The Golden Dab

A couple of weeks ago I came across this tweet on Twitter:

Since I had recently finished reading Instant Relevance: Using Today’s Experiences to Teach Tomorrow’s Lessons by Denis Sheeran, I knew I needed to have my PreCalculus students do this activity. We were days away from reviewing the trig ratios and I knew this would be an engaging and fun way to have them practice.

I quickly did some research on The Dab. Sports Illustrated published a helpful article on The Dab’s history in sports. While there is some disagreement over the originator of The Dab, most people agree it originated in the Atlanta hip-hop scene. There are also some fun celebrity videos in which people are taught to dab: Jason Derulo teaching James Corden around minute 7:05 and Ellen Degeneres teaching Hillary Clinton.

Then, I got to work putting together the actual lesson. Special shoutouts to Matt Vaudrey for his amazing Mullet Ratio lesson which inspired some of the format, and Lisa Bejarano for her feedback and input to the lesson itself.

The General Lesson Outline:
-Look at images of dabs and ask students which is the best one? Try to figure out what makes a dab, a dab.
-Continue debating. Is one dab dab-ier than another? The dab-iest?
-Calculate the dab angle of some famous people (gallery walk style around the classroom)
-Calculate their own dab angle
-Decide whether or not a “golden dab” angle exists

See slides below for a better understanding of the lesson flow:

PDF Version of slides: golden-dab
Powerpoint Version of slides: golden-dab

What actually happened?
Most students were immediately engaged in The Dab Debate and had an opinion of which dab they liked the best. However, a few immediately told me that The Dab was dying (or was already dead according to which student was asked). This was sad to hear. But there were enough students thoroughly debating for their favorite dab that the “silliness” of the conversation took over the room and we proceeded at full speed ahead.

I quickly learned that I had a very different opinion of what makes a really good dab than my students do. For example, I don’t particularly like Cam Newton’s dab because his arm lines have different slopes:

cam

However, my students immediately told me that the second arm doesn’t matter. Doesn’t matter AT ALL. This kinda blew my mind. In fact, sometimes it looks like the person is trying too hard if the arms match perfectly. Such as tennis player Victoria Azarenka:
victoria

I think her dab is great. My students on the other hand, said things like: “She forced it.” “She looks like she practiced that for hours.” They are a tough crowd, but know much more about The Dab than me, so they are the experts here.

I asked for some clarification on having both arms line up. This is okay sometimes. It was hard for them to describe, but they were very adamant that it couldn’t look like you were trying to hard. Their dab advice: Look confident. Look comfortable. Be natural. Just hit it.

So, with that advice, we set about measuring and calculating the dab angle of Cam Newton together. Ignoring the second arm, the triangle we drew looked like this:
cam2

Each student had a ruler and made their own triangle for Cam’s dab on this handout:
dab5
Download handout here: golden-dab-handout

Each student picked two side lengths and the appropriate trig ratio to use. We also had a brief discussion about similar triangles and why this method of using trig ratios based on side lengths measured from a picture would be comparable to measuring in real life. Lastly, we talked about the possibility of measuring errors and decided we were calculating “close enough” dab angles.

Then, students had the chance to choose 4 of the 6 “celebrities” located around the classroom to measure and calculate. My principal graciously dabbed for me and his image drew a large crowd.

Betty White had the smallest dab angle, around 20 degrees, and everyone agreed she was one of the best, but mostly because of who she is. Our principal’s was about 50 degrees and this also elicited a positive reaction.

I sensed that many students did not want to dab for Part 3, so I asked for volunteers and we all measured their dabs instead. Students used any of the 3 trig ratios they wanted (sine, cosine, or tangent) based on whichever side lengths of the triangle they measured.

At the end of class, I asked the big question, Is there a “Golden” Dab angle? The answer: 5/16 say yes. 11/16 a resounding no.

Here are the 5 student responses saying yes:
S1: 45 degrees. Because that is half of 90 degrees and that would be a perfect dab.
S2: I believe Cam Newton has the golden dab because he is closest to 45 degrees, 48. He looked like he knew what he was doing and looked confident, which meant he dabbed almost perfectly without overdoing it.
S3: The best dab angle is 30 to 40 degrees because it looks the cleanest.
S4: It is 45 degrees because you have maximum effect without overdoing it. You also look much cooler. While it is nearly impossible to know the exact angle while you’re doing it, you should try for 45 degrees. Practice makes perfect.
S5: It would be between 33-45 degrees because it looks the best and is the most common. But almost any angle could be a golden angle depending on the person.

General comments from the rest:
-Everyone is different and unique so for a dab to be “perfect” to you, you just have to have your own style.
-If you take another picture of the same person again, it wouldn’t have the same angle as before.
-There isn’t one exact way to do the dab.
-There isn’t one angle because everyone can dab however they want.
-There isn’t one because everybody’s arms are different lengths and people have different styles.
-It only depends on the person and confidence in doing it. They can’t seem like they’re trying too hard. The surrounding sometimes matters too.
-It all depends on someone’s surroundings, persona, swagger, and confidence. The dab depends on the person, therefore there is no golden dab angle.

We didn’t have time to work on the extension questions, but I am including them here in case someone else wants to use them.
• Can you dab at 30o? 60o? Which angle feels the most comfortable? The least? Why?
• Sketch a dab with an angle of 90o. Is this feasible in real life? Why or why not?
• If a person creates a 25o dab and their combined dab arm length is 44 inches, how high vertically would their hand be above the ground?

