Math = Love

I think I've finally gotten over my "Oh my goodness school is out and grad school is done and I don't have to do anything productive" phase. Yesterday, I wrote out a new SBG skills list for Algebra 1 for next year. Oklahoma has adopted new standards, so I had to make quite a few changes from what I used last year on top of all the normal "I don't know what I was thinking when I chose to do it this way last year" changes.

Today, I've been editing said skills list and thinking about what I want my classroom to be like next year. If you missed my previous post, I have a new classroom to decorate for next year! Due to budget cuts, we are having to consolidate our middle school and high school into a single building. Do you realize what a new classroom means? New places to hang posters! :D

So, I can say that I have designed my first new poster for my new classroom next year! While flipping through CPM's Core Connections Algebra book, I ran across a set of "Collaborative Learning Expectations" that spell out the word TEAMS. When I saw them, I instantly knew they were destined to be a poster in my classroom! (You can find out more about CPM's Study Teams Model here.)

T: Together, work to answer questions
E: Explain and give reasons
A: Ask questions and share ideas
M: Members of your team are your first resource
S: Smarter together than apart

I'm excited to start brainstorming about ways to incorporate more group work in my classroom because my new classroom will be so much more conducive to group work than my old classroom. In my old classroom, putting the desks in groups of four meant not being able to walk across the classroom because the desks were so close together. In my new classroom, it seems like I should have quite a bit of space between groups!

So, here are the posters I designed. They are made to print on letter sized paper.

I've uploaded the file for these posters here as an editable Publisher file and a non-editable PDF file. If you choose to download the Publisher file, you'll also need to download these free fonts: Londrina Shadow and Londrina Solid. If you're interested in other posters, you can find more here!

Summer: The time of year where teachers dream of all the things they'll do differently next year.

Yesterday, I posted about wanting to do a better job of group work for next year. Erin Flotte left a comment that included a recommendation for a book on group work (affiliate link). I've already ordered it from Amazon and am looking forward to diving in to it this summer.

Today, I've been hard at work creating a resource for next year because I know that my intentions to do things differently next year need to be coupled with actions to make that possible. Last week, I read a post on Amie Albrecht's blog about One Minute Surveys. It instantly brought to mind the exit tickets I used to give my students at the beginning of my first year of teaching. As a pre-service teacher, I read tons of teacher books and read every math teacher blog I could get my hands on to help me learn how to best run my classroom. All the advice seemed to point to using every minute of class wisely and bringing closure to every lesson. So, I jumped into giving exit tickets every single day. This did not last for long. First year teacher me was overwhelmed with all the tasks that teaching brings with it, and this was one thing that fell by the wayside.

I think the reason it fell by the wayside so quickly was because it was an extra thing that had to be planned every single day. Now, as a teacher going into her fifth year of teaching, I realize the importance of automating as many things as possible. I want to get daily feedback from my students. I want to get to know my students better. I want to know which concepts they are grasping and which concepts are making them grasp at straws. Sure, I could probably make up exit ticket questions off the top of my head now and be just fine flying by the seat of my pants. But, I've got a better plan.

I'm taking my favorite exit ticket questions and making sheets for each question that can be printed and chopped ahead of time. Each day, I'll be able to pull out a prepared stack of exit tickets that match what I'm hoping to learn from my students that day.

I did an online search for exit ticket ideas and compiled my favorites. These should be able to be used with almost any subject/grade level.

I've designed them to print 6 to a letter-sized page. I'm thinking this will make them easy to chop with the paper chopper.

Here are the exit ticket prompts I've come up with so far. If you have others, add them to the comments. I'll add them to the file and update it. :) [Download here!]

For the first time in a while, I'm not entirely sure what classes I'm going to be teaching next year. But, I'm 99% sure that I'm teaching Algebra 1. Oklahoma has adopted new academic standards for mathematics, so I need to adapt my previous SBG skills and units to the new standards. I'm also making changes based on my experiences from teaching Algebra 1 this past year.

If you're interested, here are my SBG skill lists for last year's Algebra 1 course. Last year, I had 8 units and 58 skills.

Below, I'll be posting my new SBG skill lists for this year's Algebra 1 course. This year, I have 12 units and 62 (If I counted correctly!) skills. There are a number of new topics that I have to address this year in Algebra 1 (simplifying and operating on radicals, arithmetic and geometric sequences, solving absolute value equations, systems of inequalities, and a much more in-depth look at probability).

I've made several key changes from last year. I greatly reduced the "review" chapter at the beginning of the year. I'm moving a lot of the things I would LIKE to review to my daily warm-ups. These are still in the works, but my current idea is to choose a different review focus for warm-ups for each month of the school year. For example, in August, I think we will start off each class period with a couple of order of operation review problems. We'll start simple at the beginning of the month and ramp up to more complex problems by the end of the month. Another month, we'll focus on integer operations for the warm-ups. I think this will help me still review these important topics without taking up valuable time that belongs to standards actually in the prescribed curriculum.

Another thing I've done is combine several learning skills into a single learning skill. For example, I used to have evaluate functions from a table, evaluate functions from an equation, and evaluate functions from a graph as three separate skills. This year, I'm combining them into a single skill of evaluating functions. I think I will still teach them separately, but I will assess them together. I'm trying not to overwhelm my students (and myself!) with too many skills.

My husband has been working on SBG skills for Geometry, so I asked him kindly for the template he was using to organize his units. I liked how he included both the new Oklahoma Academic Standards and the old PASS standards that each unit was aligned to. So, I did the same.

Are these skill lists perfect? Most definitely not. One of the reasons I want to post them now, well before the beginning of the new school year, is so I have a chance to get constructive feedback from others. So, if you're making your own plans to teach to the new Oklahoma Algebra 1 standards, or if you just like looking at other people's skill lists, I welcome your feedback!

So, without further ado, here are my Algebra 1 skill lists.
(Download the entire set of skill lists with OAS and PASS Standards here.)

Fundamentals of Algebra (FA)

Solving Equations (SE)

Relations and Functions (RF)

Linear Graphs (LG)

Writing Linear Equations (WL)

Absolute Value Graphs (AV)

Inequalities (IN)

Systems of Equations and Inequalities (SY)

Polynomials (PO)

Radicals (RA)

Sequences (SY)

Data Analysis and Probability (DP)

My Algebra 1 students are required to be able to evaluate functions from a table, equation, or graph. Last year, I taught these as separate skills. This year, I've decided to combine them into a single skill so that (I hope!) students can see that we're doing the exact same thing in each case. We're just given the information in a different way.

Last year, I played a version of evaluating functions war with my students that I haven't blogged about yet. Oops... It worked well, but it only let students practice evaluating functions from an equation. Last night, as I was laying in bed and trying to think about sleep, I started brainstorming how to make a game that incorporated evaluating functions from graphs and tables, too. I would have liked to include mapping diagrams in this activity as well, but it seemed like more of a hassle than it would be worth.

