I'd love some feedback on this tool I'm tinkering around with right now.
I was inspired by Graham Fletcher, seeing him place student estimates inside ranges, or bins if you will. My goal was to make a tool that replicated this experience, is efficient for teachers to use, and added some visual enhancements. The tool could be used with Estimation 180 challenges and was made in Desmos.
What successes might you see happening in your classroom when using this tool?
What challenges might you see happening in your classroom when using this tool?
What advice do you have for improving it?
Thanks in advance for your responses.
Bins,
303
Showing posts with label Estimation180. Show all posts
Showing posts with label Estimation180. Show all posts
Wednesday, June 28, 2017
Thursday, January 28, 2016
5th Grade Fun
Yesterday was AWESOME!
I had the great fortune of visiting Jen Sandland's classroom in the morning.
A BLAST!
The tallest student, (we'll call her Jane), came in at a towering 5'2". I was holding a part of the clothesline in my hand as the remainder of it was outstretched on the floor. I asked the class:
"How many Janes would make the length of the clothesline?"
Oh, man. You should have seen these kids talking about this? Some made guesses like four or five Janes. Naturally, I asked, "So how long are four Janes? How long are five Janes?"
I wish I took a picture of our model, but it looked something like this:
One student explained his method of adding the feet first and then the inches. It was amazing! So we came up with the length of the clothesline as a range of 20'8" to 25'10". I then had two students help me measure the clothesline against Jane's height and we almost got five Janes. That makes sense because the rope is actually 25 feet long.
We used the clothesline to talk about Day 150 on Estimation 180.
What will be the value of the finished cent sign?
The thinking, strategies, and conversations were so cool. We placed our too lows, too highs, and just rights on the clothesline. We talked about order, magnitude, and spacing. If you do Day 150 with students and you're watching the answer as a class,
PAUSE THE VIDEO WHEN THE "C" IS COMPLETED TO MAKE $0.65.
Cent Sign of Pennies from Mr.Stadel on Vimeo.
Give students a chance to revise their initial estimates. It's such a powerful experience. Pause those video answers and let students change their answers once they have more information.
Before my farewell, the students asked me a few questions:
How'd you make the video to the pennies answer?
Take a picture of the complete layout. Subtract a penny. Take another picture. Repeat.
What program do you use to make the counters on Estimation 180 videos?
Apple's Motion
What are your favorite Estimation 180's?
The music challenges. HANDS DOWN!
Did you always like math?
No. I loved music and art in school. I was just good at remembering math rules. Now, I love getting better and understanding numbers.
My question to them:
What is your favorite thing about numbers?
They are expected to answer this when I return to their class. When I return, I'd love to just blend in, if that's possible, while they are doing math centers or other activities and learn from them. Man, these kids were so fun to hang out with for an hour.
Thanks Jen! Keep up the fantastic work you're doing with them!
5th,
924
I had the great fortune of visiting Jen Sandland's classroom in the morning.
Such an engaging, energetic morning learning w @mr_stadel Thank you for sharing your love of math w my Ss! @TUSDSTEM pic.twitter.com/4j6wqgsdQU
— Ms. Sandland (@SandScholars) January 27, 2016
Jen is a 5th grade teacher in my district. Her students and I spent an hour having a blast:- talking number sense
- doing Estimation 180
- doing Clothesline math
- measuring
A BLAST!
The tallest student, (we'll call her Jane), came in at a towering 5'2". I was holding a part of the clothesline in my hand as the remainder of it was outstretched on the floor. I asked the class:
"How many Janes would make the length of the clothesline?"
Oh, man. You should have seen these kids talking about this? Some made guesses like four or five Janes. Naturally, I asked, "So how long are four Janes? How long are five Janes?"
I wish I took a picture of our model, but it looked something like this:
One student explained his method of adding the feet first and then the inches. It was amazing! So we came up with the length of the clothesline as a range of 20'8" to 25'10". I then had two students help me measure the clothesline against Jane's height and we almost got five Janes. That makes sense because the rope is actually 25 feet long.
We used the clothesline to talk about Day 150 on Estimation 180.
What will be the value of the finished cent sign?
The thinking, strategies, and conversations were so cool. We placed our too lows, too highs, and just rights on the clothesline. We talked about order, magnitude, and spacing. If you do Day 150 with students and you're watching the answer as a class,
PAUSE THE VIDEO WHEN THE "C" IS COMPLETED TO MAKE $0.65.
Give students a chance to revise their initial estimates. It's such a powerful experience. Pause those video answers and let students change their answers once they have more information.
Before my farewell, the students asked me a few questions:
How'd you make the video to the pennies answer?
Take a picture of the complete layout. Subtract a penny. Take another picture. Repeat.
What program do you use to make the counters on Estimation 180 videos?
Apple's Motion
What are your favorite Estimation 180's?
The music challenges. HANDS DOWN!
Did you always like math?
No. I loved music and art in school. I was just good at remembering math rules. Now, I love getting better and understanding numbers.
My question to them:
What is your favorite thing about numbers?
They are expected to answer this when I return to their class. When I return, I'd love to just blend in, if that's possible, while they are doing math centers or other activities and learn from them. Man, these kids were so fun to hang out with for an hour.
Thanks Jen! Keep up the fantastic work you're doing with them!
5th,
924
Tuesday, September 29, 2015
Plate of Cheeseballs
I might be the only one excited about this Estimation 180 challenge. And that's okay. If you want to play along and test out goformative.com at the same time, click here.
How many cheeseballs will fit on the plate?
*a single layer of cheeseballs
Enter your estimate, work, and reasoning here. Play along.
Cheese!
246
How many cheeseballs will fit on the plate?
*a single layer of cheeseballs
Enter your estimate, work, and reasoning here. Play along.
Cheese!
246
Saturday, August 1, 2015
CA Teachers Summit Ed Talk
I had the honor and privilege to give an Ed Talk at the California Teachers Summit held on Friday, July 31, 2015. Across the state of California, teachers attended college campuses for breakout sessions, Ed Talks, and keynote speakers. I gave an Ed Talk at the Pasadena Convention Center titled, Estimation: A Gateway To Better Number Sense. Check it out.
I also had the privilege of meeting the other two inspiring Ed Talk presenters, Nicol R. Howard and Thema Bryant-Davis. The highlight of the day for me (and my son) was that I got to meet one of the Keynote speakers, astronaut Leland Melvin!
Ed Talk,
1146
I gave an Ed Talk at the California Teachers Summit on July 31, 2015.
I also had the privilege of meeting the other two inspiring Ed Talk presenters, Nicol R. Howard and Thema Bryant-Davis. The highlight of the day for me (and my son) was that I got to meet one of the Keynote speakers, astronaut Leland Melvin!
 |
| Nicol, Leland, and me |
1146
Sunday, July 5, 2015
Open House: Week 1, Day 2
Last week was the first week of a four-week summer academy. I teach a 110-minute class, four days a week, and it's designed as an enrichment course: no homework, no tests, no grades. The class is titled Get Ready for Algebra and here's the working schedule for the four weeks.
It's a great opportunity for me to practice some of my skills; skills I once possessed and skills I learned this past year, but didn't practice enough. Initially I thought I'd be keeping some of my skills sharp, but I soon found out how rusty I am at various moves, ranging from facilitation, to instructional, to questioning. How do I know, I recorded three of the four days last week.
