# Where did the numbers go?

Back in January (yes, I’m back logged a few months) I did a professional development for 4 – 6th grade teachers.  I was asked about presenting something that could help with the ever-looming testing in the spring.   My purpose was to introduce them to the strategy of Notice & Wonder while showing them what a numberless word problem was.  I emphasized the fact that we have to slow down the problem solving.  The students need to focus on content rather than just grab numbers and add them together (I call them calculator kids). Both strategies (and my presentation) were a HUGE success.   Each teacher not only left with a base knowledge of notice and wonder, they also left with 2-3 numberless word problems to try in their classrooms.  One 5th grade team tried them out the very next day.

Fast forward a few weeks, when I met with my 4th grade teacher, Mrs. P.   We planned a lesson which would introduce the kiddos to a numberless word problem.  During our planning session, we came up with the idea of putting a bunch of problems together so that the students could review all the previous material.  Little did I know, this one planning session turned into me running between 3 different schools showing all 3rd and 4th grade students numberless word problems.

Now let’s begin with my favorite —the marble problem.  I did separate marble problems for both 3rd and 4th grades.  And both problems created the most conversation.

I got the students into a routine by starting off with “notice & wonder” before drawing any concepts or figuring any of the problem out.  I created this template to help the students navigate through the problem.  It also helped that they kept track of their thoughts throughout the process.

3rd grade  (each number was a separate slide of a powerpoint)

1. Jeanne has marbles.
2. Jeanne has marbles.  Some marbles are blue and some marbles are yellow.
3. Jeanne has marbles.  Some marbles are blue and some marbles are yellow.  The rest of the marbles are green.
4. Jeanne has 12 marbles. Some of the marbles are blue and some marbles are yellow. The rest of the marbles are green.
5. Jeanne  has 12 marbles.  3/12 of the marbles are blue and 2/12 of the marbles are yellow.  The rest of the marbles are green.  How many marbles are green?

Was a little apprehensive about doing a problem on fractions with 3rd grade, but they stepped up to the plate and were superb with their problem solving.

Here are a few pics to see…

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4th grade – each slide was a separate slide of a powerpoint.

1. Ty has more marbles than his sister, Pam.

2. Ty has more marbles than his sister, Pam. Pam has many marbles.

3. Ty has more marbles than his sister, Pam. Pam has many marbles. Louis has marbles.

4. Ty has 6 times as many marbles than his sister, Pam.  Pam has many marbles. Louis has marbles.

5.  Ty has 6 times as many marbles than his sister, Pam. Pam has 34 marbles. Louis has 202 marbles.  Who has more marbles, Ty or Louis?

By the time we got to number 3 (…..Louis has marbles.) the students were freaking out.  “Who’s Louis?”   “Why does he need marbles?”

By the time they got to the last layer of information, they were excited to find the answer.  More importantly, they knew what they needed to do.

Final thoughts….

• “Layering” the information of a word problem really helps the students focus on the content of the problem.
• It slows down the problem solving process.
• Students get to create a mini – movie in their heads before they are slapped with numbers and the question.
• The teachers noticed that by the time students got the question, they knew how to solve.  They were also able to draw out and model their thinking.
• One big AH-HA was that students don’t know how to properly give an answer.  They need to work on being specific with their thoughts.  For instance, students would tell me 7.  I asked them 7 what—7 flamingos at a dance?  7 cows jumping over the moon?  Students need to be able to write/type out their full complete answers to get credit on the tests.
• The notice/wonder routine is really inclusive.  Teachers were amazed at how many students were engaged and participating.  Everyone of the students had something to say.
• Lastly—Mrs. P did a notice and wonder talk with her students about the whole numberless word problem.  This is what they had to share….

Such a worthwhile routine especially before testing where there are MANY word problems.  Here’s hoping that all of it transferred to the test.

Crossing my fingers…

Kristen

# Divided Hearts – a 3 act

Yes. MORE HEARTS!

In my research,  I hadn’t come upon a 3 act lesson in which the students had to divide.  My 4th grade teachers wanted to see what a division 3 act lesson would look like, so I created one.  This lesson  also helped me in learning how to use more features on the iMovie application.

I ran around to about 5 classrooms in the last three weeks to try it out. The first time, I had major tech issues.  The 2nd time, I questioned  my own judgement in regards to the Act 1 movie.   By the 4th time, I was convinced it was a decent lesson.  Why?  It promoted really great discussion (Notice & Wonder), got the students showing multiple strategies in solving the problem, and as any 3 act lesson is….it was engaging!

I present to you “Divided Hearts.” (yes, those are the same heart candies from my other 3 acts.  The way I see it–I like getting more lessons out of one purchase.)

Act 1 –

Notice –  (compiled between 4 classes)

• instead of putting in–> hearts are coming out
• video in reverse?
• glass filled with hearts –>boxes pulling them out
• used 2 boxes at a time
• glass empty at the end
• candy all different colors
• the hearts were divided into different boxes
• shows one box at the end
• didn’t use hands

Wonder

• are the candies divided equally among the boxes?
• how did they get candy inside the box?
• how many candies were in the glass?
• are there an even amount of candies in the cup?
• how many candies were in each box?
• how did they fly up inside the box?

