My kids wrote a page about one math problem...

...just because I said "prove it" instead of "tell me why."  My directions were that simple, and they took 10 minutes to really dig in and do a great job. 

Yesterday, I used a matching activity from Flamingo Math to have students match piecewise functions and their graphs.  I left off the domain and range aspect because I haven't taught interval notation and I wasn't ready to focus on that aspect quite yet.  The kids worked in partners to sort out the cards.  I didn't make them record anything.  When time was up, we discusses particular graphs or equations that gave them trouble.  (One note: if you go download the activity, which you should, card E1 has the incorrect inequality symbols in the domain constraints of the function, so change them prior to making your copies.) 

Today, their first independent activity was to go back to the pile of cards and select one match.  They were to glue the cards to their notebook paper and I asked them to, "prove to me that you are correct."

I was so impressed by my kids' hard work on this assignment.  Most of them ended up filling all of the blank space on the front and many of them continued onto the back.  Some of them wrote paragraphs.  Others used lots of labels and arrows to make their point.  I'm counting it as a quiz grade; they did so well after struggling with the concept a day or two earlier.

This student wrote so much...

That she used about 1/3 of the back, too.

Clearly a different approach in doing proof from the text-heavy examples above.

One thing I need to clarify: since we've been learning about parabolas and absolute value functions most recently, they're interchanging the terms "slope" and "a-value."  Sometimes, the terms do serve the same purpose, however they've never before used "a-value" for linear functions.  We use y=mx+b.  The connection they're making is great; their terminology needs some refining. 

Have you ever had a lesson or assignment that had kids doing awesome work beyond your wildest dreams?

Mathematically yours,
Miss B

Quadratic Catapult!

My students impressed me SO MUCH today!  I am just so excited by the project we're working on and how well they've done so far.

I gave my students a table of available supplies and a budget of $50.  At the end of last week, they previewed this materials list and I showed them a Powerpoint of a variety of photos of catapults constructed from these materials.  I wanted them to do their own research, but barring me checking out mobile labs and supervising web browsing, that wasn't going to happen in school.  Too many of my students don't have internet access at home for me to assign anything for homework that requires the internet.  My pre-selected photos actually worked well because it gave us an opportunity to talk about how certain designs worked. 

Material	Limit	Cost for one	Need	Cost
Plastic Spoon	1	$10
Masking Tape	3 feet	$5/foot
Rubber Band	6	$2
Popsicle Stick	10	$3
Small Cup	2	$3
Cardboard (approximately 8”x10”)	2	$4
Wooden Clothespin	2	$5
Wooden Pencil	4	$4
Staple Remover	1	$25
Paper Clip	4	$2
Binder Clip	4	$2
Total

They started off by spending a minimum of 10 minutes planning their design before I let them "purchase" materials.  Construction was full of redesigns, and all but one group worked together well to solve the challenges they faced.  By the end of the hour we spent on the project today, all groups had a working model that they had tested at least a few times.  (Photos to come)

For those of you wondering, the approximate teacher cost for this project (for 50 students in groups of 3 or 4) was about $15, though you likely have most of the materials in your classroom already.  Substitutions are certainly possible.  No groups used a staple remover.  Few chose pencils, paper clips, cups, and clothespins.  I did want to have a large enough variety of materials that students wouldn't recreate the same design in each group.  I also had several students ask to bring in materials but I didn't allow them to do so.  I could have, and it would have increased variety, but I wanted to keep the playing field level for this project. 

One thing to note: I made a model at home just to test out my idea.  It sent the projectile about 5 feet, perfect for a classroom project.  My awesome students, however, have sent their beans flying 40+ feet (from one end of the room to the other).  It was organized chaos in my room today, but all in the name of learning.  So, if you're at all concerned about safety or the discretion that your students would use during this project, it might be good to test outdoors.  Of course, it's pouring rain for three days here, so we're testing inside and making it work.  I actually had the librarian offer her space, too, so I think we're going to try to be really quiet while we test tomorrow!