Here's what I came up with this afternoon:

Instructions:

If that image is too fuzzy or hard to read, here are the instructions in typed form. :)

Game Preparation Instructions
1. Decide how many students will be in each group.

2. Print one copy of page 2 (evaluation cards) for each student in each group. Printing these on different colors of paper will make it easier for students to sort out which cards belong to who at the beginning of the game.

3. Print one copy of pages 3-5 (function cards) for each group.

4. Laminate (if possible) and cut apart.

Game Play Instructions
1. Shuffle the larger function cards (pages 3-5) and place face down in the center of the playing area.

2. Distribute the smaller evaluation cards to each player. If they are printed on different colors, each player should get 9 cards in a matching color. If cards are not color-coded, distribute 9 cards to each player. Each player should shuffle their deck several times.

3. Turn over the top function card and place it in the center so all players can see.

4. Each player turns over their valuation card and evaluates the function at that value.

5. The player with the highest value wins each of the other players’ evaluation cards. Cards that are won go on the bottom of the stack.

6. Continue play by turning over a new function card in the center of the playing area and having each player turn over a new evaluation card.

7. If two or more players have identical evaluation cards that evaluate to the same highest value, each of those players should turn over a new evaluation card to act as a tie breaker between those players. If two or more players have non-identical evaluation cards that evaluate to the same highest value, a new function card should be turned over to act as a tie breaker between those players.

8. Play ends as soon as one player runs out of cards. The players who still have cards are considered the winners of the game. Another round may be played if time allows. (This rule keeps all students engaged throughout the game.)

If you have any questions about the rules (or suggestions to make them better!), please leave a comment at the bottom of this post!

Evaluation Cards (9 to a Page)

* Print one page per player
* Best results if each page printed on a different color
* Example: If students will be playing this in groups of three, use three different colors when you print these. If you are printing multiple sets, each group of cards can use the same three colors.

Function Cards (6 to a Page)

Graphs:

Equations:

Tables:

You can download the files for this activity here. If you download the editable Publisher version, you'll need to also download these free fonts: Qarmic Sans, Rockwell, and ArmWrestler. The PDF version will preserve all of the fonts and formatting.

One of the first things that caught my eye when flipping through CPM's Core Connections Algebra book was a team sort to assign students to groups (or study teams). In the past, I've assigned students to groups in a couple of ways. Usually, I just let my classes choose their own seats. The problem with this is friends like to set by friends when that's usually the last place they need to be sitting. To combat this, I've drawn popsicle sticks in the past for group seating. Students hate it when I do this. I like the randomness of the seating, though.

However, I really like the idea of making new seating arrangements tie into the curriculum. What if seat-changing time was also learning and practicing and talking about math time? This year, I really want to embrace the idea of study teams. Students will be seated with the same group of people for the entire unit. Thus, we'll need to pick new seats at the beginning of each new unit. (And, I've already posted about team norms here!)

Our first unit of the year in Algebra 1 will be "Fundamentals of Algebra." Our first skill will be evaluating expressions. I know this is something students have done before. The new Oklahoma Academic Standards specify that students should be able to evaluate linear, absolute value, radical, and rational expressions. This also includes non-standard operations like you would see on the ACT.
Since students will be assigned seats before we begin the unit, I want to use this as an opportunity to see what they already know about evaluating expressions. So, I've created a deck of cards that practices evaluating linear, absolute value, and a few polynomial expressions for good measure. This will hopefully give me an idea of where my students stand with evaluating basic expressions before we start throwing in radicals and rationals which can be undefined at certain values.

My goal for this summer is to create a deck of "sorting cards" for each unit of the year. This will ensure that I actually go through with my plan of changing groups at the beginning of each new unit.

Here's the first set. I promise that I double-checked for typos. But, if you happen to still catch one, please let me know so I can update the file!

Download the file here!

One of my favorite activities from this past year's Algebra 1 class was our Function Auction. When I originally did this in class, I threw it together at the last minute. This meant I grabbed a random worksheet off of the Internet and called it good. Here's my write-up of how the activity went last year.

I'm currently in an "overhaul everything" mood for the next school year. So, I decided to create my own Function Auction worksheet. I used images of functions and non-functions from released state questions from Oklahoma, Arkansas, and a couple of other states.

Here are the rules for hosting a Function Auction:

The auction catalog features 12 lots.

I also made a version with boxes around each lot.

For extra fun, make auction paddles for groups to use using colored paper and rulers or paint sticks.

Here's an example from last year's function auction:

If I haven't sold you on the idea of the function auction, I made the function auction catalog into a worksheet.

Without boxes:

With boxes:

Files can be downloaded here. For the editable Publisher file, you'll need these free fonts: HVD Comic Serif Pro and Aaargh. The PDF file will preserve the fonts and formatting.

I'm in the middle of designing my own teacher planner for next year, and I'm too excited to wait until the final product is done to start blogging about it. I love browsing the internet for pretty teacher planners. There's just something about a new planner that makes me happy inside. However, the problem with most planners that I see on the Internet is that they seem to be focused on the elementary grades. I don't need field trip planners or a zillion pre-made seating chart pages.

I started thinking about what I would want in a planner, and this is what I came up with.

* Weekly Calendars (With Lines! I cannot write in a straight line to save my life...)
* Flexibility to add more pages and move things around as I figure out what I really want/need

Really, when it comes down to it, all I want flexibility. I want to be able to change things when they aren't working. I'm tired of buying a planner and spending a year dreaming about when I get to buy a new planner because it just isn't working for me. My husband introduced me to the Arc Notebook System by Staples a couple of months ago. It's a discbound system that lets you rearrange your pages to your heart's content. You can add pages whenever you want and wherever you want. It gives me the flexibility of a three-ring binder without the annoying bulk of a binder. Plus, it lies completely flat!

I designed my own weekly spread back in May, and I've been using it to see what I *really* want in a planner. After using my own pages for a few days, I figured out what was working and wasn't working. I've redesigned my weekly spread pages, and I'll be blogging about those soon. Promise.

What I really want to blog about today is the "extras" I have made to go in my planner to keep me organized.

All of the pages in this post can be downloaded here. If you download the editable Publisher files, you'll need to also download these free fonts: HVD Comic Serif Pro and Ostrich Sans Heavy. The PDF files will preserve all of the fonts and formatting.

Address Book Pages - One thing that planning a wedding (and writing post-wedding thank you notes) taught me was that I need a better organizing system for my addresses.

Calculator Sign-Out Sheets - My school provides students with graphing calculators instead of making them purchase their own. This is largely because we are in a low socio-economic area where many families could not afford to purchase a graphing calculator for their students. I have a classroom set of calculators that serves us well. The problem arises when our students need a graphing calculator to take the ACT. In four years of teaching, I still haven't come up with a good system for tracking who has borrowed which calculator. Usually, I resort to writing calculator numbers down on post-it notes, but they can get buried in my messy desk and lost. If students seem me write down their calculator check-out in my book, they'll know that they must return it in a timely manner or I will track them down.

