# 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…

This slideshow requires JavaScript.

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

# What’s a Shape?

Back in February, I came across a blog post from Telanna about shapes.  She saw a Twitter post from Sarah Caban asking a simplistic question.

How would you define the word “shape”?

Not wanting to miss out on the bandwagon, I decided to jump in.  Considering that I have access to such a grade span, I patiently waited for the right time in each grade level’s curriculum to pop in on a few classrooms and have a conversation.    Each teacher that I chatted with was also intrigued with my master plan and wanted to see/hear the results.

Kindergarten

And so my journey of defining shapes began with Mrs. Z’s kindergarten in March.  She was right in the middle of her shapes unit (perfect timing) and so she asked the kiddos the question “What is a shape?”

Here’s a snap-shot of what was discussed….

• Some shapes are big and small.
• sometimes round— circle or oval.
• some are skinny/ thin
• different sizes
• star, heart, rectangle, square, triangle, diamond, hexagon
• shapes have points and angles.  (T asked –do all shapes have points)
• Not all shapes have points.
• shapes you can trace or cut out.
• Everything we color or write or draw is a shape.
• Shapes are everywhere because they are.

The kiddos keep having side conversations asking questions like “are they lines?” and “what about letters?”.  One child proclaimed “the sky is not a shape.”  Upon hearing this, another child replied, “but what’s in the sky?  Sun, Stars and Clouds”.

After the in-depth conversation, Mrs. Z asked them to get up and make shapes with their bodies.  First, they made a circle (or the attempt at a circle) and then a rectangle.  Some students ran up to me to show me the shapes with their fingers/hands.

Fast Forward three weeks—->>>

My next door neighbor, Ms. N, teaches third grade and upon hearing about my shape quest,  invited me in to lead the discussion on shapes.  They were also in the middle of their geometry unit, so the kiddos wanted to impress me with their growing geometry vocabulary.  They also corrected me in that they are discussing POLYGONS, not shapes.

• something that has sides
• has a vertex (corner of a shape)
• has angles—> can be 90 degrees
• has different sides
• has to have more than 3 lines
• has to be closed —-> all lines connecting
• can be a polygon
• shapes are all around us
• convex —> shape doesn’t have a cave in it
• can have a concave in it
• rectangle can have opposite sides
• can have parallel sides

I didn’t have time to go to a fifth grade classroom.  Time became of the essence for the fifth grade teachers with reviewing for CAASPP testing.

HOWEVER—- I have an a 11 year old son (5th grader) who was happy (** sarcasm**) to have a conversation with me about shapes.  Yes…this is what we do during our commute into work/school.

• shapes are in everything
• there’s no one thing that doesn’t have a shape
• shapes are the building blocks of life. (how philosophical of my son)
• have corners
• they can have an infinite number of sides, but then that might turn into a circle
• the sides are not always the same.
• there are squares, rectangles, hexagons, circles, triangles,
• rectangle has uneven sides
• square has all even sides

I asked what he meant by “uneven” and my son said that it was when one side was larger than the other.

Final Thoughts

Students in the primary grades start by being introduced to their shapes.  It becomes just identification which is the first level of learning.  By third grade, they are being exposed to more specific language and vocabulary.   This third grade wanted to impress me with their knowledge of geometry.  They had been testing out different shapes to see which would pass their definitions.  As for 5th grade, they have a broader view of what shapes are.  They have also explored 3 dimensional shapes as they discover volume.

If I had a chance to follow up with each class, I could ask the question, “what does NOT make a shape?”  It would be a great contrast to their base knowledge.  It would challenge their thinking and we could probably have an in-depth conversation about their comprehension of shapes.

A magnificent exploration.  Much thanks to Sarah Caban & Telannannalet.wordpress.com for the inspiration.

Until next time….

Kristen

# Clotheslines for Math concepts

Using clotheslines as an interactive number line has been a hot routine this year.  Last year, I slowly and carefully rolled it out into a few classrooms for use of fractions.  This school year, I’ve expanded into more classrooms, but am proud of how my teachers have especially made it work in K-2 classrooms.   It’s been extraordinary to see using a routine where you get so much “bang for your buck.”  There are a good 2-3 content standards that students have been using, let alone multiple Standards of Math Practice.

The clothesline makes sense of numbers and number placement.  I especially love the fact that it’s interactive, provokes discussion, and gives insight as to a child’s thinking.  Students are actively learning and using multiple strategies to complete the task.  And more importantly, it is a tool and a model for students to see the “big picture”.

Let’s breakdown each grade level and how they’ve used the clothesline.

KinderI’m a true believer that if you can make a routine work for kindergarten, you can make it work for any grade level.   Ever since I introduced this to my kindergarten team, they’ve come up with MANY different ways to bring clotheslines to life!  It was rough to begin with, but my kinders have now been through the routine 4-5 times and they’ve got it!   Parents are now asking my teachers what kind of math they’re doing because the kids are telling their parents about what they did.  (Score!)  In September, Mrs. Z and I started with number 0-5 first.  Within weeks, we did 0-8.  And by November we did, 0-10.  It’s imperative to point out that kinders are not working on proportionality of the numbers.  They are just working on counting and cardinality (and measurement and data).  We also tried out using the clothesline with weight.  Instead of literally putting each object in order from least to greatest weight, we kept it simplistic with the light items being placed on the left while the heavier items went on the right.  If they were sure of an item, they placed it in the middle.