Tomorrow, the groups will collect accurate data on the distance their bean travels and the time it takes to land.  We'll find an average for each of those data sets and use it to find the equation of the parabola.  I can't wait! 

Graphing Quadratic Functions: one insight

Last school year, I remember my students had a miserable time remembering the different ways that a function was transformed when they looked at the equation.  (Does minus 4 here mean that the graph goes up, down, left, or right?  Does a negative in front mean the parabola opens up or down?  Why would I want standard form versus vertex form?)  This year, I decided we needed some memory tricks for these along with our notes and our families of functions scrapbook. 

Cute trick #1 is an oldie but a goodie.  If the a value is negative, the graph is opening down, so "frowning."  Negative=frown, so that's should be an easy one to remember. 

Cute trick #2 is inspired by my kids last year who struggled with the idea of vertical stretch and shrink.  They so wanted to talk about horizontal stretch and shrink when they viewed graphs, but that's a bit backwards since an equation in the form y = 3x^2 has an a value greater than 1 which they understood to be an increase in size.  To that end, I did a little demo today in MS Word with clip art pigs.  I started with three equally sized pigs.  I kept the "parent" the same.  I changed the other two pigs based on a values of 2 and 1/2.  Tonight, I added the annotations and tomorrow this will be on my wall. 

 What sorts of tips and tricks do you share with your students to make graphing easier? 

Mathematically yours,
Miss B

Completing the Square- What am I missing?

Today I dove into a lesson that was entirely new to me.  I remember having to "complete the square" in Calculus but I don't think I was ever quite sure of the algorithm and I spent some time reteaching myself over the weekend in preparation for this week's lessons.  I even derived the quadratic formula from a trinomial in standard form- it was a thrill for this math nerd!

I tried to look for a way to make completing the square easy, fun, engaging- anything other than a long algorithm to memorize. 

Here's how my lesson went today:
I began by giving the students a "puzzle" to solve with Algebra tiles.  Could they make a square with x^2 + 6x + 9 while following the rules we'd already established for how Algebra tiles can touch each other?  The kids made the square easily and were unimpressed; after all, we'd been through this weeks ago when we started factoring!

Next, I gave the students x^2 + 4x + 6 and asked them to make a second square.  They worked at it for a while and then complained that I had given them an impossible task.  I was pleased to note that most kids started with the x^2 tile in the upper left and 2x to the left and bottom of this tile.  Instinctively, they realized that they would need to evenly split the linear term to form a square.  They tried other combinations after this and then tried to get creative- adding tiles, hiding tiles, overlapping tiles, and breaking all sorts of Algebra tile rules.   

I asked kids how many "1" squares would be necessary to make a square in the previous problem.  They knew it was 4.

We moved from these concrete examples to guided notes that worked through the algorithm.  In each step, I referred back to the models we'd made to reinforce how the algorithm matched what they had done on instinct.  And thus began the whining, complaining, whimpering, and near mutiny!  They wanted nothing to do with this lesson, don't see the point, think it's too hard, are scared of the quiz, etc, etc.  

I took as a sign of divine providence the fact that I had a meeting scheduled with my supervisor just after school.  We're writing curriculum for Common Core implementation.  Since she is just recently out of the classroom, and had recommended that I include completing the square in the course, I decided to ask what she would have done.  Her answer: she just taught the algorithm, plain and simple- not the answer I was looking for.  She was impressed by the work I'd had the kids do with the Algebra tiles but just kept explaining how important completing the square is in later math courses.  Unfortunately, I didn't get any suggestions to improve my lesson which was what I was hoping for.  I can't see completing the square being useful until at least Pre-Calc (and my students are in middle school, so that's at least three courses away) so I'm returning to the question I've been wrestling with since the weekend: is completing the square necessary at this point and are my students developmentally ready for it?  I question the wisdom of doing some problems just to say it's done.  I want to improve my lesson, so if you have any magic answers, please share! 

