Why My Kids are the Best

Today was a Monday. Last week was a crazy week, complete with a "snow" day for rain, a delayed opening for ice, a teacher inservice day, and a Career Day program. That made for an entire week with only one "normal" day, Thursday. When I walked into school today, I could see that my co-workers were dragging. No one, it seemed, wanted to be back in school this week after last week's taste of freedom. I suspected my kids would feel the same way. Thank goodness I underestimated them.

My first period class is learning how to solve equations. We're working on equations with variables on both sides. I was immensely proud of how all 20 of my kids were doing beautiful work and checks this morning. I only had to remind two kids to check their work. The students who were getting stuck were actively asking for help. This must be some sort of pre-Christmas miracle! At the end of the class, one girl spontaneously shared, "This is the first time I've ever liked math. Before, I hated it and now it's my favorite subject. My dad can't believe it because I always used to say how much I hated math." That darling earned a high five and I told her she'd just made my week!

I also really like how I had my kids do their equations today.

You know, because sometimes you just want to use a canned worksheet but you loathe their spacing and don't really see any practical reason to retype the problems.  (Does that make me a "bad" teacher?  Perhaps to some who literally make every paper their kids touch.  I look at it more as "picking my battles."  And, I've learned that I'm not very good at writing equations with a good variety of all the things kids need.  Inevitably, I leave off fractional coefficients, or negative coefficients, or negative answers, or... you get the idea.)  So, I announced to my class that I can't stand when I ask kids to write on notebook paper instead of a worksheet and someone decides to try to cram all of their work onto the worksheet, necessitating skipping steps and writing illegibly to make it work.  We wouldn't be doing that.  Instead, we put glue on the bottom and two sides of the worksheet and attached it to the bottom of our notebook page.  That left the top edge open as a pocket.  Then, we worked the problems (and checks) on notebook paper which we could fold and store in the pocket.  Happy teacher, happy kids!  This should keep lost papers to a minimum and ensures everyone is showing work.  By the way, that worksheet is ancient.  I couldn't even tell you with certainty what book it's from though I would guess Holt; my coworker ran them off for us both. 


Fast forward to my afternoon class and the kids are doing some classwork on exponential functions; nothing too inspired, really. I reminded them that page 35 in their ISN would be useful in completing the classwork. As I circulated around, I stopped and asked students how the work was going. One pair met me with a chorus of "It's hard; it's confusing!" These girls are very capable but they are so scared to make a mistake that they get in their own way. We had a conversation around the idea that they're going to have to do some things that are challenging if they want to continue to learn. That means they're going to have to get some things wrong here and there. Each time they get something wrong and struggle with it a little, they're learning. "You and I, we've been told from a young age that we're smart by our parents and teachers who love us very much. Unfortunately, that's set us up. Now, we think that we won't be able to be considered smart if we get something wrong." (The girls nod.) "That's really unfair. We need to think of ourselves as hard working and be proud of ourselves for giving full effort. We can work hard no matter how easy or difficult the challenge in front of us is, so it's something we can control." The girls agreed and they got to work on the problem that they had just a minute earlier said was, "confusing." A few minutes later when I came by again, one of them was proud to show me her correct answer. She said, "These notes are really useful. I saw the connection between the question and what we had written here and here on the notes," gesturing to different parts of a foldable we'd completed earlier in the unit. Award one point to Jo Boaler's "How to Learn Math" and one point to ISNs!

Why are your kids awesome?

 Mathematically yours,
Miss B

Today, in 7th Period...

For the past several weeks, my 7th period class has been increasingly frustrating to me.  The students are supposed to enter the room, get their warm-up papers, and work on the five daily problems independently while I take attendance, check homework, and give some assistance to those who are struggling.  This takes about 10 minutes on most days.  Recently, though, the students are being less and less independent.  They're trying to ask each other for help, comparing answers, and some are blatantly copying from others. On this type of task, I consider those behaviors to be cheating.  I thought most of this problem stemmed from the opportunity they had to influence our most recent seating chart.  So, they got new seats on Monday.  Today, the same problems were happening.  I stopped the kids and launched into a heartfelt lecture. 

"Raise your hand if you understand what I mean by 'independent work.'  Good.  Everyone knows that concept.  Who can describe it for us?" I started. 

"When you do your own work without your classmates' help," someone offered. 

"Exactly.  So that means that during this time, you shouldn't be talking to other students.  You also shouldn't be looking at their papers.  You shouldn't be comparing answers.  All of those things are forms of cheating.  I would like you all to have integrity.  Do you know what that is?"

"Doing the right thing when no one is looking," said one student.

"Being honest," another suggested.

"For sure.  I want to be proud of all of you because you show integrity.  That's much more important to me than your score.  Now, I know some of you are worried about your grades.  Some of you might be feeling pressure from home."

At this point, there are lots of small, quiet nods.  This is, after all, an advanced group.  These are the parents who will send e-mails the second their child gets an 89 instead of an A. 

"Look, I want you to keep your integrity.  I would much rather you earn a slightly lower grade honestly than get a higher score because you cheated.  I think your parents would agree.  If you're not sure, ask them at dinner tonight.  I want to be proud of you and for that you need integrity."

After this, they got back to work, and I had a kid who got a near perfect paper yesterday ask for help.  "But you did so well yesterday, what's wrong today?" I asked.  "I got help yesterday," she admitted.  I answered, "Thanks for being honest about that today.  Now let's see where you're getting stuck."

My next step is to develop a class honor code.  These kids are largely college bound.  I want them to see how important it is to be truthful and work hard.  If they don't learn that lesson now, I'm afraid they might learn it at a time it costs them a semester's tuition or more. 

Here's the questionnaire I'm going to use to get the conversation started.


How do you teach your students to have academic integrity?

Mathematically yours,
Miss B

Snow Day #1...

...or should I say, "Rain Day #1?"  It may have snowed for an hour or two this afternoon, but nothing accumulated.  We actually got more on Sunday despite the fact that we were predicted to get 2-4" today.  I used my day pretty wisely and managed to go grocery shopping, make a roast in the slow-cooker, put up and decorate my Christmas tree, and catch up with my great aunt on the phone.  It was lovely.

Tomorrow is scheduled as an inservice day.   Friday is "career day."  That means my teaching week is comprised of a 2 hour delay on Monday and a full day on Thursday.  Anyone want to take bets on how motivated to work my kids will be on Thursday? I'll be sure to do some extra active things on Thursday to keep things going smoothly. 

Mathematically yours,
Miss B

Derailing for the Sake of My Students

We've been working on equations slowly since sometime in September in my Math 8 class.  To be successful with equations, we took a detour through integers.  Now, we need to refresh our rules for fractions and decimals as well so we have the whole arsenal of rationals at our disposal since most kids are currently screeching to a halt if they see anything that's not an integer.  My initial plan was to give the kids foldables, fill in the examples, and move on. 