Before I break down an 8-minute video clip from the second day, I want to be clear:
1) It's Open House everyday in my classroom. Anyone is welcome at anytime. I observed so many teachers this year and am extremely grateful for the opportunity. I learned a lot by being an observer. Being an observer allows me to reflect on my own practices, not necessarily the person being observed.
2) Recording my Open House classes allows me to identify certain skills and improve them.
These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my own teaching. If I am to encourage other teachers at video-recording their teaching in the name of professional development, I need to do it too.
3) What professions record themselves (or other professionals) as a means to strengthen their craft? I recently tweeted some professions that benefit from recording their craft, ranging from athletes to musicians to dancers to doctors to comedians to teachers. You can only get better, right?
5) One more time: These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my teaching. Nor do I pretend to be perfect at this stuff. I just know I can be better and video recording helps immensely. If you have the stomach to continue, you'll see my notes as I reflect on my facilitation of this Estimation 180 challenge: my wife's height.
1:45
I ask the class to share a "too low" for Mrs. Stadel's height.
I try to get the class' attention about writing down 4'10" and how it's confusing... because I know students typically write feet and inches using decimal notation (4.10).
Here's what I wish I did (or could have done):
If I had done a better job of checking student work while they're working, I would have known how the student wrote 4 feet 10 inches on her paper.
I wish I asked the student how to write 4 feet 10 inches on the whiteboard.
I could have had the student write it up on the board while all the students were working.
I should have asked her why 4'10" was a reasonable "too low".
Having her share her reasoning would strengthen her voice and mine at the same time.
2:10
I received 7'10" from another student for the "too low" and asked "Is that taller than me?"
Like the previous student, I should have asked her to share her reasoning.
2:20
"Did anyone put 6'4" as their 'too high'?"
I need to capitalize on why 6'4" would be an extremely reasonable "too high".
Five students raised their hand on camera and I remember about two others students (off camera) raised their hand as well.
I should have followed up with at least one of these seven students as to why 6'4" makes sense here.
*I usually do this... argh.
2:35
"Don't share with me, share with your neighbor. Share with your group."
Why did I not say, "I would also like you to explain your reasoning behind your answer."
This would have also bought me an extra minute to check in with at least one more student. When checking in with students, I typically have them rehearse on me so I can encourage them to share whole group in a few minutes.
3:15
I began to take four estimates.
"I'm totally forgetting something."
I forgot to introduce the idea of students filling out their number lines.
4:00
I like the idea of the class filling out the same number line together on the first estimation challenge.
4:20
I explain that it's a common student misconception to put their estimate right smack in the middle of the number line, even if it's wrong.
Instead of being abstract in my explanation, I could have been more concrete by showing them an example. Let's say a student thinks Mrs. Stadel is exactly 5 feet tall (5'0"), they would still put there answer right smack in the middle. I should have put 5'0" in the middle.
Ask students: What's wrong with this?
Ask students: How can we use this number line more accurately?
I was truly lucky to get a difference of three feet between 4'10" and 7'10".
I didn't explain my thinking to students: I knew it was three feet, but didn't explain that I knew that half of 3 feet is one and a half. I should have modeled my thinking for students.
4:55
"For time reasons, I'm going to help you out"... look at me, the clock watcher. Am I really helping students out? I feel more like I'm helping me out by bailing them out. For about a minute, it's me doing the math, not the students.
How silly of me, I could have simply marked 5'10" and 6'10" on my number line breaking the distance between 4'10" and 7'10" into thirds. And again, explain my thinking.
5:10
I'll start taking your guesses.
I like when I ask students to stop me when I get to their guess on the number line.
Should I take the average? or should I have students argue it out?
I think the latter.
Here's why: that initial placeholder on the number line impacts EVERY estimate afterwards. Make it count.
6:10
I just got done taking four estimates and didn't ask for one single reason behind them...
I say, "A lot of good guesses here." because I already know the answer. I can see that the four estimates I took are in the ballpark. However, I never called on one of those four students to convince me.
6:15
I tried to dig myself out of this hole by saying, "I'm going to keep you guys in suspense."
I wouldn't say this is the best move. However, it was better than completely ignoring (or forgetting) the reasoning behind their estimates.
I went with two reasons. Half the number of guesses I received just a few minutes prior. BUMMER.
7:45
Once I revealed the answer, you can hear the "ohhs." because they were actually pretty close.
I say, "If you are within one or two inches, you should be really proud of yourself."
A student says, "Dude! I was off one inch!"
Same student, "I'm so happy!"
Maybe I missed it (or forgot by now), but a couple kids had a huge sigh of relief and were even excited about this. Seriously, that's awesome. If all we did was worry about our "answer" being exact every time, then we've lost focus on the process of estimating. Doesn't it feel absolutely awesome to have an estimate within a couple inches?
For my second day, I've seen how rusty I am and what needs improving. Moving forward:
Goal #1:
I want to cheat when placing my "too low" and "too high" on my number line from now on. Once I place my "too low", I will choose a "too high" that allows me to easily partition my number line into reasonable spacings.
Goal #2:
While students are filling out their handouts, look for 8 different students and prepare them that I'd like them to share with the class (and include reasoning):
Too low: 2 students
Too high: 2 students
Actual estimate: 4 students
Goal #3:
Ask the class who agrees or disagrees with the first estimate given.
For example, "Who disagrees with the estimate of 5'9" and would like to share why?"
Continue this with the second and third estimates given.
If you made it this far, feel free to offer any suggestions to help me get better. Thanks in advance.
Open house,
816
It's a great opportunity for me to practice some of my skills; skills I once possessed and skills I learned this past year, but didn't practice enough. Initially I thought I'd be keeping some of my skills sharp, but I soon found out how rusty I am at various moves, ranging from facilitation, to instructional, to questioning. How do I know, I recorded three of the four days last week.
Before I break down an 8-minute video clip from the second day, I want to be clear:
1) It's Open House everyday in my classroom. Anyone is welcome at anytime. I observed so many teachers this year and am extremely grateful for the opportunity. I learned a lot by being an observer. Being an observer allows me to reflect on my own practices, not necessarily the person being observed.
2) Recording my Open House classes allows me to identify certain skills and improve them.
These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my own teaching. If I am to encourage other teachers at video-recording their teaching in the name of professional development, I need to do it too.
3) What professions record themselves (or other professionals) as a means to strengthen their craft? I recently tweeted some professions that benefit from recording their craft, ranging from athletes to musicians to dancers to doctors to comedians to teachers. You can only get better, right?
What professions record themselves (or other professionals) as a means to strengthen their craft? #thinkingoutloud
— Andrew Stadel (@mr_stadel) July 1, 2015
4) I need to be vulnerable, humble, and open to improve. I intend to keep my video clips to segments shorter than 10 minutes. I picked a specific part of the class I wanted to focus on improving. Even if no one else sees your video, I hope you'll prop up a camera in your room and record 10-15 minutes of your class. Play it back and reflect. Go in the next day and make those changes (improvements) you want to make.5) One more time: These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my teaching. Nor do I pretend to be perfect at this stuff. I just know I can be better and video recording helps immensely. If you have the stomach to continue, you'll see my notes as I reflect on my facilitation of this Estimation 180 challenge: my wife's height.