Tomorrow, we'll finish our guided notes, complete a foldable to summarize the process, and try several example problems.  Wish me luck! 

Factoring Polynomials Tarsia

It's time for Made 4 Math Monday!  I have a Polynomial Factoring Tarsia/Puzzle to share today.  This mixes all of the forms of factoring that my students have been working on in the past two weeks.  I've seen lots of Tarsia examples on Pinterest but the free software is only PC compatible and I typically use a Mac.  My PC is a bit of a dinosaur, so I haven't even tried out the software yet, so I went old school on this! 

Answer Key: You'll need to check that the pieces are in the correct rotation so that the sides actually match.  The 16 pieces form an equilateral triangle.
Row 1:            N
Row 2:        A G  C
Row 3:     J  K I   B D
Row 4: O E L  F  P H  M

My other Made4Math item this week is new tubs for each table in my classroom.  We christened them today and so far, so good.  I even had a bunch of comments from my 5th period class: "Wow, you bought us new tubs!"  "Those look really good!"  It's nice to be noticed.  The materials all fit nicely when I filled them up this morning and kids didn't need much time at all to get and replace the things we used today.  I seriously hope this is my last venture into reorganizing supplies this year since we're halfway in and on the third system! 

Factoring Flow Chart

We've been factoring up a storm in Intermediate Algebra recently.  We started with my most successful use of Algebra tiles to date.  We used the Algebra tiles to learn to multiply binomials and had moderate to good success using them.  This was the first group of kids I've taught in which the group really caught on to what the tiles meant and were proficient in using them to model.  Most groups I've had before couldn't be bothered with "playing" with manipulatives; they just wanted an algorithm!  Due to our success with multiplying binomials, I started giving the kids "puzzles."  "Can you make a rectangle with area x squared plus 3x plus 2?"  They would build it and we'd talk about the side lengths.  After a few successful ventures with all positives, I added in negatives like x^2 - 5x + 6.  Then we moved into challenges that required the use of zero pairs such as x^2 + x - 6 or x^2 - 4.  From that point, we discussed how the students were building their rectangles and what connections they could make between the side lengths of the rectangles and the polynomial they were asked to create. 

Then we moved into factoring on paper.  My next post will feature a foldable flip book on which we took notes about all the steps of factoring and the special patterns. Today I'm sharing the flow chart we're using to help guide students through the process of factoring.  We're struggling a bit with the GCF but everything else is pretty smooth sailing.  I introduced this chart yesterday to remind students to start by factoring out the GCF.  Feel free to print these off for your students if you use a similar method. 

Angles Formed by Parallel Lines Cut by a Transversal Foldable for Geometry or Middle School Math

I've taught angles formed by parallel lines cut by a transversal in geometry and in my on-grade level 8th grade classes.  Students generally catch on without much trouble, but there are often a few students who have trouble matching the vocabulary to the diagram. 

Here's a foldable I'm going to use with my students in Algebra I and Intermediate Algebra this year to practice the vocabulary prior to our state testing next month.  (Eep!  Next month is March already?)  Our students need to know corresponding angles, alternate interior angles, and alternate exterior angles.  I generally include same side interior and same side exterior for means of comparison and because they're going to need them for geometry anyway, so it makes sense to introduce the vocabulary at the same time. 

Would you like to use this with your class?  Download the PDF here and enjoy.  Let me know how it works with your students. 

Mathematically yours,
Miss B

Laws of Exponents Foldable

We've been working on radicals in Intermediate Algebra since before Christmas.  The next item on the agenda is making the connection to rational exponents (and thereby also reviewing the Laws of Exponents).  My students are fairly confident with Laws of Exponents, but I thought they might like a foldable to summarize everything in one place once we add in the rules for rational exponents and have to apply all the old rules.

If you'd like a copy of the foldable I made, click here for a pdf download.  There is a small 2x2 area on each flap where you can include extra notes or an additional example problem of your own.  The inside lists a synopsis of the rules and at least one example for each type of problem.  If you use it, I'd love to hear your comments!

