Ways I use dice in my classroom

Sarah H. recently posted a photo of some items she got from a colleague, mostly large foam dice.  She asked how she can use the dice in her trig class.  I thought that was a great question and I decided to write about several ways I use dice in my class.

1. Teaching probability.  Duh.

2. Using this game board.  I can turn a set of questions into a deck of cards and students can play the game.  Everyone in the group does the problem individually, they discuss as a group, anyone with a correct answer rolls.  I'm always amazed at how much more willing kids are to do the same work when I disguise it as a game.  There are 4 versions of the board in this file: with or without directions and either in color or black and white. 



3. Assign meaning to each side of the die by typing up a key.  Students roll the dice and do the associated action.  Examples: operations on polynomials (add, subtract, multiply, divide, classify, factor, etc), trig functions (sin, cos, tan, sec, csc, cot). Here's one I used for quadratic functions that uses 6- and 12-sided dice (though you can easily change it so as not to need 12-sided dice).  Thanks to my best friend for a donation of cool dice from her Dungeons and Dragons days. 


4. This one is still not classroom-tested, so proceed carefully.  I tested it at home and I think it's a green light.  Mailing labels (like Avery 5160) are able to stick to the foam dice I bought at Dollar Tree and also unstick neatly.  That means I could write questions, equations, terms, etc. and print them on labels to stick to the dice.  At the end of the activity, I can remove the labels (possibly stick them back on the sheet for next year) and reuse the dice for a later activity.

5. As a French teacher, I've made a class set of subject pronoun dice by taking a Sharpie to some foam dice.  These big dice (roughly 2.5") are in two-packs at Dollar Tree.  I've seen red, blue, black, and yellow.

Do you use dice in your classroom?  How?

Mathematically yours,
Miss B

Headbands (Hedbandz) for the classroom

...on a Friday!
 
It's kind of funny to me that "Hedbandz" ever became a game that people pay for since I remember playing it years ago with a Post-it stuck to each player's forehead.  I suppose the lack of set-up time and ability to reuse the cards gives it some worth.

If you're not familiar with the game, each player has a mystery card that they're trying to guess by asking the other players yes/no questions.  You win by guessing your card correctly with the least number of questions. 

If you look around the internet, there are plenty of teachers who are using this game in their classrooms.  Mary,  Jennifer, and Sam have high school math versions.  For the past couple of months, ever since we played the real version at youth group, I've been looking for something to inexpensively replicate the reusable headbands.  I knew I could use strips of construction paper, but they would have to be replaced each time we played the game.  I thought about stretchy elastic headbands but thought they might be really uncomfortable.  I almost got cheap sunglasses and put Velcro dots on the bridges but decided I didn't want to have to Velcro each set of cards, nor did I want to invest $30 for this game.  I kept cruising Dollar Tree for ideas.  Yesterday, I happened upon 3 packs of foam visors. 

This has to be the simplest #Made4Math ever.  Take a visor, add a paper clip and a card, and you're good to go!  $10 for a class set is within my budget.  Totally dorky?  Yes, and I think that's probably part of the charm.  If the students wear them like visors are supposed the be worn, the taller students are going to have to tilt their heads down so the shorter students can see the cards.  Better is to wear the visors upside down (think "tiara") and the cards will be almost vertical. Similar visors are on Amazon here. 

A silly mock-up, but you get the idea.

I know I'll use this for several topics in math and in French.  Two sets of cards are in the document below, one for graphing linear equations and one for vocabulary related to functions and equations. 



How could you use this game with your students?

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

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. 

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

Sharing a Math Game

I'm not sure this is my favorite math game, but it's one I don't think I've seen online before (though I could be wrong about that).  I made it about three years ago and I've used it once or twice a year since then.  The theme today on The Teacher's Chair is to share our best games, so here you go! 

Materials:

• One game board per pair of students
• One game token per student
• One deck of question cards per pair
• Scrap paper or whiteboards with markers
• Optional: laminate the game boards or place them in page protectors/Smart Pal Sleeves

Put students in pairs and give them some question cards.  Divide the answers into two easy-to-discern categories.  Try to have close to equal amounts of each of the types of answers.  Some ideas:

• Positive and negative
• Greater than a given number and less than that number (make sure the number itself isn't an answer)
• Congruent or not (geometry SAS, SSS, etc)
• Increasing or decreasing on a given interval
• Function or not

The students take turns doing a problem and explaining their reasoning to their partner.  When both partners agree with the answer, the player who drew the card moves his marker up or down based on the key you established with the class.   The key here is that there is collaboration and mathematical discourse which is what makes this game work for me.  It is also adaptable to almost any content and certainly any grade level.  It's also pretty quick, so it would work well even if you have a short class period. 

