Category Archives: Math

M&Ms spill in Kinder

Whoa! What a week I had.  I have been scribbling enough notes in my notebook that I had to share what’s been going on.  As a matter of fact, I’m going to be working on MULTIPLE blog posts just from all the amazing things I’ve seen/heard/experienced in the past three days.

For this post, I have to talk about the wonderful things that are going on in my kindergarten classes.  My kinder teachers have been enamored with 3 act lessons…..so much that we are designing our own.  My collaborator extraordinaire/partner-in-crime, Mrs.Z and I got together a few weeks ago to brainstorm ideas.  She said she wanted to focus on having the students compare which numbers were bigger/smaller.  Specifically we looked at K.MD.2 – Directly compare 2 objects with a measurable attribute in common, to see which object has “more of”/”less of” the attribute, and describe the difference.

Here’s the video we came up with.  In the spirit of Graham Fletcher (Graham…if you are reading this, I hope I made you proud!) …I present to you M&M Spill.

Act 1 starts with this video.

Mrs. Z did this lesson last week.  I just re-taught it in another kinder classroom.  Lots of notice and wonder. (compiled from both classes)

Notice

  • they were poured out M&Ms
  • different colors
  • the package –M&Ms pic on front, not on back
  • rainbow colors
  • the M&Ms disappeared — (This was one of my favorite things they noticed!)
  • M&Ms made a mess
  • orange, yellow, blue, brown
  • hand opened package and I saw a lot come out
  • M&Ms were dumped out

Wonder

  • Can we eat them?
  • Can we count them?
  • Are there enough for all of us?
  • How many M&Ms are there?
  • Which color has the most?

In Mrs. Z’s class, there was much discussion on how we could figure out the M&M mystery of which color had the most.  One of the students whispered into Mrs.Z’s that they could compare them by color.  At that moment Mrs. Z shouted “Shut the front door!!” (She gets enthusiastic at such brilliant ideas.)  

For the 2nd Act, we gave the students this clue.  They used unifix cubes to model their answers. The students diligently got to work.  

screenshot-2016-09-30-19-51-04

Here’s the part of the lesson that is always fascinating to me. I always wonder…. How do the kids think?  How are they processing the information?  How are they going to show their answers?  And that’s when the show (the learning) begins. (And this is when I usually run around and take my photos…there’s always so much to observe!)

And here’s another thing…there were so many different ways that the students modeled their answers, that I couldn’t just pick one!!!  Take a look at how each one is significant.  

And for the grand finale (Act 3), we re-counted all the M&Ms. We had to check to see which color had the most.img_8041

Final thoughts…

  • Kindergarteners and their thoughts always intrigue me. They are inquisitive little people who see alot.  
  • I was amazed to see their conversation just on the words “Notice” and “Wonder.” Those aren’t exactly kindergarten words, but their insight as to what those words mean was incredible. (More on that in a future post.)
  • Love the process of examining one standard and coming up with an idea on how to cover it. (I can thank Mrs. Z for her marvelous mind which amazes me every time.)
  • And I can never ever ever stress the importance of collaboration.  I love bouncing ideas off of people rather than working in solitude.   Power in numbers! (Math pun!)

Until next time,

Kristen

3 Act Lessons at #SummerMathCamp

#SummerMathCamp 2016 was a busy, insightful week full of notice and wonder about math. Thirty-eight educators chose to spend a week of their summer with us exploring some big ideas in the K-5 standards. We explored number routines and math work stations. We read, reflected, and chatted about the power the SMPs bring to our teaching and students’ learning. We shared the wonder of the #MTBoS; Which One Doesn’t Belong, Estimation 180, Fraction Talks, Number Talk Images, along with our most favorite tasks from our classrooms.

One of the highlights of #SummerMathCamp was introducing our colleagues to the MTBoS’s gem: the 3 Act Lesson.

On Day 1, the campers had the opportunity to experience a 3 act task as a learner. They participated in a 3 Act called “Making It Rain” from The Learning Kaleidoscope. In addition to experiencing the 3 Act, the educators were shown Graham Fletcher’s Cookie Monster. We chatted about what happens each of the three acts. On Day 2, we showed them Jamie Duncan’s version of Cookie Monster, and portions of other 3 Act tasks. Before working in their grade level teams, we revisited the structure of a 3 Act Task and discussed the beauty of taking an everyday occurrence and finding the math in it. The next two afternoons, grade levels took pictures, made videos, and developed the storyline for their 3 Act Tasks (and in some cases a sequel.) On the last day of camp, we held a RED carpet premiere. Ok..it seemed like that in our heads. In reality, it was popcorn and soda for everyone as their work was débuted.

