Tuesday, January 28, 2014


We're finishing up our proportional reasoning unit after several weeks of exploring different representations for our thinking.  We've converted decimals, fractions, and percents.  We've made tape diagrams, grids, circle graphs, and number lines.  But, are we ready for an assessment?

Yesterday I presented a problem-solving task to my students, hoping that they would jump in with excitement and tackle the problem with some struggle but with success.  I used a task from the Shell Centre for Mathematical Education called Sharing Gasoline Costs.  Students have to use proportional reasoning to calculate the part of the total cost of gasoline for each student in a carpool.  Sounds straightforward enough.

Cue *crickets chirping* and *deer-in-the-headlights* stares across the classroom.

My excitement was not enough to carry them yesterday.  Some students gave some effort to solving the problem but most just stared at the paper with no clue where to begin. It seemed like information overload to them.  Beginning a problem is a challenge.  Some students dove into the problem and were convinced they knew the answer rapidly but hadn't considered some key factors in the proportional parts of the problem. This is the "I want to be done" group. 

Teacher is still learning that worthy tasks take t...i...m...e. Slow down. Let the ideas simmer. Afterall, I have a Master's Degree and several (ahem...) years of math experience on them, and it took me a little bit of thinking before I got the problem going on my own.

Today we're going to work on the problem in small groups with some guiding questions.  The groups are going to pool their thinking and come up with one solution and explanation for their group.

I'm keeping my fingers crossed and feeling hopeful again today. Some days, I just want to throw my hands up in the air and grab some worksheets for some "drill and kill".  It just seems easier somehow.

I think I can....I think they can....I think I can....I think they can.....

Friday, January 17, 2014


I just returned from San Diego from attending a conference by No Excuses University which is a network of schools who are promoting college readiness for all students through the development of six exceptional systems within the school.  That sounds very dry and boring - FAR from it!  The founder, Damen Lopez, was a principal who turned around his school from an underperforming to an exceptional school. He's been spreading the word across the country to help other schools to do the same thing.

Dodge became a No Excuses University affiliate three years ago after hearing a brief introduction about the program.  Having Damen come to our school and present the NEU training to our
staff was an inspirational professional development opportunity.
This trip to San Diego was no exception!

Every presenter, every aspect of this conference was top notch and a pleasure, filled with practical strategies, presented by people who are doing the work and not just theorizing about it from their ivory tower.  I can't say enough about the quality of the experience. There are NEU books to read but you really MUST go in person to get your educator battery re-charged and inspired to do great things.

My take-aways from this conference were several:
- we need to set our sights higher for ourselves and for our students (BHAG - big, hairy, audacious goals)
- we are doing a lot of things well at our school
- we need to revisit some of our systems in our school and TRANSFORM them. Tradition sometimes means RUT!

Arizona vs Arizona StateHow does your school (K-12) transmit the culture of college to your students? Do your students really think that college is possible for them? Do they understand the difference that a college education makes in the quality of their life in the long-term? Do they know college vocabulary and about the college culture?  Are they charged up about setting academic goals and achieving them?

NEU - it's for YOU!

P.S. ALL of Tucson is mighty proud of our U of A Wildcats - perfect record this season!

Thursday, December 19, 2013


It's the last day before our two-week winter break, and I can safely say that most of us teachers are as excited as the students!  I finished my 150 math notebooks, regraded the latest quiz, and now have the computer uploads to do for quarterly and semester grades and citizenship marks. I can do this with half of my brain tied behind my back.  Good thing, too, because I think that's about all I have left!

Today is going to be a modified dress code day, the dance after school, and supervision of the tutorial group until 5:00. Good thing I've got a low key day with my sixth graders!

We're doing some coordinate graphing of a "mystery picture" (ssshhh, don't tell - it's Santa Claus). We're going to do a little mental math game called Albert's Insomnia. No heavy lifting in the brain area today!

