Number Sense Conversations

I've put the elevator speeches to rest. Today's two minute speech went well... I think. As one event concludes, I'm excited to resume my ongoing thoughts about number sense and students.

Working with teachers and students, I can't help but be inundated with thoughts about things I miss, look forward to, and will be challenged with this year in and out of the classroom. However, there's one thing I crave more than anything else, and that's working with students, which usually entails having number sense conversations with students.

Today, I had rich number sense conversations with students in Math 7, Math 8, and high school Algebra classes. As I sit here and put the finishing touches on the slides for my upcoming conference workshop, Get Students to Argue in Class With Number Sense Activities, I can't put to words how valuable it is to allow students to talk about math in math class. That's an oversimplification, but we seriously need to provide our students with opportunities to talk to each other, even argue with each other. Mathematical Practice 3:

Construct viable arguments and critique the reasoning of others.

Steve Leinwand sums it up best:

These nine words may be the most important words in the entire Common Core effort. 

Last December at CMC North, I was honored to give an Ignite talk about something I'm passionate about: number sense and student conversations. It's titled: Number Sense: I Don't Like This Game Anymore.

Students are hungry for number sense conversations in math class. I really do believe. If you don't believe me, just put up this picture in your class and ask your students, "How long would it take to use all of that?" Then ask them to convince you of their conclusion.

As October quickly approaches, I look forward to seeing you at an upcoming conference this school year. In the meantime, I hope to post more about number sense.

Number Sense,
1005

Common Core Elevator Speech - Day 6

Day 1
Day 2
Day 3
Day 4
Day 5

Did you check out Steve's elevator speech on Day 5? Pretty awesome, right? Here is the second one he emailed me.

"Appealing to an audience that recognizes school math isn't working well enough."

Regardless of what you may think of the Common Core, you must recognize that school mathematics hasn’t been working for far too many students.  You’ve probably heard that the K–12 mathematics program in the United States has been aptly characterized in many rather uncomplimentary ways: underperforming, incoherent, fragmented, poorly aligned, unteachable, unfair, narrow in focus, skill-based, and, of course, “a mile wide and an inch deep.”  Most teachers are well aware that there have been far too many objectives for each grade or course, few of them rigorous or conceptually oriented, and too many of them misplaced as we prematurely ram far too much computation down too many throats. It’s not a pretty picture and helps to explain why so many teachers and students have been set up to fail and why we’ve created the need for much of the intervention that test results seem to require.

These are realities that the Common Core has been designed to fix. How? First, the new standards are common. No longer will publishers cater to a few large states and stuff their books with the union of fifty sets of demands. No longer will our assessments be developed by the lowest bidder and overwhelmingly comprised of low-level, multiple-choice items.

Instead, the prospects of a Common Core set of standards are for shorter, more web-based, better-focused instructional materials and for computer-adaptive, computer-delivered, and instantaneously-scorable constructed response-item assessments.  Second, ignore the misrepresentations and take heart in the fact that the Common Core standards are coherent. These standards replace the vagueness of strands (number, measurement, geometry, statistics, and algebra) with domains, clusters, and well-conceived grade-to-grade progressions of standards. Moreover, they are fair. Many procedures that we have come to teach at grade x, have been moved to grade x + 1, giving us all a chance to build prerequisite knowledge and slow down what has become a drag race through the curriculum. And, lastly, they are teachable. There are only about thirty standards—of varying sizes and depth—at each grade level, resulting in a far more manageable teaching load than the forty to fifty objectives per year that many of us now face.  If you care about your children, if you care about readiness for citizenship and the workplace, and if you care about our future leaders making informed decisions, you should be fighting for, not against, the Common Core.

~ Steve Leinwand

Again, I want to thank Steve for taking the time to prepare two awesome elevator speeches. Hopefully, they've inspired you as much as they've inspired me. Maybe you can use parts in your own elevator speech when the time presents itself. It's not too late to add your own in the comments. Tomorrow, I'll post the last and final elevator speech, which happens to be my two minute speech for my district. 