We’d like to share with you a sample of the awesomeness that these math educators created to use with their kids.

Third grade – “Lego Run

Fifth Grade – “Coinstar

Much Ado about Watermelons!

Day 2 of #SummerMathCamp

To feed our math brains at 8 am on a Tuesday morning in the summer, we showed this photo of some watermelons in the hopes of generating some conversation.

How many watermelons are there? How do you know?

watermelons
http://ntimages.weebly.com

This was just going to be 10 to 15 minutes of a notice and wonder conversation. Yea. We were wrong. Fifty minutes later we were still chatting about watermelons. Who knew a pile of cut up watermelons could keep 45 educators engrossed. Really, what is there to talk about—it’s just a bunch of watermelons, people.

carofmelon
Image from: weknowmemes.com

So, here’s what we chatted about.

We predicted that the most common answer would be to cut up two of the one-half sized pieces to make the missing one-fourth pieces, slide those around to make 4 whole watermelons. Then, add the other two halves to make another whole watermelon. So, the sum of 4 whole watermelons and the other whole make 5 watermelons. We thought that some version of this idea would be a good start to the day.

And that’s exactly what happened. One of the campers shared her version and just about every person in the room said, “Yup, I thought about it that way, too.”

Picture1

 

And then Shannon said, “I saw it another way. I saw 4 groups of 3/4 of a watermelon and then I added the 4 one-half sized pieces. So, 3 whole watermelons and two more means that there are 5 watermelons in the picture.” The conversation then moved to connecting Shannon’s use of the algorithm to the photo and then adding in the notation.

Picture2

Since many of the campers were happy to think about the quantity of watermelons using the algorithm in Shannon’s explanation, we thought we would pause here and push on the idea of equivalent representations. [We much preferred thinking of the watermelons as 3 groups of 1—written as 3 x 4/4.]

This provoked lots of conversation on how come we can do this. 

  • How does the image show (4 x 3/4) = (3 x 4/4)? 
  • How does the picture show Shannon’s equation: (4 x 3/4) + (4 x 1/2) = 5?

The third way that surfaced was to simply add all the pieces of the watermelons visible in the photo. We recorded it like this:  ¾ + ½ + ¾ + ½ +¾ + ½ + ¾ + ½

Picture3

Here are some of our takeaways:

  • If it’s important to the kids it MUST be important to us

We need to listen to what our kids are saying and not be on the lookout for the answer listed in the TE or for the student response that matches our preferred strategy.

  • Questions and their power

Your questions need to offer ALL kids a place in the conversation. So, in this situation we could have asked a couple of questions.

  1. How many watermelons are there?
  2. How many whole watermelons are there?

Which question lets the kids who say 8 be in the conversation?

  • Dots on ten frames and Photos of watermelons, almonds, and tangram puzzles

Math is an active subject—it’s interesting, irritating, perplexing, confusing and invigorating. It makes your head hurt when you are in the midst of the struggle and then you get to embrace the high fives when that last piece falls into place and the connection appears as a result of your hard work.

 

Until next time….

Kristen & Judy

 

Reflections of a 1st year coach

This 2015-16 school year is wrapping up ever so quickly. As I’m doing with my teachers, it’s only befitting that I complete one myself—and that’s my own end of the year reflection.  I must practice what I preach and do my own debrief.

My year in review….