Birthdays - One thing I want to do a better job of this year is keeping track of birthdays. When someone takes the time to send you a birthday card, it just makes you feel special. I want to do that more this year. I overheard a student say a couple of weeks ago that only one person had wished her a happy birthday on her birthday. Her own parents hadn't even remembered her birthday. How sad is that! This was convicting to me because I only do an okay job of recognizing birthdays in my classroom. Usually the way I deal with birthdays is this: If you tell me it's your birthday, I'll give you a birthday badge sticker to wear. Sometimes, I'll even throw in a "Happy Birthday" certificate that I picked up at Dollar Tree. What about the students that are too shy to tell me it's there birthday? I need to make a plan to recognize all of my students on their birthday. I still remember my 7th grade math teacher: Mrs. Sellars. She gave each of us a pencil on our birthday. If students had a birthday that fell in the summer months, she gave them a pencil on their half-birthday. This year, I want to recognize all of my students (and coworkers) on their birthdays. To help me keep track of this, I made some birthday tracking sheets to keep in my planner.

I haven't tested these out yet (mainly because I've yet to print all of my planner pages and assemble them.) I'm thinking that the student birthdays sheet might be too small to fit all of my students. So, I might need to redesign it so it takes up 2 pages... If so, I'll share it as well!

Future Dates - I'm always running into the problem of having a date I want to put in my planner when my planner doesn't go that far. I decided that making a sheet to record dates for the next four years should help with this. Now, I have a place to record random dates I want to keep an eye on such as driver's license expirations, teacher registration expirations, and other random stuff.

Items Borrowed and Items Loaned - I perpetually have students coming to me to borrow stuff. After four years, students have learned that if you need scissors, glue, colored pencils, markers, rulers, or any crafty stuff that I'll probably have it. The problem is that these things have a tendency to not come back. I'd track down the student who borrowed it, but I often don't remember who that was. And, I often don't realize it never came back until a week or so later. This year, I'm going to keep a log of items that are borrowed so I can ensure that they are returned. Students won't be able to leave the the room with the borrowed item until it's logged in my book.

I also created a sheet for items that other people have loaned me. It's rare that I borrow something from someone, but it does happen.

Meeting Notes - I have a new principal next year who promises that he rarely calls a faculty meeting. My previous principal insisted on having a faculty meeting every Friday. Even though there will be less meetings to attend, I still want to keep organized at these meetings. My usual approach to a faculty meeting has been to take notes on a calendar page in my planner. This is usually less than ideal. So, I designed this sheet to help me organize my meeting notes.

Student Council Meeting Notes - As Student Council sponsor, I host a usually weekly meeting for my student council kids to discuss upcoming events that they are planning. I've never been organized with student council stuff, and it makes it incredibly hard to find things later. I adapted my Meeting Notes page to a Student Council Meeting Notes page. I'm hoping this leads to more organized student council meetings this year!

Parent Contact Log - One area I know I need to improve in is parent contact. I hate talking on the phone. It scares me. But, I know that contacting parents means I will be better able to meet my students' diverse needs. This year, I am going to try to contact five parents each week (at a minimum). I wanted a place to keep track of the parents I contact and take notes on what was discussed. This is what I came up with:

Passwords - As a teacher, I have so many passwords to keep track of it's not funny. I've always relied on trying to use the same password if at all possible. This works for the most part. But, there's always that website that wants 14 letter passwords with 5 special characters or something crazy. Keeping track of my various passwords will help me keep my sanity and save time by not having to go through the "Forgot My Password" page at least once a week.

Project Planner - Okay, I'm not entirely sure what I'm going to use this for. I might use it in the student council section of my notebook to help various events such as the Veterans Day Assembly or the Annual Blood Drive. I also play a large role in preparing for the Awards Assembly at the end of the year which involves lots of small to-do list items.

Reading Log - Now that grad school is done, I think I might finally have time to start reading for pleasure again. I recently got a library card from a nearby town that allows me to access free audio books and e-books. The type column is to differentiate between e-books, audio books, and well actual physical books.

Tutoring Log - My school pays teachers to do after school tutoring, but there's one catch. We have to keep a log of our hours and the students we help in order to get paid. I often help students after school, but I'm terrible at keeping records. This means I rarely get any compensation for my time. This year, I am going to have a tutoring sign-in sheet for students to sign when they enter and exit my room. Then, I'll transfer the information (neatly) to my tutoring log.

To-Do Lists - I have designed half-sheet to-do lists for this next year. My thinking is that since they only take up half a sheet they can be inserted in the middle of my weekly spread. I've tried keeping my to-do items on my weekly spread, but that just ends up too messy. Plus, I usually have way more to-do items than space. This will allow me to change out the to-do list in the middle of the week if I need to. Of course, you can just print these, chop them in half, and use them as a normal to do list, too!

I had a twitter conversation with Kathryn Freed yesterday that reminded me of a project I want to do this summer.

...

I want to come up with as comprehensive as possible of a list of practice structures that can be used in the math classroom. Then, when I'm (or you're) looking to create an activity for a particular skill, my (or your) brain doesn't have to work quite as hard to come up with an idea!

I've tried to come up with my own list before, but I know that if we work together, we can come up with a better list than any of us could individually. When I was trying to make my own list, I started wondering about what sorts of categories these practice structures could be sorted in.

Here's the categories I came up with. For each category, I've listed a couple of practice structures that popped to mind. For some of them, it's hard to judge exactly which category a practice structure should go in. For example, a card sort can be done individually, with a partner, or in a small group. So maybe the categories are arbitrary?

Competitive Whole-Class Activities

Solve Crumple Toss
Bingo
Etc.

Non-Competitive Whole-Class Activities

Speed Dating
I Have...Who Has?
Etc.

Partner/Small Group Activities

Add Em Up
Row Games
Etc.

Independent Practice Activities

Tarsia Puzzles
Card Sorts
Etc.

Want to help by sharing your favorite practice structures? I'll compile the results (complete with links and descriptions) in a page on my blog for you to reference in the future.

If the embedded form to share your favorite practice structure doesn't show up below, please visit this link!

Thank you for all your help!

My first exposure to an open middle problem was at a CCSS workshop in 2013.

We were given the following problem (SOURCE - Page 20) to solve:

I enjoyed the challenge, but I don't think I ever used the problem in my classroom.

As I've been thinking about practice structures to use in my classroom next year, my mind keeps turning back to open middle problems. Never heard of open middle problems? Seriously, you need to follow that link!

Open Middle's website defines the problems as follows:

Of course, I read this description of "open middle" problems AFTER I took a stab at creating my own. The problem I created (and am getting ready to share with you) has a "closed beginning," an "open middle" and an "open end" because there are multiple solutions possible. I'm guessing this is still allowed because it seems like many of the problems on open middle.com allow for multiple solutions.

Okay. Time to share the problem I created.

I wanted to create an activity to help my students practice determining if a relation is a function or not a function. I also wanted my activity to perform double duty. I wanted students to be able to use the exact same activity to form relations that were functions and that were not functions.