Common Care,
156

Common Core Elevator Speech - Day 5

Day 1
Day 2
Day 3
Day 4

I have three more days of elevator speeches to share. Now would be a good time to say why I initiated this whole elevator speech series. I was asked by my district to give a 90 second presentation on rigorous mathematics standards. I will be giving this 90 second presentation on Monday at our district's State of the Schools breakfast where many community members, parents, board members, teachers, and administrators will be present. You know, all the stakeholders. In preparing those 90 seconds, I needed to push myself to come up with elevator speeches related to Common Core math standards and rigor. So Day 7 will be my 90 second elevator speech from the State of the Schools.

For Day 5 and Day 6, I'm honored to share two elevator speeches from Steve Leinwand. It was so cool to see an email from Steve in my Inbox, with him saying, "OK - challenge accepted!"

If you've followed my blog, you know I have great admiration for Steve and have been inspired by him numerous times. It won't surprise you that I thoroughly enjoy (and support) his first speech.

"Appealing to an audience that wants more for their children."

It’s only one of eight Common Core Standards for Mathematical Practice, but we can change schools and change lives if we truly implement Mathematical Practice 3:  “Construct viable arguments and critique the reasoning of others.”  In many ways, these nine words may be the most important words in the entire Common Core effort.  We can’t expect students to construct viable arguments unless we ask them “why?” and “how do you know?” and “can you convince us?”  When we ask such questions we are laying the foundation for the reasoning and justifying that represent the thinking that schools need to develop in all students.  Similarly, we can’t expect students to critique the reasoning of others unless we create classrooms where student thinking is valued and students contribute to their own learning within communities of learners.  Moreover, this isn’t just mathematics, but what needs to happen in English language arts, social studies and science as well. So when one cuts through all of the misrepresentations and politics that surround the Common Core, these powerful nine words transcend our differences and capture what every parent and every citizen should be demanding from their schools and for their children.

~Steve Leinwand 

Thank you Steve for sharing your wisdom and fervor. I look forward to sharing your next elevator speech on Day 6.

Fervor,
819

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,
339

Explain that, please.

Recently, I've given a few teacher workshops/conferences and have had the luxury of reflecting on teacher moves as I facilitate a lesson with the attendees. One of the many things we talk about are teacher responses to students.

Me: Did anyone hear me say, "No. That's wrong. You're wrong. I don't like your answer."

Attendees: No.

Me: Right. Instead, you'll hear me say things like, "Can you explain what you did here? Explain that, please. I noticed you did [this] here, please share how you got [that]. I'm curious how you came up with that. Walk me through what you did."  

I tell teachers that I'm taking the emphasis away from right versus wrong answers and placing an interest on the student's thought process and problem-solving. I continue with teachers:

Me: By telling a student they're wrong, a student can have the tendency to shutdown [I make the sound effect of a machine shutting down, "BOOOOvvvvvvvv"]. By asking a student to explain things, it shows that I'm more interested in how they arrived at their answer. 

As teachers, we know a student can be told they're wrong and it's easy for them to give up. On the flip side, when we validate a kid by telling them they're right, the student can also shut down and never reach the higher levels of Depth of Knowledge.

Recently, a workshop attendee asked me how I respond to students who have nailed the answer to a 3 Act task. First, I have them explain their problem-solving plan to me. Second, I question any details that were unclear, encourage them to be more precise, or have them explain their units of measurement. Third, I ask them if they feel confident in their answer after explaining it to me. Fourth, I validate them by simply saying, "That makes sense to me."

I don't tell them they're correct. I treat them just like as if they got the answer wrong. If that doesn't satisfy them, I respond with, "We'll find out soon if you're correct, but that (their explanation and work) makes sense to me." At this point, I offer them an extension to the task. I'd like to talk more about this later, but usually the extension revolves around the students creating something with the new knowledge or skills they have just recently gained.

After all that, please add your favorite lines when questioning students to this Google doc. I think it's also helpful we create a list of lines we avoid using with students as they explore math.

Here are a few people with other stellar teacher moves/lines to support students.
Max Ray: 26 Questions You Can Ask Instead
Dan Meyer: You Don't Have To Be The Answer Key
David Cox: Creating A Culture Of Questions
Steve Leinwand: Accessible Mathematics

BOOOOvvvvvvvv,
645

Guest Blog Posts at Estimation 180

Today, at Estimation 180, I posted some guest blog posts I collected from the beginning part of this year. I'm grateful, honored, and inspired by the stories they (or their students) shared. I hope you have time to check them out and share your story too.

