'TWAS THE DAY BEFORE WINTER BREAK....

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!

SODA SANTA

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.

THE RATIO OF TEACHING TO LEARNING

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!



HOT DOG!

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!

 

 

 

DAY IN THE LIFE OF A MATH TEACHER - MTBoS Mission

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?

WHY DO WE BLOG?

This is a response to a request from Kate Nowak who is going to be a presenter at the April NCTM conference in New Orleans. The topic is blogging by and for teachers....WHY do we do this?

I blog because.....I enjoy it more than cleaning my oven and almost any other household chore.  I would rather blog than.....fill out more paperwork and sit through presentations on teacher evaluation instruments.  I love blogging more than I like.....listening to fabricated professional development offered in my district.

Reading, writing, and responding to math teacher blogs is MY professional development.  These folks are my math department, my colleagues, my inspiration, my models.  Some of them are half my age and have half of my years of experience.  They are talented, dedicated, creative, intelligent, positive, and forward-thinking!  I can't get enough of them.  I have made more changes in my teaching due to their inspiration than ALL the years of PD I have taken in person. Need I say more?

So, Kate, thanks for the opportunity to reflect on this.  I am sure you will be an amazing presenter. I wish I could be in New Orleans in April to join together with you all.  For now, I'll just keeping working on being a newbie in the MTBoS (Math Twitter Blog-o-Sphere for all you who are not yet in the know!). It's an honor to be one of your colleagues!

http://function-of-time.blogspot.com/2013/11/tell-me-why-you-blog.html

CANDY CORN DATA COLLECTION

It's that time of year when those delightful yellow, orange, and white tidbits of pure cavity-producing candy are in abundance everywhere you look. Yes, it's candy corn!

Halloween, candy corn, math, student engagement....it's a natural combination! How do I keep the kids focused on learning when there is all of this outside excitement? Let's bring it into our lessons.

For the next few days, we'd like to gather some data  to use for math class next week. Please help us out and respond in the comment section with answers to the following questions:

1.  How many candy corns do you think are in the container?
2.  Do you like candy corn?

Thanks, in advance for helping us out! We'll report the results soon!

MTBoS Mission #2: To Tweet or Not to Tweet

This week I've dipped my toe into the Twitter water with my MTBoS Professional Devlopment crew.  I am still figuring out the platform for following, being followed, and making an effort to contribute to conversations. Still need someone to tell me how to figure out the schedule for the #chats.

I love the feeling of connection and personal contact with these mathy folks who inspire me to be a better math teacher.  It's very similar to the feeling I used to have in the "old days" when we teachers would actually go to the Teacher's Lounge and have conversation while eating lunch. (I spend my lunches in my room working with the kids.)  I miss having others with whom I can bounce around new lesson ideas.  I am the only sixth grade teacher at my school and don't share a lunch or planning time with the seventh and eighth grade math teachers so math talk is pretty limited at school. I do have a fabulous principal who is a former high school math teacher - I can always talk math with him but we know how limited his time is.

This week I jumped in with comments for a few new friends but it just doesn't feel natural to "interrupt" a conversation with people who really don't know me yet.  What I have found this week is a professional community who is willing to support me in my adventures as a math teacher, who share incredibly similar experiences, and who are eager to expand their skills and SHARE!

Now, to Tweet or not to Tweet?  I'm overwhelmed with the volume of messages every day. I don't know when these folks sleep!  LOL  I only have a "dumb" phone so my use of Twitter is limited to my computer at home.  I'm going to keep at this challenge and find my niche.  There is a wealth of ideas and support here. 

If you hear some faint chirping...it's not a cricket, it's me trying to find my way through the Math Twitter Blogosphere!

SERENDIPITY and ESTIMATION 180

I have begun using Andrew Stadel's Estimation 180 web site with my students. This is an area of number sense that many students could use practice, and this is the perfect way to get their estimation brains in shape. Andrew is one of the new faculty on my Professional Development Staff through the Math Twitter Blogosphere! Super creative and....in a word....TALL!

