# Tag Archives: clotheslines

For the past few months, I’ve been completely sidelined with another project that required my full attention and writing skills.  Luckily, the project is finished and now it’s the waiting game.  SO my apologies for my disappearance.  However, I have a few blog posts that I’m going to catch up on in the next few weeks.

As most of you know, I’m a clothesline math enthusiast.  Love the routine.  Love the conversation surrounding it.  Love that it creates student engagement.  As a matter of fact, some of you might have seen this.  Chris Shore wrote a full book about it and gave me and my school an acknowledgement.  Super cool.

When it was time for my fractions, decimals, and percent unit, I was thrilled to use the clothesline.  I wanted my students to see the interconnectedness between each of the concepts.   After I taught them the skills needed (how to convert fractions to decimals, decimals to percents and fractions to percents), I broke out the clothesline.  This time, instead of pre-designated cards, I had my students design their own.  With the use of a hundreds grid, my kids got to design color in as many squares as they wanted.  From there, they collaborated with their table groups and figured out the fraction, decimal and percent of the grids colored in compared to 100.

Once they put them on the clothesline, we had a discussion about percentages less than 1% (and what they would look like).  We also had a discussion on 200% and where that would go in comparison to 100%.  Big math argument.  One student put 200% to the right of 100%.  Other students were arguing that it should be equally spaced compared to where 0-100% was placed.  100%-200% should be the same distance.

The lesson was a success.  But I had a revelation about clothesline.  Rather than me choosing with fraction, percents, decimals to, did I increase student engagement with having students create their own?  Is there more ownership with student-created clotheslines?  More importantly, how could other grade levels create their own clotheslines?

This sparked a new category of clotheslines.  I tried out my idea with a kindergarten intervention group.  The students were enthusiastic about it.  They liked seeing how many different ways we could create a certain number.  I saw the potential of using blank tens frames.  Kindergarten also creates their own with the use of the names. (see here)

Here are my latest additions to the clothesline world.  I’ve created blank templates in hopes that our students can take ownership of their own clotheslines.

10frame

double10frame

decimal

Fraction Decimal Percent

Until next time,

Kristen

# Asilomar 2017

My math partner, Stacy and I were once again fortunate to present this last weekend.  We were invited to speak at California Math Council’s northern conference at Asilomar. We had never been to the northern conference, so we were eager to compare it to our experience in Palm Springs (last year).  I had heard that this was smaller and more intimate, but with better speakers because of its proximity to the Bay Area.

First of all, the ground of Asilomar are gorgeous.  If you never been, Asilomar was like a leadership retreat-type place surrounded with trees all the while the ocean waves were crashing in the background.  When we were checking into our rooms, there was a random deer waiting for us (no joke).   It was quaint.  It was peaceful and zen-like.

We were running into all these math heroes every step and every turn.  While backing out the car, I was close to running over Dan Meyer, Zak Champagne and Mike Flynn.  While walking to explore the beach, there was Marilyn Burns taking a stroll in maroon hat.  We helped Ruth Parker get inside our residential building.  It was like being at an  All-Star Math Camp.

Friday night we went to see and hear from Dr. Jo Boaler.  While waiting to hear from her, I ran into this guy–Chris Shore.  We’ve been planning something for next year.  Incredible guy.  We caught up with each other while Stacy listened in on Dr. Boaler.

Saturday morning came and it was our time to shine.  Stacy and I presented on the flipped hundreds chart and our work on clothesline math to about 15 teachers.  Really engaged participants.  Lots of conversation.  Lots of sharing.  We felt incredible.  It seems like we keep getting better.  We have found purpose with what we are doing.

One of our participants stopped us in the hall afterwards and congratulated us on our session.  He said that he couldn’t believe how engaging we were.  We made the session feel really personal.  We were really energetic with our participants and made everyone feel welcome.  Usually there are sessions where there are “talking heads,” but we were the quite the opposite.  And on top of all this, that we made him think about what’s going on in the classroom.

The rest of our Saturday was spent seeing other speakers.  We got to listen in on Annie Fetter and her thoughts on writing for math.  We listened in on Cathy Humphreys as she explained her dissertation on mathematical agency.  Lastly, we attended Ann Carlise and her K-2 number talks with number lines session.

Usually I look for one thing to bring home and use.  I say that if you can just gleam one thing from any professional development, then it’s worth it.  I was lucky enough to have a math partner to talk this through.  We like poking each other with questions and then come to a conclusion.

When all was mostly done, we questioned what we got out of this conference.  Stacy and I learned something far greater then what some of these great authors and math educators were telling us.