Read their stories here. 

Back to School Ignite Talk

Man, I love a good Ignite talk.
5 minutes.  15 seconds per slide.  20 slides.
Concise.  Succinct.  Compelling.

Why not do my own version of an Ignite talk at Back to School Night next year? I get 10 minutes with parents and would love to change it up a little this coming year. Trust me, after surviving last year, I think the parents deserve a better, improved, and more reassuring version of Mr. Stadel. I'll explain that last sentence in some upcoming blog posts that I'll use to debrief about the 2012-2013 school year. If you're not sure what an Ignite talk is, let me introduce you to my man, Steve Leinwand.

If you like that, check out more Ignite talks by Annie Fetter, Dan Meyer, Max Ray, and Phil Daro. These are my go-to talks when I need a math pick-me-up. Do the math, that will be a little over 20 minutes well spent, being inspired by some key people in our math community. Seriously, check out those four talks.

I'm brainstorming in this space, so feel free to share some input please. At Back to School Night, I'll start by giving a brief 30-60 second introduction of what an Ignite talk is and how they work. I'll give an Ignite talk for 5 minutes, covering any of the following things:

• Standards Based Grading (SBG)
• Noticing and Wondering
• Common Core State Standards (CCSS)
• 8 Standards for Mathematical Practice (8 MPs)
• Problem Solving
• Homework (or No Homework)
• Find my Mistake
• High School Placement Tests
• Desmos
• A healthy balance of mathematical application with procedural and conceptual understanding
• Problems of the Week (PoWs)
• Quotes of the Week (QOTW)
• 3 Act lessons
• Reassessments
• Estimation (Number Sense)
• Tangram Tuesdays
• Whiteboarding

This leaves approximately 4 minutes for parents to ask questions or something else... Have any suggestions for those last 240 seconds?

Who's with me? Does anyone else want to do a Back to School Ignite talk? There's already been some interest generated on Twitter and I started a Back to School Ignite list. Shout at me if you're in. Or is this a really foolish idea? Seth Leavitt, my new online colleague and EnCoMPASS Fellow asked if I'll post it online. I don't see why not. Maybe we can create a space for Back to School Ignite talks.

*UPDATE: Each item listed above does not correspond to its own slide. I simply listed ideas that could possibly work their way into the presentation. Some support each other. For example, when talking about the importance of problem solving, I would mention resources such as 3 Act lessons and The Math Forum's PoWs. Feel free to add to or subtract from the list.

Ignite,
930

CCSS Workshop 2013

I did my first workshop this past week (5-30-2013), discussing the transition to Common Core State Standards, with a focus on the 8 Standards for Mathematical Practice. I'm working with K-5 elementary teachers, a couple of middle school math teachers, some support teachers, and a couple of administrators in the room. I'll admit, I'm not as eloquent a speaker as Steve Leinwand, but there might be a few times where I actually make sense. I'm throwing this video out there for some feedback. I don't expect you to watch the whole thing so I've provided some chapter markers you might be interested in. At the end of the notes for each chapter, I reflect by creating a wish-list of moves I would've done differently. They come across as rhetorical questions, but feel free to chime in. However, here are a few angles I'd appreciate you considering:
What did I forget to talk about?
Where could I have been more explicitly clear?
Where coud I have used a better strategy? ...and so on.

Opener: 0:00-10:10
I use an estimation task (Day 127) to kick things off, providing teachers with the handout Michael Fenton created for estimation180.com and my students. The handout has been through many revisions and I think we have a final version that's a winner.

I use the whiteboard to write the "Too Low", "Too High", and "My Estimate" of a few teachers, asking for reasoning along the way. We watch the answer and discuss.
8:15 is a precious moment where a teacher asks, "Wait a minute! What was it (the song length answer) really?" I love how a teacher is demanding more information. I wish I spent more time expressing the importance of her question. I feel rushed because of all the workshop content I have prepared. I wish I had allowed the other teachers to address her question more. I do with my students, why didn't I do this here?

Active Notebook Part 1: 10:15-12:55
Teachers glue their Estimation 180 handout to the inside cover of their workshop Blue Book and the Table of Contents to the first sheet while listening to Can't Buy Me Love.