                                                    Click here to go to Estimation 180

In these lessons, students use the context clues in a photograph and their prior knowledge from lessons to make estimations. They are able to find out the actual measurement and see other students' estimates on the site.  I have given my students a sheet to fill out to record their estimates and the difference between their estimate and the actual answer. For some reason, the kids LOVE this! They especially love being able to get the exact answer.

Yesterday I decided to expand the lesson a little and was rewarded with some surprises along the way. After the students made their estimates I asked them to write their estimate on a piece of paper.  I then had them line up around the room from the shortest estimate to the tallest estimate. Those were the only directions - I just let them figure out the rest while I sat back and watched. One brave soul asked, "Where do we start?" and all I said was, "You'll figure it out."  And they did!

 

 My reward for not orchestrating their every move was the satisfaction of seeing their problem-solving skills in action - all the natural leaders, born teachers, and bosses of the future stepped right up. They were totally engaged, listened to each other, and completed the task of lining up without one single suggestion from me. Proud moment...

 

We then took the opportunity to talk about the range, mode, and median of a set of "live" data. Totally unexpected part of my lesson but it was one of those teachable moments I couldn't pass by. 

  

 Now for the serendipity....if I hadn't expanded this lesson with the lining up from least to greatest, I would never I have seen this...

In every class several students wrote their estimates for feet and inches as a decimal: 6 feet 2 inches was written 6.2 feet.  It never occurred to me that this misconception might come up in the writing of measurements!  Great opportunity to get this tackled - I'll be on the lookout today for anyone writing their measurements in this manner.

Changing my methods of teaching is sometimes a huge stretch for me.  Teaching an old dog new tricks is always possible.  There is no one monitoring these moments except for me (and now, YOU!). These moments are my rewards. The serendipity of learning new things is what drives me every day.  The inspiration of my Professional Development Staff keeps my passion for teaching and learning alive in the face of budget cuts, lack of technology, and the endless paperwork. 

Thanks, Andrew, for a great site that has opened up to so much more for my students and myself! 

 

 

 

 

 

 

MISSION MTBoS: The Math Twitter Blogosphere

One of the best parts of technology is the ability it gives us to connect with people. I have found a whole new community of peers through joining this challenge. While it is a bit scary to put yourself out there for (literally) the whole world to see, it is exhilarating to be inspired and supported by others

who are on the cutting edge of mathematics education reform.  While I'm not getting much professional development at ALL in my own district, these amazing teachers are my gurus, colleagues, mentors, and fellow explorers into the new frontier I've entered.  After nearly 34 years of teaching, I've found a home with the BEST of the BEST! If you don't believe me, check it out for yourself!

 

http://exploremtbos.wordpress.com/

Museum Math

While in Pittsburgh, I visited the Heinz History Museum as well as the Carnegie Science Center. (I know....it's a VACATION...what's up with the educational tour?)  Lots of math to be found at both of these places.  Here are some of the treasures....

 

 

MISSION1 - Power of the Blog

I'm stretching my skills and comfort zone.   I have joined a fun, inspiring 8-week challenge - Exploring the MTBoS. I have accepted the first mission. Jump in, head first, step into the scary void. I am new to all of this but I'm looking for growth.  Hang on...it's going to be a wild ride.
Some ideas I have rolling around in my brain for development...of course while I'm on fall break...the teacher brain doesn't stop....

Penny Wars will be starting at my school. This will be a fundraiser pitting the three grade levels against one another. Who can fill a 5-gallon water bottle with the most money? What can we do with this?  Estimate how many pennies it would take to fill it by counting pennies in smaller volumes. Estimate how much each student in the sixth grade would need to bring to fill the bottle.  There's got to be more we could do with this. 

The invasion of the 40-foot rubber ducky in Pittsburgh!  My brain is racing with questions of ratios and technical difficulties of maneuvering under the many bridges around the city!  I think sixth graders might find it fun....what do you think? Where can we go with this?
 

"Real Life" Math

Some of the math teacher bloggers that I follow started a practice of sharing their real-life math experiences on a regular basis. We all know that we use math all the time - no one just hands you math worksheets to complete - it just flows from the normal course of human events!  Here is my contribution.