Last night, however, I read Tina Cardone's Nix the Tricks cover-to-cover.  Stop now, go download the FREE book, and read it now or file it for reading before January 1.  It's important.  Essentially, it's a compilation of things that teachers sometimes teach with a procedure instead of conceptual understanding and suggestions for teaching the concept from the get-go.  The thing that teachers, students, and parents need to realize is that once you build good conceptual understanding, you don't have to worry about learning a particular procedure because they steps will naturally make a lot of sense. 

With this reading freshly in my mind, I couldn't handle it when my students couldn't explain why they convert a mixed number to an improper fraction by multiplying the whole by the denominator, adding that to the numerator, and putting the sum over the denominator.  We stopped.  We modeled three and one-third.  We showed how the whole number 3 represented 9 thirds and that together with the other one-third, we had ten-thirds. 

Then next thing students wanted to do was get a common denominator.  They couldn't explain why 12 would be an appropriate common denominator in 10/3 + 3/4.  We stopped.  I projected some fraction strips and we looked for equivalencies.  Since thirds and fourths can both be written as twelfths, that is a logical common denominator.  Many kids said they'd never seen fraction strips before, so we spent a few minutes exploring how they work.  When I asked if they wanted a copy for their notebooks, I had several enthusiastic answers of, "Yes!"  

I have to tell you that we didn't even finish that one problem in about 25 minutes.  We got so into the modeling that we didn't finish even a small part of what I wanted to get done, but our conversation was rich and dug deeper into the meaning behind the fraction rules they've been trying to memorize for years. 

Here's what I see happening in classrooms that I'd like to change.  A teacher has a set number of days to "cover" a topic.  The class spends a little time on tasks that get to the heart of the concept, but not all of the students "see" it early on.  The teacher attempts to build deep conceptual understanding but time is her enemy and she resorts to tricks to help students get through the material in time for the assessment.  Later on, the students are weak in those skills because they can't remember the rote procedures and don't understand the concept well enough to develop the process on their own. Besides the time factor, we have to realize that not all students are going to pick up on skills at the same time.  I try to build in "did you know..." moments into my lessons in which I provide the background to simple math embedded in the math we're really working on.  Most often, these are "aha!" moments I had several years after first learning the material myself. 

One of these tips that I regularly share concerns graphing horizontal and vertical lines.  As a middle school student, I was forever mixing up whether x = 6 was a horizontal or vertical line.  I think that I was taught to find the x-axis and draw a line through 6, but I just remember that being quite confusing.  At some point later in high school, I finally realized that x = 6 was a way of telling me that x is 6, meaning the ordered pairs on the line have an x-value of 6.  If I could list off a couple of ordered pairs and plot them, I could decide whether the line was horizontal or vertical.  This works so well because it's the basis for graphing lines; choose ordered pairs that satisfy the equation and plot them.  This is how I teach horizontal and vertical lines now. 

Have you nixed a trick?  Let me know and I'll make sure to pass along any comments to Tina, who is still working to add to her book. 

Mathematically yours,
Miss B

The Incredible Shrinking Notecard

I learned about the Incredible Shrinking Notecard from a former colleague who spent 40 years teaching.  During her career, she taught elementary school, then social studies, then honors English.  In advance of a test on a particularly tough topic that required a lot of memorization, she would hand out 5x8 cards several days in advance of the test and tell her students that if they kept it quiet, she'd let them use the notecard on the test.  The next day, she'd tell them that 5x8 cards were obvious and she was a little nervous that they might get in trouble if someone were to find out.  So, she'd have them condense everything to a 4x6 card.  The next day, well someone might frown on the 4x6 card and the best she could do was a 3x5.  This whole story forced her students to interact with the material several times and truly pick out the important details they were having trouble remembering.


I'm teaching exponentials right now and while I think the real world application of compound interest are valuable, I'm not sold on the need to memorize the formulas as they're so specific to one application.  Here's a template for the Incredible Shrinking Notecard that I think will be better suited to math.  I won't be telling the elaborate story; instead I'll explain why this method will help them study.  The boxes are sized to fit a 3x5 card, a 3x3 Post-it and a 1.5x2 Post-it.  If you want to use those items instead, feel free.  Copies are cheap and no-fuss, so I'm probably going to use as a left-side assignment in my ISN.  I will give the kids the little Post-it for the last box so they can use it on their quiz. A special shout-out to Kathryn F. for discussing whether or not to give notes on a quiz on Twitter tonight because that discussion got me to the place of doing this in advance of the quiz instead of having an open notes quiz, or writing the formulas on the board, or having the kids who didn't memorize things flounder. 


What study skills and tips do you share with your students?

Mathematically yours,
Miss B

Find Someone Who... Understands Transformations on Exponential Functions

We're slogging through exponential functions in Algebra.  I really think there's some merit to reordering the units and teaching quadratics before exponentials because the symmetry can be useful in graphing, although the algebraic methods associated with quadratics are heavier, so perhaps I'm wrong to consider moving that unit first. That's something to hash out later.

Anyway, my students have worked through arithmetic and geometric sequences and we've made the connection that graphing geometric sequences given a positive common ratio yields exponential functions.  We've graphed a slew of these functions and analyzed how transformations occur.  We've looked at combined transformations, dissected them, and matched these to graphs.  And it's hard for the kids.  They're really doing OK for how much has been introduced in the past few days, but they're feeling like it's hard.  So at the end of one class period yesterday, I gave out index cards and asked the kids to write down a question they had or a happy statement if they were doing fine, not really knowing entirely what I was going to do with the responses I got.

I got about half of each kind of response back and I wanted to figure out how to address the kids' questions without lecturing on some things they'd already spent days exploring on their own.  It came down to eight questions after I took out the duplicates.  The questions covered the whole gamut of exponential transformations.  At first, I thought about offering them as journal prompts for a left side assignment, but I quickly discarded that because either 1) if given a choice kids would pick the easiest question for them to answer and still wouldn't understand the question they posed or 2) if required to answer them all, kids wouldn't know what to say.  A group discussion wasn't accountable enough.  I came up with something that sort of combined the above. 

I typed the questions up verbatim, only fixing obvious mistakes (like "ship" for "shift") and put them into a worksheet.  As they finished another assignment, I had the students pick up the neon green worksheet and "interview" classmates to get the answers to the questions.  They could ask one question of each partner.  The partner would give a verbal answer.  The paper's owner would write down the response, once it made sense, and the partner would initial the response.  I reminded students that once they got going, they could share an answer they got from a partner if needed because that was now something they knew in addition to whatever knowledge they started with.  Kids who collect the answers early can continue to be an interviewee to help out classmates who are finishing more slowly and they'll all get the benefit of repeating the answers to each other as a way to reinforce the concept.  It ended up being remarkably helpful to have copied this sheet on neon paper; since the students were all starting at different times, they knew they could scan the room for someone with a green paper to interview. 



Anyway, this activity needs a name, but I think it's really like that icebreaker game called, "Find Someone Who..."

Mathematically yours,
Miss B

Make your own Tarsia

Last week, my students completed this Tarsia puzzle on rational exponents and it was a hit.  The level of difficulty was appropriate and the kids were able to do it rather independently. 