Preview of Workshop: 12:55-20:50
I attempt at working on the following question throughout the workshop,

What's our role as we reshape the classroom with the Common Core State Standards?

I share with teachers what today will not be and what today will be. On a parallel universe I share with teachers what I perceive the CCSS to not be and what I perceive the CCSS to be. Then I share a few personal items from this past school year. Seeing that I'm doing a workshop with multiple grade level and content teachers, I'm expressing the focus of the day to be the 8 Mathematical Practices and what we do in the classroom. How do we help facilitate the learning?

Estimation Task #2: 20:50-26:45
We use Day 129 where teachers see that the song length is also the track length. Listen to their reasoning. I love this! Hearing this reasoning from teachers and students is one of the many joys I get from doing these daily estimation tasks. However, I wish I did a better job (23:50) of getting the teachers to justify their reasoning and "argue" a little more than I did. I wish I created a little more tension. Check out (25:00) the excitement of the teachers as they watch the answer.

I introduce the language of creating a task that has a low-entry point and could see that many teachers had no idea what I was referring to. Not their fault. However, I like their reaction when I translate "lower-entry point" to being easier. I wish I explained "low-entry point" better. I wish I had explained it as creating a task where most, if not all students have an equal opportunity to engage with the task, regardless of their mathematical proficiency. I wish I expressed the importance of providing students with a task where math vocabulary and thinking come as a natural result of solving the task.

Math Tools & Two Uses: 26:45-33:55
I ask teachers to glue a picture of a math tool to the front of their Blue Book and write down at least two uses for each tool. They have two minutes to complete this task. After We Will Rock You, I ask the teachers for their uses instead of telling them. This serves two purposes. Yes, I have a list of uses that I anticipate them to come up with, but I want to hear from them first, selfishly providing me with additional uses that I didn't anticipate. Secondly, I'm using this activity to illustrate how students need to provide the answers in the classroom. I wish I could have given this more time in the workshop where the teachers actually used the tools in the manners they suggested. I also should have had the teachers write down all the uses we came up with.

Introduction of 8 Mathematical Practices 33:55-1:04:00
Again, I'm feeling rushed for time! Yes, I said it, "Let me talk about these 8 Math Practices real quick." Real quick? How silly of me. These practices are not something to gloss over. Don't worry, we spend ample time doing a Jigsaw activity so teachers are out finding information about them. I provided the teachers with the handouts found at Jordan School District's site. The practices are presented in a manner representative of the grade level you might teach. Thanks Fawn for this link.  I could have explained and facilitated this a lot better, but the redeeming value is hearing teachers that were appreciative of this specific activity because they were "forced" to explore the practices instead of just receiving a handout with the information embedded. If I were you, I'd skip the section (39:30-52:00) unless you want to hear some of the teachers talking in their groups as they rotate around the room to their four different stations. I'm proud of the rotation table I provided and how teachers travel together according to their "math tool." DON'T miss the "perfect high-five" at 38:10. I love that a teacher commented that "perfect" is subjective. I say this all the time to my students.
At 52:30 I give teachers time to regroup and complete the practices by receiving information from the other teachers in their group. I recap (1:00:00) and then show teachers how to create a pocket (1:01:00) inside their Blue Book so they can store a Quick Reference "teacher" version (I referred to as "adult") of the 8 Mathematical Practices.
I wish I gave more time for reflection. I wish I reviewed each practice with the whole group by having them share out loud something they learned. During the Jigsaw activity, I was told that my time with the teachers was cut short by about ten minutes so I had to hurry things along. Arghh!