Yesterday morning, I presented a warm-up problem to my students - a "real-life" math problem no less from my own life. My intention was that it be a WARM-UP not half of my class time. The understanding that I received from allowing this math experience to morph into something more was well worth while.

Here's the situation: I have those universal desks that defy group work. They just don't position well for sharing materials or being able to get into your seat without climbing. The legs of the desks and chairs have tennis balls to make them quieter and less damaging to the floor. These little bumpers prevent the legs from getting too close to each other. They get loose and become rolling objects. And they collect clumps of yucky stuff from the custodian's broom that I can't even describe....

I had the idea to begin removing the tennis balls and replace them with those little felt pads that you can by in any store. Here's where the math comes in. If the pads come in packages of 12, how many packages will I need to buy, and how much is this little project going to set me back?

I gave the problem to my students to solve in pairs, and as I walked around the room to see how they were approaching the problem, I noticed many of them were immediately drawing factor trees! HUH? Why did the students think finding the prime factorization, the GCF, or the LCM of the number of desks and chairs and pads in a package was the way to go?

I asked several of the students why they were doing the factor trees and the responses were generally to "find" the GCF or LCM.  How does that relate to this situation? They couldn't say how or why. My feeling on this was that it was the most recent mathematical concept we worked on last week. After some questioning, most of them abadoned this idea and started again.

Another common mistake was adding up the number of chairs and the number of desks (10 + 32) and then dividing by 12 (the number of pads in one package) to tell me I needed to buy 4 packages of 12 pads to complete my job.  Even some of my top-notch students made this mistake! So I asked them how many pads that was (48), and then had them count by 4's as I pointed to the desks in the vicinity. They quickly realized that this was not enough because they didn't multiply by the number of legs on the furniture.

The next thing I did was ask several groups to come to the document camera to show and explain their work. This gave them a chance to put into words a logical step-by-step explanation. Boy, this is a tough one for many of them.  To be able to go back and explain your thinking means you have to keep track of your thinking in some manner. Most of their papers looked like this:

We had an opportunity to talk about how to organize the work so that it could be easily followed by another person. This is how one student edited his work:

            

Today, we'll add the writing component to this. Perhaps, this is the most difficult aspect of the task. Writing (as I am doing right now...) takes time, thought, and effort to pull all the pieces together into a coherent form. To get the process (which happens quickly in the brain) down onto paper requires slowing that process down. Most of the students I work with have not developed that patience for the reader. They would rather that I be a telepath and cryptographer when it comes to their work!

Through all of this I didn't get discouraged because I realized that I provided a great learning opportunity for my students. I also see my skills with questioning and facilitating math tasks improving every day. It is a challenge to give up that "stage" of lecturing on a full-time basis. I am starting to see the glimmer of light at the end of the tunnel....it might be as small as a pinprick, but still there nonetheless.

Don't Forget the Math

I came across this little gem of a video by Phil Daro, one of the writers of the Common Core.  

 

 

This led to a look at the SERP (Strategic Education Research Partnership) web site of which he is a part. On this site are videos of Phil teaching a math lesson to teachers while modeling the mathematical practices. I watched the beginning clips which opened my eyes to some strategies to help my own students with solving word problems.

 

One strategy I tried this week was to give the stem of a word problem to the class and ask them to generate questions that could be answered with the information that I gave. Very interesting discussion!  I got some humorous questions, thought-provoking questions, and then the impossible-to-answer questions.

 

Isabelle is having a partyand is putting out the dessert on platters on the table. She has 15 pieces of cake and 6 pieces of pie.

 

Questions:

- How many total guests can she invite so that everyone gets one piece of dessert?

- How many guests can she invite if everyone gets one piece of each dessert?

- What is the greatest number of identical platters she can make with no leftover desserts?

- My favorite: Is she serving punch? LOL

 

I then revealed the question I wanted the class to investigate which was the third question in the list. Students worked in pairs to prepare a visual representation of their thinking as well as a written description. While the numbers in this problem are relatively easy to work with, my emphasis was to work with the mathematical practices of communication, collaboration, and reasoning. My students are still struggling with these but improving weekly.

 

Here are some examples of their work - one that is a correct representation and one that is not.

