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.

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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.

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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.

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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 –

 

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

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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

 

 

 

Standards of Math Practice in Report Cards??

Today I was at a day long meeting on report cards.  Our district is looking to align our report cards to Common Core.  I was brought in to sit with the 6th grade team.  We have 3 elementary schools that have 6th grades at their sites.  We also have 2 middle schools with 6th grade.   This year, my 6th grade elementary teachers are becoming aligned with the 2 middle schools.  And because I’m from the middle school genre, I’ve been an integral part of the transition.  Same textbooks, same curriculum maps, just different locations.

Back to the report cards….so coming into today, I knew my teachers wanted to do whatever the middle school was doing.  And I was there to advocate for them.  Game on!

We first made a “hopes and dreams” list.  They wanted consistency with middle schools, letter grades, and simplicity.   But then we looked at report cards from surrounding districts.  We realized that not many surrounding districts have 6th grade at their elementary schools.  However, one particularly interested me and it looked like this…..

IMG_6112And this is started a lively discussion.  Should the standards of math practice be on a report card?   Why are they on a report card?  How does this district formally assess for this?

One of the team said that it seemed similar to “math reasoning.”  I asked them how they graded for that.  They told me it was dependent on word problems and application.  Interesting.

And then I took to Twitter.

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Loved the feedback.  And all of the tweets validated my initial gut reaction.  I don’t think the standards of math practice should be on report cards.  Report cards are designed as a communication tool for parents to see academically how their child is progressing.   The content is what I (as a parent) would be concerned about.  The SMP’s  or the “how” they are taught/presented is for the teacher’s use.

Agree/Disagree?  Please feel free to share your thoughts.

Kristen

 

Kindergarten Rocks!

Today I spent some time in a kindergarten classroom.  Those tiny humans are inquisitive, direct, and full of spunk.  What I love about them is that there’s a whole world of wonder waiting for them and they’re ready to soak it in.

And let me tell you something about the kindergarten teachers.  They are ROCK STARS!  Especially the one I worked with today, Mrs. Z.  We spent sometime last week planning for a lesson.  She had given me a list of topics they were covering and she wanted my help to plan something.  During our planning time, I introduced her to Graham Fletcher’s 3 Act Lesson and Which One Doesn’t Belong.  We also read Joe Schwartz’s blog on the same 3 Act lesson pertaining to Shark Bait.  She was totally thrilled, but wanted to  plan her own 3 Act lesson.  Now it was my turn to be totally thrilled!

Here’s how the lesson went.

As a warm up,  Mrs. Z started the class with Which One Doesn’t Belong….except she did it Kinder Style!  What’s Kinder Style?  Kinders work on sorting by attributes.  So she posed the question “how would you sort these?”

These smart little people came up with 5 different ways to sort these dice.  There categories would be color, size, shapes (Numbers versus dots or circles), corners (big and small), and the number 5.  They were absolutely engrossed.

Next she started the 3 Act lesson that we designed.  Act 1 – She introduced Alex the Alligator (alligator – K). We needed to find out how long Alex was.   She took some guesses (which varied from 8 cubes to a million!) And then the students got to work.IMG_6029

Act 2 – We handed out the clues.  We made sure to keep grouping the colored cubes in 5’s so that they could practice their counting and cardinality.

The students vigorously got to work.  The hunt was on to find the correct number of cubes and the correct color.  As Joe Schwartz noted, it was important to print out colored context clues for those students who couldn’t read yet.

Once the students were finished, we compared cubes on the carpet.  Mrs. Z reviewed their estimations and revealed the answer on the Powerpoint.  She also went over which estimations were the smallest and the largest.

Act  3 Once the estimations were finished, she asked the students to draw their own Alex the Alligator and show how the alligator was 18 cubes long.

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Nathan drew blocks around the number 18.

 

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William drew 18 blocks on the bottom.
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Those are some ferocious teeth.  18 dots represent the cubes.

Final thoughts….

Mrs. Z and I did debrief (my favorite part) at the end of the day.  We both agreed that kinders need a story to go with the 3 act lesson.  They need context to wrap their heads around why they are finding the length, height, etc.    She also wants to create 3 act lessons that have 10 solid colored cubes plus a few more so that she could start addition problems with the kinder.

My favorite part of our debrief (and I’m paraphrasing)–

Mrs. ZI’m so glad you are helping me.  I don’t want to be that teacher that just hands out a worksheet.  I want to be better than that.  I want to keep learning.  

Well put, Mrs. Z.  I couldn’t have said it better myself.

Kristen

Math- to write or not to write?

 “Math and writing, like oil and water, seemed to have little in common.” ~Marilyn Burnsoil-water-immiscible_46d45cfae26322d3

Last week I presented on a topic that I, as a math teacher, finally figured out a few years ago.  When I had my own classroom, I was sent to a few writing workshops.  I usually entered any workshop/presentation with hope of coming out with one idea.  Luckily, the Write From The Beginning program was just what I needed to get a spark of an idea.

My middle school had been integrating performance tasks into our curriculum for quite sometime, however some of them always seemed incomplete.  Something more was missing.  It took a few trial and errors, but I started my students writing a few paragraphs on what they did.  I used the writing prompt “John Smith was absent yesterday.  Explain to him the activity and what we did.”   For an Angry Birds parabola project (teaching Algebra), I had them compare and contrast each of the methods used to find out the birds’ flight paths.  Students wrote 6- 8 paragraph essays—-IN ALGEBRA!  It was very successful!

A fourth grade teacher approached me a few months ago with the same issue.  She wanted to tackle writing in math.  I told her what I had done in my classroom and we planned ahead.  We started with a performance task (Stone%20Soup) and created a writing prompt to go with it.  After weeks of planning, I finally got to see it in action.

After watching a video about Stone Soup and reading through the performance task, the students got to work immediately.   The teacher, Mrs. P, had the students do all their brainstorming and work on a sheet.  It was there that they showed all the work and mapped out their thinking.

Once they finished and shared their work about question one, we all worked through the rest of the questions.   Not knowing how to show the work for all the veggies, I stepped into help.  We came up with a grid to show the total number of green onions, chopped meat, and baby carrots.

 

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From there, the teacher had the students do a writing prompt.  She asked the students to write their own version of Stone Soup.  What ingredients would they include to serve Mrs. P’s class of 30 people?  The students were really engaged in this part.  She got all the students to plan out on their Thinking Maps.  The students wrote these creative stories involving some expected ingredients and also some unexpected ingredients.

During our debrief of the whole experience, Mrs. P kept saying, “WOW.”  I asked her if this was a good or a bad wow.  She exclaimed, “A good wow”.  She explained how she kept wanting to quit, but something in her told her to persevere.  And she was so happy she did.  Mrs. P couldn’t believe that she covered reading, writing, and math all in one assignment.  It was incredible.

In a future post…I’ll explain the different types of writing I’ve tried out in classrooms and what my thoughts are on writing.

Kristen