I submitted this as my first entry to http://made4math.blogspot.com/.  Go over and check out the other great resources linked there if you haven't already done so. 

Mathematically yours,
Miss B

Simplifying Radicals Cootie Catcher

Back in August, I used a simple cootie catcher with my Algebra I students to help them review measures of central tendency.  I wrote the original by hand, so all I had to offer was a blank template.  The template is now available for you to download directly AND it includes folding directions.  You'll still need to write in your topics/problems/questions by hand. 

Tonight, I spent some time typing up a version for simplifying radicals.  It includes a summary of rules for simplifying single radicals as well as radical expressions involving the four operations.  There are 8 practice problems included.

You could use this a few ways in your classroom:
1. Have students complete the problems, check their work, and keep the cootie catcher as a study guide.
2. Have students work in pairs to "play" the cootie catcher game, taking turns to answer the problems.  Once both students agree that the work is correct, they can record the solution in their own cootie catcher.  They continue until all problems are complete.  This will work best if students write some numbers on the outer flaps and color the inner flaps so they're not directly choosing the problems they'll complete and there's a little bit of chance involved.   
3. Combining the ideas from above, split the class into two and distribute two versions (perhaps copied on two colors of paper).  Students solve their own problems and check with the teacher's answer key or another student who did the same version.  Two students with different colors then pair up and play the game.  As one student solves, the other student praises and coaches.  This is a version of Kagan's Rally Coach structure.  If your students need additional support, they can be teamed up with another student with the same version for the initial solving and then get a new partner for the second portion of the activity. 

We'll be doing method #3 in my classroom, but I know that not everyone is comfortable with or feels they have time for this sort of cooperative learning. 

Want your copy of two versions of this cootie catcher?  I'm trying something new to me, so bear with me and please leave a comment if it doesn't work properly.  Here's a link to the pdf file in Google docs.

Mathematically yours,
Miss B

Problem Master and Mountain Climber

My Facebook status this evening sums it up: "That was the kind of awesome day of teaching that will get me through until Christmas."

Have you ever had a day like mine when the lesson goes seamlessly (or nearly so), the kids enjoy what they're doing, you enjoy what you're doing, behavior problems are non-existent, and the learning conversations are rich.  

The best compliment I got from a kid today, "You know, Miss B, this is the highest class but we do the most fun stuff." ("highest class" = most advanced class offered to 8th grade)

So, what caused this awesome day?  Two new activities.  

The first activity was for my Algebra I class.  We have been studying probability for several weeks and it's been slow going.  Many of my students are struggling readers, so the questions are difficult for them to answer independently.  I decided to use an activity that I adapted from a math blog (I think it was ispeakmath but I cannot find the post now for anything and would love to give credit if anyone knows).  We'll call it Problem Master.

Problem Master Directions

1. Create one problem per student on the topic you're studying. (I used a mix of all the kinds of probability questions we're responsible for in 8th grade: simple, independent, dependent, sample space, permutations, and predictions from experimental probability.)
2. Assign each child a different problem.  Have them work out this problem (I used scrap paper for this step) and check the answer with you.  They need to understand and be able to explain how they arrived at that answer.  
3. Create a packet (or use notebook paper) with a numbered space for each problem.  I have 21 students in Algebra I, so I had 21 problems and a packet with that many spaces.  
4. The "Master" of the problem gets a copy of the question in green.  They glue it into the packet and show the work needed to solve the problem.  They also get a yellow sheet with 20 copies of their problem to give to classmates when they pair up.  You'll need to print one page with all of the questions once on green paper and then make a yellow sheet for each child with their problem duplicated enough times for everyone else in the class.
5. Each child then pairs up with another member of the class, they trade problems to solve, work independently to solve the problem, check their partner's answers, and they coach as needed.  
6. I had students grade each other with smiley faces for how much help they required.  
7. When a pair is finished, they return to a designated area to meet a new partner.  (Rarely was anyone waiting for more than 1 minute.  You could choose to have a secondary assignment for anyone waiting or call out switching times, but my kids were able to handle this bit of freedom because they could work at their own pace.) 
8. I had students carry their glue stick and scissors around with them.  We only cut out one problem each time we paired up instead of cutting them all apart at the beginning because I wanted to avoid them losing a pile of little yellow papers!  Envelopes or baggies would also work, but giving them an entire sheet limited my prep significantly and made it easy when we realized we would like to finish the activity in the next class period.  