 

 

 

I had randomly called on partners that wanted to share their work at the document camera and explain how they found the answer.  The first pair had the idea and understood the mathematics involved. When the second group came up, inside I cringed AND rejoiced at the same time! It was a great opportunity to teach some peer evaluation and communicating with kindness.  After the second pair shared, I asked if anyone had feedback. The audience's hands sprang up. They called on one student, and she said that their work did not make sense. How could you distribute 21 pieces of dessert on 30 plates and call them identical?  TEACHER HEAVEN!

 

Not only was it the students  who spotted the mistake and then explained it to the others, but the students all were kind in their feedback and it was received with openness!  Turning over the talking to the students reaped great benefits on this experience. The girls who did the incorrect mathematics said, "Now we get you!" A positive growth experience for everyone.

 

 

"A" is for AMAZING and ARNE

Photo courtesy of the Dodge Magnet Middle School web site.



You know how you clean the house before company comes to visit? Especially when that company hasn't been to your home before or they are someone who is special in your eyes. That's what has been happening for the last month at our school. We found out that U.S. Secretary of Education Arne Duncan and U.S. Secretary of Transportation Anthony Foxx were coming to our school on September 11 and the housecleaning began! Anything that could be polished, washed, waxed, trimmed, raked, and made beautiful was tackled. Our campus sparkled thanks to all the hard work of so many.

 

These visitors, of course, were not alone. They brought an entourage of Secret Service, staff, and the accompanying press corps that follows any big event in a community. We had local police, district security, and all our district dignitaries. The students knew we were having a special visit but they had no idea how special and wild this visit would be! This kind of activity, in their minds, was usually reserved for rock stars, multi-million dollar athletes, and movie stars.

 

The secretaries arrived on one of the school buses with some of our students. One of my sixth graders was thrilled that she sat with Secretary Duncan and shared about her science project that she was delivering to class that morning. I loved seeing that big smile of hers when she told me!   The press did their thing once the bus unloaded - then the real fun began. The kids picked up on the high energy and couldn't help but notice all the suits and ties.  We're a school with a tougher dress code than most of our schools so the lesson was not lost on them.

 

Mr. Duncan and Mr. Foxx were interviewed by one of our eighth grade Social Studies classes, played basketball on the playground with some of the PE kids, painted Kindness Coins with our Builders' Club service organization in the cafeteria, and stopped into two of the sixth grade classrooms for a closer look at how hard our students and teachers are working to implement the new Common Core standards. I have to say that as much as I wanted to just have a "normal" teaching day, I was thrilled and honored that the Secretary (and the press...) popped into my class while I was teaching the lesson on patterns. He dove right into the activity with the kids and asked about it. Right on cue, Josh told him we were looking at patterns and how to predict the number of tiles in another step. Yeah, Josh!

 

                                          Photo courtesy of Fernanda Echavarri, AZPM

 

As teachers, we all know how hard we work on a daily basis - often without words of encouragement or appreciation. When the Secretary of Education pats you on the shoulder and tells you to keep up the good work, it makes you feel like you can do most anything for the rest of the school year. Before he left, Secretary Duncan told our principal that he thought our school was "amazing." Those of us who work there know how fortunate we are to work with the best kids, parents, and staff we know. We are very proud of our "A" rating by the state and strive to be excellent each and every day.

 

I'm not a cynic by nature, but even I questioned the value of this experience and the purpose of the Secretary's bus tour. I could get all political here and talk about political aspirations, tax dollars, man hours, etc. but I won't. What I want to remember is that for a few hours, our school shone like a diamond in the eyes of the public. Our kids were in the spotlight for being so amazing. For just a little while, everyone else got to see what we see every day. Thanks to everyone who noticed there are great things happening at Dodge!

 

For more photos and information from the visit:

https://www.facebook.com/dodgems

https://www.azpm.org/p/home-featured/2013/9/11/26721-us-secretary-of-education-visits-tucson/

Least Common Multiple

We're working on finding the LCM of numbers now. After being introduced to these types of problems through the use of cycles, my students set about finding the LCM of numbers using the usual list-making strategy. Today we're going to extend our thinking into some algebraic reasoning with a little twist on multiples through pattern exploration. This activitiy is from Connected Math.