Here's the game board. 



Mathematically yours,
Miss B

Makeover- Quadratic Bridge

Mr. Stadel posted a challenge on his blog today asking us to remake a quadratic bridge problem. Sure, I thought, how hard can this be?  I've never done a makeover, but I teach this stuff!

That was about two hours ago.  That's right, I spent about two hours tinkering with ideas, doing Google image searches, revising ideas, scouring Google again, putting the document together, choosing a video clip, and having all those internal dialogues I have when I'm planning.  For one problem.

My thought process went somewhat like this.  Please excuse the disorder of my thoughts!
1.  I need a problem with multiple solutions.  Not something where anyone can say, "Yes, 8 feet 3 inches is correct."  Let's make this an open-ended question. 
2. I need a problem that makes students feel like the answer is important.  I live close to a very large bridge that is frequently the subject of controversy because of tolls, heavy traffic, accidents, and the like.  The students I teach often have parents who commute across this bridge daily.  My community is also very fortunate to have abundant water access, so lots of kids spend time with their families out on the water.  Therefore, my students would be at least somewhat invested in the idea of having a safe bridge and safe boating practices.  I also expect they'll have a good bit of background knowledge to bring to this scenario. 
3. Time to find images.  Lots of Google searching until I found pictures I liked.
4. I wanted the bridge picture to be straight on so the kids could do measurements with it (and maybe superimpose a graph on it with our TI-Nspires if I'm feeling super tech-savvy and manage to be free from crazy glitches).  I ended up choosing the Ponte Vecchio in Florence, Italy because the picture was workable and I've been there so I can add a few fun anecdotes in, possibly even a personal picture if I have one. 
5. Tides?  Yikes, I do not really know much about them other than that locally we have two high and low tides each day.  But...I'm pretty sure that they learn at least a bit about them in science class.   Something we can explore together and a good place for data collection.  This is the bit that will give us some variations in our answers.
6. What's an appropriate clearance?  The video shows that ship coming closer than I could imagine. 

All that thinking, and here's what I ended up with.  Like I said, this is my first "makeover," so I'd love to know what you think!





Mathematically yours,
Miss B

Envelopes for Interactive Notebooks that hold index cards

This week, I've been working on Common Core implementation with my school's transition team.  I'm our STEM representative, so I've been working on the STEM standards and looking at how we can integrate these across the disciplines.  It's an exciting idea for me because I remember most of my schooling was project-based and I'm glad we're heading back in that general direction, but with a bigger focus on student-led inquiry.  It's an amazing time to be in education!

Changing gears somewhat, I wanted to share a template with you that I'll be using this year in my students' interactive notebooks.  I love card sorting activities.  One of the best I've done I blogged about here back in May.  I won't asking my students to store stacks upon stacks of cards in their notebooks because it will grow way too quickly, however, I know there will be at least a few that they'll want to keep.  This envelope is large enough to store 3"x5" index cards.  Shrink it down to fit two to a page (somewhere around 65% worked for me) and you can make two small envelopes that will hold mini cards. 

So, how can you use this?  I've got three ideas for you!

1. Store cards for a card sort, vocab cards, and the like.  Simple storage.  Have students write a reflection, analysis, etc. on the other half of the page to extend a card sort beyond simple matching. 
2. Shrinking notecard!  If you've never heard of the shrinking notecard, check it out!  It's an activity to help kids get to the most important information they're learning and is an awesome left side assignment for kids to synthesize information and reflect on what elements are the most critical to remember. 
3. Two envelopes= card sorting location.  Put two envelopes on one page and write categories on the envelopes so the students can sort a pile of cards into the two envelopes.  Choosing whether a graph, table, or equation is a function would be an easy way to apply this activity.  If the students make an answer key, they can practice again and again.

Next time I do this, I'll color code everything to do with a function one color (probably green) and everything that's not a function another color (probably red).  This was the result of picking up nearby writing materials after midnight! 

I really, really wish I could direct you to the cards.  I have the worksheet as a pdf and there's no clue to who the author is in the file.  Unfortunately, several Google queries turned up nothing either.  If you happen to recognize the sheet, please leave me a comment so I can give credit where it's due!  It's a great little card sort. 

I love asking kids to justify a particular card they've sorted.  Here, it would make sense to ask them to choose one from each set to analyze specifically. 

One of my left side assignments is to make a set of cards for a card sort and I'm about to add the shrinking notecard to the list, so I know I'll use this envelope frequently.

Now, I like an envelope that seals.  A bit of masking tape made less sticky by adhering it to cloth and removing it a few times will make a good resealable closure.  If you're crafty or follow trends, washi tape would be even better for this, though more expensive. 