I ended up creating three x/y tables that have 9 missing values (3 missing values per table).

Students are given the integers between -4 and 4, inclusive, to place in the empty spots.

I designed these numbers so they could be laminated and easily cut apart. I think printing them on different colored paper than the three tables would also be beneficial.

Students are given two separate challenges to complete.

Challenge 1: Place the integers between -4 and 4 into the empty spots in the tables to form three relations that are also fuctions. Each number can only be used once.

Challenge 2: Place the integers between -4 and 4 into the empty spots in the tables to form three relations that are not functions. Each number can only be used once.

Of course, I had to print out the activity and try it myself to make sure that there were possible solutions. As I was completing the first challenge, I thought to myself "That was easy! Perhaps too easy." Then I looked at the third table and noticed I had created the ordered pair (4, 3). I had messed up on my own puzzle! So, you must be careful!

I'm super excited to try this activity out with students next year!

One of my motivations for making this activity is a certain EOI question released by the Oklahoma State Department of Education. It trips my students up EVERY SINGLE YEAR. Almost always, they are convinced that the problem is flawed and that none of the sets of data represent a function. In this "open middle" problem, I am essentially having them create functions like choice c and non-funcitons like choices a, b, and d.

I have to admit that this activity did not turn out exactly as I had planned. I took pictures of my planning scribbles to give you some insight into how this activity came to be.

Originally, I thought I would have a table, a set of ordered pairs, and a mapping diagram.

I also changed my mind about using the digits 0-9 and decided on -4 to 4.

After I created a set of ordered pairs, a table, and a mapping diagram, I began having second thoughts. In order to make a mapping diagram that could be both a function and not a function, I would have to break the normal protocol for making such mapping diagrams. This is exactly what I tell my students NOT to do.

Thus, I settled on just using tables. I had to edit some of what I had already made so that all the tables had the same number of rows.

Overall, it was a fun and stimulating process to try and make a problem that could be solved multiple ways. If you have any feedback about how to make this problem better, I'd love to hear it. And, I must give a special shout-out to my husband for testing out the activity for me and listening to me as I tried to figure out what in the world I was trying to accomplish.

You can download the files to use this activity in your own classroom here.

One of my favorite changes from last school year was to make dividers for my students' interactive notebooks. The year before last, I tried using sticky tabs to separate units. But, these just got bent up in students' backpacks. The kids weren't using them, so I stopped handing them out.

This past year's dividers were made out of a letter-sized sheet of paper. The paper was folded and glued in the notebook so that the title of each unit stuck out of the notebook for easy reference.

The very first divider had a place for students to mark off each unit as they completed it. I never remembered to remind students to do so, so most of them left it blank. A couple of students did enjoy coloring in their progress.

Each unit's pages consisted of two parts: a score tracking sheet and a list of skills that doubled as a table of contents.

A few weeks ago, Shaun started questioning me about these dividers and what I thought about them after using them for a year. I told him they were a must-have for keeping notebooks organized. I was able to help my students use their notebooks much more effectively this year because they (and I!) could actually find stuff.

The dividers made me more organized because #1) I had to know exactly what skills we would be covering in each unit BEFORE it started #2) I had to know exactly what order said skills would be covered in during each unit BEFORE It started.

Then, we started discussing possible tweaks to the dividers for next year. Since the skills are already written out and in order, we decided that the page numbers were actually unnecessary. My students weren't using the page numbers to find things, anyway.

They were using the topic dividers that I gave them at the beginning of each unit.

Next, Shaun suggested that we could put quiz scores in place of the page numbers. This would put the quiz scores right next to the skill instead of making students flip back and forth.

So, what goes on the other side now? A pretty picture, of course.

Shaun already posted the dividers he designed from his geometry classes here. I borrowed his new and updated template to make dividers for my Algebra 1 classes. Here are the finished products:

(If you're straining to read the skills, they're posted here in a much more reader friendly format!)

Files are uploaded here as (editable) Publisher files and (non-editable) PDF files. If you download the Publisher files, you'll need to also download these free fonts: Righteous and Open Sans. All clip art images were downloaded from ClipArt ETC.

After making this activity to practice classifying relations as a function or not a function, I was eager to make a similar activity to practice a different skill. I settled on creating a practice activity for evaluating functions and better understanding function notation.

I wanted to make this activity use the same integer cards (-4 to +4) that the previous activity used to save me time cutting and laminating.

I grabbed a notepad, wrote a few functions, and fiddled around with the numbers until they worked.

This is what I came up with:

Place the integers between -4 and +4, inclusive, in the missing boxes to make each function evaluate properly. Each number may only be used once.

I printed off the puzzle and gave it to my husband/lovely beta tester to give it a shot. After trying what felt like a zillion combinations, he came up with a solution. I took a look at it and realized it was a slightly different solution than I had in mind when I originally created the problem. For one of the functions, he used the same three integers I had; however, he had the integers placed in different locations within the puzzle.

We discussed the problem and decided we didn't know how long our students would stick with it. The overall idea was good, but it seemed like there was just too much guessing and checking needed. The presence of a square root symbol did mean there could only be a 0, 1, or 4 in that slot. But there were no other similar clues throughout the puzzle.

I dropped the idea for a few days until picking it back up today. I stared at the puzzle for a while before deciding maybe it would be more logically solve-able if I provided the solver with some of the input and output values.

This led to a different version. My functions were longer and more complex, so I had to change the paper orientation. That was annoying.

Instructions:

Place the integers between -4 and +4, inclusive, in the missing boxes to make each function evaluate properly. Each number may only be used once.

My husband found a solution to this puzzle in about five minutes. Given that he's one of the mathiest people I know, I'm expecting it would take students at least 15 minutes to solve the puzzle.

One exciting thing was that the solution I intended when making the puzzle and the solution Shaun came up with were totally different! For one of the functions, we used the same three integers, but we placed them in different places. For the other two functions, we used completely different sets of integers to solve each. This makes me wonder if there are even more solutions to this puzzle?

I'm not as thrilled with these as I am with the function/not a function puzzle. I just feel like these puzzles are missing something that I can't put my finger on.

If you're interested in using either of these puzzles in your classroom or trying them yourself, I've uploaded them here as editable Publisher files and non-editable PDF files.

Each file comes with a puzzle sheet and a sheet of integer squares to cut out.

Now that it's June, I'm realizing that I need to set some goals for what I want to accomplish this summer before it's suddenly August and the back-to-school frenzy begins.

Next week, Shaun and I are keeping busy with math-y things. We're attending our local math teachers' circle's summer immersion workshop Monday-Wednesday. I'm excited for a chance to spend a few days talking math and working through challenging problems with other math teachers. The workshop is at a beautiful retreat, so the scenery will be a treat as well. Plus, the fact that I get to do things like this with my husband is awesome.

On Friday of this week, we'll be attending the OCTM (Oklahoma Council of Teachers of Mathematics) Summer Conference. I'm looking forward to attending presentations and picking up creative ideas to implement in my classroom next year. I'll be sure to blog about any awesomeness I pick up!