1:45
I ask the class to share a "too low" for Mrs. Stadel's height.
I try to get the class' attention about writing down 4'10" and how it's confusing... because I know students typically write feet and inches using decimal notation (4.10).
Here's what I wish I did (or could have done):
If I had done a better job of checking student work while they're working, I would have known how the student wrote 4 feet 10 inches on her paper.
I wish I asked the student how to write 4 feet 10 inches on the whiteboard.
I could have had the student write it up on the board while all the students were working.
I should have asked her why 4'10" was a reasonable "too low".
Having her share her reasoning would strengthen her voice and mine at the same time.
2:10
I received 7'10" from another student for the "too low" and asked "Is that taller than me?"
Like the previous student, I should have asked her to share her reasoning.
2:20
"Did anyone put 6'4" as their 'too high'?"
I need to capitalize on why 6'4" would be an extremely reasonable "too high".
Five students raised their hand on camera and I remember about two others students (off camera) raised their hand as well.
I should have followed up with at least one of these seven students as to why 6'4" makes sense here.
*I usually do this... argh.
2:35
"Don't share with me, share with your neighbor. Share with your group."
Why did I not say, "I would also like you to explain your reasoning behind your answer."
This would have also bought me an extra minute to check in with at least one more student. When checking in with students, I typically have them rehearse on me so I can encourage them to share whole group in a few minutes.
3:15
I began to take four estimates.
"I'm totally forgetting something."
I forgot to introduce the idea of students filling out their number lines.
4:00
I like the idea of the class filling out the same number line together on the first estimation challenge.
4:20
I explain that it's a common student misconception to put their estimate right smack in the middle of the number line, even if it's wrong.
Instead of being abstract in my explanation, I could have been more concrete by showing them an example. Let's say a student thinks Mrs. Stadel is exactly 5 feet tall (5'0"), they would still put there answer right smack in the middle. I should have put 5'0" in the middle.
Ask students: What's wrong with this?
Ask students: How can we use this number line more accurately?
I was truly lucky to get a difference of three feet between 4'10" and 7'10".
I didn't explain my thinking to students: I knew it was three feet, but didn't explain that I knew that half of 3 feet is one and a half. I should have modeled my thinking for students.
4:55
"For time reasons, I'm going to help you out"... look at me, the clock watcher. Am I really helping students out? I feel more like I'm helping me out by bailing them out. For about a minute, it's me doing the math, not the students.
How silly of me, I could have simply marked 5'10" and 6'10" on my number line breaking the distance between 4'10" and 7'10" into thirds. And again, explain my thinking.
5:10
I'll start taking your guesses.
I like when I ask students to stop me when I get to their guess on the number line.
Should I take the average? or should I have students argue it out?
I think the latter.
Here's why: that initial placeholder on the number line impacts EVERY estimate afterwards. Make it count.
6:10
I just got done taking four estimates and didn't ask for one single reason behind them...
I say, "A lot of good guesses here." because I already know the answer. I can see that the four estimates I took are in the ballpark. However, I never called on one of those four students to convince me.
6:15
I tried to dig myself out of this hole by saying, "I'm going to keep you guys in suspense."
I wouldn't say this is the best move. However, it was better than completely ignoring (or forgetting) the reasoning behind their estimates.
I went with two reasons. Half the number of guesses I received just a few minutes prior. BUMMER.
7:45
Once I revealed the answer, you can hear the "ohhs." because they were actually pretty close.
I say, "If you are within one or two inches, you should be really proud of yourself."
A student says, "Dude! I was off one inch!"
Same student, "I'm so happy!"
Maybe I missed it (or forgot by now), but a couple kids had a huge sigh of relief and were even excited about this. Seriously, that's awesome. If all we did was worry about our "answer" being exact every time, then we've lost focus on the process of estimating. Doesn't it feel absolutely awesome to have an estimate within a couple inches?
For my second day, I've seen how rusty I am and what needs improving. Moving forward:
Goal #1:
I want to cheat when placing my "too low" and "too high" on my number line from now on. Once I place my "too low", I will choose a "too high" that allows me to easily partition my number line into reasonable spacings.
Goal #2:
While students are filling out their handouts, look for 8 different students and prepare them that I'd like them to share with the class (and include reasoning):
Too low: 2 students
Too high: 2 students
Actual estimate: 4 students
Goal #3:
Ask the class who agrees or disagrees with the first estimate given.
For example, "Who disagrees with the estimate of 5'9" and would like to share why?"
Continue this with the second and third estimates given.
If you made it this far, feel free to offer any suggestions to help me get better. Thanks in advance.
Open house,
816
Tuesday, June 16, 2015
Classroom Visit in New Hampshire
Yesterday, I had the great fortune to Skype with a second grade class and their teachers in New Hampshire.
IT WAS AWESOME!
There were about 6 students who came up to the webcam to:
IT WAS AWESOME!
There were about 6 students who came up to the webcam to:
- share their name
- share their favorite Estimation 180 challenges
- ask me a question about Estimation 180
Here are some of their favorite Estimation 180 challenges:
- Large Chocolate bar
- Surface Area of my daughter's hand ("cuz she's so cute.")
- Coins
- Marshmallows
- Lego Transporter set
- My height
Some of the questions they asked:
- How do you say your last name?
- How do I think of the estimation challenges?
- Who takes the pictures of me?
- Will you do more Lego estimation challenges?
- How many estimation challenges are there on the site? (I was asked this twice.)
- Will I continue to make more estimation challenges?
After finishing Q&A with my six new friends, Ms. Spear asked if anyone else wanted to share something. One girl spoke up and thanked me for
"...helping my brain to think more and not give up."
This warmed my math heart and made my day. I think that's a direct reflection of Ms. Spear and her colleagues who are creating a classroom of curiosity, perseverance, and risk-taking. They're raising the bar high for all of us, so anyone who gets Ms. Spear's students in the future, please continue to carry the torch and never let that flame become extinguished.
Something else warmed my heart. Ms. Spear shared that the class used estimation challenges, mohawks, and the strength of a small school community to raise money for Levi and his fight with cancer. Woah! Cool!
I thanked them for being such a polite, mature, and respectful group. As you can only imagine second graders staying seated for longer than 18 seconds is a small miracle. They were a classy group that has inspired me.
Thank you Ms. Spear and your students for allowing me to briefly visit your classroom.
You're the inspiration!
Thanks,
930
Sunday, January 25, 2015
Using Google Forms and Sheets
If you've ever used Estimation 180, you'll notice there's a Google Form on each day where anyone in the world can input their estimate. Although it's not what I envisioned when initially designing the site, it has served a purpose. And it's free. So until I have a million dollars or someone is willing to donate a bunch of money to Estimation 180 so there can be a classroom type interface like teacher.desmos.com or Pear Deck, the Google forms will have to do for now.
My suggestion: create your own form so that you can capture rich data from your students. I believe it's so important that we capture, sort, assess, and discuss student thinking. I put together three short screencasts on:
Part 2: Creating and setting up the form
Part 3: Sorting the data in a Google Sheet
Please let me know if you have any questions or suggestions to make the work flow more efficient.
