Sunday, October 28, 2012

In Search of the Perfect Man

Do your students hate fractions as much as mine do?  At this point in my career, I've decided that the evolutionary cycle has altered our children's genes in a way that the minute they see a fraction in any problem, they immediately write  "IDK"  and then skip right over it.

Well, this week I had my students literally BEGGING to do more fraction work! It was an amazing site to behold!! What is it that caused this "genetic" transformation to occur? My students were in search of the perfect man!

This project has everything a teacher could hope for: an introduction that had the students literally begging to find out the "answer", an intense buy in from my students ("Can I take this home and work on it?"),  and LOTS of contextual practice for changing mixed numbers to improper fractions, multiplying fractions,  and adding and subtracting fractions with different denominators.

It all started when I saw this: the Vitruvian man with a list of the proportions Leonardo DaVinci categorized as perfect. The list included things like:
Vitruvian Man by Leonardo da Vinci, Galleria d...
  • the length of the outspread arms is equal to the height of a man
  • from above the chest to the hairline is one-seventh of the height of a man
  • the maximum width of the shoulders is a quarter of the height of a man
  • the distance from the elbow to the tip of the hand is a quarter of the height of a man
 Now, my sixth graders are not ready for the formal study of proportions yet, but we have been reviewing adding and subtraction fractions, have been learning about multiplying fractions and about transforming mixed numbers into improper fractions, and learning about cross checking our multiplication problems. It seemed that all this would work nicely into a "Perfect Man" project.

I recruited five male teachers to help - one for each period.  All I had to tell them is that my students were looking for the perfect man and they readily volunteered. :) One teacher came into each period and the students measured them so they could do their calculations.  They all happen to be "hams" in the best sense of the word, so they really had the students going by the time they left the room. Here's the form we used to record the measurements:








In Search of the PERFECT Man Blank

If you'll notice, there's six columns, instead of five. That's because one of my sixth grade boys insisted that - since they are now in middle school - the boys really should be referred to as "men". :) With that, we decided to add one of the sixth grade boys to the list as well.


After the students recorded the measurements in each period, I typed up the list and brought it in the next day.

In Search of the PERFECT Man
 We talked about how to determine if someone was perfect in a particular area. The students decide that if the real measurement equaled the answer to the problem they set up (for instance 1/2 times the height), then the person would receive a "0". If the measurement was greater, they would put a +, along with the difference in the column and if the measurement was less, they would put a - .  Finally, students would add and subtract the numbers in the right-most column to determine which man came closest to "0" (closer to perfection). I know that sounds confusing, so here's one of the recording sheets...

Then I set the students loose.  It's rare to have 100% engagement 100% of the time, but that's what I had! I gave them very little direction about how to solve the problems, but they quickly figured out how to set up their equations ( I heard lots of "you have to multiply the fraction DaVinci said by ____'s  height..." and saw the use of lots of different strategies we had discovered to make multiplying fractions easier. They understood what each number meant and whether they had to multiply or add or subtract them. It was awesome!)


At the beginning of the fraction work, things went slowly as students worked their way through the correct strategy to use and then through the initial practice of setting up and solving the equations they set up, but as the period wore on, students became faster and much more confident in their ability to use fractions. I think they were even surprised at how adept they became at using the fractions in their calculations.

This was one of the best lessons I've ever done involving the real-life use of fractions. I can't wait to bring out the data again when we get to proportions.... I think the already deep understanding of the data will aid in helping the students understand setting up and solving proportions.

If you would like to try this with your students, you can use the blank recording sheet above and the calculations sheet I'll paste below.  If you try it, I'd love to hear how it went for you and I would love to hear of any modifications you made so I can try those next year.
In Search of the PERFECT Man Calculation Sheet

Sunday, October 7, 2012

What Happened to the JOY ?

I've always loved teaching eighth grade. The curriculum - to me - is very interesting and I enjoy helping students learn about and explore all the facets of algebra at this level. One of the things I've always found challenging, though, is the attitude many eighth graders have about school. By the time we get our eighth graders, many of them have a less than positive view of school and especially of math. Many times, this translates into attitudes of "I'm too cool to do ...." or, "I don't do....", or, in students with bigger issues, this translates into the beginnings of behavioral issues.