The conclusion: There isn’t a lot of math in this post, but there was a lot of math done in class. However, it seemed like a natural part of the conversation because we needed it to talk about a golden dab, but then collectively decided to throw it out the window as most students agreed there was no one right way to dab since everyone has their own style. But after closely comparing dabs, and ignoring personal style/confidence, many decided that 45 degrees made for a pretty good one. But the perfect one? A dab done with confidence.

This was the perfect activity to review finding angles using the trig ratios. If you try this with your students, please share how it goes! I’m curious how other students around the country view the second arm’s importance to the dab, and whether or not a 45 degree golden angle is upheld or not, or do we agree it’s all about your swagger?

#TMC16 – My Favorite

Get out your calendars and mark them now! Twitter Math Camp 2017 is being held from July 27th-30th at Holy Innocents’ Episcopal School in Atlanta, Georgia.

Having just returned from my 4th Twitter Math Camp (TMC) experience in Minneapolis, I feel the need even more to book my entire summer plans around this camp. I like to spend time in the summer with my family and friends; go to the beach; read a book for fun; nap; go to the drive-in, etc. But I also NEED to spend four days in person with my MTBoS family. The people and sessions at TMC invigorate my passions and spirit and convince me that I can conquer anything in the upcoming school year.

I can’t possibly recap everything I took away from TMC16, but here are some of my favorite takeaways. I hope they become some of your favorites too! Grab a drink, there are a lot 🙂

Favorite Pre-TMC Outing: After arrival, I adventured to the Minnehaha Falls with a small group. The weather wasn’t the best, but we had a fabulous time exploring the falls and walking to the confluence of the Mississippi River and Minnehaha Creek.

Favorite New Desmos Calculator Feature: Desmos now has audio capabilities for visually impaired and blind students. Use Command F5 for the voice option, and Option + T for the audio trace. Desmos will read the expression being typed, and then play a graph used a pitched audio representation. Kudos to Desmos for striving to be fully accessible to all users!

Favorite New Desmos Activity Builder Feature: Card sorts! Ask Desmos and you shall receive! By turning on the “Labs” option once you’re logged into Desmos, you now have the option to build card sorts within the activity builder platform. I made a cart sort for Quadratic Equations, and I can’t wait to make more and then also steal from the crowdsourced list. My group loved that we can input card sorts already created; ask students to sort in more than one way; narrow responses by asking for a specific number of cards in a pile; and ask students to analyze why someone else sorted the cards a different way. The possibilities are truly endless, and you can check out the card sort bank here.

card sort3

Favorite Passionate Educator Title: Chief Evangelist. In her keynote speech, Sara VanDerWerf challenged us to become “Chief Evangelists” for our passions in math education. Sara said, “Sharing your best with others who can benefit is a responsibility and opportunity that falls to everyone” and “To be good at evangelizing, you’re gonna have to practice.” You also need to prepare mini-elevator speeches for each of your passions so you’re ready to share, and tweak them depending on your audience (students, parents, teachers, leaders). I’m going to spend some time this summer narrowing down my list of math education passions to figure out what I want to advocate for.

Favorite Dorm Life: While not all aspects of Dorm Life at Augsberg College were glamorous (looking at you, shower stalls), I had a complete ball living with some TMC-ers for four days. Waking up and having morning bathroom chats about math ed, doing the wobble in common areas late at night, and watching the bachelorette with a huge crew were all completely memorable TMC experiences.

Favorite ELL Strategy: The snowball activity is a great way to get students writing, reading, and speaking in math class. Have students answer a prompt on paper, crumple up the paper, and throw it somewhere in the room. Each student then finds a new paper,IMG_0528
reads the response, and either 1) Adds a new idea 2) Contributes 3) Corrects something
written. After going through the cycle three times, ask students to share ideas out loud
from whatever paper is in front of them. It’s anonymous, non-threatening, and fun for students. And again, it provides them with an outlet for individual think time, following by writing, reading, and speaking. Priceless.

Favorite PD Strategy: To assess participant’s understanding during professional development, I highly recommend using the “Filling in Circles” strategy modeled by Michelle. Start by identifying the key concepts of the session, or in our case, the barriers to implementing responsive stations. Then, have participants continually reflect on the topics and fill in the circles as their learning and understanding grows. Facilitator is able to see what topics need to be discussed more, and participants are able to ask better questions about what they want/need to know. Very easy and very powerful.

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Favorite Mapping Tool: Popplet. Use it as a mind-mapping tool or to help students think/learn visually. We used it to map skills and identify gaps.
popplet

Favorite Restaurant: Pizza Luce! I had Baked Potato pizza both times we went there because it was just SO GOOD. They were also very accommodating of our large groups.

Favorite Shared Experience: Jonathan talked about how he created a shared
experience in his school by creating “Varsity Math” for his calculus and statistics

I'm on the team!

I’m on the team!

students. He branded them with shirts, stickers, and inspirational speeches; and the kids just LOVED it. They bought in. They felt like they were part of a special community… because they were. Jonathan even graciously invited all of TMC16 to join the team. How can we create shared experiences for the students in our own communities?

Favorite JLV Reminder: In Jose Vilson‘s keynote speech on “TMC16, Race, and What We’re Not Talking About,” he challenged us to lead hard conversations and be okay with feeling uncomfortable. He also reminded us that we have students who are much more capable of talking about this stuff than we are; often because they have less filters. He told us to “get out of their way” but provide an outlet to let it happen. This was a much needed reminder for me, because I often feel like I should/need to have all the answers, so when I don’t, I avoid the conversation. I know I need to work on this, and my students can probably help me. Watch Jose’s keynote here.

Favorite “Getting Triggy With It” Activity: Kristen led an excellent session on how to make trig and the unit circle not a mystery. Grab all her resources here! My favorite activity was using one triangle drawn on patty paper to construct the unit circle. Simple approach but nicely shows how all the key points are determined.