It's been a great first semester. I'm not in line with the district's pacing calendar - I'm swimming as fast as my little guppies can travel....but we have made great strides with our skills.  I'm especially proud of my students who are embracing problem-solving a little bit more and a little bit deeper.  I am so happy that I hear comments floating to my ears like these: "Math class went fast today!" "I want to re-do an assignment." I love the big ear-to-ear smiles when a student sees how well they are doing on their assessments.  I am enjoying the Wall of Champions filled with colorful post-it notes that indicate a student had 80% or better on an assessment. (Thanks for the idea, Daniel!)

2013 has been very, very good for the math teacher....Merry Christmas and Happy New Year to you all! It's a two-week break from blogging (perhaps...) but not from thinking about what comes next!

Monday, December 16, 2013


Four days til a two-week winter break, and teachers everywhere are asking..."How am I going to make it through this week?"  I must admit, I am looking forward to two weeks off as well, but I am enjoying teaching so much right now, I can't wait to work with my students this week with some holiday themed problem-solving!  I need that perfect combination of engagement, learning, and thinking to make this week enjoyable for us all.  Soda Santa to the rescue today.
Yummy Math comes through for me with this estimation activity.  Soda Santa is a display of carbonated beverage products at your local grocery store.  You may have walked past him or one of the companion displays and not even realized it.  While at my Safeway yesterday, I saw the Christmas tree design.  Normally, I wouldn't even given it a thought, but I was in my teacher-noticing mode.  I refrained from having my friend take my picture next to it. 
Yummy Math has some great suggestions for using this display for estimation, multiplication practice, and some algebraic thinking.  I wonder if we could get some geometry in there too....How many square feet of store space is required for this display?  What does Safeway charge the bottling company for this prime piece of real estate for advertising? How long does it take to put up this display? I'd like to translate this 3-D display onto paper on a grid and make a coordinate activity.
Is it math mania....or just too much caffeine this morning? 
For more soda display fun pictures, go to Flickr: The Soda Display group.

Saturday, December 7, 2013


It's been an interesting few weeks in the Old Pueblo (Tucson's nickname).  We've officially moved from summer to winter.  Thanksgiving break is over....the winter break is looming ahead (and not getting here fast enough for some!) My students are currently working on proportional reasoning.  We've have been using some of the best resources I know out there.

MATH SNACKS - Great web site from New Mexico State University with short videos and games to reinforce several math skills.  It is a developing site with materials for students and teachers.  I've used the Bad Date video that introduces the idea of ratios and Ratey the Math Cat who is an odd character that notices rates with the word PER....(purrrrr....get it?). We also used the sheet for making a rate table and then a graph of the data.  Good stuff!

One of my accelerated classes then tackled a group project yesterday from Yummy Math called Done with the Leaves...now for the Snow.  This investigation looks at proportional reasoning in another way - if the number of workers increases, how long does it take to do a given number of hours of work?  This time I asked partners to make their own table and graph to model the data in the problem. Student understanding and products varied - some students wanted to divide all of the numbers by 2. It took some questioning to get them to understand that this was not the case.  Some students made their scales for the graph with only the numbers in the data table instead of a scale with equal intervals.  This created a linear graph instead of a curved graph.  A few groups finished their graphs and are now tackling the questions, "How is this graph different from the others we just did?  Why is it different?" We'll tackle the snow portion next week.
You may have read my post about Robert Kaplinsky and his lessons.  He also has a blog which I read. This week's gem was about his experience in asking the following question of some eighth grade students:

You may be interested in seeing the video of his work with some students to see their responses.  I couldn't wait to try this out with my students and see what my sixth graders would say.  I didn't interview them individually, but I asked them as a class to write their answer on paper.  I made sure I didn't say "answer the question" or "figure it out".  I just said, "Write your answer."  The results were very similar to Robert's  - 12% of my five classes of students responded appropriately and 88% responded with a numerical answer.  It was interesting to see their faces when they read the prompt. So many looked quizzical or amused, but so many STILL used the numbers to calculate an age. So, I said, if I bring a bunch of sheep and a few dogs into the classroom, you can tell me how old I am? LOL
Why did they do these calculations?
We had a discussion each period in order to understand better how this happens.  Some students thought it was a trick.  Others stated that I expected an answer. We talked about how one of the first things we need to do when a problem is posed is to make sure we UNDERSTAND what is being asked and look at the data provided.  We have to decide what information is unnecessary and what information may be needed (how many inches in a foot, for example). Jumping into a calculation is not always the BEST way to proceed.
Most of the time, students don't take enough time to reflect in this manner - their objective is to identify the numbers, use clues as to determine the operation, find the answer....be FINISHED! Any number will do.  Check my work?  Decide if it is reasonable? Nah.
How do we help students to do this on their own? I took this one step further in several of the classes after my "a-ha" moment.  What if I hide the question and ask students to brainstorm possible questions that could be answered with the given data?  The students could generate some very good questions including ratios much to my delight!  What I also noticed is that students love to generate questions that cannot be answered:  How many sheep does each dog supervise?  Students use their imaginations to include details into the scenario that are called "assumptions" that are not valid. I believe this is lack of skill in understanding how logical arguments work. They are 11 and 12 after all.
It's been a good week for opening up my thinking as a teacher and their thinking as learners. We've been exploring Math Munch as independent study and using BuzzMath for independent practice for my intervention students. I'm so grateful for the contributions of all these talented math teachers and mathematicians.  Thanks for expanding the ratio of teaching and learning in our classroom!

Wednesday, November 27, 2013


I don't know about your students, but ours have been slightly off-kilter for the last week.  I've sensed the Holiday Fever building to a slight frenzy since Halloween.  (I'm going to blame the advertising and early onset of Christmas decorations in the store before the temperatures dipped below 90 degrees here in Tucson.) Keeping their attention during November and December is a monumental feat.  Holiday here, vacation day there, and, of course, next week we have two days of benchmark testing which enables us to have 30-minute classes for two days. (Translation: ....just keep swimming, Nemo)
How do I keep my students engaged and learning?  Yesterday I put together a lesson that caught their attention from start to finish.  It came together about 4 a.m. yesterday morning. That's usually when I can meet with my professional development team and brainstorm lesson ideas.  It all started with Robert Kaplinsky and this photo. Robert has an amazing collection of lessons that inspire me.  The key is engagement so that students are pulled into a lesson and are hooked into the math!
As soon as my students saw this picture on the screen, they were buzzing.  We launched into a Notice/Wonder activity. They didn't want to stop!  I then played the MasterCard Showdown video that Robert posted with this lesson.
While his lesson went on to create a table of data and then an equation for the function, we spun off into ratios.

I found the following information on the Nathan's site:
"Joey Chestnut of San Jose, CA, holds the world record for eating 69 Nathan’s Famous Hot Dogs and Buns in 10 minutes, and he will seek his seventh straight title this year – a world record.Sonya Thomas of Alexandria, VA, will defend her title as Female Champion.She consumed 45 Hot Dogs and Buns in 10 minutes last year, setting a new women’s world record."
The kids were truly amazed.  A few girls were just mortified at the thought of eating even one hot dog in 10 minutes.  One boy shot out, "Why would a girl do that?"  I then had students work with a partner to answer the following:

What is the ratio of hot dogs and buns that Joey can eat to the hot dogs and buns that Sonya can eat? (quick check on writing ratios correctly)
How many hot dogs can each person eat in 5 minutes?  1 minute?  60 minutes?
As always, there is a surprise in every lesson for me. I didn't think this was a particularly difficult task, and I wondered if it was actually too straightforward.  It would give some additional practice with division, multiplication and decimals.  Bonus!
The surprise was the number of students who wanted to divide by 5 to find the number of hot dogs eaten in 5 minutes, the number of students who had no idea what to divide by to find the number of hot dogs in 1 minute or wanted to divide by 9, and the number of students who had no idea where to begin on 60 minutes.  As I wandered the room each period during this task,  I had the opportunity to ask students to explain why they wanted to divide by 5 or 9.  Very interesting responses.  By continuing the line of questioning, most of them could understand the relationship between these numbers.  Finding 1 minute's worth of hot dogs consumed was most baffling. Some students were reluctant to give a decimal answer and wanted to round to the next whole number.  Would that be fair in a competition? Haven't you ever eaten a half a sandwich and left the rest?
Each class worked the entire time on this task - only stopping when we had the bell nipping at our heels.  We will be revisiting this task today with discussion and also move onto ways to display the data (tables, graphs, diagrams) in order to solve future ratio problems. 
Thanks, team, for a great lesson that provoked thinking and some formative assessment on proportional reasoning.  Have a great Thanksgiving and try not to gobble til you wobble!

Friday, November 22, 2013


Two types of people might find these blog entries we are writing interesting. Other math teachers.  This way we can see we are not alone - days are long, nights seem even longer.  And all those other folks who think we teachers work 9 to 3 and sit at our desks drinking coffee with our feet up while the kids all sit quietly and thoughtfully at their desks engaged in completing workbook pages. Hmm...

Let's see how Thursday pans out...lonnnnnnng post warning!

5:00 Woke up without an alarm. Haven't used one in years unless I am catching a plane at a crazy early hour.  Glad I went back to sleep after someone dialed a wrong number at 2:00 to wake me up.

Watched the latest episode of Walking Dead and drinking my coffee while I checked in and started grading yesterday's collection of papers:  responses to a problem-solving activity and their Estimation 180 sheets. Most fascinating response to explaining reasoning for the estimate given:  I like almonds. Too early for middle school wit.

Perused e-mail, a few blogs, and started my Day in the Life writing...

6:25 Time to make breakfast and head to the shower.

7:05 Leave home, listen to a variety of XM radio music to get my mood up.

7:25 At school, getting materials ready for class. Copy machines are busy with the other two math teachers. I'll be back.

7:55 Copies made. Principal pops in.  Can I meet with M's parents who thought they had a meeting with the sixth grade team today (it's Dec. 5) regarding their son who is failing every class.  I'm double-booked at another meeting with the school psychologist with testing results for another student. Tell M's parents he's not doing his homework but behaving better in class.

8:00 Meeting with parent, team, psychologist, and translator to explain testing results. Student will qualify for help! Yippee!

8:25 Out the door and back to the classroom. Greet the multitudes of kids in the patio on my way to the building.  It's almost Show Time!

8:44 Bell Rings and.....we're off!

8:47 Attendance, announcements over the intercom, pledge. It's our homebase time. Check everyone's planner to see that they are filling them out and give them a stamp if they are. This is the Accelerated Math Class so they are on it - don't have to cajole them.

9:00 First Period. I am just beginning Fawn's Math Talk routine in my class.  I explain how to do the visual pattern routine.  Give students time to think and write. Share with partners.  Choose three students to share their thinking aloud.

 I have students completing two independent activities while I do some intervention with students in small groups.  They are cutting apart the pieces of a graphic organizer that we will put together on Friday for our ratio notes.  Then they are working with a hands-on activity with cups of Fruit Loops to describe ratio relationships. They must model the ratio and write it three ways, then create two of their own ratios. 

Collect homework with the race routine. Give papers to my volunteer to check-in and grade. Talk to anyone who didn't bring in homework. Family dog died.  I can't find it. I know I did it.  I left it at home.  I forgot.

Minimal crunched Fruit Loops and scraps on the floor today.

I worked with over a dozen of my students to help correct their errors in dividing with decimal numbers. Did some reteaching, retweeking, and reinforcing. Corrected their errors. Changing groups, supervising the ones at their desks, answering questions.

What I didn't plan for was the rotating doors in my classroom today.....office aides in and out asking for students to come to the office for discipline issues, adults coming in to talk to kids, other teachers' students coming in/out who were sent to my room to complete work, monitor coming in to pick up kids early for lunch detention....I honestly said out loud that I wanted a quarter for every time the doors opened and closed yesterday!