First grade – tried it out with numbers 0-25.  Lots of conversation.  Teachers got insight into how their students were thinking about numbers.

Second grade – tried it out with numbers 0-50.  Lots of conversation.  What was unique is that students were using their strategies of counting doubles for a few particular cards.

Third grade – have used this with benchmark fractions.  One 3rd grade team just designed a card set with multiple representations of multiplication.  This will be tried out in the new year

Fourth grade – will be using it for fractions.

Fifth grade – one teacher used it for decimals.  The students had been doing all the operations with decimals and wanted to see their number sense when it came to placing decimals on a number line.  What happened was a complete shock to her.  Students grouped the decimals according to number of digits (for instance, .4 and .5 would group together because they have one digit.)  That completely blew my mind.  Surely, we can’t always assume that our students have a true understanding of a concept when we ask them to apply their knowledge elsewhere.

Sixth gradeteachers will be using clotheslines for integers and integers integrated with decimals, fractions, and percents.

If anyone is interested in downloading the sets of cards for their own use, look here for my sets of cards.

Until next time,

Kristen

# Change happens! Hello 16-17!

It’s a new school year!  And that means a whole new year as math coach! I say BRING IT ON!

My district has been in school for the past 3 weeks.  So much change from last year to this year.

There is something to be said about change.  Change is good.  Change pushes our practice.  It forces us to question.  It forces us to re-evaluate our situations

Over the summer, the district directors made the decision to move the coaches to the schools (rather than being in the district office).    This was a move that I welcomed considering I was hardly at my desk.  I liked the idea of being closer to the teachers, seeing sunshine again (didn’t have a window in my old office), and especially hearing kids outside my door.  I didn’t know it, but I really missed it.  It’s a constant reminder for me to keep doing what I’m doing.  And I’m in love with the school that I moved to.  The teachers are so welcoming.  They even invite me in for lunch when I’m on campus.

I’ll admit that the move hasn’t been all sunshine and rainbows.  It took a while to get a desk delivered.  (When it was delivered, it was locked.  When it was unlocked, there was someone else’s stuff in there.  Awkward!)  Don’t have a work laptop or a printer yet, so that’s caused me to keep running to the district office to get copies made and print things out from my thumb drive.

Another positive change has been that out of the 8 elementary schools, I’ve been assigned 4 schools to work with.  Luckily they’re the schools I mostly worked with last year.  A little more driving is involved with trying to hit all 4 schools, but I always come out smiling afterwards.

Now…what have I been working on?  The answer is–sooooo much. These first few weeks have been jam packed!  I got the pictures to prove it!

The first day of school, I was invited to see ten frames being used by one of my 3rd grade teams.

A few days later..I joined my 6th grade teams to sit with them in a training with a math project they are doing.  We went over conceptual lessons using integers.  Here they are using number lines.

In the first days of school, I was invited to demonstrate how to do a 3 act lesson with the 2nd, 4th and 5th grade kiddos.  (I-heart-3-acts).  And what I love even more is seeing the teachers engaged in what I’m doing.  They are eagerly taking notes, asking questions, and being students themselves.  I was also invited into my son’s classroom.  It’s so special to be able to teach your own kid.  And it was awesome for him to see what kind of teacher I really am. That’s a memory I’ll hold on to forever.

During the second week, I was asked to do a numbers talk and a number line with 3rd grade.  I love using the number line because it helps the students make sense of numbers.  They can contextualize meaning from it.  Plus I really like finding different variations/representations on a number.  I’ve seen it done at the secondary level and it really surprises me that someone hasn’t done this for the elementary level.

Last, but certainly not least, there was rice.  Yes…there was rice.  My dear friend/colloaborator Mrs. Z asked me to dye rice for her so that she can create a sensory/exploring center for her little kindergarteners.  How could I say no?   It took 3 days and 3 nights to color 60 POUNDS of RICE!  You read that correctly.  60 pounds of rice.  I’m sure there was some sort of proportion lesson in there (3 cups of white vinegar, and one bottle of food coloring= 20 lbs of colored rice), however I was so inundated with blue rice, red rice and green rice…that I’m not sure I can eat a sushi roll or have rice pudding again without thinking of this experience.  The operation as a whole took up half my garage.  But the kindergarteners are loving it.  And Mrs. Z is a happy camper.

Speaking of Mrs Z and her kindergarteners…there is great news to spread around.  She and I have been chosen to speak at the California Math Council’s Palm Springs Conference in November.  After our initial excitement, she and I realized that we have 90 minutes to fill with all the great learning we created in her classroom.   We are revising our presentation, but we are highly anticipating the whole experience.  There will be plenty more on that in later posts.

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

# 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?

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

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