See Rachel’s tweet for pictures of activity in action:

Favorite Verb: Edmund Harris and Chris Shore reminded us that modeling is a verb. It’s something kids should be doing, not something given to them. Modeling is a: Creative. Active. Process.

Favorite Physical Activity: Sara graciously brought her Backwards Bike to camp, and let me ride it as much as I wanted. If you’re not familiar with backwards bikes, watch this video. Even though I came home with several bike battle wounds, I had an absolute blast trying to ride this thing. Even after just a few times, I felt like I was making progress and coming up with new strategies to try out. Now I’m off to find someone to make one for me.

Favorite Project: Sam shared a project he does with students called “Explore Math” so they can explore math outside of school and see its beauty. He wrote about the project on his blog and shared the website he asked students to explore. It’s a “low stakes, high reward” activity. Some kids will do the bare minimum, but others will take it to levels that Sam wasn’t even expecting. His recommendation is to keep it open, keep the mini explorations mini, and don’t compare projects.

Favorite Pre-Assessment: Don’t have one yet, need to make them! Michelle led us through an eye-opening morning session about identifying the gaps in students’ understanding and then usingtrifold responsive stations to address those gaps using differentiation. I’m excited to follow Michelle’s instructions to create appropriate pre-assessments. There should only be one skill per question and as short as possible. Focus on what pre-skills students need to know in order to be successful with new content, don’t worry about the would-be-nice-to-know. The goal of the pre-assessment is so you can figure out where students are at, and provide them with learning opportunities if they don’t know, and learning opportunities if they do know (enrichment). Elissa wrote a great recap of the entire three days.

Favorite Call to Action: Tracy Zager‘s keynote speech titled “What do we have to learn from each other?” was inspiring and community-driven. She stressed that we need to stop pitting content and pedagogy against each other; we need to stop pitting elementary and high school teachers against each other. Neither of these things is productive for our community. We all have an important role in building our students’ conceptual understanding, and we need to work together to get it done. Tracy’s call to action is to analyze whom you are following on Twitter, and make sure you have a variety of contacts you can reach out to for support and to ask questions. Watch Tracy’s keynote here.

Favorite Fraction Problems: After Tracy’s talk, I pushed myself to attend Brian Bushart‘s session on fractions: a place I knew I would feel out of my comfort zone as a high school teacher. One of the reasons Brian said fractions are so hard for students, is due to practices that simplify or mask the meaning of fractions.

By finding a common denominator, you aren’t comparing fractions anymore. You’re now only comparing the whole number numerators. Cross multiplying is an example of masking; you’re getting rid of the fractions and comparing whole numbers. This masks the fact that you’re still comparing two fractions. Neither of these strategies takes into account the size of the fractions and therefore rob students of sense making. Brian then shared a bunch of strategies for how to deal with this, and I will lead you directly to his documents to learn more.

Favorite Fraction Big Idea: Another huge idea that Brian threw at us is the difference in how whole numbers and fractions are treated as adjectives and nouns. Look at the slides below for comparison.

Whole Numbers:

Fractions:

I’ve never really thought about it this way before, so this was a *mind blown* moment for me, and others at my table. Many students don’t actually gain enough understanding about fractions to realize that fractions are actually numbers and can be represented on a number line. They get stuck at adjectives (1/2 a cake) instead of moving onto nouns. This is where we need to get!

Favorite “Make It Stick” Strategy: In her session, Anna talked about the various ways she uses strategies from Make It Stick in her classroom. My favorite strategy she discussed was Calibration. The goal is to “replace a subjective experience or feeling with an objective gauge outside ourselves.” It stems from the “Illusion of Knowing” in that we think we know something, but really we only have a familiarity with it. The book recommends providing more opportunities for students to test themselves, review again, and test again. Quizzes need to be low stakes. I chose this as my favorite, because it ties in nicely with my morning session theme of helping students to fill in gaps.

Favorite Dylan Kane Confession: Dylan Kane‘s keynote speech titled “More than Resources” was one of the most honest and open talks I’ve ever heard. Dylan’s confession that he thought he was doing a good job when he started, but then realized he could be doing much better, really stuck with me. His big lesson learned was: “My intuition isn’t very good, because we see what we want to see.” Dylan was stealing all the great resources from the MTBoS, but realized that great resources do not equal great teaching. He challenged us to think about what will specifically work with our own students; and deliberately practice what we want to get better at. I haven’t come across a video of Dylan’s keynote yet, but you can access his resources here.

Favorite Upcoming Books to Read:
Tracy Zager: Becoming The Math Teacher You Wish You’d Had [Expected: December 2016]
Denis Sheeran: Instant Relevance, Using Today’s Experiences in Tomorrow’s Lesson [Expected: August 2016]

Favorite Song: Greg answered a call from the twitterverse to write a song about the cubic formula. He answered with the most epic sister act version ever… enjoy:

Favorite Student Quote: I know what you’re thinking, there were no students at TMC16 mathematicianso how can I have a favorite student quote? Well, in Annie‘s flex session on “Mathematicians: More than just white dudes” she shared this student quote: “Are there any mathematicians like me?” This question led to her creation of the Mathematician’s Project, where she showcases one mathematician every Friday (as long as they aren’t an old, white, rich, dead man) in order to show her students that anyone can be a mathematician. She includes their name, date of birth, ethnicity, background biography, major accomplishments, and math specialty. She even polled her students to see the types of people they wanted to learn about, and had students write their own mathematician bios. The shift in her classroom culture was unmeasurable.