• We figured out what kind of speakers we want to continue to be.  We need to be us. The comments from one our participants really was thought provoking.  And that was just our personalities.  We want to be personable in our sessions.  I don’t want to be a “talking head.”  If you know who we are, we are completely the opposite of that.  And we won’t change that.  That’s who we are.
• One of our expectations is that our participants walk away with something that they could use the next day.  In some of the sessions we attended as participants, that wasn’t happening.  There was lots of theory, but I wouldn’t know what to do with the information in my classroom.  Because of us flying up north, we couldn’t bring our full “show.”   I’ve been expecting our participants to look up all our resources on my blog, but I don’t know if that’s happening. How do we make sure they fully leave with something in hand?  (We have ideas).

We would go again in a heart beat.  We learned more about ourselves then we expected and that was major leap forward.  We didn’t expect that, but we couldn’t pass up processing our thoughts on the subject.

And so we continue to grow.  Onto the next conference.

Until next time….

keep laughing & keep smiling,

Kristen

# Mills, Bills, and Trill

The first week of school lesson plans usually consist of getting-to-know-you type activities.  In planning, I figured it would be a great time for exploring in math.  I hemmed and hawed about it.  At first I thought I’d do a 3 act lesson.  They are always exciting and engaging, but I couldn’t think or find one that these kids hadn’t seen in 5th grade.

But then I found this……

This was a picture I found a long while ago and kept it in my files, never knowing what to do with it.  I saw the math in it, but didn’t have a solid idea.  However, over the summer, inspiration struck and I got to work.

Have you ever asked your students about millions, billions, or trillions?  Do they truly understand the magnitude of these ginormous numbers?  It was worth a conversations.

Part one of our investigation was showing the above picture and simply asking “what do you notice and what you wonder?”

My students recognized notice/wonder which thrilled me.  Some perked right up when they saw those questions (which made me smile).  I noticed that my students focussed on the picture itself.  Some of my higher thinkers started pondering the saying.  Finally, we got to the question I was looking for….which was how many pictures are in a video.

Here’s the information we were looking for…

We decided we needed to figure out how many pictures were in a second, then a minute, and so on.  They determined that one second of video would be worth 2400 words.  And the video would have to be less than 1 minute.  One minute of video would be 1,440,000 words.   Not bad for my 6th graders.  They were getting the hang out this.

Then I asked them how long it would take them to draw a billion circles.  Saw this at a workshop given by Graham Fletcher back in January and I finally found a use for it. The students were thrilled to investigate this for sure.

With much enthusiasm, the students were jumping with energy on this one.   One girl raised her hand and asked, “are were really doing a billion?”  I looked at the clock and responded, “we got a few hours left so I don’t see why not.”  Their eyes got bigger.

First we took guesses.  I felt like I was on the Price is Right.  “I’ll say 7 hours…I’ll say 7 hours and 15 minutes.”  One group kept whispering about the question and concluded that it should take about 1 second per circle.  I loved this observation because I could tell they were not only thinking, but trying to make sense of the problem.   The class concluded that we should just try it for a minute.    Before we got started though, there was more discussion on how big of a circle they should draw.  Wouldn’t that be a factor in how many they could draw in a minute?

I started the timer and the students worked vigorously on their circles.  The looks on their faces was priceless.  They focussed, they concentrated, they were super-serious about getting this done.

When the timer went off, they counted up their circles.  We took a poll to see how many circles were drawn and the range was between 80 to 120.  For our purposes, we kept using 100.  Next, we figured out how many circles in an hour, a day, and then a year.  Finding out how many circles in a year was a bit of a doozy for them, but they persevered.  I was also happy to report that they knew how to read their place value very well.  Whew!

We even discussed what would 2 years looked like, and they told me it would only be one hundred  million circles.  “That’s not enough.”

I revealed the answer and they were floored.  I’m not going to reveal the answer in this post because I want to leave a little mystery to the question.  Go ahead…do the math yourselves.  (Answer is in the lesson PDF below).

We weren’t done yet.  For the last piece to this investigation,  I remembered this Twitter pic from Mark Chubb.   And I also saw a ripe opportunity to break out the clothesline.  I asked my students “Where would 1 million go?  Where would 1 billion go?”

After much debate and moving cards back and forth, this is what they agreed upon.  I was puzzled because they didn’t really know the relationship between billion and trillion.  I let them watch a video I found on Youtube and some referenced that when they were validating their answers.