If you're headed to CUE 2015 in Palm Springs, come check out one of my two sessions where I'll use Google Forms and Sheets to capture, sort, assess, and discuss the rich thinking and data you can receive from students.
Forms,
216
My suggestion: create your own form so that you can capture rich data from your students. I believe it's so important that we capture, sort, assess, and discuss student thinking. I put together three short screencasts on:
- Suggestions for using your own Google Form with students.
- How to make the Google Form in video 1.
- How to sort and use the data in the Google Sheet.
Part 1: The finished form
- Form fields and parameters
- Daily pic in the form
Part 2: Creating and setting up the form
- Text fields and advanced settings
- Insert the image URL into the form
- Creating sentence starters
- Using a shortened URL
Part 3: Sorting the data in a Google Sheet
- Using Add-ons, specifically rowCall to separate class periods into their own sheets
- Conditional Formatting
- Finding the average (and more) of a column
Please let me know if you have any questions or suggestions to make the work flow more efficient.
If you're headed to CUE 2015 in Palm Springs, come check out one of my two sessions where I'll use Google Forms and Sheets to capture, sort, assess, and discuss the rich thinking and data you can receive from students.
Forms,
216
Friday, January 23, 2015
@Estimation180 tweets
Why on earth would I need an additional Twitter handle (account)? I probably don't. However, it just felt right. It was time. Let me break it down:
@mr_stadel tweets will continue to be all things math and make-fun-of-Fawn.
@Estimation180 tweets will capture and share my daily estimation curiosities.
Estimation 180, the site, is a place where students and teachers can have meaningful conversations revolving around number sense. It's mainly structured around themes so teachers and students build number sense using the information from previous days or personal experiences. There's a visual introduction, a simple question, a visual payoff, and reasoning along the way. In preparing the Estimation 180 challenges for the site, many of them are brainstormed, planned, captured, and presented so they are accessible in a classroom.
As for the @Estimation180 Twitter account, I'm capturing a daily estimation curiosity, be it thoughts and/or visuals. Each day, I'll use my estimation radar to look for something I'm curious about. I'll do my best to share a visual when possible. Furthermore, I look forward to posing as many questions as 140 characters will allow. These questions can be just as important as the visual. If not more! There won't necessarily be a visual answer (payoff), but it never hurts to try. This Twitter account allows me to freely view the world in a curious way with minimal restraints.
Thanks for following me at either handle or both.
Thanks for your inspiration.
Thanks for your feedback.
Thanks for your patience as I discipline myself to look for daily estimation curiosities and share them via Twitter at @Estimation180.
Here's the first tweet:
@Estimation180,
933
The embed code for @Estimation180 feed (if you're interested):
<a class="twitter-timeline" href="https://twitter.com/Estimation180" data-widget-id="558849375049220096">Tweets by @Estimation180</a>
<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+"://platform.twitter.com/widgets.js";fjs.parentNode.insertBefore(js,fjs);}}(document,"script","twitter-wjs");</script>
@mr_stadel tweets will continue to be all things math and make-fun-of-Fawn.
@Estimation180 tweets will capture and share my daily estimation curiosities.
Estimation 180, the site, is a place where students and teachers can have meaningful conversations revolving around number sense. It's mainly structured around themes so teachers and students build number sense using the information from previous days or personal experiences. There's a visual introduction, a simple question, a visual payoff, and reasoning along the way. In preparing the Estimation 180 challenges for the site, many of them are brainstormed, planned, captured, and presented so they are accessible in a classroom.
As for the @Estimation180 Twitter account, I'm capturing a daily estimation curiosity, be it thoughts and/or visuals. Each day, I'll use my estimation radar to look for something I'm curious about. I'll do my best to share a visual when possible. Furthermore, I look forward to posing as many questions as 140 characters will allow. These questions can be just as important as the visual. If not more! There won't necessarily be a visual answer (payoff), but it never hurts to try. This Twitter account allows me to freely view the world in a curious way with minimal restraints.
Thanks for following me at either handle or both.
Thanks for your inspiration.
Thanks for your feedback.
Thanks for your patience as I discipline myself to look for daily estimation curiosities and share them via Twitter at @Estimation180.
Here's the first tweet:
What time of day is it?
How long to go a mile?
How many vehicles in a mile?
How many red lights?
#estimation180 pic.twitter.com/RvmwRD4A5U
— Estimation 180 (@Estimation180) January 24, 2015
@Estimation180,
933
The embed code for @Estimation180 feed (if you're interested):
<a class="twitter-timeline" href="https://twitter.com/Estimation180" data-widget-id="558849375049220096">Tweets by @Estimation180</a>
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Thursday, January 1, 2015
Thank You 2014
There are many parts of 2014 for which I'm thankful. Here are some math-related ones.
*Apologies if I missed someone or something. Please remind (badger) me in the comments.
*Apologies if I missed someone or something. Please remind (badger) me in the comments.
- YOU for reading this blog, giving me feedback, sharing ideas, making suggestions, attending my conference sessions, sharing stories about using tasks or Estimation 180, and being in education to support students (children and adults).
- The MTBoS for helping me continue to grow as an educator.
- TUSD for having confidence in me as a coach to support fellow math teachers.
- TPSF for allowing me to contribute to such an amazing summer learning environment.
- DLCs and Co. for being a great bunch of tech-junkies in the name of meaningful learning
- Conferences:
- GLAMC for being wonderful people, organizing great mini-conferences, and gathering wonderful Los Angeles teachers.
- OCMC for hosting highly accessible and meaningful PD opportunities in Orange County throughout the year.
- NCSM for allowing me to nerd out with Chamberlain and Kaplinsky in New Orleans.
- NWMC for a jam-packed conference of sessions in which multiple states and countries can partake in.
- CMC for holding the best conferences in the biz. I was truly honored to be a small part.
- Consulting:
- PYLUSD, Rockwood, and CUSD: thank you all for your confidence and willingness to have me work with your math teachers. I learned a great deal!
- Christopher Danielson for sending me a wonderful estimation book (still reading).
- Tracy Zagar for including some Estimation 180 in her upcoming book.
- Motion Math for making wonderful-amazing-delightful math apps for my son and me to enjoy together.
- Eric Milou, Gwen Zimmerman, Robert Kaplinsky and Dan Meyer for putting up with me during our NCSM 3-Act project and allowing me to learn a great deal from you all.
- Hannah for being the best colleague last school year.
- My niece for designing the Estimation 180 logo and artwork.
- Johnny and SPEYSYDE for helping me get my Estimation 180 shirts printed.
- Steve Leinwand for the continued inspiration and top-notch CCSS elevator speech about MP3.
- The Math Forum and the Encompass crew for the continued opportunities to connect, collaborate, and create in the name of problem-solving.
- CueThink for creating a digital problem-solving app to support students and teachers.
- Global Math Department for allowing me to frequently write a short blurb in their newsletter.
- Kaplinsky for being a great (math) friend and coercing teachers to ask for sticky note autographs.
- Fawn for still making fun of me.
- My students for teaching me.
- My family for your love and support that encompasses everything.
Thank you,
123
Saturday, November 1, 2014
Pumpkin Seeds
For Halloween, we gutted the larger pumpkin from Day 197 for two reasons:
1) To carve it and
2) To roast the seeds
*Little did I know this pumpkin would produce many number sense opportunities beyond Day 197's weight estimate.