  • I’m on all 8 elementary campuses  This doesn’t sound impressive (I work for a small district), but it was one of my goals and I achieved it.  I left my middle school math position only knowing a few elementary teachers.  It was always a hurdle (not an obstacle) to work in some way, shape, or form and get on each elementary campus.  It took a full year…but I did it.  Curiosity fostered, word spread, and my grass-roots campaign was a success. I now have around 40 teachers that I support.giphy-2 
  • More PD than a girl can ask for – I haven’t been to that many conferences as a classroom teacher.  As a math coach, I got more than my fill this year.  No regrets.  I went to the Calif. STEM conference, followed by Calif. Math Council conference in Palm Springs, a few days in Beverly Hills at a HMH Leadership Summit, and then a big finale up in San Francisco at NCTM’s annual conference.  I heard and met such influential people such as Dr. Jo Boaler, Marilyn Burns, Graham Fletcher, Robert Kaplinsky, Andrew Stadel, Emily Diehl, Annie Fetter and so many more.  My head has been spinning with everything that I’ve learned.  It’s been quite a year for my professional development.  
  • Our work – I specifically use the word “our” because I share.  I share plenty of routines, suggestions, and help, but I’m a strong believer of collaboration. My teachers and I have worked on Brian Stockus’ numberless word problems, 3 act lessons from Graham Fletcher, Robert Kaplinsky’s Open Middle problems, Fawn Nguyen’s Math Talks, situations from “Would You Rather?”, used “Which One Doesn’t Belong” pics, and so much more.  We’ve read from blog posts from Kristin Gray, Joe Schwartz, and Graham Fletcher. A big thanks to MTBoS for their inspiring work.   And our work will continue next year as my teachers are looking to push their practice further.  The upcoming year makes me giddy with math excitement!!!!giphy
  • Not just a coach – Even though my title says K-6 math coach, I have learned that this job encompasses so much more.  I not only supported, but I listened, I learned, I cried (yes..it’s true), I thought, I noticed, I laughed, and I empowered my teachers.  I’ve been their biggest cheerleader, their collaborator, their therapist, their friend, their colleague, and their shoulder to cry on.  I have also learned that my most poignant and memorable moments are not only the victories with my teachers, but the downfalls too.  And that’s ok.  We’re all learning together.  But in the end, I got my biggest rush from seeing my teachers walking taller, smiling from ear to ear, giving me high fives, and celebrating their achievements.  My teachers knew that they were doing marvelous work.   There were days where I’ve skipped lunch to run from classroom to classroom, but it’s all worth it to have seen the students benefit from the awe-inspiring teachers I work with.  The tears I’ve shed for them have been out of pure joy and excitement.  
  • Many names   Hilarity has been running amok when I walk into certain classrooms. Apparently, my teachers and their students have been giving me nicknames. It started with a kindergarten teacher calling me the Math Wizard. (Wow…should I start wearing purple cape and big pointy hat?) Fourth grade calls me the Math Master.  Not to be out done —6th graders have started referring me as the Math Goddess. (I picture myself with a white toga and gold jewelry.  Or maybe something in a painting from Botticelli. )  And lastly, a visit to some 3rd grade teachers got the me title of “The  Crack Dealer”…because my math is so good it’s like crack. (How these teachers know about crack…I don’t judge.)  I look at it as a form of sentiment.
  • Starting this blog – This blog has been such a success.  It’s been my success in that I’m documenting all the good work being done at my district.  I’m sharing ideas.  I’m being a part of a bigger network (#MTBoS)).  My teachers are enjoying that their work is being publicized.  One teacher was walking around telling people “I’ve been tweeted.”  Other teachers printed out some of my blog posts about their classrooms and posted them at their Open Houses.  And it’s been a magnificent outlet for me.  I have learned coaching can sometimes be a solitary job.  We are in the background. Our work is intangible. However this is certainly one way to connect to the bigger world out there.  

My hopes in the new school year…

  • PresentingI, along with one of my kindergarten teachers, submitted a proposal to speak at California Math Council conference.  We should be hearing by June if we are chosen.  It’s been a goal of mine to be a presenter and I’m lucky enough to have an amazing collaborator that’s willing to do it with me.  Fingers crossed.  Even if I don’t present, I’m bringing a bus load of teachers with me so that they can share the excitement and inspiration of a conference.
  • Publishing – While at the NCTM conference, I approached the Calif. Math Council booth and thanked them for my free ticket (I had won via Twitter).  We started chatting a bit. One thing leads to another and they are asking me to write an article for them because they never have enough elementary articles to publish.  I walked away with the silliest grin on my face.  How cool would it be to have my thoughts read by teachers -?  The thought is mind-blowing!
  • More – More teachers to support, more students benefitting, more ideas of professional developments (that I can give), more lessons to design, more empowering, more smiles, more laughs, more math!!!
  • This blog – Over the summer, I hope to grow the capacity of this blog.  I want to share my 3 act lessons with everyone.  I haven’t had time and some of my lessons are unfinished, however I still want to build more content.  

It’s been an incredible year of learning.  I wouldn’t change anything about it.

And, I finally have to give a shout out to my husband, son, and parents for putting up with my craziness this year.  I couldn’t do what I do without their love and support.  They are my cheerleaders.

(I’ll continue posting over the summer months as I always have plenty to say.)