Another big plan for this summer is to take a trip. Following our wedding, Shaun and I spent a few nights in Oklahoma City (about an hour away from Drumright) with plans to take a "summer honeymoon" once school was out. We've confirmed that we still want to take this trip, but we have no idea where we want to go. We *think* we want to keep driving to a minimum, but we also like the idea of spending some time at the beach. Living in Oklahoma means these are quite contrary to one another. So, if you have any great vacation ideas, leave a comment below!

What else do I want to accomplish? I think I'll resort to a list now since I titled this post "Summer List" and it's just turning out to be a collection of paragraphs.

* Complete SBG skill lists for each subject I'm teaching next year. [Algebra 1 is done!]

* Write all my quizzes for each subject I'm teaching next year. I did this for Algebra 1 and (most of) Algebra 2 last summer, and it was a HUGE life saver.

* Of course, both of these hinge on this: Figure out what subjects I'm teaching next year!

* Put together a custom planner for next year. [Already in the works!]

* Start reading more! I love reading, but grad school got me out of the habit of reading regularly (unless you count reading educational journal articles about integer operations.) If you have any great book recommendations, I'll take them, too. Please. [I'm keeping a pinterest board of my recent reads.]

* Decorate and organize my new classroom.

* Put together as comprehensive as possible of a list of practice structures for the math classroom. [Contribute to this project here!]

* Finish changing my name with the handful of places I haven't yet.

* Keep blogging regularly. This should encourage me to keep thinking about ideas for the upcoming school year.

* Work on getting into better shape. I downloaded the Runkeeper app last week. And, Shaun has agreed to go running with me. Okay, it's more like 95% walking, 2.5% running, and 2.5% whining that I'm sooooooooooo out of shape. We went run/walking for the first time on Saturday. It was tough. I complained. A lot. But, I know it'll get easier the longer I stick with it. A couple of years ago, I made a list of goals that included running a 5k. At this point, I just want to feel more fit and be able to run for more than a minute without collapsing.

* Organize/Declutter my house. After living by myself for almost four years, the process of combining households after marriage has been interesting. I want our house to feel more like "our house" than "my house that Shaun's moved into." I think Shaun might appreciate some more closet space, too. ;)

* Try out new recipes. During the school year, I tend to fall back on cooking the same old favorites. I'm always bookmarking new recipes to try. I want to actually try them now! Some recent new recipes I've tried: Quinoa Taco Meat, Moist Chocolate Cake (SOOOO good in two layers with homemade whipped cream between and on top and sprinkled with crushed oreos), and Cheesy Vegetarian Chili Mac. There's also the fact that Shaun got a bread maker for his birthday, so we're learning how to use that. So far, he's made a 2 lb loaf of white bread and a 1.5 lb loaf of cinnamon raisin bread. It's tempting to just eat fresh bread for every meal of the day.

* Come up with a system for keeping up with housework. This has NEVER been a strong suit of mine. I'm a list person, so I think I need to come up with a list that tells me what to do when. Then, hopefully I'll actually keep up with it. I think I need a list that tells me what to do every single day, what to do once a week, what to do once a month, etc.

I'm sure there's a zillion things more I want to do this summer. Okay, I'm positive there is. I'm the girl that has a six page long to-do list word document on her computer. But, I doubt you want to hear about my plans to finally getting around to framing my undergraduate diploma and my plans to finally put together wedding photo albums (and an album I bought to commemorate our one-year dating anniversary...)

I'm thinking that I will revisit my progress on these goals at the beginning of July and August to reflect on how I'm doing.

What's on your summer list?

Today was the first of three days of my local math teachers' circle's summer immersion workshop. Picture a room full of 30 elementary, middle, and high school teachers plus a smattering of university professors in a room exploring challenging problems together. This is my second year attending, and it is an absolute blast.

We had breakfast, two morning problem solving sessions, lunch, and an afternoon problem solving session. The topics we explored today were pentominoes and divisibility, cryptography, and something called polygon differencing.

My goal with this post is to share a couple of my take-aways from today. We had to take a pre-workshop survey, and one of the questions asked about what we felt were our strengths and weaknesses as a mathematics teacher. I listed teaching students to problem solve as a weakness. With this in mind, I kept a page of ideas throughout the course of the day.

Developing Norms

One of my favorite things we did was de-brief after the first session on pentominoes. We were asked to take out a sheet of paper and answer two questions.

1. What characteristics describe a good group member?

2. What characteristics describe a good problem solver?

We took our answers to these questions, shared them in our groups, and then compiled a top 3 list for our group. Then, we compiled our group lists into a set of norms.

Since I am planning to have students work in groups this coming school year, I think I'd like to do some problem solving activities the first few days and develop a set of norms at the same time. These norms could then be posted for students to reference throughout the school year.

Now, I just need to figure out what sorts of problems I want to pose to my students.

Round Robin Strategy

Another thing I quickly took note of as soon as we did it so I wouldn't forget was a round robin strategy for sharing within our groups. The facilitator provided us with our first problem and told us to work on it independently for 10 minutes. No discussing with tablemates at all. Then, after the timer went off, she announced that we were going to do a round robin. How she approached the round robin really appealed to me. Instead of asking everyone to share what they had come up with, she asked each person to go around the circle and (in less than a minute) share how he/she had originally approached the problem. We weren't supposed to share what we had discovered in the ten minutes we had been working on the problem. We were only supposed to share our initial thoughts. It was very interesting to hear where everyone in the group had started. This provided insights into how others were thinking that normally wouldn't be shared because they weren't polished/proved/or even right.

When I just ask students to share final answers without how they got there, I'm doing a disservice to my students. This reminds me of the book Making Thinking Visible (affiliate link) which I read in early 2013. I pulled it back out this week and started it again.

Looking forward to sharing more takeaways soon!

Originally, I'd planned to blog after each day of the math teachers' circle summer immersion workshop. But, it turns out that driving one hour to the workshop, spending eight hours doing and talking math, and driving one hour home makes for a satisfying but exhausting day!

Here are a few more of my take-aways from our three day workshop. If you missed the first installment, you can find it here.

Giving Rules is Tricky

On the second day of the workshop, we were introduced to a game known as The New Eleusis. The game was shared by Martin Gardner in Scientific American, but he did not invent the game. We were given an 11 page handout including rules of the game, but our facilitator said he would demonstrate how to play the game so we wouldn't have to read the rules packet. We were invited to join around one table where we would watch a game and learn the rules of the game.

The first thing I noticed is that I get very frustrated when I'm given a bunch of rules to learn, but I don't get to practice them right away. Trying to see over other people's heads to watch a game that was going on is NOT the same as getting to play the game myself. How often do I do this to my students, though? I give them steps to solve a problem, then we talk about those steps, we write those steps down, and then maybe finally they watch me do a problem following the steps. They must feel exactly like I did while watching others play this game.