However, I wanted to push them further.  I inquired why each of the cards was equally spaced.   Were there an equal amount of numbers between each number?  Some answered yes.  Some were completely puzzled.  Rather than beat the horse to death, I wrote a few new numbers on cards to see if they could show me the relationship.  I wrote 0, 10, 100, 1000.     The conversation got a little more exciting because my students were dealing with numbers they could relate to a bit more.  Unfortunately I forgot to take a picture of the final clothesline and specifically where they moved the cards.

Final thoughts…

• We hear how the US and other countries have trillion dollar debts, but how many people truly know the size of that number.  It’s quite “ginormous” but how does it relate to millions and billions?
• The students loved that they got to “investigate” something tangible.  They could all draw circles.  It was an easy task that they all handled.  It was hilarious to see them take it so seriously.
• The idea of the trillion clothesline was spot on with the investigation, but I saw many blank stares because the students couldn’t really fathom a trillion.  Instead of beating the idea to a pulp, we went with something they were familiar with based on their discussion and reasoning.
• This showed their lack of knowledge in how 10 related to 100 and so on.
• Considering this was the 2nd day of school, this showed that we will be making math fun, accessible, and worthy of their attention.   Many of my students said this was their favorite thing of the day.

Here’s the lesson if you’d like to try it out for yourself.

Until next time,

Kristen

Welcome back to a whole new school year!  I’ve spent the whole summer steadily preparing for my new assignment and it’s one that I’m embracing.

Here is it…the night before my first day at a new school, new routines, new students, new colleagues—actually, they aren’t that new to me.  I’m supposed to be trying to rest up and review my plans for tomorrow and all I can think about is “I have to blog about this!”

To catch you all up….I used to be a middle school math teacher for 16 years.  The last 2 years, I was a elementary math coach.  Now I’m going to conquer teaching 6th grade, but at an elementary school.    I get to be with little kiddos again.  Ok…my kiddos won’t be so little, but I get to experience the joy, the smiles, the high-five moments, and the celebrations that come with learning.

This transition was tough at first.  In the months following my decision, I had weeks where I was raring to go and then weeks when I was doubting myself.  I kept asking myself if I made the right decision by heading to an elementary school.  My 6th grade buddies at the other elementary schools were cheering me on every step of the way.  And with positive mindset, much support from the other 6th grade teachers, and lots of studying over the summer, I’m ready for my challenge.  This is going to be an awesome year.

In diving into this new experience, my inner elementary teacher started coming out.  I spent a good 2 months planning for decorating my classroom.  One of the kindergarten teachers at my site asked me back in March, “what’s your theme going to be?”  My reaction was “Theme?!?!?  Middle schools teachers never did a theme!?!?!?”  I go home and tell my husband about the conversation and he starts looking up things on Pinterest (he is totally a teacher’s husband!).  Low and behold, he holds up this picture….

My classroom is completely decked out with college stuff for my theme.  I created something from nothing.  All of what I’m about to show you is because of this single picture.    As a matter of fact, I’m calling it Acosta Academy.  I’ve had colleagues come in to see my progress and were completely floored with what I had done.

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I also had a revelation.  I put more energy into putting together this elementary classroom than I had in all my 18 years of teaching.  I embraced the belief “Go big or go home!”  More is more in elementary.

And in the little time that I’ve been in the elementary community, I’ve learned so much.  For instance, who knew that you could buy Walmart flat bed sheets for \$5.00 and they were big enough for your bulletin boards/walls?  And I’ve discovered the joys of lamination.  It’s such a magical treat.  I can’t get enough.

And I’ve created some goals for myself for this year….

1. Integrate 3 Acts, Which One Doesn’t Belong, Estimation,  Clotheslines, Open Middle, Numberless Word Problems, number talks and engaging math activities/stations into my math curriculum.
2. Learn and implement Google classroom as well as other Google tech with my students (Recently took a Google Cue Launch workshop and will be taking the first test soon)
3. Conquer my fear of teaching English/Language Arts.  It’s a monster.
4. Find creative activities for partnering my kids with kindergarteners.  The kinder teacher and I have a few great math ideas/activities.
5. Use my time in the classroom to embrace the joy, to foster curiosity, and to give my students the best for their last year at elementary school.

On a side note, I’m proud to announce that my kindergarten collaborator and I have been asked to speak at 2 conferences.  One of them will be at Calif. Math Council’s northern conference in Asilomar.  The other is at the Southern California Kindergarten Conference in February in Pasadena.

I’ve also been asked the speak at my alma mater, Frostburg State University.  Sloop Institute on Leadership & Excellence has asked me to present on “Empowering Others.”  I love the topic choice and have already outlined what I’d present.  Even though the conference isn’t until March, it’s never to early to brainstorm.