Last year, I was moved from eighth to sixth grade. I was disappointed because I truly do love the curriculum at eighth grade. However, I spent the summer reacquainting myself with a sixth grade scope and sequence I hadn't dealt with in ten years, with the common core standards for sixth grade, and with a variety of the new type of approaches and assessments being used at this level.

I've been working with my sixth graders for a month now and I've come to realize that there was one thing about sixth graders that I forgot in my almost ten years spent with eighth graders. They're wonderful!!!! I am having sooooooo much fun with them because they are just so joyous about everything we do! I don't care how small the activity is that I've planned, I always get numerous responses of "that was fun" or "thank you for teaching me that" or "I've always wanted to know that". They come into the class excited for the day, asking what we're going to be doing, and - for the most part - diving right into the activity of the day with great excitement. It's making my teaching days very fun and very rewarding in a way I hadn't experienced with my eighth graders.

This leads me to my question in the title....What Happened to the Joy ???? I've been asking myself this a lot for the last few weeks. Where does this exuberance, this joie de vivre, this love of learning new things go? The last group of sixth graders I taught had it, this group has it, other sixth grade teachers tell me their students have it. Eighth grade teachers tell me their students, as a group, do not.

Why? Is it all developmental? Is it something we "do" to them at school as they get older? Is there anything we can do to change it?

This is an incomplete blog post because I simply don't know the answers. But I would like to. And I think this is an important question worth examining....

What are your thoughts?



Sunday, September 30, 2012

It Happened on Wednesday

Dating can be a lot of work! We want to find out all about the person, find out what makes them tick, what they want in life, find out if we're compatible in the ways that are important to us.... When you first start dating someone, it takes a while to get to know him or her and even longer to start catching glimpses of their heart. For those of us who have been lucky enough to fall in love, those first glimmers of love probably resulted when the preciousness of the person we were dating first became apparent. And we cherished those beginning glimmers because they were signs of what we hoped might be a long-term relationship.

Isn't it much like this every time we start a new school year? In a sense, we do the same things with our students that we do when we first start dating someone. We observe behaviors, we talk, we ask questions, we search for shared connections, we watch for that elusive synergy that happens when we know them and they know us well enough and have built the beginnings of what we hope will be a classroom of students who can learn from us and learn from each other.

Every year I seem to get one class that takes a little longer to build that synergy with. This is usually the class that is filled with more behavior problems than most or filled with students who are suspicious of anything or anyone that comes along with the word "math". This year, for me, that period is my fifth period class. The class is large (35 students), is approximately 3/4 boys, and has more than its share of behavioral issues. We have practiced classroom procedures far more times than my other classes and I've had to use my classroom management skills with this class in a different way than my other classes. In short, they have been a lot of work!!!

But then it happened. Last Wednesday, I was out in the hall helping a student who couldn't open his  locker. The bell rang, which meant that class was to begin. Normally, I'm in fifth period when the bell rings, reminding students to get their supplies out, reminding them to start the warm up, asking boys to stop playing with the air outlets..... On Wednesday, I walked into my room a couple of minutes after the bell rang expecting to find chaos. Instead, I saw 35 students sitting in their seats working on their warm up and happily SINGING along with Colin Dodd's "Powers" video. I stood at the door for a second listening to them sing "five times five times five times five is 625" and my heart melted; the preciousness of who they were overwhelmed me. And so the relationship begins...

Saturday, September 22, 2012

The BEST substitute plan ever! :)

I don't know how your school operates, but at the school I teach at, we have to have two emergency days of substitute plans available. These have to be generic enough that students could use them at any point during the year and they need to have the type of content that provides opportunity for new learning or practicing things already learned.

I've always struggled with these type of plans in that I want to make them educationally valuable for my students and easy enough for my substitute to implement if I was not available to give more input.