What do you notice?  What do you wonder?   What will the 20th step look like? When will the total number of tiles in a step equal 576 tiles? Explain how you found that answer. 

Then there is another pattern to explore:

 

Once again, what do you notice?  What do you wonder? What will the 20th step look like?  When will the total number of tiles equal 110?

 
Here's my graphic organizer and an exit ticket for Least Common Multiple.

Arrays, Number Puzzles, and Factor Trees

This week my students are tackling a task I came upon from the Georgia Performance Standards web site resources. It caught my eye because my students need a LOT of work with the mathematical practices especially collaboration, communication, persistence, and reasoning. This task fit the bill for all of those skills while they practice factors, multiples, and factorization. Students work in small groups (we're working in pairs). They have three sheets of paper to share with rectangular arrays, factor trees with missing numbers, and puzzle cards. The goal is to identify the number of each representation and match them.

There are several entry points for this task - some easier than others. Most students wanted to tackle the word puzzle cards first but then realized that the other two sheets were much easier to do first and then use as clues for matching up to the word puzzles. There is a second group of cards for those that finish quickly - although no one in my two advanced classes finished yesterday. My other three
classes will begin this activity today.

Today we will finish up this activity, make posters of the matches, and present their findings with some discussion by the students to justify their answers.

For our math notebook, we will make a number puzzle of a mystery number for others to solve.

Here is the link to the file:
https://ccgpsmathematicsk-5.wikispaces.com/file/view/4-6_Arrays_Number_Puzzles.pdf

 

 

Gosh, I Love Math!

The following is from an e-mail I received from one of my math colleagues at school this week.

 

"Ben B. just turned to me while doing a Word Problem Workshop and stated:

'Ya know Ms. M…a math class is the only place someone can buy 80 watermelons and no one questions their motives. Gosh, I love math.' "

 

I just had to share that with all my mathy friends because THIS is the fuel that keeps our fires burning in teaching.  When I hear something like this, I forget about all the paperwork, the long hours of planning and grading, the meetings, the paperwork, the frustration of not having enough time....did I mention the paperwork? I especially love knowing I had a teeny part of that young man's enthusiasm for math as he was my student two years ago and now I have his sister in my class. Ben, you make me want to be a better teacher!

 

This week some of my students told me that my class always goes by quickly. I take that as a great compliment from a sixth grader. The days that drag by for me are the ones where I am not engaged, not interested, and am bored.  The day is endless when I sit and watch them take standardized tests....*yawn*. I am enjoying their attitude towards learning these days. I know that the group work and discussion, the discovery of concepts through the messy mucking about is ALL worth it!

 

Gosh, I love math!

 

Interactive Student Notebook - Exponents

 

After dabbling in interactive student notebooks over the last two years, I have made a more dedicated commitment to using them with students. Here is our latest entry when reviewing exponents this week. We did a review of the content and took notes on the right side of the notebook page. The next day I gave the students this to fold in half and glue onto the left side as an independent activity that also served as an assessment while I worked with small groups. The cartoon idea was a hit with the creative side of the kids and a great reminder for the power of exponential growth!

Math Munch - My Latest Discovery!

In my early morning searches of wonderful ideas on the internet, I was delighted and a little intimidated when I came across Math Munch.  This is a wonderful blog which invites kids into the coolest math experiences outside of the classroom. As the authors point out, readers don't just read in class, they choose to read outside of class. There are places to go for more books to read - libraries, book stores, collections in the home.  There are book clubs and forums to share the sheer pleasure found in reading.  What is there for the hungry math student? This is a site dedicated to opening the world of math that is all around us.  I have so much to learn from reading this site! Be sure to check it out.

Math Munch TED Talk   

Prime Factorization Success!

Following the frustration this week was a deeply satisfying "ahhhhhhhh" moment on Tuesday. My students were learning about prime factorization. I pulled together a few pieces from several great lessons. One idea came from an ace teacher, Jen Runde!  http://www.rundesroom.com/

I started the lesson by holding up a bag marked with 300 on the outside. I asked the students to do an "I Notice, I Wonder" journal entry to spark some interest. After some sharing, I revealed the colored shapes/numbers in the bag.  More "I Notice, I Wonder" writing and sharing. I was hoping students would notice there were only prime numbers and the fact that you could use those numbers to get the product of 300.  Paydirt!  At least one student in each class came up with the primary ideas. Never say for the students something they can say!