There’s more exciting plans coming in the 2018-2019 year, but I’ll wait to report on that when things are more finalized.

Until next time,

Kristen

# Cents clothesline

Recently, I was invited into a 2nd grade classroom to work on money (2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately).   The teacher wanted to try out something new to go along with this standard.  My suggestion was to try out the clothesline.  Let’s see if students could put different variations of coins from least to greatest.  It totally make cents (1st bad money pun)

And it went splendidly.

Each student was given a card to work on.  They calculated the total amount and put their answers on a post it note.  When they were ready, the hung their cards on the clothesline.

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When they were finished, we went over each card and made sure that we added each coin correctly.

At the end of the session, they students asked why they were doing the activity now (they were well passed their money unit).  I answered by telling them how many skills were involved with this activity.

• recognizing each coin and its value.
• practicing their addition skills with one and two digit numbers
• comparing and ordering the numbers
• showing equality with some of the coins (for example- 1 dime is the same as 2 nickels which is the same as 10 pennies)
• realizing what happens when you have more than 100 cents.

After my answers, I realized how much “bang we got with our buck.” (2nd bad money pun).  This activity had a lot going on it.  And all we did was put up a string and gave them cards.   But the thinking that went on was nothing less than incredible.

Until next time,

Kristen

# Names on a clothesline

It’s incredible to have teachers take something you introduced them to (in this instance–the clothesline) and see what they do with it.  And I can’t emphasize enough to my teachers that they should use whatever I give them and make it their own.  I usually tell them to “make it work for you.”  And then, they invite me in for me to see how they made it work.

In this instance, it’s Mrs. Z, my kinder all-star.  Mrs. Z decided to type her class list of students’ names onto cards and see what the kiddos would do with it. How would they want to put their names on the clothesline?  Quite a innovative way to make use of the number line.  I was curious too

.

I assumed they when asked, the students would want to put them into alphabetic order.  Seemed like an obvious choice.  Nope…alphabetic order didn’t even come up as an idea. Instead, the students decided to count their letters in their names and put them in order from smallest name to longest names.  “Medium is in the middle,” I had one student tell me.  Got it! Thanks for explaining.

And little by little, they started placing their cards. And they did really well.  Yes these pictures look like that are incorrect because they are not in alphabetical order.  Remember though that they were putting them in order by number of letters in their name.

And one night for a parent evening for kindergarten, I saw this.

.

So much fun to see.  What a thrill to see one of my routines expanded and used.   This only proves that there are so many possibilities to the clothesline activity.

Until next time,

Kristen

# Kinder clothesline with 6th grade

Some of my 6th graders went back to kindergarten.  They didn’t know it and we didn’t tell them till the end of the activity.  The teachers and I just wanted to do it out of sheer curiosity.   And it turned out to be a curiosity that was worth exploring.

Let me back up a bit.  Just last week, I led a workshop on the clothesline activity.  I like starting off with the teachers trying one out on their own.  I pulled out my weight cards that were used for kindergarten.  These cards are filled with colorful pictures of a bike, building, tree, a leaf, and other objects.  Students are asked to order the objects by weight (the lightest being on the left and the heaviest objects toward the right).

When I tried this out in kindergarten, we had the students put their cards in 3 basic categories—-light weight, medium weight, and heaviest weight.  We were not looking for precision.   However, 6th grade brought in the precision aspect.  Because they have more background knowledge, they were not only integrating math, but science, social studies, and language arts.  The 6th grade teacher also told me that this was great because the students were persuading their peers as to which order the cards should go.  They had been working on argumentative statements in the weeks prior to this activity.  (Gotta love when you can bring more than one curriculum into an activity—I call it “more bang for your buck!”)

Let me give you a visual…

Kindergartenput these in the “light category”.  No arguments from them.

6th gradeargued whether the leaf or the feathers should be switched.  One student brought up the fact that the leaf was made of water and the stem makes it heavier.  Another student claimed that there were 2 feathers compared to just one leaf.

Kindergartenput the train in the heavy category although some questioned whether it was a toy train or a real train.

6th grade put it in the heavy category althought argued whether it was a toy or real.  One student said it was a toy because of the multi-colors.  Another student argued back that it was real because of the smoke coming out of the smoke stack.  Another student questioned whether it was made of wood or metal.

Kindergarten put this card in the heavy side.  No questions/arguments.

6th grade put this card on the heavy side, however others had issues with it.  One student wondered if it was a toy plane.  Another students said there was blue sky behind it and so it was real.  Another student said the weight might vary because we don’t know if it’s full of people.

Kindergartenput this on the heavy side.  They said they have seen these trucks on the roads and highways.