What surprised me after each class was how fascinated the students were with showing the video in reverse.  Some of them couldn’t get past that.  However, I later told them that if I showed the video forwards, it would show how I’m adding hearts to the cup.  That might give them the idea of addiction or multiplication.  That wasn’t my intent.

Act 2

Before I continue with the lesson…take a moment to look at how many hearts are laid out. Take it all in.  Stare at those hearts. Those hearts and that layout became the bane of my existence for a few days.  I must have laid out those hearts and recreated the Act 3 video a good 4-5 times.  Sheesh.  But anything for the betterment of the students. Ok..rant over.

There were a range of strategies seen in every classroom.

Let’s start with these two… there were  a few students who didn’t know what else to do but start by counting out 168 candies.  The student on the right decided to use small lines.  It must have been exhausting to keep so many counted.

A few more strategies popped up that I have no explanation for (see below).  I had the students try to tell me about their work, and I was still stymied.  It’s not very often that I walk away still scratching my head.  I know they were onto something. If I had more time, I would have spent more time with them.

And then there were some who saw patterns and were making sense of what they had to do. They were avidly checking their work frontwards and backwards.  The 3rd student worked on her multiples until she got to 168.  She kept on persevering and that’s what mattered most.

ACT 3

Without saying a word to any of the students, I showed the last clip of the lesson.  At first, I heard groans because they thought they’d have to sit through 5 minutes of watching this random arm separate 168 hearts into 8 boxes.  However, once the video sped up, the fascination with movie making came back.  And when they counted the last hearts that fit into one box, the classes excitedly yelled “Yes” with a round of high fives.   That’s the moment that you eagerly anticipate as a teacher.

Final thoughts

• Technology is evil.  Always have a back up plan.  Because I save my videos to Vimeo, I was able to save myself and the lesson.
• My teachers have been learning just as much as I learn from the teachers and the students.  Some of them never knew of lessons that create so much discussion and intrigue.
• Don’t want to ever count hearts again. I’m good for awhile (until next February).

There is always more to come.

Until next time….

Kristen

We have been on spring break this past week, however I had a hankering to write about other previous experiences in classrooms. Back in January, I had been asked to help with division  in a 4th grade classroom.  She wanted a fun activity to help the students.

I introduced the class to a game I called Division War.  With the help of Uno cards, the students had the opportunity to create their own division problems.   The student who had the largest quotient wins the round.  The concept is similar to what I had heard from Robert Kaplinsky in a session on Open Middle.  However, unlike just challenging students with an Open Middle concept, I like to rev up the engagement a notch with a little friendly competition.  The students don’t know that they are working on a DOK level 2 or 3.  They think they’re just playing cards.

To get the students started, Mrs. P and I played one round on the whiteboard.  I chose the numbers 8, 7, 7, and 2.   I asked the students where I should put my numbers.  They were pretty random with where to put them and this is what it looked like.  What I also liked about this part is that they had to identify which part was what.  We used our math vocabulary to make sure we were all talking about the same parts of the problem.

Then Mrs. P went with her green cards.  She chose 4 cards which were 4, 4, 5, 2.  The students helped her put the numbers in some sort of arrangement.  She happened to get a bigger quotient than I did.  Mrs. P won that round.

Now rather than just letting them start to play, I wanted to push their thinking a bit more.  I asked them if there was any way that I could win that round. Could I switch any numbers around so that my quotient beats Mrs. P’s quotient.   Some suggested to just rearrange the numbers in any order and hope for the best. However, one student finally came through.  “You put the 2 in the divisor and make the largest number possible in the dividend”  Bingo!  There’s the lightbulb going on!

The kiddos started playing.  It was great to see them having so much fun with a simple rendition of war but with Uno cards. I guess the novelty of having me help out and a competitive spirit really got the best of them.

Just as I was musing on the high level of engagement, Mrs. P came to chat with me.  “We have an issue. One of the groups has figured out how to get the highest quotient without doing any of the math.”    Well…now you have my attention.   We marched over to the group and I asked them to explain what they were doing.   One student told me that he didn’t need to solve the rest of the problem because he pulled a one and put it as the divisor.  He knew he had won.

Then I heard this from a boy at the same table…”That’s cheating–he’s using one in the divisor.”  The boy sat there smugly like he had figured out my secret.  (I was laughing on the inside–loved it!)

As I walked away to check on other groups, I overheard Mrs. P trying to get the students to show their work.  She then threw them another challenge.  Mrs. P asked them to play another few rounds but with finding the smallest quotient.

Mrs. P ran over to me and told me about her discussion.  I looked at her wide-eyed and gave her a high-five.  That was actually a brilliant twist to my plan.

In our debrief, we encountered one hiccup.  How do we get the students to show all their work?  The group that figured out the “secret” would just choose 4 cards, look at them, and declare a winner without actually doing any of the calculations.  I consider that a good problem to have.

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

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.

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.

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 –

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