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?


Tuesday, August 28, 2012

Risk your Fraction Skills

Next week, I begin my school year with 180 sixth graders (36 students per class).  My district has provided a scope and sequence that builds from where sixth graders should be starting the year skill-wise. It assumes that most students will need a brief review of adding and subtracting fractions before we launch into multiplying and dividing.  Over the years, I've learned not to count on the fact that assumed prior knowledge is in place and so I want to do a pre-assessment to double check where my students' skills lie. I really hate to throw a test at my students the first couple of weeks and - when trying to think of another way to preassess - I remembered a game I saw on Sue VanHattum's blog a while ago. Sue's game (Risk your Algebra Skills) was aimed at algebra students, but I used her idea to focus on my students' fraction skills.
Risk Your Fraction Skills
The idea of the game is that students risk up to 100 points that they will get the first question correct (they should make their bid BEFORE they work the problem). If their answer is correct, they add the points to the beginning 100 points; if they're wrong, they subtract.  They now have a new total from which to bid.  The winner of the game will have the highest point total.

The reason I like this game as a preassessment is because it gives me two important pieces of information:
  • How confident the students are in their skills of adding or subtracting fractions or mixed numbers with common and different denominators  (Where do THEY think they are?)
  • The actual skill level of the students (Where are they REALLY?) so I can differentiate my instruction and products, as needed
It also disguises the "test" in a way that will distract my test phobic students.

I'm looking forward to trying this with my kiddos .... a test disguised as a game....FUN! :) If it works well - it might be a way of disguising other sorts of assessments. If you try the "game" I'd love to hear if you think you got the same sort of information you would get from a normal test.

UPDATE: Here's an Order of Operations one ...


Risk Your Ooops

Sunday, August 26, 2012

WANTED: Dead or Alive

 
How many times do we - as math teachers - have students bringing their friends to the classroom between classes, after school, or at lunch just to show them a project they're working on? How many times a year do we have students ASK if they can come in at lunch to work? Maybe in art class, maybe a photography class.... but math? Hardly ever! Last year, I had students doing just that: asking to come in and work on their own time and bringing their friends in to show them their work. AWESOME! The project occurred over a three day period (we worked on it for about 30 minutes each day - rough draft and then final) and it was one of the best investments of time I made; the outcome was amazing!

Direct Variation functions seem to throw my 8th graders for a loop every year. The easy part is recognizing equations in the y=kx form or even the y/x=k form; but in the past, for some reason, every time they saw something like y=x/4 on a test and were asked to identify the type of function in was, they thought it was a direct variation - just because it was a fraction. I know they could stop a minute and reason through the equation and realize that it wasn't, but you know eighth graders! :)  I wanted to come up with something that would allow my students to explicitly think about equations that "fool" them into thinking they are something they aren't. Who else often does that? Criminals! And so...

I had my students create wanted posters for direct variation. I started out by showing them different wanted posters (they liked this!) and we talked about the different things that needed to be on a wanted poster for it to be effective. I then set them loose. And they had a blast! I've inserted some pictures below so that you can see some of the final products they came up with. There's a range of posters from my low-level kids up through the ones functioning at a much higher level. I like the fact that you can see - fairly quickly - what each student understands about the function and what misconceptions they might have. 

Each day, we worked on some fairly focused practice, both in the warm-up and in the practice activities, and then we spent the rest of the period working on our posters. It was fun to walk around, chat with my students, ask them some leading questions when they were stuck, and help streamline their ideas, when necessary. 
Several things:
  • I was surprised that many students weren't sure what "alias" meant. We spent some time talking about that, both during the powerpoint showing different wanted posters and, again, as I walked around the room while they were working.
  • We needed to spend some time talking about the terms "disguises" and "m.o".  Some of my students LOVED the phrase modus operandi and used that term on their posters. 
  • My low-level kids needed a little extra support in the writing phase, but - for the most part - they excelled in the illustration part of the project. :)

It doesn't matter how fun a project is if it doesn't produce the results you're looking for. I waited six weeks after we did the posters (so I could test for long-term learning vs short-term "remembering") and then I gave my students an assessment to see if they were still struggling with recognizing direct variations. The results were amazing - less than 6% of my students showed any indication of needing any reteaching at all! I think that makes this project worthy of another visit next year!










Tuesday, August 21, 2012

R squared equals one

Do you have a friend or colleague who always has the perfect analogy for any situation? I do. My friend, Clark, can come up with perfect analogies for any situation in a second. And they're always clever. I have another friend who comes up with analogies equally quickly; however, they never seem to make sense. To her, the analogy is perfectly clear. To the rest of us? Clear as mud!