Another thing that was great food for thought for me was the fact that group we were watching started playing the game without knowing all of the rules. The facilitator had the first person in the group play a card without telling them what type of card they should play. As game play progressed, more rules were given out. Starting to play a game without knowing all of the rules made me feel very uncomfortable. I'm still not sure how this applies to the classroom environment, though.

The game turned out to be fun and challenging, but it took soooooooooooooo long to learn how to play the game that I'm not sure it is worth it. John Golden has created a version of Eleusis called Eleusis Express that makes the game shorter and easier to play and understand. I haven't played this version yet.

Don't Fill in all the Blanks

At the workshop, we were given a list of problem solving strategies in the back of our folders. The first thing I noticed was that not all of the problem solving strategies were filled in. In the past, I've been quick to hang up a list of problem solving strategies on the wall or on a bulletin board. What I should really be doing is letting students develop their own list of problem solving strategies. As students use different strategies, we should post them in the classroom as a reminder.

Let Students Create Their Own Examples to Test Conjectures

The first activity we did with the Four Color Theorem was to try and color a map of the western United States with as few colors as possible. I thought the use of pieces of chopped up colored card stock was brilliant with this activity! Of course, we had to ignore the east coast since it was too small for our small pieces of paper. Our facilitator said he uses giant posters of the entire United States when using this activity with kids so can still used the small pieces of paper.

This was a fun activity, but the twist I really liked was when he asked us to take a ruler and draw our own maps to color. We had to start by drawing five lines randomly from edge to edge on our paper. Then, we figured out the fewest number of colors we could use to color the regions. Then, we addeded a sixth line and repeated.

I think I do a lot of activities like the first map in my classroom. I don't do enough activities were I let my students test the conjectures on their own examples as in the second map.

Life is Better with Pi Shaped Cookies

No further explanation necessary.

Last week, Shaun and I were able to attend the Oklahoma Council of Teachers of Mathematics Summer Workshop at OSU-Tulsa. We attended some great sessions, and I've decided that the best way to not forget what I learned is to blog about it! Over the course of the next few weeks (months?) I want to write a blog post about each session we attended and what I think were the major take-aways.

The first session we attended was on high yield geometry routines, and it did not disappoint! The idea of a "high yield routine" interested both of us, and we *think* Shaun will be teaching geometry next year.

Dr. Utley wasn't able to be there, but John Weaver did an excellent job demonstrating and engaging us in the high yield routines. He recommended the book High-Yield Routines from NCTM (affiliate link). When I looked it up after the conference, I was sad to see it was directed at K-8. I haven't purchased it (yet) because of that reason. Is anyone familiar with it to know if it can be applied to high school?

First, we heard a bit about what high yield routines lead to in the classroom.

Here were my main take-aways (as told by the furious notes I was taking during this session!)

High yield routines must be used early and often to be most effective.
High yield routines should be used in class from day one.
High yield routines offer access to the BIG ideas of math.
High yield routines offer a deep understanding of concepts.
High yield routines should be used to build your classroom environment.

John also made an analogy that I found very thought provoking:

Estimation is to Algebra as Spatial Sense is to Geometry.

My first instinct was to think that we don't do that much estimation in algebra. But, then I got to thinking about how I get SO frustrated when my students arrive at an answer without checking to see if their answer is even reasonable. I need to have my students do more estimation. I need to build this into my classroom as a routine.

In regards to vocabulary, I especially liked John's quote: "Vocabulary is the hill I've chosen to die on." I need to do a better job in my classroom of ensuring that students both value and use proper vocabulary. I haven't done a word wall in a few years, so I'm wondering if this should be part of my initiative again?

Okay. Enough of my random thoughts for things I need to do a better job of next year. Are you ready to learn about these high yield geometry routines?

Quick Draw

This idea is based on the book Quick Draw by Grayson H. Wheatley (affiliate link). The teacher's job is to flash an image on the screen for three seconds. Then, when the image disappears, the teacher tells students to "draw what you saw." It sounds simple, but seeing it unfold in person was powerful. I looked over at Shaun's notes after we did our first Quick Draw activity, and he had written "Do this!!!"

Here are some much more detailed directions:

Here's the first quick draw image we were asked to draw:

After seeing it on the screen for 3 seconds, I was able to easily draw it in my notes. I didn't need the extra 3 seconds to look at it again. Instead, I just sat there thinking "How in the world could I use this in algebra class?"

What really got my attention was when John started asking people to describe what they had saw and drew. The things I was hearing others describe was not what I saw at all! I had seen a square with a triangle inside it that had a vertex at the midpoint of the top line on the square. Other people were describing how they had seen an equilateral triangle with two right triangles formed from the sides of the equilateral triangle. When I realized that different people can see the same image very differently, I began to see even more potential for using this in the classroom!

One more thing about the equilateral triangle thing - this led to an awesome discussion about whether the surrounding shape was a square or a rectangle and if we could prove it. So much math talk about of a simple one minute task!

So, I'm sitting in this workshop feeling kinda silly because I should have realized that different people might see the same image differently. Then, we do another one:

Again, I'm able to draw it easily on my paper. I see a small square inside a larger square with straight lines connecting the vertices of the small square to the corresponding vertices of the larger square. Then, the facilitator starts asking others to describe what they saw. I'm blown away when others start describing seeing 3-D objects. One lady saw a "room." Another lady saw a truncated pyramid. Yet another person saw a lamp shade.

The book Quick Draw (affiliate link) has a collection of these images to use. Here is a sampling:

And, here were some of the benefits of this high yield geometry routine:

I did some searching online and found a few more sources of quick draw images if you want to try them out in your classroom before investing in the book.

A summary of Quick Draw by the author - includes a video of the structure in action!

Journal Article Including Several Quick Draw Images
NCTM Article About Quick Draw

I was so impressed with how much geometry vocabulary and math talk came out of this simple routine. I can definitely see how this is an activity that can be used throughout the year to gauge how students' vocabularies and spatial senses are developing.

After discussing Quick Draw, two tweaks to the activity were suggested:

1. Have students construct the image on a geoboard. This would make it easier to discern between squares and rectangles.

2. Instead of asking students to describe what they saw, have a student describe to the teacher how to draw the image on the board.

Quick Build

We also talked about a variation of Quick Draw known as Quick Build. When we had entered the room where the workshop was, we had been given a set of 5 snap cubes. We were all immediately curious about what the snap cubes might be used for.

Here's the type of image that would be shown to students during a quick build session:

Just like with Quick Draw, the object (or picture of it) will be shown to students for 3 seconds. Then, it will be taken away so they have a chance to draw it/build it. Show students the image for another 3 seconds for them to fix their drawings.

You have several options with Quick Build:

Have students recreate the 3-D figure using Snap Cubes
Have students draw the 3-D figure using Isometric Graph Paper
Have students draw the "top view" of the figure.
Have students determine the volume of the figure.
Have students determine the surface area of the figure.

I'm sure there are many other options, but these are the only ones we discussed.

At the bottom of this article, there is a video of this activity taking place in a classroom.

Fold-N-Cut

I'm really sad I didn't think to take any pictures of this activity while it was being presented. So, I'll try to explain it to the best of my ability.