On Thursday, I was sick! I came down with something awful and was unable to make it past lunchtime. (Can you catch things from fellow twitterers?? I seem to be getting whatever it is you all have had. Just sayin ..... :))

The day had already been planned out, so I didn't need to create any lesson plans. But what I stumbled upon was the greatest emergency lesson plan ever! :)

My students are just finishing up their study of order of operations and - as a final review before the assessment - they had requested that they get to play RISK again. I blogged about this game in late August. It's a great way to preassess or practice a skill. Well... it's also a great activity for subs to use!

My substitute was wonderful! She has a math background and is exceptionally good at teaching a class of totally unknown students. She has subbed for me many times. As wonderful as she is, she still has to deal with students testing a sub, multiple students asking to leave the room, or students refusing to work - all the things subs normally have to deal with. Yesterday, NONE of that happened! I got a nice long note from her RAVING about the RISK game and asking if I minded if she took one of the forms to use in other classes where teachers might have left incomplete plans. She thought the game could be used at any level of math. She said that when she announced what they were doing that day, they all yelled "YES"! She mentioned that she has never had NO behavioral issues in all the years she has subbed and that she had 100% buy in from the students (they LOVE this game!) --- no one even asked to leave to go to the restroom or get a drink because they didn't want to miss bidding on a question. AMAZING!

So, RISK is going to be one of my emergency plan lessons. I'll include a quick warm up, an explanation of the game (although she said she didn't have to explain it at all... they all quickly got to work on their ten problems), and I'm going to include a generic RISK sheet (I've inserted one for you to use below)  so I can change the type of questions the sub will use as the year progresses. I think I'll go ahead and come up with the 10 questions for our next three or four areas of study and, as we get through those, then come up with the next three or four... By the end of the year, I'll have a year's worth of RISK games ready for emergencies.

AWESOME! :)



Risk Generic

Friday, September 14, 2012

What Time Is It?

I have a wall of clocks in my room.Each clock has a different math "theme" with all sorts of expressions that equal each of the 12 hours of the day. My students love these clocks! They enjoy trying to figure out how each expression (most waaaay above their level of thinking) could possibly equal the number it says it does. I decided to take their interest in the clocks and use it to my advantage.


We're midway through our exploration of the order of operations.  I wanted to give my students a chance to breathe (mentally) and allow their learnings to cement in a little. I wanted to have an activity where they could practice what they've learned so far and where I could see what they knew.

I remembered a clock activity that Fawn did with her students last year and decided to morph her idea into an activity for my students. I told my students that each group was going to design their own clock. The assignment was met with lots of interest and excitement! I explained that - instead of each number on the clock - they would write an expression that demonstrated their ability to use the order of operations correctly.

First, I had each group grab their mega white board and use it to plan what expressions they were going to use.  This was a great use of the boards! I heard lots of great math talk and saw lots of wonderful collaboration as they struggled to come up with expressions that would work.


As the groups worked, I was able to walk around and eavesdrop on conversations. It was wonderful to see my students trying different expressions, analyzing why some weren't working, arguing for their way of solving, and rejoicing together when they finally found one they all agreed worked. Fabulous!

As each group finished their planning, they got a
blank clock face to write their expressions on.
They then decorated them as they chose and then proudly displayed them on a wall for all to see.

I was really happy with how this project turned out. The students were able to work at a fairly high level of analytical thought, they were able to be creative, and they were able to practice their group communication skills (my sixth graders still need LOTS of practice with this). :)

There were lots of benefits for me as well. Instead of grading 173 papers with several problems on each paper, I was able to simply walk around, talk to my students, write some quick notes about problem areas I was seeing (exponents!) and make notes on individual students. The project turned out to be a wonderful formative assessment opportunity for me.  I learned all I needed to know about where each individual student was and  I was very easily able to see where some reteaching was needed, what areas the students had totally mastered, even found a couple of students who are ready for some extensions.

Next week.... way more practice with exponents, a little more practice with parentheses, I'll throw in some embedded parentheses and, finally, throw some dreaded fractions into the expressions.

If you try this activity, I'd love to hear how your students reacted and I'd love to get any suggestions for making the activity better next time.

Below, I've put a few more examples of student work and a blank clock, just in case you'd like to try the project.


















Monday, September 10, 2012

Exit slips du jour


We all struggle with how to formatively assess our students in a way that doesn't take up too much class time, but still allows us to get the information we need to plan future learning opportunities. One way to get this information is with a targeted exit slip.