Lots of people are having trouble viewing the document to download it.  Please try this link if you can't use the embedded box.com file.  

What will you have students put in this envelope? 

Mathematically yours,
Miss B

Solving Equations Pinch Cards

First of all, thanks to @druinok who blogs at statteacher.blogspot.com for motivating me to write this post (and being such a good encouragement on Twitter as well).  Follow me if you like; there's a button to the right now. -->

There was some discussion on Twitter tonight about response cards.  I can't stand fumbling and missing pieces, so individual cards are not for me!  I prefer a pinch card.  If you're not familiar with them, they are long thin strips of paper (like cutting an 8.5x11" into three vertical strips).  Answers are located along the strip.  These are general usually, such as A-D for multiple choice, True and False, etc. 

Last school year, one of my favorite uses for pinch cards was solving equations.  My kids were Struggling (yes, with a capital "s") with understanding which operation to do when.  I made simple pinch cards with the four basic operations, combining like terms (now "collecting" like terms for CCSS), and distributive property.  We would look at equations and decide which step to do first.  One or more students would explain their answers and we would reach a consensus.  Then we would work together to solve that step and use the pinch cards again for subsequent steps.  I kept it to the four basic operations at first and it worked well.  Then we added in the CLT and distributive property.  We had 100% engagement (and even if at first they were copying their response from a friend, at least they were putting effort into getting the right answer)!

Here's the file.  I recommend printing it double sided so you and the kids can both see what was selected.  Laminated cardstock would be your best choice for durability. I kept them in table bins but you could also punch holes and keep them in students' binders if you'll be using them frequently.




How have you used pinch cards or response cards in your lessons?

Mathematically yours,
Miss B
 

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! 

If Barbie Were as Tall as Me- A Lesson in Proportional Reasoning

This lesson idea isn't new; it's easy to find many versions of it all over the internet. In fact, I was inspired by a post from fellow teacher Fawn Nguyen.  Here's my spin on it.  My students need to review proportional reasoning this year, so I wanted to focus on application since they got the basics of how to cross multiply and solve last year.

I started by collecting some Barbies and Kens.  Thank goodness for generous teachers in my district and our fabulous e-mail network!  I got 5 Barbies and Kens in no time.  I bought one more at Goodwill for $1 and now I have enough for each table in my classroom to have one.  I'll try to pick up a few more when I can find them (clothed) for $1 or so.  :)

Students will work in their table groups of four on this project.  They'll need to select one student in their group to serve as the human reference.  That student's height will be used and their silhouette will be traced on bulletin board paper.

Next, students will carefully measure and record data on Barbie's body measurements.  I selected six data points I'd like them to collect and superimposed them on a coloring page of a Barbie doll.  They'll write proportions to find out how large these body parts would be if Barbie were enlarged to their height.  Then, they need to work as a group to make a scale drawing on chart paper.  I'm planning to have them place their scale drawings next to the silhouettes to show off how unreasonable Barbie is.  I'm also curious to see if this pans out in a similar way with Ken or if he's more reasonably made.  His abs are unusual, that's for sure!

A screenshot of a portion of the diagram students will use. 

The individual portion of the project asks students to write a letter to Mattel explaining their findings and requesting changes in Barbie's physique so that it will be more true to life.

Since it's Monday, I'm posting to made 4 math.

EDIT: There's a follow-up to this post here that contains files you can download.  

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!  
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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

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! 

Measures of Central Tendency Cootie Catcher or Fortune Teller

First, a PSA: Tomorrow is the first day of school!  Hooray!

Back to your regular programming...

I've seen some academic uses of the so called "cootie catcher" or "fortune teller" and I decided to make one for my kids to use this week as we review measures of central tendency in Algebra I.

Here's the basic template I made in Word.  If you want the file, please just leave me a comment and I'll be happy to share   download the PDF from Google Docs.  Obviously, you could just have your kids fold a plain one and write things on it.  I don't know my clientele yet, so I'm doing most of the work for them this time. 

The four corner squares are labeled mean, median, mode, and range.  These are the measures of central tendency and variation that my students should have mastered in 7th grade.  Generally, they come in pretty well prepared on this topic, with some of them mixing up the "m" words.

I filled in everything but the solutions and definitions for them.  There are 8 data sets given and there are places for the kids to write in the mean, median, mode, and range for each of the sets.  My plan is for them to work in partners to "play the game" and collaborate on finding the answers for each data set, only recording their work if they both agree.  They can then take this home as a study guide/review game.   The colors on the words are just pretty.  The colors around the data sets and answers are there to keep the kids from getting switched around. 