Favorite Icebreaker: Amy taught us an amazing new icebreaker that I can’t way to play with my students when school starts called “Go Ahead – Break the Ice.” Break students into small groups, and give them three minutes to collectively come up with a favorite book, movie and game. Then, have students list all the ways they came to the decisions they did. This leads into a great discussion on group norms and how to work with other people. Some of the decision-making strategies were: “strong arming, time pressure, majority rules, brainstorm, survey, throw out ideas until they stick, pickiest gets the choice, narrow the choices, help those who aren’t speaking up, make sure everyone has a voice, etc…” It was a really fun activity to get to know your group, and have time to talk about group dynamics.

Favorite Day of the Year: Hannah loves celebrating birthdays and she shared some great ideas for celebrating in the classroom. She does birthday shoutouts on the board and buys cheap birthday seat covers. She sees increased positivity in her classroom culture and her students love it. She also uses birthdays to talk about what is and is not a function:
birthdays

Favorite My Favorite: I can’t really put into words out much Glenn means to me in this community. Watch his talk here, and be as thankful as I am that he didn’t turn around.

Thank you to everyone who helped make my experience at TMC16 an amazing one! Much MTBoS love ❤

And of course, the end of camp song and dance:

Experiencing the Engineering Design Process through a Math Lens

NCTM Annual Conference 2016 – San Francisco
Friday, April 15, 2016: 2:45 PM-4:00 PM Moscone 2008

Description: The emphasis on turning your math classroom into a STEM one can seem daunting. How can we bring in engineering authentically? Experience the engineering design process through a math lens and learn how to transform meaningful tasks, such as Barbie Bungee and Catapult Launchers, into challenges worthy of an engineering design team.

Slides: NCTM16 Slides

Handout (PDF): NCTM16 Handout PDF
Handout (docx): NCTM16 Handout docx

Other tasks that could be adapted to the Engineering Design Process Framework:
Barbie Zipline (Pythagorean Theorem, Rate of Change)
Amusement Park Rides (Circular Motion)
Hotel Snap (Surface Area, Profit)
Tinfoil Geometry (Surface Area)
Make Your Own Visual Patterns (Functions)

[The below activities can be found in various textbooks or online sites]
Bouncing Ball Investigation (Exponential)
Mini Golf Hole Design (Angles, Reflection)
Buried Treasure Maps (Triangle Congruence)
Food Container Design (Geometry)

Polynomial Art Project

While doing a quick search on the MTBoS Search Engine for lesson ideas on using algebra tiles, I came across this really cool project idea from Hoppe Ninja Math. She had her students create works of art using the algebra tiles, and I just knew that I had to have my students do the same.

We played around with the algebra tiles for one class period and experimented with adding and subtracting polynomial expressions.

Algebra Tiles

The next day, I introduced the project guidelines and drew a practice image on the board (see my lovely dog below).

IMG_8749

Then, students started creating! Most began by using the actual algebra tiles to play around with building different images. Then, they sketched their designs on the paper and recorded the number of tiles they would need. After writing and simplifying their expression, they cut out the necessary amount of algebra tiles from color copies of these printouts that I made:

In all, I gave students 1.5 class periods to work on this task. Some students completely finished during this time, and the rest finished for homework or came in during homeroom or after school to work on it.

The finished designs were so awesome that I had such a difficult time choosing which ones to show off:

Overall, I loved this project for a few reasons: 1) My students loved it 2) They were able to practice simplifying polynomial expressions 3)…in a creative manner!

One change I would make for next year is regarding a simplified expression that equals zero. Many of my students thought it would be really fun to create a design in which all of the tiles negated each other and simplified to zero. This is fine in my book; however I would still want those students to write the entire expanded expression on their artwork, and then show that it equals zero. Some did this, some did not, but it would be an easy change to implement next time.

If you try this, please tweet me some pictures; I would love to see them!

Find Your Perfect (Absolute) Match

For the final week of the Explore MTBoS challenge, I am going to share my lesson on Absolute Value Functions written in piecewise notation.

mylesson

Learning Target for Students: I will be able to write the equation of an absolute value function using piecewise notation.

At this point, we have spent many days graphing absolute value functions from tables and directly from examining the vertex form equation. We have also discussed the characteristics of absolute value functions.

When students entered the classroom, this warm up problem was posed to them:
Screen shot 2016-02-08 at 11.48.29 AM
I chose this problem as our “throwback” because I wanted students to recall how to find the domain and range for a relation, since this skill would be necessary for today’s lesson involving the domain intervals for the pieces of the functions. After giving students a couple minutes to think about their answer, I switched up the problem so that the third segment had an arrow at the end; this allowed us to talk about how the domain and range would change if the line continued on forever.

At this point, I gave each student his/her own graph (I quickly removed extras once I had taken attendance for each class period. Only one class had an odd number of students, so I partnered up someone who been absent for 2 days with another student.) Here are the 20 that I pre-made:


I asked students to examine their graph, and briefly examine the graphs around them. What is similar about your graphs (linear, slopes, restricted domains)? What is different (slopes, y-intercepts, equations)? Students copied their own graph onto this sheet, in the box labeled: “My Linear Function.”

Students wrote the equation for their line, and determined its domain. Then I told students that right now, they were alone. Their graph was alone. But that somewhere out there, it has a perfect match. I showed students how if they folded the graph at the x-value of the domain interval, they would be able to line it up with another classmate’s graph, to create a new function. I directed students to find their match, and sit with their new partner.