Until next time,

Kristen 

No numbers…no problem for Kinder

Just when I think that the year is coming to an end, and all the outstanding math is coming to a close….one teacher always surprises me.  Mrs. Z is at it again….being an exceptional kindergarten teacher.  She’s tackled the 3 Act lesson, she’s mastered the 100’s chart, and now has been experimenting with numberless word problems.  She had taken a particular interest in them after I had introduced them to her through Brian Bushart’s blog. Mrs. Z’s work is always intriguing and I’m always thrilled to be invited to watch.

On the first day of her new venture with a numberless word problem…Mrs. Z created her own and posted this..IMG_6872

First Mrs. Z posed the question “What’s a numberless word problem?”  The students quickly raised their hands and answered “words turn into a problem”, “something you have to read,” and “no numbers.”  Mrs. Z went on to explain how she was going to be telling a story and that they had to figure out the missing parts.

She had the students close their eyes as she read the story to them.  She then had them discuss what they had pictured in their heads with their partners.  Next they discussed as a whole class what they envisioned.  Once everyone had a picture of what was happening, Mrs. Z started asking the class what good numbers they could use. As you can see in the pictures below, the students came up with different combinations of numbers to add.  They also proved how they could add them up.

One student tried to answer “TWENTY HUNDRED MILLION!”  Mrs. Z calmly replied “that many would not fit in my yard.”

After finishing her circle map of possible answers, she had the students try their own.  And this is what they came up with.  Love seeing them verifying their answers at such a young, impressionable age.  

Mrs. Z was completely thrilled with the results as was I.  She asked me for feedback, and the only thing I could think of was to try giving them an answer to work with and seeing what combinations they came up with.  Would they work with number bonds, manipulatives, or draw out their answers?  

A few days later, she wanted to try again and invited me in to watch.  Here’s what she first posted.

IMG_6953

First, Mrs. Z started with notice and wonder.

Notice –  It’s about cookies.  I see sight words.

Wonder – What kind of cookies were there?  Did he get sick?  

She once again practiced with different combinations that make up 12 cookies.  They even discussed whether or not zero cookies were eaten on Monday and 12 cookies were eaten on Tuesday.  

One student wanted to come up and show the class how he counts his numbers together.  All the students had a turn showing Mrs Z. what combinations make up 12 using unifix cubes.

 

Next the students were given a similar problem about more cookies eaten by George.  This time he gorged on 18 cookies.  They were asked to find out all the possible combinations of 18 as they could. 

They were given unifix cubes to start with.  This table decided to first count their cubes to 18 and compare (to make sure they were all the same).

IMG_6967

Once they counted out their cubes, the kiddos got to work.  The table I sat at needed help, so I engaged them a bit.  I told them to close their eyes and break their stack of cubes.  After they opened their eyes, they counted their two stacks of cubes.  

 

The highlight of my two days with kindergarten was one sprightly pony-tailed girl named Lauren.  She ran up to me after she had finished her work and proclaims “PICTURE TIME!”  I nearly fell out of my chair in laughter.  (Do you think the kids know me or what?!?!)IMG_6968

 

Until next time,

keep smiling & keep laughing!

Kristen

A Series of 3 Acts in Kinder

Mrs. Z and I have been hard at work since being back from spring break.  We have been planning 3 act lessons on subtraction and more measurement.

The first 3 act lesson was designed with the concept of subtraction.  We collaborated and designed a lesson on popping balloons. I blew up 10 balloons, made a video with my son popping the balloons, and was all ready.  Seemed like everything should go as planned.  NOT!  Due to technical difficulties, the video didn’t 100 percent run correctly (audio and image were out of sync).  Ugh.  It was really a bummer.

However, there’s always something to learn despite a down fall.  Mrs. Z and I did learn that we need to take the time to plan our delivery of the lesson.  Maybe we were overconfident with all that we’ve accomplished.  We needed to stick with the basic coaching model of planning, delivery, and debrief.

And so that brings us to our lessons for this week.  We first brought back Alex the Alligator.  Mrs. Z wanted to have the students use another unit of measure besides the unifix cubes we had used before.  We used the yellow and red chips as a different type of unit.  (Check it out Remember%20me-alex).  The premise is that Alex couldn’t see behind him and wanted to know how long he was.