In fact, they enjoyed the Tarsia so much that I decided to make some blank templates.  Last night, their homework was to design a Tarsia with any problems that involved the laws of exponents.  Today, they got some time to work in teams to verify the accuracy of their puzzles.  Then, I collected them and checked through to make sure they were in fact correct.  I found about 25% of them were perfect.  The others typically had a small mistake.  I made copies of the correct puzzles and we'll make them available for practice tomorrow.  One of the best parts is that the students have helped me out by differentiating the puzzles- some are much harder than others and I'll let the students know which are which so they can choose based on their comfort level.  I can see using this for many other concepts.  I might also make this available as an "early finisher" activity and provide a list of potential topics. 

Here are the templates.  (Yay, I've posted something to #Made4Math for the first time in a long time.) I started my students off with the triangle template due to the complexity of the exponent problems we've been working on.  The squares would be appropriate for shorter problems or for students who need an additional level of difficulty. 



How do you use puzzles in your classroom?

Mathematically yours,
Miss B

MTBoS Mission #1: A favorite problem

Hi to anyone who's visiting thanks to the Explore MTBoS blogging event.  If you haven't heard of MTBoS, it's short for Math Twitter Blogosphere which is essentially a bunch of math teachers who like to connect online and share their best resources and ideas to advance the profession.  Or something like that.  It's loosely organized and self governed, so there are no official rules!

Anyway, welcome and thanks for reading.  I've been blogging about my professional life for a little more than a year.  You can find me here at iisanumber.blogspot.com and also at my 180 blog where I try my best to put up a short post from my classroom each day.  I'm also on twitter, handle @iisanumber. 

Sam asked us to respond to this prompt as our first of eight weekly challenges:

• What is one of your favorite open-ended/rich problems?  How do you use it in your classroom? (If you have a problem you have been wanting to try, but haven’t had the courage or opportunity to try it out yet, write about how you would or will use the problem in your classroom.)

I chose a semi-open ended problem, but one I like very much.  I think I first wrote it about three years ago when it was a completely bland word problem.  For your comparison, I left that page as the third page of the document.  It harkens back to the days of ECRs (Extended Constructed Responses) in MD curriculum.  It's interesting to look back on old things and revise them!

In the problem, students are first presented with two competing movie rental plans and asked to compare them.  An improvement I made to the original problem was that I presented the data in different forms so students have to work from a word problem and a table simultaneously.  After students compare the two plans, a third plan is introduced in the form of a graph and the students are asked to make further comparisons.  Finally, they are asked to create their own plan and advertise it to the appropriate customers.

I used this task a few weeks ago after my students had worked on a quiz about systems of equations.  I liked that different students chose different representations with which to compare the plans.  It was a nice way to get a secondary assessment of how my students did on the systems unit.  I noticed that their most common issue was figuring out the equation based on the table.  Many of them erroneously chose the cost of one DVD per month as the y-intercept instead of recognizing that the monthly fee is based on renting 0 DVDs. When I noticed the error in their equation, I would ask them to verify their equation using a number of months on the table and each time they noticed their total was too high and they were able to reduce the monthly fee to the correct amount. 

The main reason I chose to write my post about this problem was a comment from one of my students.  T said to me after he turned in his work, "You know, Miss B, at first I didn't really get the problem.  But I sat and thought about it for a while and tried some things and then it just made sense and I could do it.  It challenging but not too hard."   I like to strike that kind of balance whenever I can, and I thought I should share this problem because not only did I feel like I was expecting a certain level of rigorous thinking from my kids with the task, but they articulated the same thing to me.  

If the file would be helpful to you, you are welcome to download it from box.com below. Let me know if you have any feedback that could make it better.  Thanks!


Sam's second question was all about what makes your classroom unique.  I won't go in depth with my answer since we were asked to choose just one prompt, but I think this post sums up my answer AND backs up my colleagues' assertions that I am a math nerd.   :)

Mathematically yours,
Miss B

Distributive Property and Combining LIke Terms

Thanks to Julie and Nora, I was inspired to introduce combining like terms and the distributive property to my students using some manipulatives.

I started with a grocery bag (one of the ubiquitous freebies emblazoned with a company logo), a dozen ziplocs, some buttons, some paper clips, and some cap erasers.

Like Nora suggested, I set up some ziploc bags with a few items and I made several identical ziplocs.  To make it easy for my students to differentiate between the bags from a distance, I placed a piece of colored card stock in each bag.  The set up is illustrated on the ISN page below. 

Students volunteered to come up one at a time to place items in the grocery bag or remove them from the bag.  They could only touch one kind of item per turn (so Ziplocs with yellow paper, loose buttons, Ziplocs with red paper, etc).  We started with combining like terms using just the loose items and tried three practice rounds.  Each time, I asked the students how many of each item were in the bag before we showed how to write the answer algebraically.

Then I introduced the Ziplocs to the activity.  We discussed how parentheses group items in math just like the clear bag was grouping the items.   Some of my students erroneously thought that we could show multiple identical bags by using an exponent but with some follow up questions they decided that multiplication was what they really needed.  Again, as we wrote our expressions, I had students predict the simplified expression before we wrote the work algebraically.

The real magic happened when they had a homework problem like 9[5 + 2(x + 3)].  I asked, "if the parentheses are represented by the ziploc bag, what would the brackets represent?"  They told me the brackets were modeled by the grocery bag.  "How many grocery bags would we need?"  They decided they would need nine grocery bags.

I wish I had done this activity using pennies as well.  If I had, I would have made them each worth 1 instead of assigning them a variable.  One point of confusion I saw after this activity was what to do with an expression like 12 + 5x.  Many of my students tried to make that 17x and I think we would have done well to have constants in the original lesson.


Thanks to Julie and Nora for the inspiration.  I was so excited about this lesson that I immediately shared it with my colleagues.  This is the best part of the MTBoS- great lesson ideas at your fingertips, tried out by real teachers!  

Mathematically yours,
Miss B

K'Nex Linear Programming

I love linear programming.  It's actually applicable to the real world (huzzah!) and it's multifaceted enough to keep my interest.  I get bored of math problems that I can solve mentally without much thought.  Linear programming presents something with enough layers that I have to get out pencil and paper (or Desmos!) to do some of the calculations. 

The problem with linear programming is that my students don't appreciate the layers of the problem.  They view linear programming as too many steps and too much work.  They may not fully appreciate how useful it can be, even though they can completely understand that a business would like to maximize profit or minimize cost.

I tried to address this problem today with a small K'Nex experiment.  Essentially, I wanted to give the kids the resources of a linear programming situation and ask them to solve it without the system of inequalities.  The handouts I used are embedded.  They're sized for composition books. 



First, I had students attach the scenario to their notebooks and create a table.  You can see this in the photo below. 

I gave each group a bag with the amount of K'Nex specified in the question and asked them to build combinations of "bots" and "quarks" based on the restrictions in the scenario.  Most groups latched on to the idea of needing to use as many pieces as possible, so they didn't record many pairs that had lots of left over pieces.  After about 15 minutes of building and recording, I had groups report out.  There were a couple of cases where students didn't agree about the maximum profit, but in every case they were able to find their error.  Either they used more pieces than they were given because they didn't physically build the models, or they made a simple calculation error. 