Original graphs:
IMG_8615

Post folding:
IMG_8616

With perfect match:
IMG_8617

Students then shared everything they knew about their original line with their partner, and transferred the new information into the box: “My Partner’s Linear Function.” At this time, I asked students to recall earlier in the year when we studied piecewise linear functions, and how they were able to write the equation of each line segment. We talked about how they had not noticed that an absolute value function could be thought of as a composition of two linear pieces, until this moment. We talked about how easy they found it to write the equation for their individual piece, and it wasn’t much different adding in their partner’s piece. Students combined all the information to create “Our Absolute Value Function” and made observations about the two different forms the equations could be written. Most students recognized the the connection between the y-intercepts from piecewise notation as being the distance from the vertex (h units away from k).

When we tried another problem, I gave out yellow post-its so that students could hide part of the function, and focus on one line at a time. Some students prefer to use colored pencils to highlight the different pieces, so I also encourage this option.

I had every intention of giving students this exit ticket at the end of the period, but time ran away from us and I didn’t want to cut our earlier conversations short.

Screen shot 2016-02-08 at 11.49.15 AM

This is the second time I’ve attempted this activity, and I would do it again next year. I love how student pairs are determined by who is their perfect match, which gets my students to work with someone they usually don’t, and they know it’s completely random. I love how it’s close to Valentine’s Day, so we had a silly time with the idea of the Perfect Graph Match. I love how each student physically started out with only one line, and then did some paper folding to pair them with another. I love how this visual representation really shows the separation of the pieces, and that it’s a shared experience we can refer back to during the rest of the unit. And I love how it starts by activating students’ prior knowledge about lines, and how they could use that information in this new setting.

Would love to hear any feedback about this lesson, and if you try it in your room, please let me know how it goes!

Day in the Life of Ms. Kohn Take 3

For Week 1 of the Exploring MTBoS blogging initiative I decided to document one day of my life. Although I’m just posting about it right now, this day occurred last Thursday (1/14/16).

adayinthelife

5:11 am Alarm goes off. Hit snooze.

5:20 am More snoozing.

5:29 am Get up and get ready. Orange juice is my morning power beverage. Check email/facebook/twitter while eating my cereal. Forgot to pick out an outfit the night before so I waste a good ten minutes staring at my closet. No food in fridge for lunch, that means I’m buying today.

6:20 am Put out trash and leave for work.

6:28 am Arrive at school. Check mailbox and help a substitute teacher find her way.

6:32 am Arrive in classroom. I am amped up for today! We are doing one of my favorite lessons and following it up with a Desmos Activity Builder lesson that I can’t wait to try. I make some last minute edits to the activity, and queue up all the browser tabs I’m going to need for the day.

6:50 am Students start entering the building and my classroom. I immediately get bombarded with demands to know how many jelly beans are in the container. I refuse to tell them.
IMG_0324
They know the winner is going to be announced today, but not until 7:25 am I say. Last minute guesses are welcome. Students hang out in homeroom, play board games, and experiment with my Eno board which is now up and running.

7:20 am Homeroom officially begins. Take attendance. Two students absent. They’re going to be sorry they miss today’s lesson.

7:25 am The bell rings to go to first period, and without speaking, I simply go up to the white board and write down the correct number of jelly beans: 1472. Students from the other two homerooms next door come in to see the answer. There is yelling; they are excited! They still don’t know why we are playing guessing games.

7:29 am This is the 1st of 5 times I am going to do this lesson today. I teach five sections of STEM Honors Algebra 1 to 9th graders. It will get better as the day goes on, as I observe and adapt to how my early students respond to it. Today is the first day of our unit on Absolute Value Functions. The beginning of the lesson can be found here, minus the project part (they’ll get this later). After we dissect the jelly bean situation, I show them this Estimation 180 problem, and we guess again. I take predictions for the shape of the graph and this time they think they have it all figured it out. The shape will be a V, but skinnier! No, wider! No, a check mark! Because there are fewer under-guessing options! We are on to something:
sweetheart graph

At this point, they are ready to explore and play around in Desmos on their own/with a partner. This was my first attempt at duplicating someone else’s Activity Builder and using it in my room. Overall, I was pleased with how it went, but would definitely make adjustments for the future. Some students finished early. I wish there were more challenges, such as what happens when you throw in negative signs. I tried to throw this question in as the day went on, but it didn’t work because I had already made a class code. I also wish I had a question about the absolute value vertex form equation with h and k. So that students could be more specific when they described how the function transforms. Here are some of their descriptions:

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We ran out of time at the end of class to debrief (my fault), and we don’t have class again until Wednesday (1/20), so to be continued!

8:17 am Period A ends. 4 minutes passing time. Run to bathroom. Head to STEM colleague’s room for our common planning period. Our big Winter STEM Expo is tomorrow, so we are doing last minute prep work. Edit presentation rubrics and chat with 10th grade team about last minute details.

9:12 am Period C begins. Algebra 1 take 2.

10:05 am Period D begins. Algebra 1 take 3. Four students actually leap out of their seats when the number of sweethearts in revealed.

10:53 am Lunch! Rush to teacher’s cafeteria and order my turkey wrap. Ask for cookies too. Get a slight look of disapproval when I reject the offers for pickles, apples or carrots as an additional side. No, just cookies please. I already have lettuce and tomato in my wrap. Eat lunch with math colleagues. Discuss our losing the powerball last night.

11:22 am Period E begins. Algebra 1 take 4. By this time of the day, we have some cheaters. Students from earlier have given away the answer, but I weasle out some confessions and we move on with the activity.

12:21 pm Period F begins. Algebra 1 take 5.

1:08 pm Period G begins. My prep. Finally. It’s been a great day but I’m exhausted. Today’s lesson was a high energy one. I always try to show the same enthusiasm with my last class as the first, but sometimes it can be difficult. Check personal email. Finish editing STEM rubrics. Take care of emails. Chat with STEM Director.