After showing the students the hook (Alex with one chip), Mrs. Z took estimates.  What I really liked about this part of her lesson was that Mrs. Z has been talking to the kids about what a reasonable answer is.  Usually her kinders love to give her an estimation of “ONE MILLION!”  Now she’s honing their estimation skills to a more likely answer.  IMG_6520

Act Two/Three of Alex involved having the kids see what too many of the counters looked like.  From there, Mrs. Z’s plan was to have them figure out the correct amount.  She figured that they could figure it out themselves if we left the picture up.

IMG_6523

Here’s where the lesson got dicey and we quickly realized it.  Mrs. Z asked the students if they could draw Alex and the number of counters (like her previous lesson).   Some of the students just started drawing their own alligators and measuring their own drawings.  Some were doing what we had hoped by drawing an alligator and showing us he was 14 counters long.

We also remembered that we gave them 11 x 14 paper last time instead of an 8 x 10. Like I said before…despite any down falls, we always learn something.  That’s what makes any of us want to be better.  We debrief, we learn, we plan something better for next time.

A few days later, we planned for the Cookie Monster.(cookie-thief-smaller-numbers-color-correction-2).  Rather than just doing another subtraction lesson and doing a subtraction sentence, Mrs. Z suggested we try this lesson with number bonds.   (Side note – I love collaborating with Mrs. Z in that we can start planning for a lesson and discuss different strategies, but then come up with something new.)

Act 1 – First Mrs.Z introduces Cookie Monster and shows the video.  The students love the video and we start to do a notice/wonder.  Here were their responses….

  • I think there’s 0 cookies left.
  • The boy ate them (we asked how does he know) –I heard him eating them.
  • They’re all gone (again–how do we know?)
  • The boy was hiding – he left 2 -3 because he was full.
  • The box is long…so it must hold 10.
  • The box was closed so it must have been a full box.

Next we went to the carpet to estimate the number of cookies.  Again, Mrs. Z asks, “What’s a reasonable answer?”

IMG_6602

Some students were still having trouble figuring out an estimation, so Mrs. Z said “show me with your hands what the box looked like”

IMG_6603

Act 2 – we showed the students how many cookies were actually in the box (to start with).

IMG_6604

Then we showed them how many were not eaten.  And promptly, the students started with their number bonds.  It was terrific in that the students were visualizing what 2 numbers combined to make 13.

And as the grand finale, Mrs. Z had them complete a number sentence.  And to prove their answers correct, the kinders started a number line and crossed out 6 “cookies” to show that there were 7 eaten.

IMG_6610

What brought the house down was showing this video of Cookie Monster baking. We must have watched it 2-3 times.  Go and see it here….Cookie Monster and Siri.

After a week of 3 Acts, here are a few thoughts…

  • No matter how well you do plan for a lesson, technology will somehow fail you.  Ugh. Go with the flow and make it work.
  • Planning the delivery of a lesson is important.  By the third go around, we made sure we knew how the conversation was going down.  The 3rd lesson had much more flow to it.  There was a rhythm.
  • Clarity is imperative.  Being specific with our instruction helps.  However, when things don’t go correct, be resourceful and turn it around.
  • A shout out to Mrs. Z because she’s really forward thinking with her students.    Her students know to they must prove their answers (or show the evidence).  For instance, how do we know you have drawn 13 circles?  She has them number each circle.  Perfect for the CCSS.

This week, I’m off to NCTM for a few days.  I’ll catch you all in San Francisco.

Until next time…

Kristen

 

Division in 4th grade

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.

IMG_5937

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.

IMG_5938

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!

IMG_5939

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.

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

 

Flipping the Hundreds Chart

***March 2017 Update —this blog post got published in the March 2017 CMC Communicator—click to download—> Mar2017CMCrHundredsChart****

A few weeks ago, Mrs. Z (my kinder “rockstar”teacher from a previous post) was telling me how she wanted to work more with the hundreds chart.  She wanted her students to make connections from one to 100 and see patterns.   She uses her “placemats” from the textbook series, but she wanted more.   She showed me her hundreds chart which was the usual 0-100 from the top down.

A week later, I came to Mrs. Z with an idea I had read from Graham Fletcher.  His post called “Bottoms Up to Conceptually Understanding Numbers” was about the hundreds chart being inverted.  Instead of starting at the top with 0 or 1, the first line started with the numbers 91-100.  It completely makes sense conceptually.  If you keep adding more numbers together, what happens?  They get bigger or rise.  Since when, if you add numbers together, do you head further down a chart?