I tried an exit slip in class today that worked really well. I asked students to rate their engagement in the lesson and their understanding of the objective (I can evaluate expressions using the order or operations). This is an important step in getting them to metacogitate (think about their thinking - don't you just love that word?? :)) and become more evaluative of their learning. We spent a bit of time discussing what it means to be engaged in a lesson and had a really good discussion! Students then picked one of two problems to work so I could formatively assess where they are at. I wrote one problem with an exponent and one without. Exponents are still tripping up some of my kiddos and I don't want that to keep them from showing me what they know about the order of operations.

It was really easy to sort the slips into two piles: one pile of students who are ready to move on or try some more difficult problems and a pile for ones who need a bit more work. Tomorrow, I have a differentiated activity planned and the piles made it really easy to put students into groups at their approximate ability levels.

I've pasted the template (with my learning target and math problems) below. It's easy to simply change the learning target and problems and you'll have an exit slip ready for whatever unit of study you're teaching. If you teach in a district, like mine, where having data to show growth for each student is important, you can file completed slips away and pull them out as needed.

Exit Slip

Friday, September 7, 2012

Visions of PEMDAS Danced Through my Head

I woke up in the middle of the night with visions of lesson plans dancing in my head. Earlier in the day, I had gone over and over my plans, trying to find the best method of introducing my new crop of sixth graders to the infamous order of operations. I struggled with whether to use PEMDAS or not (I normally use a different acronym), but I really wanted to use Mr. Stadel's PEMDAS video; I knew my students would love it! Since I've started using foldables, I really wasn't happy with the normal graphic organizer I might have used and so I began searching for a foldable that fit my vision. Alas, nothing could be found and so I finally gave up, resorting to my tried and true graphic organizer.

Fast forward to the vision that woke me up...... My brain had been working on the problem while I got what little sleep most of us are used to the first few weeks of school. I saw the perfect foldable in my mind; now, I just had to construct it!

Have you ever tried to design a foldable at 3:30 AM???? It's far more difficult than one might expect! :) I wanted to make sure that my foldable emphasized the fact that multiplication and division are done as we move left to right through the equation and that it is true for addition and subtraction as well. In my mind, I could finally see what it needed to look like, but my brain just couldn't get it onto the paper.  Finally, at 4:45.... Success!  Here's what it looks like all folded and nice after one of my students constructed it today ....




Notice that the P and the E flaps extend across the foldable, but the M and D share a row, just as the A and S do.  I wanted to make sure that students graphically saw this on the foldable. And it worked!

I had students choose a color for writing the "P". They then chose a different color for the "E". They picked a third color that they used for the "M" and the "D" because, as my students said, they share a row. :) The fourth color was used for the "A" and the "D" for the same reason.
















After we made the outside of the foldable, we turned to the inside. I wanted the students to label each step and we also worked through a problem together.











Once we finished the right side of our INB (our input side), we turned to the left page (our output).
We worked through a problem together, labeling each step as we went. Students then worked through a couple of problems on their own, underlining each step. Finally, I had the students answer a generalizing question at the bottom of the page.

All in all, this was the smoothest introduction to the order of operations I've ever experienced. Students LOVED the foldable, they LOVED getting to choose the four colors that they would use with intentionality (my word, not theirs :)), and I loved how easily students picked up the idea of doing multiplication and division and then addition and subtraction as they moved from left to right in their expression! :) :)  Success!

Here is the elusive foldable pattern I came up with early this morning.....


PEMDAS Foldable
Just cut out the larger rectangle, cut out the black spaces, and then cut on the dotted lines. Fold the smaller flaps in towards each other and fold the larger flaps across the foldable to the right.

I would love feedback..... If you try the foldable, how did it work for your students? Did you make any changes or modifications that worked well?

Some things I'm wondering.... How can the process be streamlined for my sixth graders (Some of them take forever to cut the foldable and even to write a single sentence!!!) but still keep the educational value intact?  What are the "have to haves" or the "have to do's that I need to keep in the lesson so that my students get that innate sense of the steps (especially MD and AS)? Suggestions? Ideas?