The analogy of my blog's name is perfectly clear to me. The danger with sharing the analogy with you is that you might read it and respond, "Clear as mud!"  :)
 
The coefficient of determination (r squared):
  •  is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph.  
  • represents the percent of the data that is the closest to the line of best fit
  • is a measure that assesses how well a model explains and predicts future outcomes
  • is expressed as a value between 0 and 1. A value of one indicates a perfect fit and therefore a very reliable model for future forecasts. A value of 0 would indicate that the model fails to accurately model the dataset.
Every day we put our "model" on the line and we test it, hoping for an r squared of one.  We design (what we think is) the perfect lesson with just the right learning target and just the right set of activities to get our students there, and then we go for it. While we are teaching, we check for outliers, for students that wander near the line of best fit, for students that are right on the line, and students who don't even make our graph. A reflective teacher then tries to account for as much of the variability as we can, hoping to get close to that perfect value of 1.

That is what I try to do every day. Achieve a one.  Sometimes I get close. A few times, I've been near 0 and had to start all over the next day. Every once in a while, I "score" a one. And we all know how wonderful that feels! To me, those 1's come with the synergy created between the art of teaching and the science of teaching. They are hard-won. And they feed me (professionally) like little else does.

I hope to share my 1's with you, as well as my 0's and all that falls between. I hope to hear about yours as well. We'll rejoice in our 1's while sharing our strategies, activities and thoughts and we'll analyze the 0's so that - the next time - our outcome will be different.

Looking forward to the journey...

RACKO

One of the main areas I need to assess the first week of school is how well my sixth graders understand fractions, decimals, and percent. I know my students will be all over the board in this area and so I think I'll play a game of RACKO with them. Here's how it works:

  • I'll divide the class into two teams.  
  • We'll shuffle the cards and then deal out 8 cards to each team. As I deal them, I'll place them in the order their drawn on the rack (hence the name RACKO) on the board. 
  • A student from the first team draws a card and can either discard it or replace one of the cards in his/her team's row.( The goal is to be the first team to get all their cards in order.)
  • Now, the second team has a turn. It goes back and forth until one team gets their cards in order.
Fun!
While the class is playing, I'll be listening to the conversations in the teams. Who seems to have a grasp of the equivalencies? Who doesn't seem to have a clue? Who always seems to consistently offer the correct suggestion? Who remains quiet? Who can replace a card correctly by themselves? Who needs help from the team?

We'll play this a couple of times and then - another day - I'll put students into smaller teams to compete - maybe two person teams and then, eventually, one person playing another. If you plan on doing this, copy each set of cards in a different color; that way, clean up is easy!

The beauty of this game is that it can be adapted quite easily. You can:
  1. Make a set of all fraction cards if you are working on ordering fractions or on common denominators.
  2. Make a set of square root cards mixed with whole numbers or even numbers with decimals.
  3. Make a set of integer cards, mixing positive and negative numbers.
  4. Make a set of decimal cards. This will really help pull out misconceptions about place value and decimals.
The possibilities are endless. The students love this game and it's one of the best ways I've found to pull out misconceptions and examine them as a class. I love any game or activity that can do that; it is difficult to affect change at a deep level until both the students and I understand what misconceptions are held about the concept we're learning.



Friday, August 17, 2012

Foldables vs Graphic Organizers

On Tuesday, I attended the online presentation Julie did on using foldables in our interactive notebooks. I liked the variety of foldables Julie showed us and I think they would be fun for my students. I appreciated the fact that the foldables would be useful in helping my students process new content and that my students could use them to practice and to study for assessments.

Earlier, I had gone through some of my old math lab materials, looking for some things to send to someone who is teaching a Math Lab this year. I found a whole set of graphic organizers/guided notes I use with my lab students. They really like them because it makes the content fairly explicit and helps them to make connections they might not otherwise make.  I pulled out one on the angle relationships created when a transversal crosses a set of parallel lines (I've used it for years and don't know where I got it; if it's yours, let me know and I'll cite you).  It looks like this:
Transversals Guided Notes

And here's what it looked like when filled in (after some hands-on activities and practice) and glued into our notebooks.
Now, there's absolutely nothing wrong with this: it pulls all the important content onto one handy page and helps my normally scattered students focus their thinking and pull together connections they've made along the way. However, I thought it might be more useful for my students if I turned it into a foldable. So, here it is.... my first foldable! :)
I designed it so that after students take notes on it, it can be folded and opened up a variety of ways so they can us it to study for assessments. On the left, examples of each angle pair relationship is colored in. On the right, students describe the relationship as congruent or supplementary, and in the middle, students write out the relationships.

When opened like this, students see the same of the relationship and they can see if it is supplementary or congruent. Facing that page is a blank diagram so they can practice finding the angle pairs.

After they name the angle pair, they open that flap to see if they were correct. I like this; it gives them immediate feedback.
All folded up, ready to be taped into their notebooks.
While I really like using graphic organizers and guided note forms, I think this foldable is a much more valuable tool for my students. I like how interactive it is and I can think of tons of ways students could use it in class after they use it to take notes on.

Since this was my first foldable and I'm still learning (Julie-you forgot to tell us how looooooong it takes to get everything organized and lined up just right! :)),  I would love feedback. Where could I improve on the design? Would there be a better placement of information so that it would be even more useful to our students? And - for those of you who are farther along on this journey than I am - do you have any hints for streamlining the process?