A hint if you try this: organize your bags so that a group has only one length rod and one shape connector.  I had some students who were trying to make "different bots" by connecting the pieces in different ways.  I had to review the definition of a bot with them and explain that the construction didn't make a difference as long as the materials were consistent.  I think this issue would be muddled by offering different shapes and sizes of K'Nex to one group.  It's also helpful when a piece ends up on the floor as you can more easily glance around and see which group it might have come from. 

I heard many students say they enjoyed the activity and from listening to discussions around the room, I feel like I introduced this in a way that was concrete enough that most of my students grasped the concept of linear programming before we got to the algorithm.  Yes!

Tomorrow we'll use the other pages from the embedded file to take some notes of all the steps of a different example and we'll use that process to verify our solution from today's exploration.   In my experience, the hardest part for students is choosing the variables and writing the inequalities for the constraints. 

What's your favorite toy to bring into the classroom?

Mathematically yours,
Miss B

My best tip on Interactive Notebooks thus far!

I am loving using Interactive Notebooks by a large.  The one thing that does bother me is that my kids are still not all that fast at getting things assembled.

Tonight, I came up with a simple solution to keep things moving.  Legal paper!  I've heard that other teachers like to use half sheets, but I don't think a 5.5" by 8.5" piece of paper is quite enough space for most things I want to include.  I realized, though, that legal paper would cut in half to 7" by 8.5" which just leaves a small margin of extra space when the sheet is glued into the ISN.  All I'll need to do is to format the handouts two to a page and chop them in half.  Huzzah!  Now, to find out if the school has legal paper hiding anywhere...

To give you size comparison with a regular composition book.  I didn't attach it because I don't have my model notebook at home, but it leaves about 3/8" on each side and the bottom with a bit extra up top so there's room for a title. 

Here's a KWL chart that you can print on legal paper.  Font is Arial Black which should be standard for almost everyone.  I used KG Shadow of the Night on mine, but not everyone has it installed.  :)



What's your best time-saving ISN tip?

Mathematically yours,
Miss B

Using Visual Patterns to Introduce Linear Functions

A few months ago, I found visualpatterns.org and I knew it would be useful as I started linear functions with my 8th grade students. 

Here's how I've used it.

First, we learned what functions are and practiced completing function tables given a function.  My students are weak in computational skills, so that was important to tackle before we got too deep into  linear functions.  Then, we used the steepness of stairs to explore the concept of slope.  Once we'd learned to find slope from a graph, table, two ordered pairs, and word problems, I was ready to introduce linear functions.

I had students start with pattern #2.  They built the pattern with unifix cubes and completed a recording sheet.  The recording sheet asked them to find the number of cubes used in the first six terms of the pattern and then it jumped to the 15th term.

As I circulated around the room, I saw some students were building to get to the 15th term while others noticed the numerical pattern and chose to complete a table.  I also saw several students who were off by one or two blocks on their answer.  One student had written 30 (the correct answer is 29).  We had a rich discussion which I'll try to capture here.
T: So why is the 15th term made with 30 blocks?
S: Because it's 15 and 15. (She gestures horizontally and vertically.)
T: Can you build it and show me?
S: Like this.  Student builds an L shape with approximately 12 blocks on the horizontal and 7 on the vertical.
T: Would you explain how you made that?
S: I just added some blocks on.
T: Why did you add that amount of blocks?
S: I don't know; I just added some.
T: OK.  Did you notice a pattern happening when you built the first four objects?
S: You put one on each end.
T: Could you try that here to get to the 15th term?
S: Yeah.  Student builds correct 15th term as we count out loud which term number she is on.
T: So, how many blocks did you use?
S: 30.  (Student answers immediately without counting the blocks used.)
T: Could you count them?
S: But there's 30.
T: Please count them so we can be sure.
S: OK.  1, 2, 3, ..., 29.  That's not right.  1, 2, 3, ..., 29.  Hmm.  Student picks up another block and adds it to her construction.  30!  There's supposed to be 15 and 15. 
T: Why are you changing what you built?
S: Because it's wrong.
T:  Before we decide that it's wrong, let's look at a smaller object.  Look at the third term.  How many are there?
S: 6. (immediately)  Oh, no.  There are 5.
At this point, the student sitting across from her can't take it any longer.  He interjects his observations.  
S2: Look, if you take the L apart, there are two equal lengths with the one block in the corner as a connector.  Student 2 models what he's describing with the blocks by taking the L apart and showing Student 1 that the sides are equivalent if you remove the block in the corner.
S1: OK, but why isn't it 30?
S2: Because you have to have that corner piece, too.  
T: Have you noticed any mathematical pattern in the first few terms?
S1: It's adding 2 each time.
T: And do you notice anything about the kinds of numbers that are in the table?
S1: They're all odd.  So 30 couldn't be on the list.

Our conversation actually went on a bit more, but I wanted to capture this part because I thought it was really good.  I was a bit shocked at how difficult this process was for Student 1.  I was also pleased by Student 2's observations as I suspect he'll do well as we make the connection to slope and y-intercept next week.  I think next week I'm going to ask Student 1 to use a new color for each term so she can see clearly what she has added in each step.

As we wrapped up this pattern, students graphed their data points.  I asked them what they noticed.

• It's a line.
• It's positive.
• It's a function because it passes the Vertical Line Test. 

No one said, "the slope is 2" but they'll certainly catch on to that next week as we examine a few more patterns and write down our observations. 

Edited 7/23/15 to add my recording sheet:



And a second version I used with Algebra I:

 

Thanks to Fawn for offering such a helpful resource! 

Let's see if I can make this coherent...

We're now four weeks into school and I've been using interactive notebooks with my students for the last three weeks.  They are new to me and to my students, so I expected some growing pains. 

Today, two of my students told me that they prefer the way they took notes last year (copious notes on looseleaf).  I'd be lying if I told you I wasn't a little crushed.  I left out my disappointment when I talked to them about it.  I asked why they preferred the notes last year and it seemed to boil down to the fact that they like direct instruction with lots of examples.  I thanked them for their input, said I would take it into consideration, and told them I appreciated them talking to me about it because I know it takes a lot of courage for middle school students to have that kind of conversation with a teacher. 

I have to say that I don't disagree with the girls that a few more examples over the most recent topic (solving systems of equations) would have been helpful for some students.  The thing I'm now trying to figure out is how I make that work with the interactive notebook.  I don't want to have students take lengthy notes only to later condense them in the notebook because that would take so much time.  I also don't want to do a few examples on a foldable that is saved and a few others on a sheet of looseleaf that won't ever be seen again. 

My other issue with this comment is that my school is trying to ever so gently move away from direct instruction.  While it has its place, we know that there are lots of other ways that students learn and express their knowledge that are much more dynamic and engaging. 

If you use Interactive Notebooks, how do you find the right balance between overly condensed notes and lengthy notes?