We worked on this activity for almost an hour of our 90-minute block.  The kids were engaged the whole time and were taking their responsibility seriously.  They weren't happy that we didn't have enough time to finish and begged to get more time next class.  I'll happily oblige because they were doing an awesome job!  
---

With my morning class going so well, I worried some about the potential of my afternoon class.  After all, could I manage two new group activities in one day without pulling out my graying hairs?

This activity probably exists out there in one form or another, but I invented it last night without any direct inspiration.  It's called Mountain Climber. 

My students were very complimentary of my artwork.  Bless them for loving my scribbles!  Coming soon, there will be a picture of the poster we used to track our progress in the "game."  For now, just picture a crude half-mountain drawn on poster paper.  Starting at the bottom and going up the side, there are labels reading "level 1,"  "level 2," all the way to "level 10" and the groups all have a little mountain climber clip art icon colored a different color that they move up the poster.  

Mountain Climber Directions

1. Each group is assigned a different colored marker.  My grouping scheme is discussed here.  I used groups of 3. 
2. Create a variety of problems/tasks related to the topic you're working on and level them from easiest to hardest.  Put each problem on a separate page (half page, etc) and make enough copies for the number of groups you'll have.  I chose to make 10 problems, but this can be adapted to the difficulty level of the topic and the amount of time you have. 
3. Students provide notebook paper.  Pass out one record sheet per group and one copy of the level 1 problem to each team. 
4. Students work in their groups to solve the problem.   Group roles are recorder (writes on record sheet discussed below), messenger (delivers paper for corrections), and scorekeeper (keeps track of group progress).  
5. As the students work on a problem and reach a consensus, the recorder fills in the record sheet, the messenger brings it to the teacher for checking, and the scorekeeper moves the mountain climber up a level when they get a problem correct. Give them the next level of problem when they get a correct answer.
6. I emphasize accuracy over speed in this exercise.  You can see there are three columns on the right of the record sheet.  The first time the group gives me their paper, they get 3 points for a correct answer.  Each subsequent time, they earn less points.  This is a good motivator to help them reach a consensus before bringing me the paper!   The team with the highest point total at the end is declared the winner.  I do not care who finishes the 10 problems first.  

The kids were very excited to play Mountain Climber.  I teach a competitive group in Intermediate Algebra, so they all wanted to be fastest.  Some groups started to realize that they needed to slow down and read the questions carefully so they could get their points.  I had one instance of a team that tried to "divide and conquer" on a problem.  I marked an X in their first box for that problem, and they went back to helping and coaching each other as I'd asked.  Despite that one very minor incident, the activity went well and the kids again begged me to let them finish next class. 

My students want to do math problems.  That's my definition of winning! 

Mathematically yours, 
Miss B

Classifying Systems of Linear Equations.

 I set my students to work today on a sorting activity for systems of linear equations.  Systems is a review topic from Algebra I, but a topic that still gives many of them trouble.  I gave the students this paper to cut apart:

After a few minutes of cutting, I gave them this chart onto which they pasted the vocabulary and examples after solving the systems on the reverse of the paper.  

 They ended up with a chart like this one. 

What worked well: The students were able to self-check because they knew there would be two of each type of system.  Since there were 6 graphs, the students had a couple of opportunities to practice the solutions to each kind of system. 

What needs improvement: I should have labeled the systems and graphs with A-F prior to copying the sheets; I had the kids do the labels instead.  The kids complained that the graph paper was too small, though most of them managed just fine. 

