estimate and not a guess?
HOW would you go about getting the information to make an estimate and not a guess?

The second I do this...

I know WAY more information. It's no longer a guess.

Think of other senses that could be used to make a better estimate. 
*One scenario would be something along the lines of me watching the customer(s) before me to see how they held the bottle. How did they shake the bottle? How many people at the table used ketchup and how much?
But that's just plain weird...

Sure, pick up the bottle. Formulate an answer and be ready to back it up with a reason. Don't skip this reasoning part. The bill depends on it!

Let's now move to the answer. Let's say we have more information now.
How would you describe your answer?
How might someone else describe their answer?

Could we say any of the following?

• It's half full.
• It's about 3 squirts.
• It's two-thirds empty.
• It's about a pound.
• I could eat 5 french fries with that.
• It's about 8 ounces.
• [insert other]

Here's where specificity matters. How should we agree to quantify the amount of ketchup in the bottle? Should we agree at all?

This ketchup bottle context is one of the simplest contexts I've come across in awhile. Here's why:

• The question is straightforward.
• You demand more information to do anything better than a pure guess.
• With one small piece of information, your guess should now be an estimate!

In case you're wondering about the time of day, I don't think it really matters here. The bottle was about a quarter full and this was at breakfast time. It's not like someone went around the night before and filled every ketchup bottle. Which begs the question: 

Is it more efficient for an employee to go around lifting all of the ketchup bottles to determine if it needs refilling or should they just wait until a customer says, "The ketchup bottle is empty, can we get a new one?"

Why haven't you seen more Estimation 180 challenges that deal with weight, density, etc? They're tricky to capture. I wish I could fix that, but I digress. I'll put that onus on you. 

My charge to you is:

No matter what grade level you teach, bring in an item like the ketchup bottle. Ask a simple question where the answer is pure guess and students demand more information to make an estimate. Literally, keep track of all the questions/demands students formulate. Report back.

Classroom (or lesson design) application:

• Design lessons with less. (notice "less" is in "lessons")
• Ask straightforward questions that demand more information.
• Use information to move away from guesses and into estimates.
• Is it more effecient to go around asking our students what they're stuck on and re-filling them with information or should we wait until they realize their stuck and we help them get unstuck?

Lots for me to think about. Feel free to chime in with some advice. Thanks.

Ketchup,

1248

P.S. This reminds me of one of my favorite jokes:

A momma tomato and baby tomato are walking down the street. The baby tomato falls behind because it's going slower. The momma tomato turns around and stomps on the baby tomato, yelling "Catch-up!"