San Diego Conversions

I was in San Diego, California the past few days doing the whole San Diego Zoo and SeaWorld thing with the family. We had a great time, but that's not the point of the post. There were definitely a handful of opportunities to capture some math moments, but I've found it more important to contain myself (mathematically) when I'm with family and make the most of our time together. Here are the two things I captured and want to share.

Number 1: 
We were waiting to board the Wild Arctic Ride (virtual helicopter ride) at SeaWorld and watched this video. There were subtitles in Spanish for our spanish-speaking (reading) friends. However, they go along with the helicopter pilot.

Here's Act 1:

When I saw the the number behind the black box, I thought, "Is that right? Is 400 miles per hour really ### kilometers per hour?"
Are they correctly converting for our Spanish speaking friends? It turns out that 400 miles per hour is about 643.7 kilometers per hour.

Here's act 3:

What do you think? Should I keep the black box there? Should I delete it?
I feel this is one of those moments where I don't insert a black box and we simply ask students:
Is 400 miles per hour really 600 kilometers per hour?
I'm curious about students arguing about this one? or would they even care?
What difference would 40 kilometers per hour make?
Where do you stand, on any of it?

Number 2: 
The great thing about San Diego is there are tons of people from many different places of the world. San Diego has an international airport and many places of interest besides SeaWorld and the zoo to contribute to this melting pot. I loved listening to all the different languages being spoken throughout the day. Therefore, it didn't surprise me when I walked into the pool area for the first time on our trip and noticed a few interesting things. I couldn't help but think how wonderful it would be to use these in any math classroom, specifically Math 6. The first thing you see as you enter the pool area is the jacuzzi. I couldn't help but notice the depth:

Okay class, check this conversion. It ends up making sense and I appreciate the use of meters for pretty much everyone outside of the United States. Seriously, I simply have such a hard time understanding why the United States uses inches, feet, yards, miles, etc. I digress.

Here's the (very shallow) pool:

Let's look a little closer at the depth signs around the pool. The deepest part of the pool is 4 feet or 1.2 meters. Okay class, check this conversion. Looks pretty legit, right?

So, if you saw a depth sign with 3.5 feet, what would you put the meters conversion at? How would you order these pictures with your students? Which would you present first? second? third? or would you give them all to your students at the same time? Would you cover up one of the measurements (like feet) and only show them one measurement so they work on finding the conversion. Here's the 3.5 ft depth sign.

Okay, if you do the conversion, 3.5 feet is 1.0668 meters. Obviously, someone was following their rounding rules. A few questions pop into mind here:
Should we round up?
Would it be wiser to round to 1 meter?
How much of a difference does roughly 4 centimeters make?
Could they not use a slightly larger tile and put 1.07 meters?
These questions aren't the only questions, nor the most profound, but I'm still curious.

There's one more crazy thing about this pool I had to capture and share. How did they get away with this? 

Look closely. Inside the pool is a depth of 4 feet (1.1 meters). Outside the pool is a depth of 3.5 feet (1.1 meters). WHAT?!!! Now reflecting, I should have had my wife take a picture of me next to the sign to get the water level and measure how deep it actually is here. I don't know about you, but 6 inches is definitely more significant than the 4 centimeters we discussed earlier.
At what point does an error like this matter significantly enough to change it? 6 inches? 2 inches? 12 inches? and in what direction: shallower or deeper?

How would you use any of these images or video in your class to help facilitate discussions or arguments regarding conversions?

SD conversions,
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Des-man

Today, students had about 90 minutes to work on creating their Des-man. Des-man was the brainchild of Fawn. Desmos then teamed up with Dan Meyer and Christopher Danielson to create a suite of classroom activities, one of them being Des-man. I've done Des-man before, but not with the Desmos classroom. Let me just say, it's awesome!

