Fun With A Sticky

Earlier this year, I wrote about Fun With A Dot and A Line, a Math 6 lesson I loved because it had:

• A simple question/task.
• A competition.
• Student creativity.
• Students assessing the work of each other (accountability).
• Students defining the necessary vocabulary/rules.
• Students determining the necessary tools to help solve the task. 

As my 7^th graders approached surface area, I prepared a few activities in preparation for File Cabinet. Here is one of those activities. I give you Fun With A Sticky:

Launch:

Hand each student a 3” x 3” sticky as they enter. Post the following on the board:

Explore (creativity):

A few students might do something like this.

Give the class a hint or two (if they need it):

1. This can be done with four lines.
2. Think Tic-Tac-Toe

Here's what we're going for:

If a student is still clueless, encourage them to look around and see what their classmates are doing. As the teacher, keep your eyes peeled for students who are approaching this with some creativity. Sarah and Pricila used the straightedge of their binders to draw lines. Gerardo tried folding the sticky in thirds like this.  

Student accountability:

When done, have each student write their name on the back of the sticky. Have each group of 3-4 students decide who has the best 9 squares and bring that one sticky up to the teacher. In no particular order, place them under the document camera for all students to see. Without sharing, ask each student to quietly (mentally) pick the top 2 stickies they feel have the best 9 squares. 

Vocabulary/Rules:

Ask students for input. 

Me: "Without telling me which stickies you’ve picked, how are you determining which sticky has the best 9 squares?" 

Jesus: They drew straight lines.

Carla: They are perfect squares.

Have the class define a perfect square.

Carla: Each side is the same length

I now had students take their top 2 and pick their favorite one. Somehow get your students to vote; little sheets of scratch paper, SmartBoard Responders, iPads, etc. I labeled each sticky alphabetically to avoid “this” sticky and “that” sticky. I had each student stand up. I then said, "Sit down when I say the letter of your sticky with the best 9 squares."

Necessary Tools:

They narrowed it down to about 3 stickies and gave great rules for finding the best 9 squares.

Me: What tools can I use to make it even more precise?

Student: A ruler. 

Me: Ok. What do I measure and what am I looking for on these stickies?

Here’s where you get students to discuss (or discover) how each square should have a width of 1 inch and a length of 1 inch. In other words, you’re defining a square inch with your students. Okay, there will be some "squares" that are just garbage and can be eliminated by eyeballing them. However, here's where you get to be dramatic with your students. Get them worked up. Ask them which ones you should measure. Mess with them a little and joke with them how they're unable to determine the correct "squares". Have fun with it. Either way, make sure students see the squares being measured. If I had more time, I could have redistributed the stickies and passed out rulers for the students to measure each other's "squares". You can see from this picture that the winning sticky note had a total of 3 "perfect squares."

Congratulations to my winners! They received a brand-new whiteboard marker.

Here’s the icing on the cake (and lesson design telling me something wonderful just happened):

• Itzco wanted a chance to do it again. He'd been sleepy in class all week.
• Genesis wanted a ruler if we did a second round. Let's just say her attitude toward math all week was subpar and she has difficulty being a self-starter.
• Students wanted a chance to improve and try again. Especially students who initially drew ridiculous "squares".

There it is, Fun With A Sticky. Here's that list one more time:

• A simple question/task.
• A competition.
• Student creativity.
• Students assessing the work of each other (accountability).
• Students defining the necessary vocabulary/rules.
• Students determining the necessary tools to help solve the task. 

Sticky,

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SBAC on Steroids?

California is an SBAC (Smarter Balanced Assessment Consortium) state. This last week my school started the SBAC Field Tests and I was a Test Administrator for my 7th grade classes. Before I continue, let me post part of the Security Affidavit I had to sign.

That's right, I will not divulge the contents of the field test. However, I will first refer you to last year's post where I made a video comparing released CST questions and SBAC practice questions.  Here's a reminder (screen shot), comparing just two questions. 

This week, I felt like my students were looking at SBAC practice questions that were on steroids. Since I can't speak about the SBAC Field Test questions, I took my Deodorant 3 Act task and put what I think the SBAC steroid version might look like. I have nothing against SBAC. I tried to create a similar task that had rigor, complexity, and mathematical modeling.

First, my Deodorant task goes like this:

Act 1: How long will it take to use all of that deodorant?

Act 2: Data from the first 4 sticks. 

Act 3: The answer is still in the works. 

Sequel: How many sticks of deodorant would a person use in one lifetime?

Here's how I'd see this same task presented SBAC-on-steroids-style. 

I walked away this week, thinking our students need to do many things.

1. Read the story. 
2. Decode the text.
3. Understand the question.
4. Organize the data.
5. Retrieve and access the correct skill(s) or skill set.
6. Apply the necessary skills.
7. Perform the correct operations with the above skills.
8. Interpret their answer.
9. Explain (and articulate) their answer.