My 4.5 year-old son helped gut the pumpkin with me. We gathered as many seeds as possible and set them aside for the roasting process. The recipe I use can be found here. Before mixing the seeds in olive oil and seasonings, I lowered the pan down to my son and asked how many seeds he thought there were. [How many do you think there are?]
His pile actually makes sense to me and definitely looks close to 100, give or take. Now that we've made a pile of his "one hundred" seeds. I ask:
Seeds,
225
P.S. Thanks to Christopher Danielson and all he does at #tmwyk!
1) To carve it and
2) To roast the seeds
My 4.5 year-old son helped gut the pumpkin with me. We gathered as many seeds as possible and set them aside for the roasting process. The recipe I use can be found here. Before mixing the seeds in olive oil and seasonings, I lowered the pan down to my son and asked how many seeds he thought there were. [How many do you think there are?]
Me: How many seeds do you think there are?
Son: Well, ...[thinking for a few seconds]... there's definitely more than a hundred.
Me: How do you know it's more than a hundred?
Son: It just looks like more than a hundred.
Me: Make me a pile of seeds that would be about 100.He takes his hands and makes a pile toward the bottom of the pan. I can't contain my excitement to see what he has done.
His pile actually makes sense to me and definitely looks close to 100, give or take. Now that we've made a pile of his "one hundred" seeds. I ask:
Me: How many piles of 100 seeds do you think we can get?I see he's a little confused by my question, so I ask it differently.
Me: How many piles do you think we could make where each pile has 100 seeds?He starts to think, but by this time, my almost two year-old daughter sees the pan of seeds is now at her level, so she comes running over and wants in on the action of moving seeds. I thought our conversation was derailed as I brought the pan back up to counter height. But my son keeps it going. He didn't necessarily attempt to answer my question (which is fine by me). He took it in a different, pleasantly unexpected direction:
Son: What if we could get 10 piles?
Me: Do you mean ten piles of one hundred?
Son: Yes!
Me: Are you asking me how many seeds we would have if we had ten piles of 100?
Son: Yes.This blew me away. Where'd this come from?
Me: Well, ten piles of one hundred seeds would mean we have a thousand seeds.
Son: A thousand??!!
Me: Yes.
Son: What if we had twenty?
Me: Twenty piles of 100 seeds?
Son: Yes.
Me: Well, what two numbers make twenty? Ten and...
Son: Ten!
Me: Right. So if ten piles make a thousand and another ten piles make a thousand, we would now have two th...
Son: ...ousand!
Me: Right.
Son: What's 100 piles?
Me: You mean, what's one hundred piles of one hundred?
Son: Yea.
Me: That would be ten thousand.My wife chimes in.
Wife: No.
Me: One hundred piles of one hundred? Ten thousand.
Wife: Wait. You're right.And our kids are now off in the other room playing and getting ready for going outside and looking at Halloween decorations before trick or treating. So many cool things happened:
- I love how we pursued my son's questions and not mine.
- I love that he was fascinated by the word "thousand" even if it didn't make sense.
- Because he thinks a "hundred" is big.
- I love how we started with actual seeds (concrete) and went way more abstract.
- I love how my wife had the best estimate in the house [375 seeds].
- I love how the "pumpkin seeds" estimation challenge is just large enough so you can't accurately eyeball the amount and it's just small enough where it wouldn't take me an absurd amount of time to accurately count.
My wife and son watched the video answer this morning. My wife's response:
This is perfect for my [1st grade] students!
We paused the video when we saw ten groups of ten and paused it again when I made a larger pile of one hundred seeds. He struggled with making sense of final amount.
Me: How would you say that number?
Son: Forty-eight eight?
Me: How many piles of one hundred are there?
Son: Four.
Me: So we say "four hundred" and let's count the piles of ten together. Ten, twenty,..
Together: thirty, forty, fifty, sixty, seventy, eighty,
Me: And. Wait. There are only eight in this last group. So we say eighty-eight. Four hundred eighty eight. Say that.
Son: Four hundred eighty eight.
Me: Great. Let's go make breakfast.Here's the recipe again and some pictures of the process.
 |
| Seasonings! |
 |
| Ready for the oven. |
 |
| Roasted and ready to eat! |
225
P.S. Thanks to Christopher Danielson and all he does at #tmwyk!
Monday, September 22, 2014
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:
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
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
Sunday, July 20, 2014
Estimation 180 Gear
They're here! Estimation 180 t-shirts and stickers! Yes, I'm excited.
Estimation 180 was born out of my love for number sense and visual mathematics. In addition, it was important I help my students develop better number sense and see the world of mathematics in a different way. Little did I know, the site would make its way into classrooms across the United States, Canada, and other parts of the world. Thank you all for tweeting or emailing your experiences as I find it so cool that students are exploring number sense in your classroom and having mathematical conversations, sometimes even constructive arguments.
It makes my math heart full of joy to see other teachers do amazing things with Estimation 180 and beyond. Please make some time to check out blogs like Joe Schwartz, Jonathan Claydon, Mary Bourassa, and Megan Schmidt who are just a FEW of the teachers taking the idea and running with it. Teachers like Michael, Hedge, Dan, Robert, John, Matt, and others spread the Estimation 180 love when doing teacher trainings or presentations. I couldn't be more appreciative and grateful. Thank you! Chris Harris even shared some bacon estimations to a roomful of parents one weekend. I love how the site has become an instrument to help teachers create a classroom of curiosity with students, building number sense along the way. In addition to daily estimation challenges, the site has many of the lessons I've developed over the past few years.
These shirts are just another extension of my passion for number sense. As I present at conferences and give teacher trainings, I'm excited to give away some t-shirts to attendees nailing estimation challenges built into my workshops. Likewise, stickers are available for you to stick some number sense in your favorite place. This is how I roll!
I'm not in this to make money. This is more of a hobby to go along with the site. I would be eternally grateful if you decide to buy shirts and stickers and spread the Estimation 180 love. Head over to the Estimation 180 store and check out the shirts, their sizes, and how easy it is to order.
Nuts and Bolts:
If you're interested, I think it'd be good to be transparent on the nuts and bolts behind the t-shirts and stickers. If you're not interested in the nuts and bolts behind the t-shirts, skip the rest of this post and check out the t-shirts and stickers.
No outside party is financially backing Estimation 180. AND I don't plan on charging for using the site, ever! Therefore, I have done everything I can think of to make these shirts as affordable as possible, because I'm not in this to make money. Any money made from shirts and stickers would go back toward web costs associated with Estimation 180 and the free t-shirts and stickers I would pass out at conferences. As you can imagine, it's been one huge math task keeping track of expenses in order to set reasonable price points for the t-shirts and stickers so that teachers can afford them.
$20 for a shirt gets you a lot! You get a high-quality shirt for one. This price also includes tax and shipping. It also looks like I can throw in a sticker with each t-shirt order. Sweet! This $20 also goes toward the cost of the blank shirt, printing, mailing envelopes, and labels (mailing and return).
$2.50 gets you a high-quality sticker. This covers the cost of getting the sticker made, the envelope, labels, and postage. Of course, if you order two or three stickers, it's a better deal.