As the teacher, I could see every students' work in real-time and display it up on the projector for all to see if need be. That's a really slick feature on top of the already amazing Desmos. It's like math euphoria! It was a blast to see students work 90 minutes straight, being as creative as possible with their Des-man (or Des-woman). After three weeks, Desmos became a very familiar tool for students because they used it with tasks like Barbie Bungee, Datelines, Hit the Hoop, Vroom Vroom, Stacking Cups, and more. I'd like to showcase a few creations for you. Enjoy!

Thanks Fawn, Desmos, Dan, and Christopher for a wonderful and creative math experience. Lastly, I want to thank my students. Today, you guys helped each other out, persevered, asked for advice, freely explored, had fun, and wanted to know more about functions, domain, range, circles, sliders, and more!

Desmos is great about asking for feedback. I have some observations and am curious. Maybe I'm missing something, but I noticed some features from the regular desmos calculator missing in the classroom. Maybe these are upcoming features:
Students couldn't duplicate functions. How come?
Students couldn't create (use) tables. How come?
Students couldn't create folders or text boxes. How come?
Students can't share their Des-man (email, link, etc.). How come?
As the teacher, I can't keep the Des-man (functions included) for each student. How come?
As the teacher, I'd love to have access to each student Des-man, especially if I want to send it to that student or share at a later time.
Thanks for listening, Desmos!

Des-manian,
1035

Tools: Helpful & Unhelpful

Not sure I made the best teaching move today, but I had to try it. We explored Dan Meyer's "Will it hit the hoop?" task(s).

Act 1: Roll "Take 1"

• Agree on the question, "Will he make the basketball shot?"
• Ask students to make a series of guesses for a total of six takes.

Act 2: Ask for information
I typically ask students to think of information they would find useful in answering the question. Today, I went somewhere else with Mathematical Practice 5. I asked students to make two lists:

• List 1: Math tools that would be UNhelpful.
• List 2: Math tools that would be helpful.

This is the fourth and final week of the summer academy. My students have been exploring many math tools. I'll list the activity/task with the prevailing tool(s):

• Class height: Measurement, mean, median, mode, range
• Number Tricks: inverse operations
• Bucky the Badger: Tables
• Barbie Zip Line: Pythagorean Theorem, wrong models
• Taco Cart: Pythagorean Theorem
• Barbie Bungee: Measuring, Data collecting, Tables, Line of best fit, slope-intercept, Desmos
• In-N-Out Burger: Slope-Intercept, Functions
• Styrofoam Cups: Functions, slope-intercept
• Stacking Cups: functions, slope-intercept, Desmos
• Basketball shots: guess and check, tables, linear systems, Desmos
• Datelines: functions, Desmos, linear inequalities
• Vroom Vroom: Measuring, Data collecting, Desmos, function of best bit, quadratic equations

As you can see, many of our tasks were dominated by slope-intercept and Desmos. I didn't find their lists surprising.

I love how some students thought Desmos would be helpful, while others thought it'd be unhelpful. Those that found it unhelpful, wished you could insert images into Desmos so they could use sliders to find the path of Dan's shots. Boy, were they happy when they discovered you could import images. My first class was split down the middle: half thought slope-intercept might be useful and half didn't. It took a few convincing students to explain why Vroom Vroom was an example where a linear function was unhelpful.

Overall, I'm pleased with this approach, but I wouldn't do it with every task. It might confuse students that there's only one way to solve a task and detract from the importance of MP 5. I thought this was a fitting opportunity for students to mainly see the difference between a linear function and quadratic function. Specifically, I wanted them to see the advantages of using sliders in Desmos with a quadratic function instead of a linear function. I think students need to shuffle through their tool belt often and pick the right tools for the right task. I think today it was necessary. Dan has written about this or breaking students' tools. Moving forward, it's a matter of using this strategy at relevant times and not overusing it. However, I might be wrong altogether. That's where it's your turn to chime in...

Tomorrow: Des-Man!

Tools,
1125