1:55 pm School day ends. Go to advisor meeting about upcoming school-wide dance. Return to classroom. Approximately 40 students have elected to stay after school to make trifold posters and last-minute changes to their STEM projects. My coworker has been supervising all of them while I was at the meeting. Spend afternoon giving advice on projects and printing, printing, printing for them.

3:55 pm Write passes for the late bus and start kicking kids out. They are nervous but ready for tomorrow. Here’s a video released after the Expo!

4:15 pm Say good-bye to final students. Clean classroom.

4:30 pm Pack up and head out. Run errands. Sit on couch. Breathe. Check email/facebook/twitter. Make dinner. Have plenty of time to write this blog post… but don’t do it. Take the night off. Watch an episode of the Blacklist (okay, okay, three episodes).

10:00 pm Bedtime.

If you want to read about other past days, check out these posts:
Take 1 – November 15th, 2012
Take 2 – November 18th, 2013

NCTM Regionals Nashville – My Favorite

After a whirlwind trip to Nashville attending the NCTM Regional Conference, I was able to check two items off my bucket list: 1) Go to Nashville 2) Present at an NCTM Conference. I had a great time presenting on strategies for teaching English Language Learners in math class, and will be posting more about that later. However, I want to first share my favorite moments and takeaways from the rest of the conference.

Favorite Airport Art: The Dancing Sound Wave
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Favorite Robert Kaplinsky Quote:
It’s actually impossible to pick just one. I’ve been following Robert’s work for years, and I was very excited to finally get a chance to see him in action. Robert’s session was “Motivating Our Students with Real-World Problem-Based Lessons” and we worked our way through the famous In-N-Out Burger problem. I did this activity with my students a few weeks ago, and they are still talking about it. It was so rewarding to see Robert lead us through the activity, and explain all aspects of the lesson. He stressed that you need to start with application (the burger), and then marry the context with the math content. My favorite quotes:

  • “Convince me that you’re right or convince me that I’m wrong.” – Math Practice 3
  • “You should be spending most of your time figuring out how to implement your lessons rather than what the lesson is going to be.” – So true. Robert stressed the need to anticipate what the students are going to do and think so that you are ready to react and respond.
  • “My goal in life is to be the least helpful teacher ever.” – This is something I know I need to work on. Students need to struggle, and I need to let them. It’s a necessary reminder to focus on the hints we can give our students (because we’ve planned for the lesson implementation) that are just enough to keep students going, but not enough to deny them of how they’ll feel after successfully solving a tough problem.

Favorite Teacher Move:
Robert demonstrated how he gives enough wait time after asking a question. He physically counts down five seconds by putting his hand in the air and then bending one finger down at a time. Wait time is so important; this move is easy to implement and it makes you accountable for all five seconds.

Favorite Meal: Brunch at The Pancake Pantry

Several people, (and Taylor Swift!), highly encouraged me to visit the Pancake Pantry. I was told I would need to wait in line, but that it would be worth it. I waited for one hour, and then treated myself to Banana Nut Muffin and Caribbean pancakes. Very worth it.

Favorite Card Sort:
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Kimberley Williams presented a session titled, “Are We There Yet? Increasing Rigor in the Math Classroom.” She discussed Webb’s Depth of Knowledge (DOK) and explained how you could increase the rigor of a task depending on the type of question you ask, using the DOK chart. We looked at several examples of how one topic could be portrayed at each level:
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But the most helpful part to me, was when each group was handed a set of cards and asked to sort them among the different levels. It can be difficult to differentiate between them, so it was helpful to discuss with my table. I could see this activity being done with staff members at school to help everyone figure out the levels.

Here is the card sort:

Favorite Non-Session Activity:
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I loved volunteering at the Math Twitter Blog-o-sphere booth and helping newbies learn about all the awesomeness the MTBoS has to offer. Check out the Exploring MTBoS website here!

Favorite Task Progression:
Brian Shay ran an excellent session titled, “How to be a Super Model-ing Teacher.” He led the crowd through this Illustrative Mathematics Task:

The session reminded me to check out several great sites for modeling tasks that I don’t often check: Illustrative Mathematics, Mathematics Vision Project, and NRICH.

Favorite HonkyTonk:
Line Dancing at the Wild Horse and practicing the Texas A&M Yell Chant with some fellow MTBoS-ers!

Favorite Estimation Activity:
How old is Athena, the goddess of wisdom? How old is Nike, the goddess of victory, perched in Athena’s right hand?


Found at the Parthenon

Favorite Session: Kate Nowak’s “Plan a Killer Lesson Today”
Kate started off the session by asking everyone to think of a topic we dread, and I immediately thought of Radicals. Simplifying them, adding them, everything. I dread it. And she said her goal was to find ways to adapt lessons we already have, so that we’re not throwing out all our “standard” lessons and just starting over. Kate’s suggestion is to invert the lesson: You do, Y’all do, We do.

Her strategies for inversion:
-Ask about a pre-requisites
-Ask the question backwards first
-Give sample items with the question
-Engage in MP8

I have seen and used some of Kate’s work before, but I’ve never really thought of the lessons as strategies that I could use in my classroom… until now. I really needed to hear her thought process and think about how this could work in my classroom. I’m going to re-write my lessons on radicals so that I start by asking the question backwards first. I am going to give students a set of radical statements that are true, and ask students to see if they can fill in some blanks to create more true statements. Stay tuned for a future blog write-up.