Mrs. Z stared at the idea intently as I sat quietly.   I can see the wheels in her head processing.  Let’s do it! she exclaimed.   We ran over to her chart and swiftly switched the numbers around.

IMG_6240

Yesterday, I eagerly arrived to her classroom to observe.  I could hardly wait to hear the  talk.   What would the kids’ reactions be?  Would they notice?

The students sat on the carpet and Mrs. Z asked “what did you notice about the 100’s chart?  Turn and talk with your partner for 30 seconds.”  The students were engrossed in conversation.  The little ones were totally on-point and taking turns sharing their view points.  Afterwards, she congratulated them because that was “the best conversation they have ever had.”  She then took answers from the students.

Here’s what was said…

  • Why are they mixed?
  • Why are they at the bottom? Number 1 is at the bottom.
  • The number fairy must have come.
  • The numbers are backwards. 1 is supposed to be at the top like the calendar.
  • 10 used to be up there (top right).
  • I think you switched them.  It would take forever to switch them.  Maybe the math wizard did it (FYI–they call me the math wizard.)
  • We’re counting backwards.
  • Why is 100 up there and 10 is down there?
  • It’s wrong.
  • We are past the 100th day so the chart flipped.

I was definitely impressed with the students’ observations.

Mrs. Z then took it a step further.  She got out a bag of skittles and a jar and drops one in the jar.  She asked the students what would happen if she kept dropping more into the jar. “The jar fills up and there’s more Skittles,” one girl explained.   So, Mrs. Z filled up the jar with Skittles.  Now there were a bunch of Skittles that were “higher than just 1 Skittle.”

Wow…this was amazing and awesome conversation.  The kinders are rock stars.

And just when I thought we were done, IT GOT EVEN BETTER!

Mrs. Z had the students show her what 100 looked like with their bodies. (I later learned that this is called TPR – Total Physical Response.)  They all stood up straight and tall.  She asked them to show her what 50 would look like.  They all hunched down half way.  She asked them what 10 would look like.  Most of the kids sat down with their hands in their laps.  Mrs. Z then asked them what 0 would look like.  All the kids laid completely down on the carpet.

Oh…the learning didn’t stop there.  Mrs. Z was on fire.   She pulls out her water bottle and asks the kids to estimate where her water was.  IMG_6260

They guessed around 50.  Quickly catching on, I grabbed my soda bottle (which was close to full) and asked the students where my soda was.  Most guessed 90.  I asked them what would happen if I drank some.  I immediately started gulping as much as I could in a few seconds (I don’t recommend this, however anything for the betterment of our students).  The students looked at me in shock, but guessed 70 or 80.

And just as we got done, one girl runs up to Mrs. Z and shows Mrs. Z her socks.  The wee little one explains that her socks are 100 and 0.

IMG_6261
This little girl showed us her socks.  The one sock that rises past her knee represents 100. The other sock represents 0.

Holy  hundreds chart!  Mrs. Z and I were giddy with excitement during our debrief.  But we had more work to do.  She wanted to probe their thinking further.  We wanted to see if they would pick up on any patterns.

Day 2 – today Mrs. Z continued the conversation, however she tweaked the hundreds chart to look like this.

A number talk generated with the following observations….

  • I see 10’s
  • We’re counting by 10’s
  • Zeros are in a line.
  • There’s a one zero going up and then 100 had 2 zeros.

After changing the papers to show a new row of numbers, the students said they could see 1’s.  One boy said, “I see numbers counting down and getting smaller.”

Next Mrs. Z handed the class to me.  I told the students that we were going to play “guess my number.”   The excitement was in the air!

Mrs. Z and I used an activity we found on Math Wire (100 board), except we used an inverted 100’s chart.   We figured we wanted to keep consistency with what we just showed them.  We also wanted to see how many of them truly knew their numbers up to 100.  The students were going to follow the directions of the arrows in order to find what number I was “thinking” of.

This math wizard used her magical powers to pull numbers out of the air.  The students waited with baited breath as I told them which direction to go. Because we used the inverted 100’s chart, we ran out of space (see 29 with 4 down arrows).  The students thought I was tricking them.  They were being fooled.  Well, this math wizard can’t fool any of them.  They are way too smart for me.

IMG_6275

I haven’t yet debriefed with Mrs. Z about the past 2 days, however I can report that it was really worthwhile for her to take a chance.  As I have said before, those kids are inquisitive.  They do notice details.  And lastly, kindergartens are no fools.

Until next time…

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