Square Dance

I recently debriefed with a fellow (teacher I support) about two activities focusing on Squares, Square Roots, and Irrational numbers. Let's build number sense. Here are the goods:

• Clothesline activity using these cards
• Square Dance desmos activity

She ran both activities with students, starting with the Clothesline activity. She used the cards linked above for students to first place the visual representations on the number line. It looked something like this:

Followed by:

Students then completed the first 7 screens in the Desmos Square Dance activity. Screen 6 includes a validator when done correctly, compliments of Nathan Kraft.

*Please note that part 1 of the activity uses only whole numbers as rational numbers. I highly recommend using the activity as a launching point for students to know that perfect squares include other rational numbers like fractions and decimals. 

Back to Clothesline:

This week she will use the next set of cards for irrational numbers. It might look something like this on the number line:

Followed by:

Back to Square Dance 

Students can build better conceptual understanding of irrational numbers in the desmos activity. Also look for teachable moments throughout the activity. 

*Please note screens 11 & 15 include non-repeating and non-terminating decimal notations. 

Screen 11

Screen 15

Just like Screen 6, Kraft-y validators are included on screens 12 & 16.

Two closing thoughts:

1) My fellow was so happy to use these conceptual representations with clothesline and desmos. 

2) She hasn't seen students making mistakes like she has in the past. Here's an example (crossed out) of a common mistake she has seen regularly in the past.

If you have time, head over to this post and have your students play War with the Rational-Irrational cards provided.

Dance,

945

Clothesline Cards Hit the Floor

A colleague and I stumbled upon an opportunity to strengthen number sense with students using a double clothesline. The video says it all:

 *For more fun with clothesline math, go to Chris Shore's designated site: clotheslinemath.com

Floor,
831

5th Grade Fun

Yesterday was AWESOME!

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

Jen's students have done a few Estimation 180 challenges this year. Therefore, I assumed they already knew my height. WRONG! So, we started with estimating my height. The best part of the conversation was helping students deliver their answers like 6.2 as 6 foot 2 inches. It was sooooo cool to hear students catch themselves, and work at eliminating the decimal point when referring to feet and inches. Once they found out my height, I took three student volunteers for the class to estimate their heights?
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

Make It Happen

"This could have easily been a two- or three-day activity."

I literally just met with a fellow who made this comment after we debriefed on an activity she prepared for her sixth grade students. This comment was the result of how rich the activity was. The math was rich, students were collaborating, there was student thinking, great visual representations and she did a wonderful job facilitating the activity based on 6.NS.C.6.A.

I'm sure you can relate with the sentiments expressed by this teacher. You had an activity where students would benefit from it and you wish it could go on forever. I remember experiencing this too. Here are two solutions to this [great] challenge:

Short-term:
Subtract your homework, guided practice, and housekeeping stuff from your Classroom Clock for that day (and maybe the next day).
*I'll blog more about my definition of a Classroom Clock soon.

Long-term:
Do bits and pieces of this type of activity most days of the year so students are more and more familiar with these concepts and practices.

I prefer the long-term goal! (and assigning extremely little-to-no homework EVERY day)

Example:
In this case, the teacher prepared a Pear Deck activity where students would drag colored lines to represent the placement of fractions and their opposites on a number line.

The ratio of students to devices was 4:1. After each Pear Deck slide, the teacher provided a validation slide displaying the correct placement of each line. In addition to the pear Deck activity, she also had a clothesline number line across her room where students interacted with these same fractions in a different yet still dynamic way.

The teacher's learning objectives were met with this activity, but let's move toward retention. We talked about doing this more each day. (long-term solution). Here are some specific ways:

• Make these activities the two-three minute warm-up at the beginning of class each day. 
• Do them as a transition in your class. For example, "I need you to put your notebook away, get your whiteboards out, and when you're ready, place 3/10 and 7/5 on a number line." 
• Make them an exit activity before student leave for the day.

If you agree to provide students with access to rich math, find ways to make it happen more often.

Long-term,
159

Clothesline

Dear Chris Shore,

Thanks for introducing Tustin Unified to Clothesline during your awesome professional development workshop!
You, Math Projects Journal, and Clothesline rock (David Lee Roth style)!