I had more bags with other numbers: 18, 30, 48, 56, and 75. I had the students work with partners to figure out the prime numbers in each bag I held up. They recorded their ideas in their interactive notebooks. We also talked about how we could find all the other factors of each number by combining the prime factors. This part of the lesson came from an article, "Moving Beyond Factor Trees," by Terri L. Kurz and Jorge Garcia in Mathematics Teaching in the Middle School. This was a powerful lesson for students. Rather than starting with factor trees and teaching a procedure, the students were able to discover through their intuition and understanding of prime numbers, how to do the prime factorization! Today we'll add the exponential form to the factorization.

Thanks to my online colleagues for the great ideas!

 

Frustration....

Yesterday's experience was frustrating....oh, yeah...teachers feel it.  So many students are reluctant writers to begin with.  Now I'm asking them to write in math class. (Are you kidding me?)

My two classes yesterday turned in mixed results of their Cat Walk problem.  It was clear that those that had quite a bit of work on paper had adult guidance. That's ok with me as long as the student can explain. Not all could do that.  Many of them had no written explanation of their reasoning. If I look at their papers, it's up to me to put some logic and order to the scribbling of numbers and calculations to follow their thinking. We had a talk about why it is important to explain your thinking. It is an expectation to be clear in oral and written language in order to be college- and career-ready. If you can explain your thinking, you demonstrate deeper understanding. This is going to be a growth experience for us all.

How do you move students along in their ability to write in math class?  Ideas? Suggestions? Let's pick each others' brains!

Prime Time

The last two weeks have been incredibly busy - Open House, first progress reports, four new students and papers to grade. Getting back up to full-speed is really time-consuming!

I'm spending a great deal of time thinking through my lessons to make them top-notch. I'm still having a hard time estimating the amount of time I need.  On paper, it looks like there is plenty of time to accomplish all that I plan for the students.  In reality, I'm biting off too big of a chunk! I have forgotten about all the little things that are not "planned" parts of the class period that absorb all those precious moments.  Prime time gets shorter after attendance, passing out flyers, homework, picture packets, dress code issues, explaining progress reports, and handling all of the spur-of-the-moment student crises!

Today I am looking forward to a discussion with two of my classes on the Problem of the Week. They have had about a week to think over the Cat Walk problem from the Math Forum website. http://mathforum.org/ The problem is one of proportional reasoning - a cat takes a different amount of steps than a dog to cover the same distance. Students are to find the distance a cat will cover in 24 steps. I am curious to see the methods of approaching this problem.  The students are going to share their work and talk about their reasoning.

I wonder....
   How many students will have their homework.
   How many students communicated their thinking in writing.
   If I can lead this discussion by allowing the students to do most of the talking!
   If students will enjoy the process of tackling a more difficult problem without being led through
       the steps.
   If they will gain the ability to persist even when it is challenging.

I am prepared to keep at it! I know that my students can get better at solving problems. I need to persist even when the going gets tough just like they do! We are ALL in the learning process here.

The other task today is to continue our work with prime numbers in all classes. We're entering vocabulary into our math notebooks (Frayer Model) while I work with small groups.

I wonder.....
    If I have bitten off too big of a chunk today? All I can do is monitor and adjust, right?

Twist on the Penny a Day Problem

I had to share this with all of you. You probably have seen this problem in another form.....do you take the offer to earn money by doubling the amount you earn each day starting with a penny or do you take a million dollars for the month?  Muhhahahahahahah...

Taming the Dragon

There is a paper dragon snarling and breathing fire in a folder somewhere on my desk. It is known as THE PACING CALENDAR.  It roars a few times throughout my day and begs for attention. It reminds me at 2 a.m. that I'm not covering enough curriculum in order to do it all. I've fed it a few tidbits this week to keep the flames of stress to a flicker, but the dragon demands attention at the most inconvenient times.