Favorite Grand Ole Opry at the Ryman Singer:
Again, impossible to pick just one. I was lucky enough to attend on a night when five (5!) Hall of Famers were performing, and they were honoring Jean Shepard for her 60th anniversary as a member. The show was simply magical.
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Favorite Guideline for Increasing Task Rigor:
During their session on the “Impact of Task Design on Students’ Attitudes about Mathematics”, Ziv Feldman and Jeneva Moseley recommended several guidelines for increasing task rigor:
-Ask students to provide multiple solution strategies
-Ask students to provide mathematical justifications
-Ask students to create their own examples and non-examples

Although I use these strategies often, it was how they asked students to provide another strategy that really stood out to me. See part c below:
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I love how simple the phrasing is, yet it creates the need for a second method.

Favorite Design Principle to Develop a Problem Based Learning Classroom:
Geoff Krall shared five design principles for developing a problem based learning classroom, and it was the 5th one that really got me: “Don’t go it alone.” He said partner up, select 2-3 tasks that will produce rich student thinking artifacts, implement, and debrief. You need to have an “accountability buddy.” So rarely do we actually have time to debrief a lesson on our own, let alone do it with a colleague. It was another useful reminder to focus on lesson implementation, and the value of teamwork.

Thanks to NCTM and all the presenters for a great conference that completely reinvigorated me as we head into the winter season!

#TMC15 – My Favorite

Although I just returned “home” from a California adventure that included visits to Santa Cruz, Big Sur, Anaheim, Los Angeles and Claremont… I actually felt like I was home while attending this year’s Twitter Math Camp (TMC). It has become my must-attend event of the summer, and I plan the rest of my break around it. Doing math and talking about math with such passionate and inspiring educators propels me into the new school year on high speed. Next year’s camp will be held at Augsburg College in Minneapolis from July 16-19, 2016 and you can bet I’ll do anything in my power to attend.

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It always take a bit of time to wind down from TMC; it’s information overload in the best way possible. But it’s unreasonable to think that I will return to my classroom in 5 weeks and implement everything I learned. These are my largest takeaways from TMC, and “my favorite” memories/quotes/highlights, that I wish to carry with me during the year.

Favorite Disney Picture(s): Pre-TMC, I spent a whirlwind 16 hours at Disneyland and California Adventure Park with Casey, Connie, Nicole, and Meg. We mapped our course through the parks to maximize the number of rides/attractions we could see in one day. And of course, when we weren’t tweeting while waiting in line, we talked about teaching math.

Favorite Price is Right Group: It’s a very long process of signing waivers, getting nametags, and being interviewed by producers for a potential spot on the show, but in the end it was worth it to check this item off my bucket list. We cheered and yelled prices at the contestants, and you can watch how it all played out on November 2nd!
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Favorite Morning Session: I made the decision to attend Elizabeth and Chris‘ morning session on “Creating a Culture of Exploratory Talk” and it was the perfect decision for me. I have been attempting to hold better classroom discussions, but this session provided me with specific strategies/structures to use with my students to get them to have richer conversations. I have selected Elizabeth’s Talking Points Activity as my #1TMCthing, so I will be writing another blog post about that in the next couple weeks. In the meantime, here is our morning session wiki page, and here is one of Elizabeth’s posts about Talking Points.

Favorite Debating Activity: Table Debates. During the exploratory talk session, Chris shared his numerous activities for bringing debate into the math classroom. He shares many of his strategies on his website. An argument is comprised of two parts: a claim and a warrant. You can turn almost any statement into a debateable question by adding words such as: best/worst, always/sometimes/never, most, weirdest, biggest/smallest, etc. When students are table debating, they are given a problem or situtation, and two possible opinions on the topic. They must state their argument for the opinion on their side of the table. This is my favorite strategy because students might not always agree with the opinion they are given. However, they need to figure out a strong argument to support that opinion. I feel like many of my questions can be easily rewritten in this format, so it shouldn’t be too difficult to implement this activity this year.

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Favorite Must-Watch TED Talk: In Fawn’s keynote, she shared a quote from Rita Pierson’s TED Talk: “Kids don’t learn from people they don’t like.” I’ve come across this TED talk before, but never actually watched it… until now. The quote nicely highlights Fawn’s recommendations for good teaching: fast (in terms of returning emails, feedback, etc); fair, friendly, firm, and funny.

Favorite SMP Posters: During his talking on Teaching the 8 Practices, Chris shared his SMP posters and had us analyze them. Chris boils down all the CCSS into two words: Thinking and Communicating. The posters all have the same format and are designed specifically for our students. My favorite part of each poster are the questions in the bottom left corner. These are questions that not only can our students ask themselves to determine which practice they are doing, but we as teachers can ask them as we develop lessons and tasks.

Favorite Jumping Picture: Taking jumping pictures while traveling is kind of my thing, and I found a jumping partner in Connie. She shared my general enthusiasm for just having the best time ever no matter where we were, and it resulted in epic pictures like this one (the burgers were great too!)

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Favorite Math Mistakes Activity: Andrew’s session on Math Mistakes and Error Analysis provided me with a great opportunity to analyze the value of mistakes and how we can use them to help our students learn. My favorite activity of Andrew’s is when he gives students a handout like this:
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Every problem has a mistake. Every problem. Students must analyze the structure of the problem to build their conceptual understanding, based on what is currently incorrect. Students must fix the mistakes once identified and justify their reasoning. Read more about this activity on Andrew’s blog.