UPDATE 1/6/13: The files shown below are available for download as a pdf.  I've marked the graphs and systems A-F as indicated above.  Thanks for visiting!   

Implementing Rich Mathematical Tasks

My school system is partially through the transition to Common Core Mathematics.  Our lower elementary grades have fully transitioned, HS Geometry has transitioned, and 8th grade has transitioned to the point where we're teaching both the old and new together this year!  As part of the transition, 8th grade students who previously passed Algebra I in 7th grade are enrolled in a course we've titled "Intermediate Algebra."  The course resembles traditional Algebra II in a lot of ways and is designed to fill the gap that would be made by students moving directly from our state's Algebra I/Data Analysis curriculum into CC Algebra II.

One of the expectations for the course this year is that I provide my students with rich mathematical tasks with an open-ended quality.  I was a bit hesitant to get started with these as the students I teach haven't had many experiences with open-ended problem solving.  I feared they would be frustrated by the lack of rigid structure and be very needy.

Here's how I organized the task process in my room.

1. I presented the concept of a mathematical task as different from a BCR (the style of constructed response used on MD state testing which is quite formulaic) and explained to them that there are so many correct ways to answer a task that they should answer a task in the way that makes the most sense to them mathematically.  I stressed that I was not going to be answering lots of questions during this task, so they were to rely on their group and "figure it out."  (I still coached a minimal amount when groups were quite astray, but I wanted them to feel independent.)
2. I assigned groups of four, making sure each group had at least one or two strong math students and a mix of boys and girls.  (Side note: I use pocket charts for grouping and it has been a breath of fresh air this year.  Something about this system, perhaps the groups being on the wall when kids enter the room, has kept the whining/eye rolling/ugliness entirely at bay this year.  I so much as mention the word "group" and their little heads spin to the back wall to check out who they'll be with, but they don't complain!)    
3. I presented the task they were responsible for, indicated the variety of materials available, and set them to work.  
4. After 30 minutes the first day, none of the groups were even close to fully answering the question.  Most had talked for 90% of their time and written very little.  All the groups stayed on topic and remained focused during that time frame.  
5. The next day, I made some general comments about the task and gave a small insight or two into the problem to give a few hints related to common misconceptions.  The groups reconvened and were charged with finishing their answer. 
6. We did a jigsaw grouping to share out.  Two students stayed put and presented their group's work to two students who came from a different group.  We rotated again so all students had a chance to present and a chance to review another group's work.  
7. The original groups had some time to debrief about what they would change after getting input from other classmates.
8. Homework was to write a reflection on the process. 

The tasks I'm using this year are from the Dana Center.  This is a great PDF resource to download if you teach Algebra I or II, or possibly even pre-Algebra with motivated students.  You can scaffold more or less depending on your group of students and the relative difficulty of the task.  This week, students worked in groups of four on the "Extracurricular Activities" task, part B.  The task gave students a scenario and asked them to write a function to model the scenario and find its domain and range.  From my description, I'm sure you're wondering why I needed to devote even 15 minutes to this problem.  We actually spent nearly 90 minutes in class spread over two days plus one night's homework on this task.  Here's why: 

• The problem is embedded into the task in a way that students must make meaning of the situation.  Since the meaning wasn't immediately clear to the students, most every group restarted or made significant revisions to their work during the process.  (Make sense of problems and persevere in solving them.)
• Students have various ideas about the meaning of the problem and how to go about solving it, so they have rich discussions. My students were holding each other accountable for their ideas, asking pertinent questions to better understand their classmates' points of view.  (Construct viable arguments and critique the reasoning of others.)
• Students were able to use any of the materials in the room, so some groups gravitated toward calculators, while others preferred to sketch a graph by hand or write out a table.   (Use appropriate tools strategically.)
• The real world context leveled the playing field in an unexpected way in at least one group.  I overheard one student who is a weak math student leading his group through this task at the beginning because he was the only one with the real-world background knowledge to understand the problem.  His more "book smart" teammates were lost without his guidance.   He was more engaged in this task than I've seen him since school started. 