Find My Mistake: 1:04:20-1:13:00
I made an executive decision to skip the model lesson I had prepared for the worksop. I'm glad I didn't skip the Find My Mistake segment of the workshop. I'm very adamant about teachers finding the mistake quietly here. I encourage them to share with each other before we review with the whole group. I give props to Michael Pershan for mathmistakes.org. You can hear kids in the hallway, alerting me that our workshop is coming to an end very soon. We listen to each other make corrections or talk about the misconception and why us teachers are good at knowing the content we teach. We're constantly telling students what their mistakes are and telling them how to fix it. Let's switch that role. Make the students find, correct, and tell each other what the mistakes are, especially items that use algorithms. Remember, most of the teachers here are elementary teachers. I also point out that I haven't been jumping for joy every time a teacher gets an answer correct. Instead, I try my best to throw it back on the class for what they think, allowing them to critique the reasoning of others. I love how estimation and number sense is addressed with teachers on how to help encourage students to avoid these mistakes.
I hit a nerve (1:10:45) when I was asked, "What about simplifying?"
I could very well be wrong here, but my current understanding is we (as teachers) are to allow for multiple representations of the correct answer, unless explicitly instructed otherwise. In other words, ten-eighths is just as acceptable as five-fourths.
I wish I reviewed with the teachers the importance of doing an activity like this quietly and individually first, before group discussion. I wish I expressed how much I love group work and collaboration, but need to remember both teachers and students need that quiet time FIRST. The worst is being in a group where one person dominates the conversation and you don't have time to think or worse, problem-solve. I wish I had covered this with the teachers.

Summary: 1:14:15-1:19:00
I provide teachers with a fill-in-the-blank handout to glue to the inside of the back cover. Again, watch their reaction when we get to "low-entry" point. I hope I drive it home when referencing the "Cent-ed Whiffle Ball" task I recently did in Geometry. I remind myself and the teachers to listen to the students. I'm constantly working on allowing students to finish their thoughts. Don't cut students off or finish their sentences for them. I ask teachers to create a couple of goals. I provide the teachers with a list of resources found here. I like how they (at least some of them) want another in-service/workshop.
I wish I emphasized the importance of knowing the 8 Mathematical Practices better and to use the summer to better prepare for next year. I wish I had more time to pump up these points in the summary. I wish I had more time!

Unleash yourself in the comments if you will.

Thanks!
729

Estimation180 site

Its official: I've launched estimation180.com

The Google doc was a temporary holding place for my daily estimation challenges. I'm proud to announce that I will be updating my daily estimation challenges through this site. The site is way more interactive than a Google doc spreadsheet... and quite possibly, more fun too. You can make estimates, share your reasoning, see how others estimate, and more.

The goals of the site:

1. Document my daily estimation challenges.
2. Create opportunities for teachers & students to build number sense together.
3. Share!

What you can do:

1. Click on a picture.
2. Read the question.
3. Look for context clues.
4. Make an estimate.
5. Tell us how confident you are.
6. Share your reasoning (what context clues did you use?).
7. See the answer.
8. See the estimates of others.

The most important part is step #6. It's so valuable to a classroom when students share their logic or use of context clues when formulating an estimate. After you make an estimate, feel free to give us a brief description.

I've posted the first 15 days and will continue to update the site. Go do some estimating, build some number sense with your students and throw me some feedback if you find any glitches or ways to improve it. I want to sincerely thank Fawn Nguyen, Nathan Kraft, Chris Robinson, Michael Pershan, Dan Meyer, and Steve Leinwand for any help, inspiration, and/or feedback you've given me regarding estimation180.com You all are amazing!

Happy estimating!

Estimation 180

Estimation initiative:

[*UPDATE: www.estimation180.com has gone live]

Last year I willingly started adding an estimation question to my daily warm-up, inspired by Steve Leinwand, Dan Meyer, and a monthly ASB gag we did a few school years back. Everyday, I greet my students at the door and hand them a 3x5 index card for their warm-up. They get the first 2-3 minutes of class to complete the warm-up exercise and estimation question. The first question reviews the previous day's skill. As for the estimation question, last year I was putting questions that were comparable to fun facts and students had no context clues for making logical estimates. It got silly. Here are some examples:

• How many miles is the California coastline?
• How long does an elephant stay pregnant?
• How many In-n-Out Burger restaurants are there?
• How many miles from the Earth to the Sun?
• etc.

Stepping back over the summer and really fine-tuning the goal of estimation (improving number sense), I began using estimation questions that were more relative and provided better context clues. Every chance I get, I use a picture or something inside my classroom that will allow students to make logical estimates. Here's today's (Day 10):

I've had to cover up the bottom half of the screen now because students come in and immediately want to go for the estimation question. They want to come up to the screen and do weird measurements, or ask me factual questions, and they flat out forget about the first question. I don't blame them. It's fun. Once we go over the first question (favorite yes/no), I usually have students give me estimates that are too low or too high and then we "go right at it." "Who thinks they got this?"

