Like I was saying in another blog-post, I’ve been exploring the different ways and types of writing that could go on in a math classroom. Last year, I was asked to present on the subject.
This is a topic I dabbled in when I was in my own classroom, so I was pretty excited to share with my elementary teachers.
It’s been a question that’s been in everyone’s heads for such a long time. How do we incorporate writing in math? I know that it should be done, but I wanted it to have be meaningful. I wanted it to be authentic. A student’s writing is one way for us to see inside their heads. What’s going on in that brain? How is he/she approaching problems?
As a parent, I’ve seen my own son come home with those “write to explain” questions at the bottom of his worksheets. Usually his answers are short and blunt. Or some of us have seen writing like this…
Yup…this kid is going places. I do appreciate the humor in this, however this is not what we are going for.
Some elementary teachers have admitted to me that they usually skip the “explain” questions at the end of the homework. And let’s admit it…what student completely takes ownership of those questions at the end? How much thinking/reasoning are teachers seeing out of those questions? It’s not happening.
We need to get our students’ buy-in. We need them to take ownership. We need them to be engaged in the problems. We as teachers have to be creative. As William Zessner said, “Writing is a way to work yourself into a subject and make it your own.”
So here’s a few ways I’ve engaged students into writing.
Performance tasks/PBL – Performance tasks are a perfect way to engage a student into a problem. It’s a spring board to have them create their own writing. This is a 4th grade task that one of my teachers tried out. Stone%20Soup A teacher can cover at least 3 subjects in one task.
Exit cards. I have used exit cards to ask questions. I think of it as an extension of a number talk. For instance, explain to me that 17 x 28 is greater than 16 x 29.
Error Analysis. One question I ask students as closure is “how will you know when you’ve learned this?” Usually I get answers like “when I get an A on the test.” I’m never convinced. I’m looking for the student to give me the answer of “when I can show/teach you the concept.” I’ve created a template that can change with the concept. For instance, here’s one on division. Div Err Analysis
Start with the answer...I haven’t used this one yet, but I’ve seen a few versions of it. Let’s say that you start with the answer of 6. The student has to write a math story to go with it. I see this especially for 1st and 2nd graders who need practice with their addition and subtraction (and also writing).
I know I don’t have all the answers. I’m just starting the exploration. I would welcome others to leave comments as to how they tackled this topic.
Some of my 6th graders went back to kindergarten. They didn’t know it and we didn’t tell them till the end of the activity. The teachers and I just wanted to do it out of sheer curiosity. And it turned out to be a curiosity that was worth exploring.
Let me back up a bit. Just last week, I led a workshop on the clothesline activity. I like starting off with the teachers trying one out on their own. I pulled out my weight cards that were used for kindergarten. These cards are filled with colorful pictures of a bike, building, tree, a leaf, and other objects. Students are asked to order the objects by weight (the lightest being on the left and the heaviest objects toward the right).
When I tried this out in kindergarten, we had the students put their cards in 3 basic categories—-light weight, medium weight, and heaviest weight. We were not looking for precision. However, 6th grade brought in the precision aspect. Because they have more background knowledge, they were not only integrating math, but science, social studies, and language arts. The 6th grade teacher also told me that this was great because the students were persuading their peers as to which order the cards should go. They had been working on argumentative statements in the weeks prior to this activity. (Gotta love when you can bring more than one curriculum into an activity—I call it “more bang for your buck!”)
Let me give you a visual…
Kindergarten – put these in the “light category”. No arguments from them.
6th grade – argued whether the leaf or the feathers should be switched. One student brought up the fact that the leaf was made of water and the stem makes it heavier. Another student claimed that there were 2 feathers compared to just one leaf.
Kindergarten – put the train in the heavy category although some questioned whether it was a toy train or a real train.
6th grade – put it in the heavy category althought argued whether it was a toy or real. One student said it was a toy because of the multi-colors. Another student argued back that it was real because of the smoke coming out of the smoke stack. Another student questioned whether it was made of wood or metal.
Kindergarten– put this card in the heavy side. No questions/arguments.