Mathematically yours,
Miss B

Notebook Check

It's time to start checking the contents of students' Interactive Notebooks.  My plan is to check them roughly every three weeks beginning this week.  I have just shy of 80 students, so I'm planning to check 20 notebooks Monday through Thursday during a normal notebook check week and to get any stragglers on Friday.

I shared a rubric during the summer that I'm using with my classes.  Today, I guided my students through their notebooks and pointed out the portions that needed to be complete prior to my checking the notebooks.  Several students realized they had a few portions to complete or improve before their first grade. Tomorrow, we're going to all mock grade our notebooks before I collect any.  I want the students to grade their notebook and then see if my grade matches theirs. 

One expectation that I have for my students is that if they do not earn full credit for completeness on a notebook check, they must catch up prior to the next notebook check.  In other words, if they didn't have pages complete for notebook check #1, those pages will roll over into notebook check #2.  Double jeopardy?  Perhaps.  However, I feel like it's the best way to truly hold students accountable for staying on top of everything. 

To help with this notebook check process, I posted this sign in the classroom.  The reverse side says "next week" so I can post it prior to the notebook check also.  The main thing here is to include the page numbers so students have direction as to what they need to look over prior to notebook checks. 

This is my #Made4Math Monday entry.  I think it's been three or four weeks since I've posted one, so I'm happy to have something to share, however small.  Want the file?  Here it is ready to print. 

Mathematically yours,
Miss B

Day 11- Now for something totally unexpected

When I created my list of left-side assignments this summer, I assumed that some would be more popular than others because kids would assume that they were "easy."  I did not expect that the first time I assigned a choice of left side assignment that I would get items of as high a quality as I did. 

Here's a song about Standard Form, to the tune of Justin's Bieber's "Baby." 

I was also impressed by a couple of comic strips, a set of flashcards, and by the student who typed his page-long assignment with one hand since no one was home to help him and he is in a giant splint following a sports injury. 

Get their attention!

In my last post, I noted that many of my students this year are "orange" personality types and kinesthetic learners.  Since my classes are already larger than normal and I now know I've got some big personalities, I recognized the need to get a good "attention getting" method into place.  I don't have the loudest voice, so calling for their attention isn't quite immediate and I hate using bells!  Kagan recommends a two-part chant and lots of teachers have success with a clapping pattern.  I have always felt awkward trying to use something like this in 8th grade, but I'm going to get over it! 

I've heard the chants like, "One, two, three, eyes on me" but they seemed too elementary.  The best one just popped into my head yesterday!  I'll use that famous military cadence, that goes, "I don't know but I've been told..." I'll chant, "3 point 1 4 1 5 9" and the kids will continue in the same cadence, "2 6 5 3 5 8 9." 

Not only will I get their attention, but they'll memorize 13 digits of pi in the mean time! My neighbor in the adjoining classroom said it sounded good through the wall- she thought I was doing a song! 

Follow up to Multiple Intelligences Survey

Yesterday, my students completed their Multiple Intelligences Survey but we ran out of time to actually discuss the results.  Today, we got to that part.  One of the points I wanted them to understand was that a low score in a certain intelligence doesn't mean that they will automatically be unsuccessful in that subject.  Rather, they will have to be looking for opportunities to express what they know through the other intelligences.  Kids who have a low mathematical score can be successful in math class, too. 

Visual-Spatial?  Draw diagrams to get your point across. Build models.  Use manipulatives.
Verbal-Linguistic? Have a discussion.  Explain.  Write sentences. 
Musical?  Sing a song.  Tap out the math to a beat. 

You get the idea. 

As we wrapped up, I asked the kids if any of them discussed what we had done at home.  About 1/3 said they had, and a few mentioned giving the surveys to friends or parents out of curiosity.  The most interesting comment came from a girl whose mother also works in education.  She said her mom is finally going to let her listen to music while she studies because it aligns with her learning style!  How cool is that?!?

Have you surveyed your students to determine their learning styles and multiple intelligences?  How did it go?

Mathematically yours,
Miss B

Learning about my classes

For the "getting to know you" portion of the beginning of the year, I thought I would focus on some things that could really inform my instruction this school year.

I collected some great ideas from the MTBoS, of course!  In the spring, I took a class on personality and I read "Showing Our True Colors" which helped me understand the behaviors of many of my students last year.  By the time in the year that I took the class, I had observed my students enough to know which color family they belonged to, but this year, I thought it would be nice to start the year with that info.  Thanks to Sarah at Everybody is a Genius and Sarah at Math Equals Love for sharing their ideas and links on the topic as well as learning styles and multiple intelligences.  I took the surveys and summaries and condensed them into a little booklet (three front and back pages folded in half).  We worked through it today.

Here's how I did it.  I introduced the notion that I wanted the students to know how to help themselves when it comes time to study and I want to be able to teach them in the ways that work best for them.  I pointed out that when the time comes that some of them need individual help, I'll be able to give them a method tailored to their needs if I know how they learn, think, or show their skills.

We started with learning styles because I thought kids might have had at least some background knowledge there.  I explained that some of us learn by hearing, others by seeing, and still others by doing.  They took the survey.  Then, I regrouped the students so they could sit with other people with the same learning style.  I asked them to read the provided tips and tricks for that learning style and to discuss how they had used those before or if they wanted to try any that were new.  We shared out.  Interesting, the visual learners in one class were quick to ask if they could write notes on the paper.  I pointed out that they asked to do that because they're visual learners! 

Next, we did the true colors personality questionnaire.  It's the hardest one for the kids, so I put it in the middle.  If I'd done it first, they would have been overwhelmed.  If I saved it for last, it might have been a struggle.  We modeled how to fill out the chart.  They had several words that they weren't familiar with but the nice thing is that there were lots of familiar words that they could lean on even when one word in the group was unknown.  As it turns out, "impetuous" was on the test they'd just taken in language arts.  Someone asked what it meant and I explained that it meant making decisions without thinking of the consequences.  A cheer erupted- most of them had gotten it right on the test!  Once the students had completed that questionnaire, I had posted colored papers around the room to correspond to the true colors.  Each kid found his group, wrote his name on the colored paper so I could keep a list, and they discussed if they were like the description.  The crazy thing is that 39 out of the 58 kids I teach in the afternoon are orange.  Oh my goodness, we are going to need to move and be very active this year to learn!  The funny thing is that even on the first day, I could tell I had a lot of energy in the afternoon groups!

Finally, we did the MI survey.  We didn't get to the analysis yet- that will be tomorrow.  We did fill out the graph shown in the picture below.  Tomorrow we'll talk about MI and learn our strengths there.

I'm so glad I did this!  I feel like it's going to be such a time saver as I plan lessons this year because I'll know better how to approach them.  Hopefully this will turn into less kids needing reteaching less often because I'll meet their needs the first time.  I'm also super happy that this year I decided to implement an interactive notebook.  I think it will appeal to my orange students and all of the kinesthetic learners. 