Hold up a sheet of paper to your students. Fold it in half with the top edge of the paper coming down to meet the bottom edge of the paper. Whenever you do this activity, the fold should always be at the top.

Take a pair of scissors and cut the folded paper. Our facilitator cut a triangle off one corner, a square out of the bottom, and a quarter-circle out of another corner.

Then, it was our turn.

Draw what the paper would look like when it was unfolded.

We repeated the activity with a paper that had been folded into fourths.

We were warned to NOT ask students to share strategies with this activity. Some students will discover that they can simply draw what the folded paper looks like and then perform a reflection/rotation of that image to end up with what the unfolded paper will look like. While this is awesome, once students start doing this the activity will lose a lot of its charm.

Where's Polygon

Another activity we discussed was called "Where's Polygon." I've included the instructions from the presentation below, but here's the general gist of it.

Display a blank coordinate plane for students to see. At the conference, this was done with a document camera. If you have access to a projector, you could use different colored dry erase markers on the board. If you have a SMARTBoard, just project the coordinate plane on there.

Before beginning, have a specific polygon in mind - exact coordinates!

Your color coding will feature four colors. One color for points outside of your polygon. Another color for points inside of your polygon. Yet another color for points on the edge of your polygon. And, a final color for the vertices of your polygon.

As students call out ordered pairs, color them accordingly. This continues until all the vertices of the polygon are found.

Now that circles have moved to the Oklahoma geometry standards, I think it would be fun to throw a circle into this activity to see how students react. Of course, a circle isn't a polygon, so that would be a bit mean... I see such potential for this routine to grow with students throughout geometry class.

Guess My Rule

This activity pulls from an awesome problem found in Michael Serra's Discovering Geometry (affiliate link) text. Students are given a set of images that are examples of widgets and a set of images that are non-examples of widgets. Then, they are asked to determine if other images are or are not widgets.

Next, we saw how we could use polygons to make our own problems like this.

Sadly, I never got to figure out what John's rule was because we ran out of time.

There were a few more routines in the presentation that we didn't get a chance to get to, so I'm afraid I don't have all of the details. There were slides for them in the original presentation, but I had trouble filling in the missing pieces myself. You can find the entire presentation here (open the folder titled High Yield Geometry Routines).

This is my second blog post recapping sessions Shaun and I attended last week at the Oklahoma Council of Teachers of Mathematics Summer Conference. Be sure to check out my previous post on High Yield Geometry Routines!

The second session we chose was called Fun Functions by CPM.

The Bug Problem

We began the session by checking our understanding of what a function is. I took a picture of the PowerPoint slide, but it didn't come out readable at all. So, you'll have to put up with my re-creating the slide in Microsoft Paint...

Image Source: Buel P. Colton, Zoology: Descriptive and Practical(Boston:D.C. Heath & Co., 1903) 18

I was shocked at just how many teachers in the room voted that this was most definitely not a function. Then, I started thinking about what my students would say if I gave them this question. The thought was not pretty. My kids need to know more about functions than just the vertical line test!

Function Machines

The first activity we did was to order function machines.

Here were our four functions:

Of course, they were printed on function machines and laminated for durability. (And, for the record: laminated papers are really hard to photograph in a bright classroom!)

CPM has posted these function machines as a free PDF on their website if you're interested.

Source: http://pdfs.cpm.org/stuRes/CCA2/chapter_01/CCA2%20Lesson%201.1.1%20RP.pdf

Our task was to arrange the functions so that when a 6 was dropped in the first function machine that the last machine's output would be 11. This led to some good conversation in our group about which functions couldn't be last.

CPM also has a PDF version of this activity with an easier set of functions that I plan on using with my Algebra 1 students this year.

Silent Board Game

Next, we moved on to an activity called silent board game.

When we entered the room where the session was held, this laminated sheet was taped to the wall:

The idea is that the teacher puts up an incomplete input/output table.

Here's the one we used in our session:

I got this image from page 8 of this file from CPM that features several pre-made Silent Board Game tables.

As we played the game, I realized it truly was a silent board game. The facilitator would hold up her dry erase marker until someone raised their hand. Then, she would hand them the dry erase marker. They would walk to the board and fill in an output value. If the output value was correct, there would be silence. IF the output value was incorrect, there would still be silence. But, the teacher would walk to the board and erase the incorrect value.

This continued until the board was filled. Then, we moved on and silently filled in the rule for the function and the functions' growth rate.

I'm honestly not sure how this activity would play out in my classroom. Would my students stay silent and engaged the entire time???

One participant in the session suggested a tweak to this activity: have a graph where students plot each point after adding it to the table. This could help students see if the function was linear, exponential, etc.

Function Walk

After the Silent Board Game, it was time to get out of our seats and do a function walk. Our facilitator suggested that this was a great activity to get students outside. If doing it outside, she suggested that we could draw the axes of our coordinate plane with chalk.

Since she works for CPM and does this presentation frequently, she had taken two rolls of ribbon and written the values on them to serve as axes. I thought this was quite ingenious!

We were each given a laminated index card with an input value filled in. Different people received different colored index cards. I was in the red group.

The purpose of the color-coding became clear when we got our handouts. As a person with a red card, I would be helping to graph the equation y = 2x + 1.

We took turns graphing different functions.

Here's my spot on the x-axis before we moved to our appropriate spots.

And, here's a picture of the rest of the red group in action:

If I end up teaching trig again this year, I think I'd definitely like to do some kinesthetic graphing of trig functions.

There were several other activities in the handout that we didn't get to. A copy of the handout for this presentation can be found here.

For the past few days, I've been recapping various sessions that Shaun and I attended at the Oklahoma Council of Teachers of Mathematics Summer Conference. So far, I've recapped High Yield Geometry Routines and Fun Functions. Today, I want to share what I learned from a session called "Taking the Practice Out of the Worksheet" by Judy Schwarz (her name is misspelled below). There are SO many good ideas in here! Apologies in advance for the picture overload that this post is sure to become!

I guess I didn't read very carefully because I didn't realize this was a geometry session. Thankfully, even though a lot of the ideas are for geometry, they can be modified for any math classroom. The facilitator just happens to teach geometry, so that's what form most of her ideas are in.

If...Then Posters

The first idea that Judy shared was to have students make "If...Then" posters at the beginning of the school year. She said she often has students do this before they've ever even talked about conditional statements. If I remember correctly, she usually has students complete this as homework. But, if you have access to a stack of magazines, you could even have students do it in class during the first week.

Here are some examples she brought to show us:

And, here are my interpretations:

If you eat spicy food, you need to brush your teeth.

If you own a lot of dogs, you have to buy a lot of dog food.

If you get caught drinking and driving, you will end up in jail.

The facilitator said she hangs these up around the classroom for instant decorations. Then, when they begin the unit on conditional statements, she has students work problems from the posters made by their students instead of from the problems in the textbook. Students will have to pick a poster from the room and write the converse, contrapositive, etc. By starting with real-life examples, students are more engaged. Eventually, they do move on to the problems in the textbook.