With all of my math heart,
Andrew

*Check out Chris' post on Clothesline (link coming soon).
**I highly recommend inviting Chris to your district/school for math workshops.

Where do I begin?
I used to have a number line in my old class. But it was static. All of the benchmark numbers were taped to the wall. I used it often, but not often enough.

Flash forward to Chris' workshop last week. He introduced Clothesline using this great quote from Tim McCaffrey:

"Clothesline is the master number sense maker." says @timsmccaffrey according to @MathProjects. Good call Tim! pic.twitter.com/bVvvJz7CtX

— Andrew Stadel (@mr_stadel) August 19, 2015

You better believe my ears perked up when I heard "master number sense maker". Check it out!

When I worked with teachers in Irvine today, my ice breaker was asking the teachers,

"How long does Dyson think it should take you to dry your hands with their machine?" 

I've never posted this picture online because it's my favorite ice breaker to do with teachers at conferences and workshops. However, I will use the context to illustrate how I introduced Clothesline to about 150 teachers, coaches, administrators today.

As teachers were discussing, I went around and asked

• two teachers for a guess that's too low (3 and 5 seconds)
• two teachers for a guess that's too high (30 and 40 seconds)
• four teachers for a guess that's just right

I used a big black marker to write the numbers on the red papers for the first four teachers with their "wrong" answers. I then had them place the red papers on the 25 feet long clothesline hanging on the side wall. I had the last four teachers write their "just right" guesses on the green slips. 

You'll notice the green slips might be hard to read from a distance. I did this on purpose so that we could get the visual effect (from a distance) of placing their green slips accurately on the clothesline using correct spacing (sorry, no pictures), based on where the red slips were originally placed. I reminded the teachers that this is a dynamic number line. You can move the numbers along the clothesline as you please. Please note that the teachers (in this case) were doing all the work, thinking, critiquing, and adjusting. In other words, students should be doing the same in my class as I help facilitate the conversations.

Throughout the rest of the day, I worked with teachers grades 7-12 during three breakout sessions. Therefore, I made a handful of cards for each breakout session to correspond to numbers or expressions relevant to them and their content area. Here's a sample:

I love when Chris used colored papers to focus on the numbers being placed (or in question). Notice the "benchmark" numbers are on white paper.

THE ROPE
The clothesline is 25 feet long. I think this is plenty long. I went to Home Depot and bought a 100 ft. clothesline. I made three cuts to make four lines of 25 feet. I used a flame to burn the ends of the rope so they stay in tact.

THE CLOTHESPINS
I noticed Chris used these to stack equivalent values together vertically. Brilliant. See above for examples that could stack.

THE NUMBERS (or expressions)
NCTM suggests using 3x5 cards, but then you have to use more clothespins, making the number line more static. Chris suggested using strips of paper. Using strips of paper allows the number line to be way more dynamic, allowing the numbers to slide along the clothesline or making it easy to place the numbers or take them off without the use of clothespins.

VARIABLES
Many teachers loved the idea of using variable expressions. Here's how I determined x for each group. I asked the three teachers in possession of the variable expressions to share how long they had been working in the district. For example, three teachers shared 12, 13, and 15 years. Therefore, 40 was the value of our variable, x.

FUTURE USE
Whenever I give a professional development workshop for teachers from now on, I will be using Clothesline. IT'S AWESOME! It is a master number sense maker. If I happen to be at your district or school doing PD, I'll bring a handful of clotheslines to raffle off (or give away). At the end of my last session today, it was awesome to have two excited calculus teachers be extremely thankful for receiving a clothesline. One walked away saying, "I'm going to use this Wednesday." Their first day of school! Calculus!

Last, but not least, test it out at home if you have the chance. My five-year-old son and I had fun this past weekend. He threw me a few surprises.

Clothesline 1
I just tossed up a few numbers on the clothesline for him to first get acquainted with the idea of numbers on the clothesline. "Move the pieces of paper so they make sense to you."

Clothesline 2
My son caught me off guard when he pursued something he was interested in. 1, 2, 3, 6.
"What?"

Clothesline 3
I wanted to see how my son did with spacing the numbers.
"Show me where four and five go."

I'd love to hear about your Clothesline experiences.
Check out Kristin Gray's great post from the other day. I love how much she anticipates student thinking in preparing for a successful Clothesline activity.

Clothesline,
930