During the last period of the day, my principal came in and we got to talking about what a nice group of kids I have in that class.  I told her how surprised I was by their learning style results (about 50% auditory, 20% kinesthetic, 30% visual) and how utterly shocked I was that so many of the kids in Advanced Algebra are orange.  She's gold, so her eyes bugged out a little at those numbers, too!  She really liked what I did in class today; she even asked to take a copy of the booklet with her.

Here's a look at the front of the booklet that I made.  The front cover is courtesy of Sarah from Everybody is a Genius. 

Tomorrow's the big day!

Summer has come and gone and tomorrow will be the first day of school for my new 8th graders!  This year, I have 21 students in Common Core 8th grade math, two groups of 29 for Advanced Algebra I (really Common Core Algebra I), and a yet-to-be-determined class list for French I. 

I'm excited and ready, but I'm already looking forward to a nap! 

Measures of Central Tendency Cootie Catcher Update

The most popular post on this blog came out of a whim to make a cootie catcher for an activity with my homeroom last year during the first week when we get our homerooms for extra time.

Since then, people have asked for a printable and for rules for the "game."

First, here's a scan of my cootie catcher.  No, it's not typed or fancy, but at least it's filled in!


Second, the rules of the "game."

Give each student a cootie catcher.  Partner kids up.  One person chooses an outer section, the other spells its vocab word opening and closing the cootie catcher with each letter.  The first person then chooses an inner section and the second spells that color, again opening and closing.  This time when it's opened, the first person must choose a color and calculate one of the measures of central tendency, explaining it to his partner.  If they agree, they record the answer and switch roles.

I've also done this with simplifying radicals for a different class.  I made two versions on two colors of paper. Kids worked all of the problems independently, checked them on an answer key. This allowed for some coaching among the student and differentiation of levels.

I hope this file is a help.  Sorry it's taken a year for me to finally get it scanned and uploaded!

Officially back to work!

It was the Back to School kick off today at work.  We had our district wide meeting, complete with a visit from our State Superintendent.  Her visit meant a lot to me; we're a very small county compared to others in our state and not located close to the state offices, so it's unusual for us to get that kind of attention.  The central office had also organized a wellness fair for us.  Frankly, that just added to our stress because we wanted to get to our schools to work, but I have to admit that it was well executed.  At the end of the day, we met with our grade level team to discuss some of the mundane back to school items such as schedules and locker breaks.

I went back to school at 3 to do some work.  My room is so close to being done!  Tomorrow for sure it will be; I'll stay until it is.  I will need Thursday for curriculum work!

Here's a peek at my classroom library.  I bought a "real" bookcase last year to replace some very pathetic plastic crates.  It makes me happy that I can offer a good number of choices and have a dozen or more math-specific books that the kids can choose.  Of couse, those are the ones I featured on the top!

What are your favorite books for middle school math classrooms?

Mathematically yours,
Miss B

It's no wonder I always feel busy!

On Friday, I was talking with a colleague about the upcoming school year and the changes we're going to face, especially in regard to additional record keeping.  She said she was planning to make herself an afternoon checklist so that she would be sure to have everything done before she left the building.  She joked that it was because she was getting old, but I told her I could also benefit from such a list.  

This afternoon, I sat down to type out a list of the things I do after school.  Note that actually planning lessons and grading papers don't figure into this list.  I aim to do those things during my planning period or at home.  This list is just the other aspects of my job.  While I was at it, I also made my morning routine list.  I get to school about 45-55 minutes before the students arrive, so there's also time then to grade a small stack of papers or pull together some ideas for an upcoming lesson plan.  

Morning Routine
 Print lesson plans and papers to be copied
 Check mailbox, sign in, and deliver copy requests (We don't make our own copies; we have a staff member who runs the photocopiers.)
 Update boards
 Check e-mail
 Deliver TAP work (TAP is our in-school suspension)
 Unlock calculators


Afternoon Routine

During waves: ("Waves" are our dismissal groups.  We have 4 waves and the process takes 15+ minutes.  I typically have a handful of kids in my room who will be able to help with some of these tasks.)
 Change the date
 Lock calculators
 Attendance in Power School (We do this every period, but I have a tendency to forget the last class of the day every now and again.)
 Check e-mail
 TAP list, gather work
 Log parent contacts
 Photo 180 (This should be done during the day, but I'll have a back up reminder if I forgot earlier.)
 Label and file missed work (This should have been done during the day, but I'll also collect work for students with upcoming absences at this time.)

After waves: (I'll continue the list above and add in these tasks that aren't well suited to completion during dismissal.)
 Check mailbox
 Math Maintenance
 Daily grades in Power School
 Weekly files up-to-date
 Student files up-to-date

What does your routine look like?  

Mathematically yours, 

Miss B

Guess Who- Linear Functions

I was hopping around the MTBoS this afternoon and I happened to reread a post by Sarah from several months ago in which she listed some thrift store/garage sale finds she was planning to use in her classroom. Among those finds was a Guess Who? board game which reminded me that I had purchased the same thing a long time ago and hadn't yet remade it into a math game.  

Guess Who? was a staple in my house when I was a child and I can remember toting it to many a babysitting gig, too.  It was perfect as a two-player game since I was an only child and just had to find one other person to play. I always wanted to be Maria because she looked the most like me, even with the funny green beret, and I learned a lot about probability by calculating the best questions to ask in order to eliminate about half of the people at a time.  

Sorry for doubling up on Made4Math this week, but I couldn't bear to wait for next Monday to write my post after making this beauty!  

Here's what my $3 at Goodwill and several hours of my evening got me:

Truth be told, the red one's not done yet.  :)

The family that owned this game before me must have been a tiny bit compulsive. ;) They had glued the character cards to the yellow flippers. I pried each one loose and then slid my card in along with the character card. The back of the flippers show the question mark design of the Guess Who cards and I was able to use cheap paper instead of thick card stock.

If you want to make your own set on another topic, just measure the cards and make a table with cells that size. I found these cards were 1 1/8" wide and 1 3/8" tall, but be sure to check if you have a different model of the game. The one I had as a kid had much larger cards.  Before I had this game board, I made a paper version using file folders for linear inequalities in my first year of teaching and it has been a classroom staple.  I made it all by hand, so I might not be able to blog it for a while.

I'm sharing the files I made below. Included are directions for how your students could play this game even without the game board. After all, this is cute, but who is going to buy a class set, right? I figure I'll make this one cute, draw a couple of kids names to play with this set, and let the rest of the kids play the modified way.  Now that I know I can modify them, I'll pick up another set or two if I see them at Goodwill again because I'd like to make one for quadratic functions for my Algebra class.  





This game ties in nicely to a couple of 8th grade standards:

• CCSS.Math.Content.8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
• CCSS.Math.Content.8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

How have you repurposed games in your classroom?

Mathematically yours, 

Miss B

Problem of the Week: Absences

I'm not sure this will become a regular feature, but I've now written two posts that explain how I want to deal with an issue of classroom management.  I sort of like the title "Problem of the Week" but I suspect these won't be weekly, even if I do feature this regularly.  Let me know what problems you'd like me to tackle.  :)

This post will focus on how to handle make-up work for absent students.  Currently, I have a hanging file organizer for each class that contains handouts for students who were absent.  Read more about them here.  I like this system and it's made it much less likely that I need to sort through files to find papers for children.