As a teacher of many ELD students, I can safely say that the following steps are already challenging; 1, 2, 3, 8, and 9. Don't get me wrong. I believe in literacy, but I wouldn't want language to be a barrier when assessing a student's mathematical abilities.

Hear this though: Students must make sense of the problem before they can use mathematical modeling to predict the answer. Then, they must articulate how they got their answer. I would consider this expectation the new norm.

I'm not done. I could totally see SBAC taking this deodorant task and creating an additional question that would complete my 3 Act. Check out this doozy.

We're looking for students to drag numbers to both axes, use a line of best fit, make a mathematical prediction, and explain everything again. The only thing I left out of this question was for students to write an equation for the line they draw. 

I have more to say about this, but that's enough for now. I'm already thinking about how to better prepare my students for these types of questions, which should be my next post. If you have any thoughts, please share. If you've made it this far, here's a preview of Act 3 for my deodorant task. Don't worry, I keep my shirt on!

Steroids,

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Get Students to Argue in Math Class

I recently submitted my speaker proposals for both 2014 CMC conferences. One of my proposals is for the following session:
Title: "Get Students Arguing in Math Class with Number Sense Activities."
Description: Get students to productively argue about math situations. Participate in number sense activities requiring students to construct viable arguments, critique the reasoning of others, and use sense-making. Get ready to throw down.

I also had to answer a few questions justifying the session and connecting it to the CCSS and 8 Mathematical Practices. I provided the following connection:
The presenter will use number sense activities to get participants to construct viable arguments and share their reasoning like students. Using presenter-made tasks (Estimation 180) and other online resources appropriate for grades 3-8, attendees will be able to see the importance of student reasoning and creating productive discourse in the classroom. Teachers will also be provided with sentence frames and stems for all students, especially English language learners.

I'm really excited at the thought of this session getting accepted so I figured I would jot down a few ideas here and see what you all have to contribute. Even if I'm not accepted, I think every math class has to have students productively arguing at times. Doing estimation challenges with my students has been so beneficial for them to get better at the art of arguing. However, I know it could be better. I'm not sure if you've ever experienced it before, but it's a treat to stand off to the side or in back of a group of students arguing about a question in math. They have no idea you're nearby because they are so caught up in the argument. Don't get me wrong, it's not like they're swearing at each other and calling each other names. They are having a rich discussion, sharing conjectures, examples, counterexamples, etc. and I have the pleasure of spectating. I usually turn to an innocent bystander (nearby student) and whisper, "Awesome, look at them arguing. Isn't it great?" The student usually looks shocked that I'm happy their classmates are arguing. I love it!

I'd like this session to place a big emphasis on two mathematical practices:
MP 3: Construct viable arguments and critique the reasoning of others.
MP 1: Make sense of problems and persevere in solving them.

I plan to break these two practices down more in my session. For now, I feel I need to focus on three major parts to arguments: having excellent content, capturing the arguments, and indirect facilitation.

Content: There's a wealth of content available, but I think the more controversial the point of contention, the better. One of my favorite moments in math class was when we did Mathalicious' Datelines lesson. Students were arguing about which celebrity shouldn't date another celebrity because of the age discrepancy. Some students disagreed about the rule of (n/2) + 7, especially since I was teaching 14 year-olds at the time. It was awesome.
Here's my current list of resources that have given my students great things to argue about:

• Estimation 180
• Mathalicious
• Would You Rather 
• by John Stevens

My kids went nuts arguing about a similar question to this "Would You Rather" found here.

These don't have to be full-on lessons. They can be warm-ups, math talks, used during classroom transitions or to break up your direct instruction, etc. I'm really looking forward to using @MathCurmudgeon's site MathArguments180.com
Imagine your students arguing about which student should pack your parachute based on this data.

Another up and coming resource is Open Middle by Robert Kaplinsky and Nanette Johnson.

What resources would you add to my content list?

Capture: I need to capture these arguments for a few reasons. Students need to listen to other students argue, especially from different classes. My memory is very porous, and I can't remember what students say verbatim. Students can listen to the recordings and pick a side, or provide their own agreement or dissent. I'd also love to share student arguments with other teachers, especially at this session. How do I capture this?

I just downloaded Voice Memos for iPad onto my school iPad. I will test it out next week with students. Wish me luck. Here are the features I'm optimistic about:

• It will record in the background while another app is running.
• It was $1.
• I can pause the recording.
• I can trim audio clips.
• I can sync with Dropbox.

Have any tips for capturing student arguments?

Facilitation: Here's where I need to do a better job. For many of my students, English can get in the way of them articulating their point. I'd like for students to listen better to each other and respond accordingly. I want to hear what they have to say. I want them to be a contender in their disagreement, but I don't want them to be held back because of language deficiencies. Therefore, I need to provide them with sentence starters and stems. Fortunately, these can be used with any student. Here's a few:

• My opinion about this is _____________.
• I could argue that _____________.
• I disagree with your statement that _____________ because _____________.

Have any stems or sentence frames you're already using with students to help them articulate their thoughts?

Argue,
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