*Important note: my buddy Johnny from Speysyde was in charge of printing the t-shirts and he did a fantastic job! Please cruise by his site. It's all about the sustainable lifestyle:
I think you'll truly enjoy your shirt. I am!
Gear,
1047
Estimation 180 was born out of my love for number sense and visual mathematics. In addition, it was important I help my students develop better number sense and see the world of mathematics in a different way. Little did I know, the site would make its way into classrooms across the United States, Canada, and other parts of the world. Thank you all for tweeting or emailing your experiences as I find it so cool that students are exploring number sense in your classroom and having mathematical conversations, sometimes even constructive arguments.
It makes my math heart full of joy to see other teachers do amazing things with Estimation 180 and beyond. Please make some time to check out blogs like Joe Schwartz, Jonathan Claydon, Mary Bourassa, and Megan Schmidt who are just a FEW of the teachers taking the idea and running with it. Teachers like Michael, Hedge, Dan, Robert, John, Matt, and others spread the Estimation 180 love when doing teacher trainings or presentations. I couldn't be more appreciative and grateful. Thank you! Chris Harris even shared some bacon estimations to a roomful of parents one weekend. I love how the site has become an instrument to help teachers create a classroom of curiosity with students, building number sense along the way. In addition to daily estimation challenges, the site has many of the lessons I've developed over the past few years.
These shirts are just another extension of my passion for number sense. As I present at conferences and give teacher trainings, I'm excited to give away some t-shirts to attendees nailing estimation challenges built into my workshops. Likewise, stickers are available for you to stick some number sense in your favorite place. This is how I roll!
I'm not in this to make money. This is more of a hobby to go along with the site. I would be eternally grateful if you decide to buy shirts and stickers and spread the Estimation 180 love. Head over to the Estimation 180 store and check out the shirts, their sizes, and how easy it is to order.
Nuts and Bolts:
If you're interested, I think it'd be good to be transparent on the nuts and bolts behind the t-shirts and stickers. If you're not interested in the nuts and bolts behind the t-shirts, skip the rest of this post and check out the t-shirts and stickers.
No outside party is financially backing Estimation 180. AND I don't plan on charging for using the site, ever! Therefore, I have done everything I can think of to make these shirts as affordable as possible, because I'm not in this to make money. Any money made from shirts and stickers would go back toward web costs associated with Estimation 180 and the free t-shirts and stickers I would pass out at conferences. As you can imagine, it's been one huge math task keeping track of expenses in order to set reasonable price points for the t-shirts and stickers so that teachers can afford them.
$20 for a shirt gets you a lot! You get a high-quality shirt for one. This price also includes tax and shipping. It also looks like I can throw in a sticker with each t-shirt order. Sweet! This $20 also goes toward the cost of the blank shirt, printing, mailing envelopes, and labels (mailing and return).
$2.50 gets you a high-quality sticker. This covers the cost of getting the sticker made, the envelope, labels, and postage. Of course, if you order two or three stickers, it's a better deal.
*Important note: my buddy Johnny from Speysyde was in charge of printing the t-shirts and he did a fantastic job! Please cruise by his site. It's all about the sustainable lifestyle:
Our mission is simple. To spread awareness and advocate an eco & social sustainable lifestyle through the creative collaboration of culture, music, sport, art, adventure & travel.I declined using some of the premium web store features my host offers, such as shipping calculators, tax calculators, and other premium web store features. This drastically keeps the cost of the shirts at $20. For each purchase and transaction, Stripe takes a small percentage from my side. There is no additional cost to you. Their service, similar to PayPal, makes each transaction secure, safe, and easy.
I think you'll truly enjoy your shirt. I am!
Gear,
1047
Wednesday, July 2, 2014
Barbie Zip Line
Inspiration from Matt, John, and Jedidiah helped me shape my Barbie Zip Line task today. Whenever I prepare new tasks for my students, I have been trying to keep mathematical modeling, student ownership/creativity, performance tasks, and openness in the back of my mind. That's a lot, right? Plus, there's a hundred other little things, but let's focus on the list above. As I reflect on today, I'll share how I would improve this for next time.
Supplies (in order of attachment):
Buy enough rope so that you can have lengths that are 10 feet apart. In other words, have different rope lengths: 30 ft., 40 ft., 50 ft., 60 ft., etc. This will play well into the mathematical modeling part of the task (see below). It will also help make it easier to get the pulley systems on and off of the zip line. Solving the task yourself will also help determine the rope lengths you'll need for your school site.
The task (handouts found here):
Depending where (and who) you teach, some students have been zip-lining before. Ask! It never hurts. Maybe they can share their experience. Plus, this gives you a chance, at some point (if you feel necessary), to talk about how they're sitting in front of you, ALIVE, because someone was able to do some solid math and build a sound enough structure for them to zip line on. Just sayin'.
I low-balled my students today on their budget. I should have raised it to $2500 or $3000. Figure out what will work for your site. However, this mistake allowed me to give some early finishers an extension: find a more reasonable starting budget.
Here are the opening costs of your zip line company:
Students had to receive approval from their Summer Academy principal by showing their designs. I highly encourage this move. Students see someone else taking a vested interest in their learning. The principal gets an informal glimpse of your classroom. And students have to be prepared to explain the math and their problem-solving approach. If your principal is unavailable, get someone else: teacher, custodian, campus security, etc. It could be you, but you're already doing the formative approval (assessment) in class.
All these prices can change depending on your tastes. I included a liability insurance just for fun. The materials for the harness and pulley system need to be of high quality, so don't make them cheap. $50 might have been too cheap. The most important material is the steel cable (rope). This will help create multiple solution strategies. It's beautiful. Overall, I was pleased with my price points.
I found that having students create three rides is essential to this task. At least three rides. Sometimes tasks generate such a strong focus on the ONE CORRECT WAY to construct an answer or problem-solve. This adds pressure and can rob students of discovering mistakes or playing around with numbers. By creating separate zip lines for both certain death and boredom (getting stuck), it does many beautiful things.
Students innately know what type of zip line would kill barbie: a steep zip line. They can sketch that on their whiteboard, no problem. On the flip side, students have a good understanding of a boring zip line: practically a horizontal line. They can also sketch that on their whiteboard. Both sketches can be done without using numbers, formulas, or mathematical notation. It creates an entry point for all students. So here's what they had to say:
Students were able to draw steep zip lines, label the height 20 feet, guess the ground distance to be about 5 or 10 feet, and use the Pythagorean Theorem to calculate the length of the cable (hypotenuse).
Mathematical Modeling and Multiple Solutions:
Students were able to design their own zip line by playing around with the numbers between their certain-death zip line and boring zip line. I told them to dream big on the whiteboards as if money wasn't a factor right now. Most did. Most.
I had a couple groups first figure out the cost of all the materials ($700) and subtract it from the $1500 budget, giving their group $800 to spend on cable. With $20/foot, they could use 40 feet of cable for their zip line. They identified the height and the hypotenuse of the right triangle. Impressive.
One of these two groups felt this wasn't enough cable and it was still too steep. Michelle had been zip-lining in real life so she knew. This was my mistake, but it turned into an opportunity for me to extend this task. I asked them to create a new budget for me so the cable was longer, but within reason. If you need more of an extension, have them come up with a formula to determine the amount of cable and distance on the ground, given a specific amount of money.