I was very proud of my students this week.  I wasn't really looking for their work as the final product.  I was hoping to see them demonstrate the eight Standards for Mathematical Practice.   I highlighted a few above, but I can honestly say that I saw all 8 standards in play during this process. 

Some students were already asking to do more tasks on Tuesday before we finished our first task.  They loved the interaction and I loved how involved they felt in solving the problem.  

The joy of a rich question

I was considering the first unit for my Intermediate Algebra class and how I could enliven it.  My first unit isn't even really part of Intermediate Algebra but rather part of my state's 8th grade curriculum.  Because I teach high school courses in middle school, I'm responsible for delivering two courses worth of curricula in one school year.  Thankfully, we operate on a schedule that allows a year-long every day block of 88 minutes for math and reading, so I can get it done. 

I'm challenging myself this year to find a really rich question to ask near the beginning of every unit with the intention of answering it throughout the unit.  Today, I started my measurement unit with my students.  Our state standards require students to find the area of composite figures composed of polygons and circles and to find the volume of cylinders.  I posed the following question to my students: "How much would it cost to paint the ceiling throughout the school?"  Our school is highly irregular in design thanks to its age and at least three renovations/additions of which I'm aware.  The map is far from rectangular; my room is a trapezoid and our cafeteria has a wall that bows out in an arc.

I set the students to work in a Think, Pair, Share in which they had to list factors we would have to consider when evaluating the cost.  I meant to take photos of their posters.  They'll get added to this post when I get back to my classroom.  Here are a few of the "obvious" answers and some highlights that show they were really thinking about this in depth:

• The area of each ceiling tile and number of ceiling tiles
• The amount of paint per can, its cost, and how much surface it would cover
• The amount of masking tape, plastic sheeting, brushes, rollers, stir sticks, paint trays, ladders, and gloves needed. (I get the feeling these kids have painted before!)
• The salary of the crew, how long it would take to paint, and when the painting would happen
• How the lights would be treated, if at all.  (This was a point of great contention.  Some students thought it was a fabulous idea to paint the lights and give everything a blue cast.  Others thought they would like regular white light in the classroom.)
• What kind of paint would be necessary. (They realized that the gym has a different type of ceiling than the classrooms and that they would need to research the proper materials.)
• The need to consider HVAC and proper ventilation. (They pointed out that we would waste A/C if we left the windows open to let the fumes escape.)

I was very impressed with their quick brainstorm.  Now I would like to hone this into a class project that culminates with a presentation to our principal.  She used to be a math teacher, so I think she would appreciate it.

My next plan is to have them consider the list they made and decide what math skills they know that will help them with each aspect.  I see applications of area, perimeter, volume, proportional reasoning, and likely percents (when items are on sale or using the percent of ceiling covered in lights in my room to predict the amount covered in the whole school).  Just my luck, all of these are within my curriculum.  :)

Students will then work on determining the area to be covered.  I know we can do this with the maps of the school that we have, but I think I might be able to use my classroom GPS units at some point to get measurements on the outside corners of the building to help the students calculate the total area of the ceiling of the school.  I honestly don't know much about how the GPS units work and need to learn what to do with them.  That's a goal I have for this year.  I did buy a book of lesson plan ideas so I could try to incorporate them this year. 


Next, I will divide the class into teams, each of which is to research one area of interest (paint type, salary for workers, other materials, color selection) and provide two or three options for the proposal along with their recommendations for which one is the best choice.

At that point, we can put together a PowerPoint as a class and (I hope) "brief" our principal on the idea in our teams.   

I really doubt we'll be painting anything, but it's food for thought! 