What is all this talk about dragons? It is my greatest enemy in being an effective teacher: TIME. I don't feel I ever have enough of it in each class period, in the week, in the school year. Just not enough time to do it all the way "THEY" say it should be done. 

What I am relaxing into is the concept that digging deeper into student thinking and problem-solving takes time. If my students are to really benefit from that hour with me, I need to give them space, opportunity to make mistakes, find ways out of their misconceptions, and support to try again.

The sweetest sound that slays the dragon came yesterday....I could have cried or leaped into the air with a backflip! While working with a partner on the Arranging Tables problem, a fledgling of mine SHOUTED and threw his hands in the air, "I got it!!!!" I went over to him and his partner, and we talked through his solution. Although it wasn't quite correct according to the criteria, they persisted and persisted until they figured out one of the possible solutions! VICTORY! That really doused the whimpering dragon's fiery breath on my desk!

What I saw yesterday from all five classes was total ENGAGEMENT for ALL learners. I saw persistence. I saw students willing to record their thinking by using diagrams. I heard focused conversations about math problem solving.  Teacher Heaven. I took a deep breath and told them we would keep working on this problem on Monday. (The dragon backed up into the cave and let out a whimper...) We are about the work of developing our mathematical brains here. We are not in a race to some finish line. The lessons that these students are learning through this lesson are invaluable for the long-term.

My students are inspiring me. The damsel in distress is ME - thank goodness they are willing to come to my rescue!

Arranging the Tables

This morning we are going to dive into a review of factors and multiples through a task I found on the NRICH math web site. 

http://nrich.maths.org/964



The task is to find a way to seat those 44 people with no empty seats at any table. I want students to find a way to record their thinking and to explain their final answer in sentences as well. There are multiple ways to make the arrangement so early finishers will be asked to find more ways. Are there any patterns to finding the ways?  Does knowing the factors of 44 help you to solve this task? Why or why not? Are there factors of other numbers that are useful? What are they and why are they helpful?  We can have some group sharing of solutions with feedback from peers.

 

Students will add their solution to their notebooks, and we will also make a Frayer model of their vocabulary words - factors, multiples. I've got an exit ticket prepared to check on their understanding of factors. Sounds like more than enough for one lesson - probably two! Oh, yeah....some time today we're having our first fire drill! Thanks for letting me think through my lesson with you all.

Dodge Middle School - An "A" School for Another Year!

Just wanted to brag about our school this morning - we received an A grade for the hard work of our students and staff. We are so proud! I have the priviledge of being a part of this great group. We are the only middle school in our district to have an A rating. This is no easy task - we are a magnet program and our students are chosen by lottery. Our student body is "like a box of chocolates" - we never know what we're going to get! Some think that we get to pick and choose, and that's why our students achieve so much. Not so! It's a lot of effort, commitment, and focus by students, parents, and staff!  Here's to all of you!

http://dodgemagnet.weebly.com/

Interactive Student Notebooks

Interactive Student Notebooks are another great tool that I am implementing this year.  I have always had students keep a notebook, but it has usually just been a place to take notes and do a little practice. As I have been looking at all the amazing ideas on Pinterest and on teacher blogs, I have come to realize what a powerful asset an ISN can be in my class. My hope is that kids will take ownership of their notebook and see how it can help them deepen their learning. They may even use it for homework or studying. Ahhhh....a teacher's dream!

So we started by getting the basics pulled together in the notebook.  All of this takes time, and I am impatient. I feel like I should be getting "more" accomplished in the area of curriculum. I have to keep reminding myself that time spent on procedures, routines, and the basic structures for the year will pay off in the long run!

I have borrowed and stolen all the great ideas for my notebooks from other teachers who are so kind to publish on the web. Thanks to you all for sharing! I will post throughout the year to share my victories and a-ha's about this new process.  For today, we're putting the last of the pieces - a sheet to keep track of their progress on standards, an "iPocket" for those unglued pieces, a reference sheet for geometry formulas, and finishing two reflections. That ought to be enough to keep us busy today!

If you see that I have used your idea, would you give me a shout-out so that I can give you credit?
I must keep better track of where I have gotten these great ideas!