Once I get about 8-10 estimates, I reveal the answer and it's so cool to see how the students react. "Ohhhh, I was sooo close." Or "I was way off!" Either way, I ask the student or students who were close to explain their logic. It's fascinating how kids think.

For today's, I snapped a picture of a measuring cup full of almonds (my new favorite snack). Tomorrow, they'll estimate how many are in the jar from CostCo. Estimation should build. The whole first week we talked about height, based off my height. 

Day 1: What is Mr. Stadel's height? They don't need a picture for that.

Day 2: What is Mrs. Stadel's height? They needed a picture for that. 

Day 3: What is my son's height? Another picture.

Day 4: What's the height of a lamppost Mr. Stadel is standing near? etc.

The first four days used my height as a frame of reference. Check out Estimation 180 (Google doc will be replaced with estimation180.com )and you'll see what I mean. My estimation initiative is to begin documenting my 180 days of estimation, simply titled Estimation 180. Seriously, do I need one more thing on my plate right now? No. However, I do this every day and would love to share this stuff and receive feedback. Estimation is important to me. I've already seen student improvement with number sense in just 10 days of school.  

I'm starting small here, but would love to expand this idea: stay tuned. In the meantime, check out the spreadsheet catalog (tab at the top).

[UPDATE: estimation180.com is live. Forget the spreadsheet!]

Number sense,

1056

Distance, Rate, & Time [Giddy Up!]

Last week I finished Steve Leinwand's Accessible Mathematics. It's a quick, easy, informative, realistic, and applicable read. Get on that!
This week I planned on diving into Standards Based Grading while restructuring some things for next school year. Well, there's still time for SBG. Instead, I've been churning out some new 3 Act lessons with:

1. Some outtakes to the hexagonal Pencil Cup lesson and...
2. The beginning of some distance, rate, and time lessons

There's a plethora of resources out there dealing with d = rt. Therefore, I thought I'd try and put my little spin on the whole roundabout. Keep checking my Distance, Rate, & Time album for updates.
Giddy up to summer!

Ferrari Ride - Act 1 from Mr.Stadel on Vimeo.

Go the distance,

1140

Estimation is Key

First Day of summer school.
This morning, I snapped a picture of a portion of our school parking lot. My intention: use it as the daily estimation question included in the warm-up.
Q: How many total parking spaces are in the parking lot?

We did our warm-up. I first asked for numbers that were too low and didn't make sense. Then too high. Finally, I asked for their estimates, but didn't validate any responses. We then jumped into our lesson for the day: ESTIMATION.
Opening the lesson, I asked my students to think of one good thing and one bad thing about estimation. Here's what they listed.

Good:

• Doesn't have to be correct
• It's easy
• Can be made mentally
• It's an educated guess
• "It's free! It doesn't cost you anything." (Oh, I added that one)

Bad:

• Not precise
• Could be wrong

After comparing the pros and cons, the good guys won! Estimation FTW!
Why?
It gives anyone a chance to cast an answer based upon specific information. It's a starting point. It keeps your number sense in check. It allows the brain to think abstractly for a brief moment. It's free!

We went outside and delegated the work. Students counted staff, reserved, preschool, handicap, and ordinary (unlabeled) spots. We got a total of 141 parking spaces. One kid was two away with 143 as his estimate. Go figure. Another kid was in the five hundreds. Go figure. After the empirical data produces the answer, we always circle back to our original estimates. It's important for students to see the difference so they can improve their number sense and estimation skills for next time.

Tomorrow, we extend the lesson: convert those itemized numbers into percentages in order to make a pie chart of the allocation of parking spaces.

Check it: Steve Leinwand Case 4: Number Sense
He hits some great points at 2:25. It's worth watching the whole thing in my opinion.
Steve exclaims about estimation, "We need to build that into ALL the things that we do!"

Think how many times a day we estimate:
Time to get ready in the morning. Time to get to work. How long is this darn red light? How long before I get my cup of coffee? How many? How many? How many?

Please share with me!
What can I do to make estimation better with my students?
How do you use estimation effectively?
How do your students benefit from it? (or not)
What are some other daily estimations you make?

Estimate,
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