Before they could go outside and test their zip line, students had to complete this list:
I had students transfer their work to their graph paper composition books before they took it to the principal. I'll insert some pictures:
Here's the permit:
It was a blast! Students loved it. Here's another extension:
Have students design a system that gets the pulleys and/or dolls back up to the top of the zip line.
By the way, I did teach the Pythagorean Theorem in there somewhere. Where? You might ask. I don't remember: ALL throughout the task. Use discretion. Some students need it first. Some need it after you've let them mess around on the whiteboards.
Zip,
1152
Supplies (in order of attachment):
- Barbie doll, or an action figure like G.I. Joe, Superman, or Captain America
- Velcro: One-wrap (don't get Sticky Back)
- Carabiners
- Swivel Spring Snap (optional)
- Fixed Pulley
- Rope (thin enough to fit through the pulley)
Buy enough rope so that you can have lengths that are 10 feet apart. In other words, have different rope lengths: 30 ft., 40 ft., 50 ft., 60 ft., etc. This will play well into the mathematical modeling part of the task (see below). It will also help make it easier to get the pulley systems on and off of the zip line. Solving the task yourself will also help determine the rope lengths you'll need for your school site.
The task (handouts found here):
Depending where (and who) you teach, some students have been zip-lining before. Ask! It never hurts. Maybe they can share their experience. Plus, this gives you a chance, at some point (if you feel necessary), to talk about how they're sitting in front of you, ALIVE, because someone was able to do some solid math and build a sound enough structure for them to zip line on. Just sayin'.
I low-balled my students today on their budget. I should have raised it to $2500 or $3000. Figure out what will work for your site. However, this mistake allowed me to give some early finishers an extension: find a more reasonable starting budget.
Here are the opening costs of your zip line company:
All these prices can change depending on your tastes. I included a liability insurance just for fun. The materials for the harness and pulley system need to be of high quality, so don't make them cheap. $50 might have been too cheap. The most important material is the steel cable (rope). This will help create multiple solution strategies. It's beautiful. Overall, I was pleased with my price points.
Students innately know what type of zip line would kill barbie: a steep zip line. They can sketch that on their whiteboard, no problem. On the flip side, students have a good understanding of a boring zip line: practically a horizontal line. They can also sketch that on their whiteboard. Both sketches can be done without using numbers, formulas, or mathematical notation. It creates an entry point for all students. So here's what they had to say:
Leyla: We have a chance to see what not to do.
Trevor: It reminds me of when we do Estimation [180] and you ask us to give a too low and too high. It helps us find a reasonable number in the middle.
Deena: It shows us what a wrong answer or zip line would be.
Students were able to design their own zip line by playing around with the numbers between their certain-death zip line and boring zip line. I told them to dream big on the whiteboards as if money wasn't a factor right now. Most did. Most.
I had a couple groups first figure out the cost of all the materials ($700) and subtract it from the $1500 budget, giving their group $800 to spend on cable. With $20/foot, they could use 40 feet of cable for their zip line. They identified the height and the hypotenuse of the right triangle. Impressive.
One of these two groups felt this wasn't enough cable and it was still too steep. Michelle had been zip-lining in real life so she knew. This was my mistake, but it turned into an opportunity for me to extend this task. I asked them to create a new budget for me so the cable was longer, but within reason. If you need more of an extension, have them come up with a formula to determine the amount of cable and distance on the ground, given a specific amount of money.
Before they could go outside and test their zip line, students had to complete this list:
Here's the permit:
It was a blast! Students loved it. Here's another extension:
Have students design a system that gets the pulleys and/or dolls back up to the top of the zip line.
[insert video here]
Zip,
1152
Monday, June 30, 2014
Fun With A Name Tent
As I ask my new students to make a name tent with an 8.5" x 11" sheet of paper on the first day of Summer Academy, I think, "Let's have a little competition." This wasn't in my lesson plan. Ha!
If you haven't noticed, I have become obsessed with classroom competitions. Here are two posts in case you missed them:
Fun With A Dot and A Line
Fun With A Sticky
Therefore, I'm adding today's post of Fun With A Name Tent to the "Fun With A" series. A name tent looks like this:
I use name tents for teacher trainings or on the first week of class with students so I can quickly learn their names. Right as I tell my new students to make a name tent, I announce, "Let's see who can fold their name tent into the best thirds?"
Game on!
If you have read (or remember) my two posts from above, you know this activity will go something like this:
Here are some whiteboard shots of my lazy writing as I quickly jot down what students say. It's fascinating.
I handed each group a name tent that was in the running for the best thirds. Some groups used inches and some groups used centimeters to measure.
I didn't care nor tell them what unit of measurement to use. I walked around and questioned which unit of measurement they were using and asked them to explain why they chose that specific unit of measurement. We later had a discussion (almost arguments) about which made more sense for this task. Most students eventually were convinced by their peers that centimeters would be more accurate here. My second class had two tents that were extremely close, but couldn't tell which was better:
We had to compare 0.5 centimeters to 0.25 inches to see who had the smallest error, Leyla or Srihitha? It was awesome! We had to decide if we wanted to convert the inches to centimeters or vice versa. You can see that Leyla won by 0.135 centimeters. DANG! Those are some good folds.
Next, I introduced them to Estimation 180 by estimating my height. They'll be keeping track of their estimates in their compositions books.
My favorite part was this exchange:
My favorite was Mansi. She suggested that we multiply the number of students (20) by 5 feet since most students were about 5 feet tall. Then we add or subtract the difference of each student's height in relationship to 5 feet. We started a Mansi column in our Google spreadsheet. This would make for a pretty cool lesson on integers.
Before we went outside, I had the students get in order from what they thought was shortest to tallest. If you keep track of the data in a spreadsheet, use the spreadsheet to verify their order: another great tool from a spreadsheet.
With this organized data, you could do a lesson on mean, median, mode, and range. Even mean absolute deviation if you're up to it. Another great part was Dylan noticing a student was absent today. "We don't know the height of the kid who isn't here today."
You could take this task and apply the mean or the mode. Have students predict the height of the absent kid. Furthermore, you could segue into probability if you like. What are the chances the absent kid is the mean height? the mode height?
How sweet of my first class, they wanted to include my height in the total height. We went outside and looked for an area long enough to fit our calculated total height of approximately 103 feet.
We went a little bit past 103 feet because some students were considerate enough to avoid placing their feet next to someone else's head. The dismissal time was rapidly approaching so I let it slide. One clap on three for Reese. She had the closest estimate of 102 feet.
One. Two. Three.
CLAP!
Thirds,
1050
If you haven't noticed, I have become obsessed with classroom competitions. Here are two posts in case you missed them:
Fun With A Dot and A Line
Fun With A Sticky
Therefore, I'm adding today's post of Fun With A Name Tent to the "Fun With A" series. A name tent looks like this:
I use name tents for teacher trainings or on the first week of class with students so I can quickly learn their names. Right as I tell my new students to make a name tent, I announce, "Let's see who can fold their name tent into the best thirds?"
Game on!
If you have read (or remember) my two posts from above, you know this activity will go something like this:
- Students get time to create their best thirds.
- Students decide in their group (of four) who has the best name tent.