6th grade– put this card on the heavy side, however others had issues with it. One student wondered if it was a toy plane. Another students said there was blue sky behind it and so it was real. Another student said the weight might vary because we don’t know if it’s full of people.
Kindergarten – put this on the heavy side. They said they have seen these trucks on the roads and highways.
6th grade – put it on the heavy side. Questions of whether or not it was a toy were brought up. Another student asked it if was filled with anything because that would make a difference. For instance, the weight would vary if it were filled with feathers versus bricks.
Kindergarten – put this in the middle category. They did wonder if it was filled with anything.
6th grade– Wondered if it were filled with anything. One student said that when she bought a new backpack it was filled with paper to make it look full. Another student said it could be filled with books.
One last thing. We did not say a word about this being a kindergarten activity to the 6th graders. We just told them to put the cards in order from least to greatest. At one point, an exasperated student exclaimed “THIS IS SO COMPLICATED!”
Below is the final clothesline that the 6th graders “settled” on. (There were some that were still not happy with the outcome.)
If you’d like to download your own set of weight cards..gohere.
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 1starts 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)
they were poured out M&Ms
the package –M&Ms pic on front, not on back
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
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.
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.
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!)
Last weekend, I attended a memorial service and a birthday party on the same day. The range of emotions went from sadness and tears to laughter and smiles –all within hours of each other.
Of course during the service, my mind started wondering to all sorts of places. The deceased was a father of a teacher who had encouraged his children to get a college education. Upon hearing this, thoughts of how I became an educator started entering my mind. It was my father who told me “Education is the one thing that no one can take away from you.” That one piece of advice has been my mantra during my career as an educator. And it’s importance seemed so tangible that I wanted to be a part of it. I wanted to pass on such knowledge and make a difference in childrens’ lives.
Education is a gift to all of us. We have heard that adage of “it takes a village to raise a child.” There’s beauty to that sentiment. We are all educators–whether we are teachers, parents, grandparents, young, old, male, female, or human beings. We all have something to teach and instill into each others lives. We all have something to learn from each other. Some of us—myself included—have been fortunate to make a career out of it. It’s an extraordinary feeling to instill one memory, one quote, or one smile into someone’s life. I knew of the joyous feeling of teaching teenagers for much of my career, but now my work with adults is even more satisfying and humbling.
And that brings me to the birthday party I attended later on that evening. The festivities was for a former student who looks to me as her mentor. She was one of my favorite students of all time. Why? Because she may not have been smartest or fastest math student that walked into my class. But she was one that showed the most heart and gave me the most effort. She was/is the definition of integrity. She made me strive to be better teacher. And I have found that those kind of students are few and far between. And as an educator, you never know what kind of impact you have made on any child.
And so, as I sat there at her Sweet 16 party, I didn’t see my former student. I saw a young woman whom I was lucky enough to cross paths with. I sat there with pride because I had something to do with her life. I hope that I made a difference in her life as I did with many others. I hope everyday that I’m making a difference when I coach my teachers with their math curriculum. I hope that the joy, the excitement, and my love of math (#mathnerd) gets passed onto them.
I’m suddenly lost for words as to how to close this essay/blog post. So instead, I decided to include pictures of past students, current students, and people who have been educators in my life. I write this with the greastest humbleness because not only have I’ve been their educator but they have been mine. All of these people inspire me to be the best teacher I can be. We all have something to learn from each other….and I’m grateful to be any part of that learning process.
Until next time…keep learning, keep educating, and make a difference,
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.
#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.
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.
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!!!!
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 akindergarten teachercalling me theMath Wizard. (Wow…should I start wearing purple cape and big pointy hat?) Fourth gradecalls me theMath Master. Not to be out done —6th gradershave started referring me as theMath Goddess. (I picture myself with a white toga and gold jewelry. Or maybe something in a painting fromBotticelli. ) 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…
Presenting – I, 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.)
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.
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.
***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.
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?
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.
“show me what 40 looks like”
Students were “growing” from 1-100.
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.
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.
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.
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.