Favorite Good Teacher vs. Great Teacher Distinguishing Feature: Ilana Horn’s keynote titled “Growing Our Own Practice” was inspiring and informative. Among sharing many discoveries found during her studies, she shared three key features that differentiate between the good teachers and great teachers she observed: Teacher Agency, Empathetic Reasoning, and Ecological Thinking. My favorite among these is Teacher Agency. Ilana emphasized that great teachers state their problems as actionable items. The example she shared is how a teacher views the problem of a student finishing his/her work early. A great teacher does not discuss this problem as having fast vs. slow kids. A great teacher discusses this “problem” in terms of the task itself, and the value of finding group-worthy tasks that engage all levels of learners and include extension possibilities. As I start a new school year with another new principal, I want to remember this mindset: how can we take a problem and turn it into an action item?

Favorite New Desmos Activity: This is actually a trick. I can’t tell you about my new favorite Desmos activity because it hasn’t been released yet. But Eli gave the TMC crowd a sneak peek, and let me tell you, it’s amazing. It will change your teaching life. Stay tuned, it should be released sometime next week.

Favorite Data Table: In his session on Vertical Non-Permanent Surfaces, Alex shared this data table from Peter Liljedahl’s research:
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Hopefully this convinces you to head to your nearest home improvement store and purchase some shower board panels if you haven’t already!

Favorite Debriefing Partner: At the end of every day, Rachel and I would meet up for the walk/drive back to the hotel, and immediately begin sharing everything that happened during the day. It was one of the times of each day that I treasured most. We needed that time together to gather our thoughts and really process everything we learned/experienced. Since we didn’t end up attending a single session together, we were able to double our information intake. Thank you for being the perfect roommate, Rachel!
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Favorite Piano Bar Song: Sweet Caroline. John requested it, someone else vetoed it, more money was thrown into the pot, and then we had an epic singing contest between both sides of the room. We owe a huge number of thanks to PianoPiano in Claremont for entertaining us each night.
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My Favorite My Favorite: Matt shared his strategy of using music cues to help students “become self-directed learners.” I won’t go too in depth because Matt graciously wrote a very extensive blog post about it. Within his post, you can find a google folder with all the music he uses, and a list of the cues in which he uses music. I would like to try implementing 2 or 3 of these this year, but I am definitely overwhelmed trying to figure out the technology to make this happen in my classroom easily. If I can get it working, I know I want a music cue for: “Take out your chromebook, go to student desmos, type in the class code.”

Favorite Quotes:

  • “Find what you love. Do more of that.” –Christopher Danielson
  • “Bad teaching is not knowing that what you’re doing could be better.” –Fawn Nguyen
  • “Build connections so we’re not surviving in the classroom, we’re thriving.” -Fawn
  • “De-front your classroom.” –Alex Overwijk
  • “Don’t stress so much about how to make things debatable. Just throw the word ‘best’ in there and let it go.” –Chris Luzniak
  • “Strive for a Process Reward System, instead of an ‘Answer’ reward system.” –Chris Shore 

Thank you to the TMC volunteer planning committee! This special conference would not exist without all your hard work, and we are all better teachers because of it!

3D Desmos Designs

About a month ago I wrote about how I use Desmos Des-man to introduce an algebra graphic art project. I have done this project for several years now, but this time, I added a special twist… After making a design in Desmos, the students used Creo Parametric to create models of their designs which they 3D printed!

Step 1: I taped four sheets of graph paper together so that students would have a large work area. They chose a theme and started drawing. The only requirements I gave: there had to be at least one image per group member with at least 8 equations (at least 2 quadratic and 2 absolute value) and 2 inequalities

Step 2: Students divided up the drawing and started determining the equations. Some students physically cut their image apart so they could work on it at home.
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Step 3: Students took turns inputting their equations into one Desmos calculator. This took a bit of time since the students could not all be the same calculator at once. Most of the groups would save the Desmos image as a PDF to google drive, and then share that file with their group members.

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Step 4: All of my students take an Engineering class where they learn how to use Creo Parametric. I also took a PTC STEM Certificate Program this past semester where I learned the basics of 3D modeling. I had each student start with a basic rectangle and they uploaded their Desmos image to the rectangle. Then they traced the outline and extruded the lines. That’s it! Some students who are very comfortable with Creo decided to add special features and colors.
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Step 5: I printed the designs using our Stratasys uPrint machine and the students created 3-Dimensional Displays to showcase their work.

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Some groups did not complete a 3-Dimensional Display, so I will be turning their designs into magnets!
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My students were so engaged in this project and so proud of the models they created. It felt so natural to have them continue working with their Desmos designs and turn them into actual 3d prints. One aspect of the project that I didn’t stress with the students this year was the scale of their models. Next year I will have students determine a group scale, so that each component of the image fits together better.

I feel very lucky to have access to a 3D printer at school, and I will be looking for new ways to bring 3D printing to my students naturally. If you have any ideas, please share!

Update: I shared this project during Twitter Math Camp 2015. Here is a video of my presentation:

My Take On Desman

One of my favorite course projects is the Graphic Art Project. Students will design an image on graph paper, write all the equations for it, and type them into Desmos. To intro this assignment, I have students complete my own version of the amazing Desmos Des-man activity.

Instead of having students create their own Des-man, I ask them all to recreate this picture:
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The main reason I start by having all students create the same face is because this is a review activity for us. At this point in the year, students have learned to write equations for linear, absolute value, and quadratic equations. They have also studied domain and range restrictions. I want them to practice these skills, and not just guess/play with the sliders/numbers to see how the equations transform. Each student is given this sheet to show any work they did to find the equations:

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The Teacher Desmos interface allows me to see very quickly who gets it and who needs help (see above). Some students will play around and choose their own colors, or add additional inequalities. When they are all done, we move on to Part 2, and I let them create their own designs. This year we are trying something special for the final product and it is still in the works… so, to be continued!