Building Vocabulary with a Word Wall

I think most teachers are familiar with word walls.  I've seen elementary teachers organize them alphabetically.  For my math students in middle school, I organize the walls by unit theme.  Each unit we study is assigned a color so students can look for related words in the group.  We make use of our word walls in countless ways, but here are just a few:

1. I place all of the words for a new unit on the wall.  As we work our way through a unit and learn a new concept, students try to guess which word could have that meaning.  This often guides us through a discussion of prefixes, suffixes, and roots as students break down the words and try to make meaning from them.

2. Students refer to the wall to help them recall words that have slipped their minds and for spelling.

3. Because I am lucky to have two metal walls, my words are most often individual strips with magnets on the back.  We take them down and use them for games.  One favorite game is the fly-swatter game.  Give a representative from each team a fly-swatter (clean, of course), scatter the vocabulary words on the board, and give a definition, example, non-example, drawing, etc that the students have to match to the correct word.  It's fast-paced and they get to smack the board, so they love it!  My rules are that they may only smack the board and they must alternate turns smacking words (otherwise it looks like whack-a-mole gone bad and the kids don't pay attention to the words).

4. Review/Study.  I give a final exam so I encourage my students to use the word wall to identify their weaknesses.  They can read through the words and decide what to study based on what vocabulary is most difficult for them.  This is true for unit tests and quizzes as well.  I also find my students using the word wall when they help each other.  They are frequently overheard asking each other about the words and the responses typically include the related words.  I love hearing my kids use their vocabulary! 

I have experienced a few set-backs with my word walls in the past.  First, the words get a glare once laminated so they can be hard to read.   Sometimes I end up with students who have trouble reading at a distance even with really large font sizes.  So, readability is a big problem in my classroom.  Second, the students can't take the wall home so they don't have that resource when they are completing assignments outside of my room.  In response to those issues, I decided to do a little more with vocabulary this year. 

New to my class this year will be personal word walls.  Hooray!  I designed a template to look like a brick wall complete with a graffiti title.  Kids will be responsible for adding words to their wall when we first learn them in class.  Each unit will be written in a different color and the kids will be able to place the words how they want to on the sheet though I'll encourage them to group like words in some way instead of randomly scattering them.  I'm going to have the kids lightly shade or outline the boxes with colored pencil when they feel they have mastered the term.  To me, that means they can describe/define it clearly, draw it accurately, and spell it correctly.  I think we'll need two or more copies to fit all of our words depending on the course as each size holds about 75 words.  When I taught Geometry in the past, we had nearly 300 words, so we would have needed 4 of these.  I'm going to make this double sided and copy it on cardstock.  They'll keep it in a sheet protector so they can use it to quiz themselves by marking things off with a dry erase marker. 

Here's the file.  You'll need the font "a dripping marker" for the title (or just choose a font that you already have).


  

Now, as we keep the personal word walls, we'll also keep up with the one in the classroom.  I want the students to take more ownership this year, so I'm toying with the idea of letting them write the word strips.  The problem is that they wouldn't all be pretty and uniform and I don't know if I could handle it!   I made a matching title for the word wall in the graffiti font I used on the worksheet.  I'll report back and let you know who is making the word strips, me or the kids. 

If you would like to use this with your class, leave me a comment with your e-mail address and I'll send you the file.  

How do you organize vocabulary with your students?  What makes it meaningful to them?  I'd love to hear more strategies that work with math.

Miss B

Welcome!

Thanks for visiting my new blog.  I currently teach Pre-Algebra and Intermediate Algebra at a middle school and as I was beginning to be inspired for the new school year, I found I had lots to share.  While Pinterest is fun, I needed a place to share my own creations. 

I chose "i is a number" for the title of my blog because it gets at my love of math and sounds like poor grammar- one of my major pet peeves.  Teaching students about i last year for the first time was such an experience!  "Really, kids, it's a number.  I promise!"

I don't know how regularly I'll get to update as the school year progresses, but I'm looking forward to networking with other secondary math teachers, especially any with PBL or STEM experiences to share.  I hope you find something here you can use and that you let me know if you do.  Thanks again for visiting! 

Miss B