Why does this system need to change?  Well, I realized that it works well if the make up work is all on handouts.  But what if the missing work was from a textbook, used manipulatives, was a game, etc?  It's near impossible to put those items in the pocket.  I realized a little "while you were out" form would greatly improve my communication with students who had been absent.

I'm not a paper work fan.  I do know, however, that there are always a few helpful students who want some extra responsibility.  I'll let those students fill out the forms based on our daily agenda (always posted on the chalkboard) and collect the day's handouts for the absent students.  At the end of class, they can place the papers and form in the class file.  I hope this will foster a spirit of helpfulness in my class.

Here they are as an editable Word doc.  It's this week's #Made4Math!


No cute fonts or anything today- my school-issued laptop died yesterday morning and  I suspect it needs a new hard drive again (this happened in December, too).  For now, I'm making do with my 6-year-old dinosaur of a PC until at least tomorrow and realizing how unaccustomed to PC I've grown in the past 5 years since I started working in a district that only uses Mac. The timing on my poor computer's demise couldn't have been much worse since teachers report back to school on Tuesday and I know our tech office is probably being bombarded with requests from all directions.  Say a prayer that the tech guys will be able to resurrect my computer and its files once again.

Mathematically yours,
Miss B

Fishy math in NBC's The More You Know about Graduation Rates

I've always had a soft spot in my heart for NBC's "The More You Know" public service announcements because they give short messages of encouragement which are a great break from typical advertisements.  When I saw this PSA, featuring Al Roker of Today, on Sunday during Meet the Press, I was vacationing with my family.  "What a great math problem to share with my classes this year," I exclaimed to my father.  He couldn't understand what I was talking about.  Watch for yourself and see if you took from it what I did.



Did you catch the math in there? "If we don't double the number of kids graduating from high school in the next 8 years, our country won't be able to compete globally." My knee-jerk reaction was, "Does he realize that's impossible?" We're already well above 50% of our students graduating. Take this article from NEA Today that cites the graduation rate at 74.7% in 2010.*  Doubling that, we'd graduate nearly 150% of the eligible students in a given year.  That's some fishy math. 

So, perhaps the answer here is that we need to look at the actual number of children.  If the birth rate is increasing significantly, the math could work out correctly.  I looked up the number of births in the US in 1992 (when students who graduated in 2010 would have been born), 1995 (2013 graduates), and 2003 (2021 graduates, "8 years from now").

1992 (class of 2010): 4,084,000 births
1995 (class of 2013): 3,892,000 births
2003 (class of 2021): 4,089,950 births

We can see that the birth rates dipped slightly in 1995, but are quite close in 1992 and 2003.  Let's take those children born in 1992.  Since 74.7% graduated:  4,084,000 births  • 74.7% = 3,050,748 graduates.  Unfortunately, I wasn't able to find graduation rates for years after 2010.  If we assume that graduation rates stayed relatively constant over the past three years, 74.7% of 3,892,000 births = approximately 2,907,324 graduates in 2013.  If we double this as Mr. Roker suggests, we'll need to graduate 5,814,648 students in 2021, which amounts to 1,724,698 more children than were born in 2003. 

What about immigrants?  Surely we have children graduate from American schools who weren't born in the USA.  Using some data from this site, I found that there were 40 million immigrants in the US in 2010 of which 6% were ages 5-17.  That equates to 2.4 million school aged immigrants or roughly 200,000 per grade.  If they all graduate, we still need to find 1.5 million additional students to graduate in order for the math to work!  It seems that my initial reaction was correct: there's no way to double the number of students graduating from high school in the next eight years.  Let's strive to increase our graduation rate and continue to reduce the achievement gap that we've been whittling away at for years. 

Going back to the original claim, I'd like to know what the threshold is for the USA to "compete globally."  Are we aiming for inclusion in the top 10?  Top 5?  First place?  I wasn't able to find that information on the NBC website.  You can compare high school graduation rates from around the world at this site.  Currently, Portugal and Slovenia are tied at 96% with the highest graduation rate and the USA ranks 21st.  If we were able to reduce the number of dropouts by half, our graduation rate would be about 87%, good enough for us to be tied with Hungary for 13th place. 

While I'm criticizing the math offered in the first sentence of the spot, I find there's a lot of truth in the rest of the spot and the text on the website below the video.  We do need to provide our nation's children with qualified, capable teachers.  Not only do we need to recruit new teachers to the profession, but we also need to support veteran teachers.  So while this clip touches on some valid points, I'd like to see the first sentence revised.  I suspect the good people at NBC meant, "We must decrease by half the number of students who don't graduate from high school on time."  Granted, that might be too verbose for a 15 second spot, but I'd still love an attainable goal!

Mathematically yours,
Miss B

* This Bloomberg Businessweek article lists the graduation rate as a percent of freshmen who graduate on time and has a nice graph to show graduation rates over time.  I won't be using 78% as I believe it excludes children who drop out prior to high school.

Ch- ch- ch- changes

I spent the last week vacationing in San Diego with my family.  We enjoyed the weather, the zoo, the U.S.S. Midway, and much more.  As soon as I got home today, I wanted to head over to school.  We weren't allowed in our rooms until this week, so I wanted to get in there as soon as I got home to get a handle on what I need to tackle in the next week!

I found a few changes are under way for 13-14.  First of all, a new interactive whiteboard system was hanging on the wall.  Surprise!  I had a SMARTboard that never truly cooperated with my computer, so I called it the "dumb board" and used it as a screen mostly.  After countless failed lessons ("OK, everyone, it looks like my computer's frozen, so I'll just switch over to a paper copy and the document camera..."), I threw in the towel and I don't think I used it once last year.  It was about 8 years old, so I suppose it was time for a modern replacement.  I just didn't know I was getting one!  Now we'll be trained next week how to use these darlings.  I'm hoping we get some new software too; the SMARTnotebook software was never my favorite. 

We're becoming a PBIS school, so we're going to have a school-wide "acknowledgment" system instead of grade-level incentives.  It sounds really promising, taking the better aspects of what we did before and making them consistent throughout the school.  I think we'll be getting rid of our grade-level economy as it would be largely redundant.  That's a bit sad, but it had its flaws, so I'm happy to try something new. 

Oh, and I totally rearranged my classroom.  I moved my desk to a different corner, put some cabinets in different spots (they're large and on wheels), and still have no idea where my document camera should live.  Right now, I think I want to try to keep my old projector to use with it so I can project from my computer and document camera simultaneously.  Good idea?  Bad idea?  I'd love input. 

Other big things on the horizon for 13-14 are:
1. NBCT process
2. Teaching the new Common Core for 8th grade math (and refining the CC Algebra I course I taught last year)
3. Implementing Interactive Notebooks for the first time
4. Continuing my role as STEM representative for my school and presenting follow-up inservice on STEM/PBL to the rest of the staff. 