Here's the front....
Transversals 2
Here's the back...
Transversals 1





Sunday, August 5, 2012


THE HIDDEN AGENDA

I’ve taught for quite a few years and I’ve learned that no matter how wonderful an activity is, there is much a teacher needs to bring to it that, in my opinion, goes unsaid in most lesson plans and ideas. A few years ago, I mentored a group of teachers who were interested in learning more about brain-compatible instruction and about ways of increasing relevance for their students.  A couple of teachers would try the things we worked on in our weekly meetings and would come back to report less than stellar results when others were reporting the opposite. Finally, I went in to observe some teachers who were reporting success and some who weren’t. I quickly realized the problem.  Although everyone was implementing the activities correctly, some teachers went no farther than implementing the activity itself. 

 I asked one particular teacher what she had learned about her students and about what they knew/didn’t know from observing their involvement in the activity. She wasn’t sure what I meant and so I explained to her what I was thinking and observing during the lesson (who was on or off task, who got the “point” of the activity and who needed me to ask a leading question or two, who wanted me to tell them the answer, who didn’t do anything at all, who seemed to have a misconception that needed addressing ….) She said to me, “ I was just trying to implement the activity correctly; I didn’t know I should be watching for those things!" 

Her comment caused me to stop and reflect on my own teaching practices and how to make what seems apparent to me apparent to everyone else, whether it be a teacher I am mentoring or a class full of students I’m teaching. As I share some of the activities and lessons I’m using, I’ll try to remember to share some of the “hidden parts” of the lesson. For most of you, it will be things you are already thinking or doing; for one or two of us, it might make the reason behind the lesson a bit more apparent. I know it will help me as well as it will remind me of what my overt and covert intentions are and will help me focus more intently on those goals.

All of us best process information in one (or more) of several ways; one category of those are our visual learners. I enjoy using this activity to see who in my classes tend to be good at picking up information visually.  I’ve used it on and off for years and have no idea where I got it. I do know that it was intended to be more of a brain challenge, but I use it in the way I’ve described above.  I use the Sherlock activity to begin a discussion about how we all might learn a little differently and to talk about our learning styles and preferences.
Sherlock 1

I hand out the first picture of Sherlock Holmes’ room and ask students to observe it for a bit of time (I’ve tried 3 minutes and 5 minutes… adjust the time to fit your particular students). At the end of the time, I collect the pictures and I give them the blank one with the questions. I then give them a period of time to draw in the objects as they remember them. At the end of the time, I project the original diagram on the Smart Board and have students circle all the ones they got correct. We then begin a discussion about ways we like to learn and that even though someone may have got very few correct, if I gave them a similar activity where I described where everything was, they might get them all correct – we all simply learn best in different ways. And that’s okay.  I want to set a tone of openness and acceptance as we all discuss how many we got correct and how we feel we learn best.  Finally, I ask the students to reflect on their own preferred ways to learn and I have them write me a short paragraph telling me how they feel they learn best and telling me how I can best help them this year. This will be their exit slip.Sherlock 2


Now, here’s what I do while my kids are busy… I’m watching and learning. I’m learning sooooo much about my students, about my class make-up, about how each particular class relates to their fellow students … Here’s what I’m watching for…..

1.        Are all the students involved? Who is looking around the class or out the window (or whatever) instead of participating in the activity?
2.       Who is very focused and studying the diagram intently?
3.       Who simply HAS to talk with his or her neighbor as they process what to do or process how many he or she got correct?
4.       Who has to check in with me to see if they’re doing it correctly?
5.       Who seems to want to sit back and observe what everyone else is doing before they jump in?
6.       Who calls out comments as they’re working?
7.       Which students simply can’t concentrate for the short time period you give them to study the diagram? What are they doing? Getting up? Beginning conversations? Fiddling with their “stuff”?
8.       As I walk by to see how the students are doing, who wants to talk with me or show me something? Who wants to simply work without interruption?
9.       As we discuss our findings, who wants to share? Who seems to want to add their comments more than expected?
10.   Which students try to steer the discussion off topic?
11.   Which students don’t share at all?

Now, check the writing the students do for the exit slip.
1.       Which students write well? Poorly? Who struggles to communicate their thoughts?
2.       Which students invested themselves in the writing task? Who sort of blew it off?
3.       Were students able to stay on topic or did they meander all over the place?
4.       Who didn’t write anything at all?

By the end of class, I have a pretty good feel for the class as a whole and for my individual students. I’ve already discovered some potential challenges I might have with each class and I’ve begun thinking ways I might structure each class to help with those challenges. Tomorrow, when we talk about class norms, routines, and expected behaviors, I already know where I might need to focus a little differently with each class. I know which of my classes are more social, which might need more prodding during discussions and which classes have students who need a little more help (and I already have an idea of who it might be best to pair them with). All in all, a very fun and productive first day activity!