Handed out tonight's homework. Clean-up.  Time's up!

Three minute passing period.....start again!

The day is a large blur ....All five classes are pretty much like shampooing - lather, rinse, repeat! I read e-mails from staff, parents on the fly in between all this.  One parent wants a meeting - says I never responded to her request. Principal has forwarded her unhappy e-mail to me. Must solve this problem in my head in under one minute.....I never got a request. She requested that meeting with me and another teacher via the other teacher.  Request lost in translation. Quickly send off e-mail - let's meet Friday at 4:15. Why not?  It's Friday...I don't have a life anyway!

12:08 Lunch time. Today is my day to have lunch detention for anyone who did not bring a homework assignment during the week.  Ten little monkeys join me for part of lunch time.  Not a bad number out of 150 students and homework 4 days per week.  Sweet partner brings lunch for me, and we eat at the table while I help a few other students who come in and want to re-do quizzes and/or get help on homework.

12:20 Dismiss detainees....finish gobbling lunch. Run to the office to use the little girls' room, check mailbox, and get back to class before the bell rings at 12:41.

The afternoon is a repeat of the morning on this day.  It's more like a hamster on the wheel......

1:45 Ahhhh....my planning time! I tried to shuffle through the mountain of papers on my work table so that I can find the tutorial folder for the kids for the afternoon.  I prepare the work the kids are getting and answer more e-mails. Don't have time to organize the mess....I move it to another area. Three colleagues come through the room to discuss various issues....so much for my prep time.

2:50 Last period of the day....another set of accelerated students. They are my bright, verbal, creative, most rambuctious of the day! Smart. Keep me on my toes. They are the ones who can't handle Fruit Loops without throwing them. ***grrrrrr*** Tonight is not my night for the custodian to sweep my room (only happens every other day).

3:45 Clean up, pass out flyers for the Pizza fundraiser tonight, collect their R&R cards (behavior recording card) and send them out the door.

3:50 Bell rings and the afterschool mandatory detention kids who are failing a class start arriving.  I have all the kids grades 6-8 who are failing math plus a few kids who are failing Language Arts. Two other colleagues have the rest of the bunch. Take attendance. Separate kids as much as possible. Talk to the three boys who have some behavior issues about my expectations.  Teacher arrives with our math volunteer (former teacher) who is here to help. Get materials passed out. Everybody starts working.

We are circulating, offering help.  I help one of the boys who is having trouble figuring out what 4 + 5 is.....These are the numbers he got from estimating some fractions. Ironic that he can do one thing but not the other. 

My behavior boys keep turning around, wanting to talk, and now want to start the Potty Parade. I remind them that they were to take care of that before coming to tutorial.  Lots of lip from them. Move one to another area while I keep helping kids with math.  The Potty Parade is allowed to start - "You have two minutes" I say.  This begins the parade of everyone who now MUST use the bathroom.  One doesn't come back in two minutes. I talk with him.  I get more lip.

Move one of my sixth graders to a desk that is halfway in the hall. It's my friend M from earlier this morning. Glad he stayed to get caught up on something.

4:50 Can't come fast enough.  We collect all the work done. Kids scatter to the bus or to their rides.

Time to sweep the floor and wash off the desks from the Fruit Loops. Gather my pile to sort and finish grading at home. Last check on e-mail crises. 

5:15 Out the door and on my way home.  Call a friend in Minneapolis on the ride home to de-compress from my day.

5:35 Home at last. Wonderful partner has dinner ready. We eat like civilized people at a table.

6:00 Wash dishes, put away leftovers. Pull out pile of work from school. Sort, grade, write comments, record papers.  I am especially pleased at the re-tests of two students whose grade jumped from 45% to 80% due to the extra effort!  This makes the whole day worthwhile!

8:30 Done.  Put a fork in me. Look at some personal e-mail. Get in bed.

11:00 Still trying to get to sleep....

Is it Friday yet?