Bring it on, 13-14!  

Mathematically yours,
Miss B

180 Days

I just saw a fun idea over on Twitter and I'm going to (try to) jump on the bandwagon this year, along with everything else I'll be doing in 13-14.

Much like the 365 bloggers or Project Life scrapbookers, I'll be posting once a day for the 180 days of school.  You can expect lots of these to be just photos with minimal captions.  I'll try to keep up with semi-regular posts of interesting ideas and thoughts as well.  To see all of my 180 posts, just use the tab at the top of my blog. My first day of teaching is August 26th, but I might start with a few sneak peeks of my classroom the week prior. 

Based on suggestions from a few other bloggers, I'm starting an additional blog for these 180s so they'll be easy to view.  You can find it here: iisanumber180.blogspot.com.  Come on over and follow it so you can have a look inside my classroom everyday. 

Several other tweeps are going to do this as well and I'll add links to their 180s below.  If you're joining in, leave me a comment with a link so I can add to this list.  Also note what subject/grade you teach if it's not clear from your title.  Thanks!

170ish Days of Math (Out of the Zone)
180 days of Math Post-its (Teacher Leaders)
180 days of Geometry (Crazy Math Teacher Lady)
180 days (Restructuring Algebra) 
Peek Inside my Classrooom (druinok)

Problem of the Week

My Problem of the Week is how to handle when students all finish at different times.  It's inevitable, but only now am I finally getting a system together to handle it.  Read my last post for details. 

This post is all about my new Problem of the Week.  I think I tried something like this my first year, but it was more like a problem of the month, hardly anyone ever attempted it, and I might have abandoned it after 4 months.  Not a win at all!  I'm coming back with a better plan this time around.

First of all, I'm making a set of 40 problems (and my answers) this summer.  No need to search for them mid-year.   I've collected some interesting problems from Mathcounts and Exeter, along with a few other sites.  As I'm thinking through this more, I think I'm going to need some open-ended questions to really make this take off, so if you have good sources, please let me know. 

Second, I've totally rethought the process.  See, I could have kids do the problems on their own, turn them in to me, wait for me to check them, tell them if they're right or wrong, and move on.  Who does most of the work in that scenario?  Me.  And goodness knows I don't need another stack of papers to check!  Who should be doing all (or most of) the work?  The kids.  Enter the new system: each week, I'll post a new question to the POTW bulletin board area.  Students will be encouraged to write up their solutions and post them to the bulletin board themselves.  Then (and this is the part that I'm most excited about) other students will be encouraged to respond to the solutions posted and tack their responses to the board.  They can ask questions or make comments.  If I can get it to take off the way I envision, there will be a mess of notebook paper surrounding the question.  (Construct viable arguments and critique the reasoning of others, anyone?)  On Friday, we'll tear down the week's work and start fresh on Monday.

Third, I want this "discussion" to happen among my classes.  Currently, my school groups students into homogeneous classes for reading and math.  The students know this.  They also know which teachers or classes are "high" and which are "low."  I once had a student tell me, "You know I'm not good at reading because I am in Mrs. ___'s class."  I teach a middle-low group (8th grade math) and the two highest math groups (CC Algebra I).  I'd like to have these students conversing about math via the POTW board so that the students in a lower group see that they can contribute just as much as the students in the higher classes. 

Do you use anything like a problem of the week?  How does it work in your classroom?

Mathematically yours,
Miss B

What to do with the early finishers?

Let me start by saying that even writing this is making me cringe.  I’m going to share what I perceive to be the most troubling problem in my classroom and what I’m planning to do to combat it this coming year.  Your input is valued and appreciated!

I’ve gotten better at teaching over the past five years, but there are still some things that I know I need to work on to make me feel like I’m doing as good of a job as my kids deserve.  One of those things is a better plan for kids who finish early or late compared to the rest of the group.  Here’s how it goes down all too often:

Ted doesn’t really need to show his work on these problems.  He does the math in his head and understood it from the get-go.  Racing through the assignment, he makes a calculation error or two, but conceptually gets it and finishes when most of his classmates are just about halfway through.  I engage Ted in conversation about the work when he lets me know he’s done.  I help him discover his errors and try to delve deeper into the meaning and application of what’s been done.  Children who aren’t yet finished have questions for me, and Ted picks up a book to read, helps a neighbor, passes out graded work, takes a bathroom break, or gets started on homework.  Or in the case of some students, Ted gradually becomes a minor distraction.    

No matter how great the earlier part of the lesson was, this is not how I want Ted to spend his time in math class.  I want him to be engaged with the material the whole time.  Other teachers at my school seem to get around this time inequity by assigning lengthy packets every week or two.  Students who finish classwork ahead of their peers then work on the packets while those who need more time to finish classwork end up taking the packets home as homework in addition to the daily assignments.  I don’t see this as a solution because the inequity is shifting to the home and the work in the packets isn’t requiring much application as they’re usually the joke/puzzle worksheets.  

This is one of the issues that has been on the back burner because I could sort of justify "it's only a few minutes" and because teaching five different courses plus a variety of interventions over the past 5 years didn't leave me gobs of time for solving this problem in a way that would work for me.  Getting this fixed will help me feel like I'm making the transition from "novice person who tries to teach a lesson" to "maybe kinda sorta a real teacher."  My beloved college professor asserted that one can teach a class, but one is not truly a teacher for at least seven years.  The closer I get to that magical number, the more I understand what he meant. 

During this, my sixth year, I’ll be making a few subtle changes to alleviate as much of this early finisher as I can.  I’ve made a “When you’re done” poster set to help guide students to appropriate and meaningful things that they can do when their work is complete.  It's hard to believe I didn't have something like this before, really.  You're welcome to download it in either Word or PDF.  As always, I use Noteworthy which makes Box get the pagination wrong because it changes the font of the Word documents, so the PDF is ready to go but the Word doc can be edited to suit your classroom.  

As you can see, some of the choices are based on the Interactive Notebooks I’m starting this year; I expect that students will use the INBs and add to them during these “extra” minutes.  I’m also halfway done a set of problems for my “Problem of the Week” bulletin board.  They’re a compilation of problems from Mathcounts and Exeter along with a few other sites.   More on the Problem of the Week in this post.  I tried to keep most of the items to a higher level than just "do an extra practice worksheet."  There is the expectation that they catch up on anything they might owe me, but after that the tasks are open-ended and higher-level. 

I also realize that this problem would be largely addressed by shifting away from the algorithm-practice-repeat method.  I’ve been working over the past two years to incorporate more inquiry-based lessons into my classroom but I’m not doing these every day all the time.  Practice will continue to have its place in my classroom and while it does, kids will need varying lengths of time to complete that practice. 

It’s hard to write a post that’s self-critical, but in doing so I feel like I’ve given myself a clearer understanding of what exactly the problem is, why I feel it’s a problem, and how I can start to change it.  Pretty good professional learning for free, if you ask me!  Thanks for reading and please let me know if you have other ideas for engaging those early finishers. 

Mathematically yours,

Miss B