Category Archives: number talk

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.

watermelons
5 watermelons

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.

IMG_6332
4/5 or 1/5?

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

 

Share your thinking!!!

I love it when my teachers take an idea and run with it.  Not only did a teacher run with it, but added even more to a suggestion.   And that’s what I saw today.

One 4th grade teacher that I’ve been coaching (Mrs. P) had asked me to work with her on number talks.  She had wanted me to demonstrate a few on division and fractions before she tried one herself.  And that’s exactly what happened.  A few weeks back, I did one on division (one that I’d seen on the Teaching Channel) and I did another one on fractions.   I whole heartedly admit that they didn’t go as well as I had wanted, but we live and learn.

This week, we continued our work on number talks especially with fractions.  We went back to the basics.  We watched a video online (Dr. Jo Boaler) and went over the purpose of the talks.  Instead of over-complicating matters, we agreed to simplify the process.   Let’s use number talks to gauge where the students were in regards to their background knowledge of fractions.  Perfect.

We started off with a visual from Which One Doesn’t Belong.IMG_6186

I sat back and listened intently to what the students were saying.  One student says “It’s not about which ones don’t belong, it’s about which ones DO belong.”  Mrs. P asked him, “How so?”  Some of the students noticed that the top two fractions were equal.  Some students noticed that the bottom two were improper fractions.  They also noticed that the bottom two weren’t equal but similar (being improper fractions).  The students loved to agree and disagree with each other as long as they voiced their reasoning.

Mrs. P and I debriefed really quickly at the end of that session.  She had the biggest smile on her face as did I.  It was a success.

But then the awesomeness kept going!

She asked the students to create a thinking map with another WODB on fractions.IMG_6188

She turned the whole idea of numbers talk with WODB into a full class activity.  Each student had to first pick a fraction (that they thought didn’t belong) and then write down their reasoning.  The students were interviewing each other.  There was tallying going on.  There was “writing in math” happening!

This was incredible!

Some examples –

 

IMG_6189
The check marks represent how many agreed with that statement.
IMG_6191
The students even interviewed me.

IMG_6193

Here’s why I think it worked –

  • With number talks, you may not hear from every student.  By doing this, the teacher got to see/read about their knowledge of fractions and get every students’ participation.
  • Teachers have difficulty figuring out how to incorporate writing into math.  This was one example of how to overcome that.
  • Students are using math vocabulary to explain their reasoning.
  • In this class, the students don’t always collaborate well.  This gave them time to work together.

Mrs. P and I have been on this math journey together.  She’s the type of teacher who wants to push her practice and just do better with “mathy” stuff (her words).   I appreciate that we can have real conversations without worry of judgement or pressure.   It’s exciting on my end to see her grow as a teacher.  She’s one of the reasons I love being a coach.

Kristen

 

 

 

Number Talk Images

Can I just say that I can’t get enough of visual math routines?  Or do you call it a number talk image?

Some call it a visual number talk.   It’s a picture that’s shown with a known quantity.  Students may start by making observations and ask questions that are lingering in their heads (AKA Notice/Wonder–thanks Annie Fetter!)  Once their questions are answered, they may try guessing a number that’s too low.  Next they’ll try to guess a number that’s too high.  The last number they’ll write down is an actual estimation.

Why should we do this?

  • Develops students’ understanding of quantity
  • Give numbers meaning
  • Help students see the relationships of numbers to one another
  • Support an understanding of how numbers operate

The conceptualization of quantity is foundational to number sense. As students’ abilities to visualize amounts improve, their number sense improves. Their strategies and mental math become efficient and quick.

Once I was introduced to this routine, I was ADDICTED!  It became a mission of mine to find my own pictures.  My goal was to develop a collection of everyday items (thanks Target!) that any other ordinary human would pass up.  Well, this April Fool has you covered.  Every now and then, I stumble across something and take pics like a crazy person.  And yes, I will sit there and count.

So here is something I came across during the after-Christmas sales. How many storage boxes are there?IMG_5834

Just in time for Valentine’s.  How many hearts are on the front side of this bag?

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If you are interested in more of these, I suggestion Andrew Stadel’s Estimation 180.  And if you are interested in more images ,Pierre Tranche’s Number Talk Images is really cool.

 

Oh…and not to leave you hanging.  There are 60 storage boxes and 388 hearts.

Kristen