Again, you can download the blank template here if you missed the link above!  If you'd like the filled in copy (in my lovely handwriting, sorry), you can get it from my updated post.

How do you make review activities fun and unique to keep kids motivated?

What to do about "I'm done!"

We all have experienced the joys trials of teaching a group of students who work at very different paces.  There are those children who must be encouraged, coaxed, and refocused so that their work gets finished.  There are the kids on the opposite end of the spectrum who, it seems, have finished the worksheet before their classmates have even managed to get started.  What to do with the children who finish early? 

Obviously, you want to ensure that they're producing their best work and not rushing through an assignment simply to be finished.  I had one child who was such a pro at finishing everything quickly that I always saved my classroom chores for him (passing out papers, sorting things, taking a note to a classroom, etc).  It helped him to have something physical to do because he was very prone to getting into trouble and pestering other children within seconds of being finished his work. 

Other than classroom chores and the overused, "read your free reading book," there weren't many options in my classroom for early finishers.  I decided that this was the year I needed to make it happen! 

I'm going a totally different route with my Early Finisher choices.  I'm putting together brain teasers, puzzles, pentominoes, tangrams, 24, and the like with instructions for a short activity.  It's sort of an homage to elementary school math centers.  Each center will be stored in a zippered pencil pouch that the kids will select and take back to their seats.  I think the fabric pencil pouches will hold up and be easy for the kids to use.  I put a binder ring though the zipper on each pouch so it's easy to hang.  My hope is that these stations will build logical and spatial reasoning which are applicable across many subjects.  The start-up cost for me was about $20 for the pouches ($1.50 each at the discount store in my town, probably at Dollar Tree but not worth the drive for me) because I already had the other materials.  Most of them were sitting unused because I either didn't have enough for the whole class to use at once or because they weren't strictly related to my curriculum.  This is a step in the right direction!  I hope to create enough materials so I can swap these out mid-year.  Every term would be awesome, but I don't have enough materials for that just yet. 

These pouches are left over from previous students.  I purchased 12 more (not pictured) for a total of 16.

I also set up my classroom library in a much more inviting way than in years past.  I stacked some file crates sideways and used them as my bookshelves.  I placed some books related to math in a display.  I was so close to selling that pink locker storage piece because the pockets are so deep when it occurred to me that I could stuff the bottom with paper so items would sit up higher and be visible.  Duh!  My library last year, in comparison, had all of my books piled in one crate that was placed under a chair in a corner.  Not exactly inviting!  I could use some better books; most of what I have is so dated I don't even want to pick them up.  I will try to make it to a library sale this year in hopes of adding some attractive books to the collection and I'll go through my books at home to see if I have any that are age appropriate for the kiddos. 

Finally!  A classroom library with a bit of character.

Do you have any great ways to keep kids' brains active when they've finished their assignments?  Please share what works for you.

Miss B

"Everybody In"

Engagement was a hot topic at my school last year.  Our test scores are great (10th middle school in the state overall, 6th in the state for 8th grade math, and the best in our region of the state) and we're really working on reaching that last 5-10% or so of kids. 

I certainly don't think I invented this idea, but I don't remember taking it from anyone else, either.  So, while I can't give credit, I'll bet there's someone who thinks I should.  I call this, "Everybody In."  While everyone in the class should be focused in at all times, we know that's not reality.  We all teach kids with attention problems or those that are simply disinterested in the topic at hand and are having a hard time getting into the lesson.  "Everybody In" is my way of getting 100% participation and a quick check for understanding. 

This poster (crude as it is) reminds kids of our signals. 

 

During Everybody In, all students must raise their hand(s) when a question is asked or a statement is made.   The left hand raised represents an answer of "no," a disagreement with the statement, or a negative number (since we do a lot of integer work).  The right hand raised represents "yes," agreement, or a positive number.  My kids know that they are supposed to "ride the roller coaster" when they are unable to decide.  This tells me they've considered the statement or question and are in need of some support. 

Just to be totally goofy once in a while, we'll add left and right feet if we're working on a topic that naturally lends itself to three or four categories (for example, types of angles).  It gets the wiggles out even while they're in their seats! 

Now, this isn't going to get at your higher-order questioning.  However, it will let you test your class on simple facts to make sure they've got them straight before you delve deeper.  It's great for vocabulary, think alouds, and class discussions.  Follow up by asking someone from each side to defend their selection. 

Oh, and if your principal just happens to walk by when you're doing this, you're going to look awesome.  After all, it will look like 100% of your kids are ready to answer your question.  Which they are!  

How could you use Everybody In as a part of your lessons?  What words or phrases would you use for the left and right hands? 

Miss B