6th grade – put it on the heavy side.  Questions of whether or not it was a toy were brought up.  Another student asked it if was filled with anything because that would make a difference.  For instance, the weight would vary if it were filled with feathers versus bricks.

Kindergartenput this in the middle category.  They did wonder if it was filled with anything.

6th grade Wondered if it were filled with anything.  One student said that when she bought a new backpack it was filled with paper to make it look full.  Another student said it could be filled with books.

One last thing.  We did not say a word about this being a kindergarten activity to the 6th graders.  We just told them to put the cards in order from least to greatest. At one point, an exasperated student exclaimed “THIS IS SO COMPLICATED!”

Below is the final clothesline that the 6th graders “settled” on.  (There were some that were still not happy with the outcome.)

Until next time….

Kristen

# Clothesline Fractions

Fractions is one of the “F” words in math.  (The other is functions, but I’m not working with that grade level).   Whenever these two words are said, teachers usually groan with frustration (that other F word). Understood because both can be hard to understand for students.  Part of my job is to turn that frustration into FUN!

Third grade has been working on their fractions for the past 4 weeks. This week I went in to work with them.

First I started off my visit with a number talk using a picture that has been floating around Facebook.  This picture had the potential to initiate lots of discussion and it surely didn’t disappoint.

I let the students just stare at it awhile. Rather than taking observations and questions right away, I like my students to just have quiet time to internalize what they’re seeing. Next, they shared with their elbow partners their thoughts and questions. Then, I let them share their thoughts with me.  Watermelons provoke lots of discussion (who knew?).  Lastly, I asked them what possible question I could ask of them.  One of the teachers rose her hand and said, “how many watermelons are there?”  Being picky about words and vocabulary, I politely added to her question.  I asked the students “how many WHOLE watermelons are there?”

Here are some of the highlights of the three classes’ discussions….

• I see eight pieces of watermelon.
• They are in a square.
• It looks like an optical illusion. It’s kind of like the 4 outside melons are the frame and the half melons are the picture.
• Some of them look like Pac-Man
• How are they standing up like that?
• Finally, the quietest girl explained how she saw 5 watermelons.

Onto the class activity.  The third grade knows I come with something different, innovative, and unique.  I like to surprise them.  I didn’t invent this idea.  As a matter of fact, my inspiration was from a workshop I had attended given by Andrew Stadel.  He introduced me to Clothesline Math.   I wanted to use this idea of an interactive number line with fractions.   I envisioned a single clothesline with students approximating where to place certain fractions between 0 and 1.  However, one question lingered.  How can I maximize the engagement with the whole class in this activity?  Print out 30 fraction cards?  With my active imagination, I saw kids running for the number line, tripping over each other, and ending up in one gigantic entangled web of limbs, fraction cards, and rope.  Yeah…that wasn’t happening.

After a trial run in my office, one of my colleagues suggested that I put up two clothes lines.   LIGHT BULB!!!  That was it!  Split the class up.  13-15 kids working on a number line was a much better option than 30 kids per one number line.

So happily, I strung up two number lines in the classrooms (one in the front and one in the back).  I printed out about 20 fraction cards on colored cardstock.  I not only used unit fractions, but also chose equivalent fractions, and pictorial fractions.

The students were stoked and excited.  I promised them that they weren’t being timed (don’t like to pressure students with that element) but emphasized that they needed to work as a team.  Off they went.

One of the teams decided to analyze and read all the cards first.  Good strategy.  Other teams just started grabbing cards and ran for the line.  One of the teachers approached me and asked if the kids could use their fraction bars.  My compromise was to let them work for 10-15 minutes first before using their fractions bars.  They ended up only using their fraction bars to check their work after their number lines were completed.  Very resourceful.

Here’s something I found intriguing.  One of the kids clipped together these two cards as equivalent fractions (see below).  He saw the picture as 1/5.  I intended for the answer to be 4/5, but could a student validate this as equivalent fractions?  I asked one team this question and none of the kids wanted to take ownership of it.  I think they were embarrassed to admit to it in fear that they would be wrong.

As a closing activity, we did a “would you rather” question.  Would they rather eat 2/3 box of cookies or 4/5 box of cookies?  They could write out their reasoning on the paper.  They were allowed to use whatever strategy they could to validate their reasoning.   I didn’t get to see how these turned out as my time ran out with each class, but my hope is that it was worthwhile.

After the excitement of the day, my mind is reeling with other concepts that could be used on the number line.  The third grade teachers also want to use the clothesline concept for other topics.  This especially excited me because it means I’m empowering my teachers to try new things in their classroom.

Kristen