- Students vote (whole group) by eyeballing the tents and make a prioritized list.
- Students define how we decide the best thirds.
- Students define what to measure.
Here are some whiteboard shots of my lazy writing as I quickly jot down what students say. It's fascinating.
I handed each group a name tent that was in the running for the best thirds. Some groups used inches and some groups used centimeters to measure.
Next, I introduced them to Estimation 180 by estimating my height. They'll be keeping track of their estimates in their compositions books.
My favorite part was this exchange:
Brianna: Will you tell us your height?
Me: No.
Brianna: What?
Class (disappointed): Ohhhhh!
Brianna: That's not fair. Then why are we doing all this work?
Me: I understand. I said I'm not telling you my height.And then BAM! I take out my measuring tape!
Me: Brianna, stand on your desk chair and you can measure how tall I am.
Brianna: Oh, cool!We proceed to estimate my wife's height and then we estimate the TOTAL height of the class. This was fun. I asked, "What would be useful to know and how would we go about getting it?" borrowed from Dan.
My favorite was Mansi. She suggested that we multiply the number of students (20) by 5 feet since most students were about 5 feet tall. Then we add or subtract the difference of each student's height in relationship to 5 feet. We started a Mansi column in our Google spreadsheet. This would make for a pretty cool lesson on integers.
Before we went outside, I had the students get in order from what they thought was shortest to tallest. If you keep track of the data in a spreadsheet, use the spreadsheet to verify their order: another great tool from a spreadsheet.
With this organized data, you could do a lesson on mean, median, mode, and range. Even mean absolute deviation if you're up to it. Another great part was Dylan noticing a student was absent today. "We don't know the height of the kid who isn't here today."
You could take this task and apply the mean or the mode. Have students predict the height of the absent kid. Furthermore, you could segue into probability if you like. What are the chances the absent kid is the mean height? the mode height?
How sweet of my first class, they wanted to include my height in the total height. We went outside and looked for an area long enough to fit our calculated total height of approximately 103 feet.
One. Two. Three.
CLAP!
Thirds,
1050
Sunday, June 15, 2014
A Few Updates
Update 1:
I finally finished Act 3 for my Deodorant lesson. I hope you check it out and can give me some feedback; I think it could be much better with your help. If nothing else, check out how long it took to use 5 sticks of deodorant. Mathematical Modeling should really be at the forefront of this task. It might appear linear, but I would bet a year's supply of deodorant that an adolescent's deodorant use will be far different than mine. I also guarantee students will think of variables ranging from climate to age to geographical location to genetics to more. I think you'll have some excellent conversations with the deodorant task. My favorite part is the sequel: How many sticks of deodorant would one use in a lifetime?
Way back when this task first started, I opened up a little estimation competition in the comments at 101qs. Don't listen to a word Nathan Kraft says. The person with the closest guess would win an Estimation 180 prize. With so many close estimates, the following gentlemen will be the first to receive the new Estimation 180 stickers, hot off the press!
Congratulations to:
1st place: Chris Robinson (May 14, 2014)
2nd place: Robert Kaplinsky (May 5, 2014)
2nd place: Michael Fenton (May 15, 2014)
3rd place: James Cleveland (May 3, 2014)
Update 2:
Estimation 180 will be getting a facelift and other updates over the summer. Here are a few things to look out for:
The new logo was done by my niece. I love her simple design, the two 180 degree arrows, the metric reference, and her idea to transform me into a stick man. That reminds me, I still owe her a pizza!
I hope to get a few t-shirts made too. You can sport them at your next PLC, department meeting, casual Friday, or math conference. Any takers?
Update 3:
I've accepted a Teacher On Special Assignment (TOSA) position with my district for next year. It's a bittersweet feeling at this point. On one hand, I'm very excited because I'll be working at various secondary sites throughout my district, collaborating with other math teachers, helping design lessons and implementing various technology. My official title will be a Digital Learning Coach. I hope to seek advice from people like John Stevens, who have been doing this for some time now. As I pack up my room, I already miss my own classroom and students. However, I look forward to learning a great deal from the teachers I will be fortunate to work with and the students I'll be able to interact with at each site.
Updates,
243
I finally finished Act 3 for my Deodorant lesson. I hope you check it out and can give me some feedback; I think it could be much better with your help. If nothing else, check out how long it took to use 5 sticks of deodorant. Mathematical Modeling should really be at the forefront of this task. It might appear linear, but I would bet a year's supply of deodorant that an adolescent's deodorant use will be far different than mine. I also guarantee students will think of variables ranging from climate to age to geographical location to genetics to more. I think you'll have some excellent conversations with the deodorant task. My favorite part is the sequel: How many sticks of deodorant would one use in a lifetime?
Way back when this task first started, I opened up a little estimation competition in the comments at 101qs. Don't listen to a word Nathan Kraft says. The person with the closest guess would win an Estimation 180 prize. With so many close estimates, the following gentlemen will be the first to receive the new Estimation 180 stickers, hot off the press!
Congratulations to:
1st place: Chris Robinson (May 14, 2014)
2nd place: Robert Kaplinsky (May 5, 2014)
2nd place: Michael Fenton (May 15, 2014)
3rd place: James Cleveland (May 3, 2014)
Estimation 180 will be getting a facelift and other updates over the summer. Here are a few things to look out for:
- New logo
- New fields for entering student estimates
- Clean spreadsheets containing "other estimates"
- Updated Lessons
- Search by Categories
- Sentence frames for student reasoning
The new logo was done by my niece. I love her simple design, the two 180 degree arrows, the metric reference, and her idea to transform me into a stick man. That reminds me, I still owe her a pizza!
I hope to get a few t-shirts made too. You can sport them at your next PLC, department meeting, casual Friday, or math conference. Any takers?
Update 3:
I've accepted a Teacher On Special Assignment (TOSA) position with my district for next year. It's a bittersweet feeling at this point. On one hand, I'm very excited because I'll be working at various secondary sites throughout my district, collaborating with other math teachers, helping design lessons and implementing various technology. My official title will be a Digital Learning Coach. I hope to seek advice from people like John Stevens, who have been doing this for some time now. As I pack up my room, I already miss my own classroom and students. However, I look forward to learning a great deal from the teachers I will be fortunate to work with and the students I'll be able to interact with at each site.
Updates,
243
Friday, April 18, 2014
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:
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:
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:
Argue,
339
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:
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.
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?
- My opinion about this is _____________.
- I could argue that _____________.
- I disagree with your statement that _____________ because _____________.
Argue,
339
Tuesday, April 8, 2014
NCSM 2014 Day 1
Day 1 of NCSM was yesterday and here’s something I found interesting. Robert Kaplinsky, Dave Chamberlain, and I were walking back to our hotel room from the conference and I saw this clearance sign to the entrance of our hotel. I have been known to do estimation challenges before with clearance heights, not once, but twice.
I thought to myself, "There's NO WAY that thing is 6 foot 4 inches!"
I walked up to it and thought I should hit my head. Nope.
Okay, I’ll stand on my toes. Nope.
Okay, what’s going on here?
Why is this mislabeled? What’s your theory?
I’ll admit, this made me a little suspicious of the other clearance height challenges I’ve captured. Is this worthy of Estimation 180?
Photo bomb!
Suspect,
852
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