I love this idea, and it kinda makes me sad I'm not teaching geometry...

Stump The Teacher

Next, Judy shared an activity she uses occasionally with her students: Stump the Teacher. It goes as follows:

* Give students a textbook section to read. Set a timer.

* When the timer goes off, the teacher closes his/her textbook.

* Students take turns asking the teacher questions that could be found in that textbook section.

* If a student is able to stump the teacher, he/she gets a small prize. (Judy says she gives 1 point extra credit when a student is able to stump her.)

* After the teacher feels like she has an idea of the students' understanding of the concept based on their questions, the tables are turned. Now, the students close their textbooks and the teacher starts calling on students to answer questions.

This activity gets students reading and re-reading as they try to formulate questions to ask. Students need to think about what the main ideas of the lesson are and what common sources of errors might be. The teacher makes sure to pull out important ideas not brought up by students when it is his/her turn to ask questions.

A quick google search led me to another more thorough explanation of this activity.

I don't use textbooks in my classroom, so I'm not sure how I'd apply this structure to my classroom. If I could find an interesting article that relates to a topic we are studying, I might could see myself using this structure to ensure that students actually read the article. Hmmm...

Top Ten List

This next idea is so simple, but I think it's definitely a keeper!

At the end of a chapter or unit, have a students make a list of the top 10 things they learned. This could be done as a homework assignment, or you could give students a few minutes in class to complete.

Then, put students in groups. They must each read their top ten list to the group and compile a top five (or top three) list that is agreed upon by all members of their group.

Judy claims that this simple activity gets kids talking about math and justifying their answers. The discussion helps kids really concentrate on what the key ideas of the unit were.

Remember my interactive notebook dividers for next year? I'm already thinking about replacing the bit with the pretty picture to be a place for them to record their top ten list.

Around the World

This is an idea I've used in my own classroom, but I've always referred to it as a "Scavenger Hunt."

Sheets of paper are placed around the classroom. Each sheet has a problem and an answer (to a different problem.)

Students choose one poster to start at. After working out the solution to the problem on that poster, they search the other posters for the poster containing the appropriate answer. Then, they solve the problem on that poster. This process continues until you circle back around to where you started.

Picasso Polygon Portrait

Students are given a set of requirements of what must be in their self-portrait. Students MUST use a ruler when completing the project.

Here's what a finished portrait looks like:

Students peer grade each other's projects using a rubric.

I really liked Judy's explanation of how she has her students peer grade each others' projects. She takes up all of the projects, shuffles them, and hands them back to students to grade. She makes sure that best friends aren't grading each other's work. Students use a copy of the rubric to grade another student's project. When students are done grading, they take the original project and the rubric and deliver it to the student it belongs to. Each student looks at the rubric and decides if they agree with the grade they have been given. If a student disagrees with the way they have been graded, they take a colored sheet of paper and staple it to the top of the project with why they disagree with the grade the other student gave them. When the teacher is entering grades, he/she just need to double check the projects that have colored sheets of paper on top.

Leap Frog

The next activity we did was called Leap Frog. This was a review game that was totally new to me. That's always exciting to experience at a conference!

Each student is given a deck of cards. This will be their answer bank. Judy suggested printing each deck on a separate color of paper. If this isn't feasible, have the first set of students who use each deck write their initials on the back of each card. Then, if a card gets dropped in the floor during clean-up, it can easily be reunited with its friends.

Students arrange their desks in a circle, and each student lays out their deck of cards.

We played Leap Frog around two rectangular tables. This worked, too.

A problem is projected on the board.

When a student figures out the answer (or what they think the answer is) they grab the answer card and hide it so none of their neighbors can see.

When time is called, each person compares the answer card in their hand with the answer card in their neighbor's hand. The teacher announces the correct answer. Everyone returns their answer card to the deck in front of them. Those students who got the answer correct stand and rotate desks to the right.

The goal of the game is to be the first student to make it all the way back to where you started by "leap frogging" over other players.

The facilitator said she has used this with great success with her Pre-AP Geometry classes. I can definitely see the competitive nature of this activity working for more advanced students. But, I'm not sure if I'd want to use this with my Algebra 1 classes. I can see my IEP students getting very, very frustrated. My trig and statistics classes, on the other hand, would probably have a lot of fun with this.

Some of the audience members expressed that making up a deck of cards was too much work, and they suggested having students write their answers on a dry erase board.

One other concern I have with this activity is that I think it might be a tad bit too easy for students to cheat. I was sitting right next to Shaun, and it would have been very easy to just wait for him to pick up his answer and pick up the same answer. Of course, students can cheat with many review games by just looking at what their neighbors are doing. I guess the only person they are punishing is themselves.

The last few things we did during the hour-long workshop was to circulate between three tables with more ideas of practice activities that don't involve just doing a worksheet. Each table had a sheet explaining each activity. Instead of trying to put each activity into my own words, I'm just posting the picture I took of each sheet.

Sorting Activities

Self-Checking Activities

Miscellaneous Activities

I really liked having the line on a transparency where students could just move it around. I thought this was super clever!

And, that's a wrap. This was such an awesome session to attend!

Can you believe it's already July?!? I'm not entirely sure where this summer is going. Shaun and I just got back from our vacation earlier this week, so I thought it was time to post an update regarding my progress on my Summer To-Do List.

Table Rock Lake - Branson, MO

As for our vacation, we decided to head to Branson, MO for four nights followed by four nights in Little Rock, AR. It was nice to get away and play tourist for a little over a week. Plus, Shaun got to double the number of US states he has visited. We also thoroughly enjoyed not having to worry about dishes, laundry, or other household chores. I'd also say we didn't think any about school, but that would be a blatant lie.

I took my recently purchased copy of Designing Group Work: Strategies for the Heterogeneous Classroom by Elizabeth Cohen (affiliate links contained in this post) with us along with two highlighters, and I completely devoured the book on vacation. After I blogged about creating some groupwork posters, Erin Flotte left a comment suggesting this book as a great resource. Within a day or two, I had ordered it from Amazon. I chose to order the 1994 2nd Edition because it was significantly cheaper on Amazon. But, I ended up loving the book so much that I kinda wish I'd bought the 2014 3rd Edition.

A couple of years ago, I had decided to implement groupwork in my class. I made posters for group norms and group roles, but I never actually ended up following through on it. Sure, my students sat in groups, but they weren't doing real group work.

I had thought that I wanted to do groupwork because it would be beneficial for my students. Reading Designing Groupwork showed me why groupwork is actually effective. And, it showed me how tricky it is to pull off effective groupwork.

The best thing about this book is that it doesn't just stop there. It gives specific things you can do with your students to teach them how to work effectively in groups. I've already decided one of these activities is going to be my first day of school activity. But, more on that in another blog post!

Let's get back to the point of this post: updating how my summer is going. As I mentioned earlier, Shaun and I enjoyed a lovely vacation. Shaun has been recapping our vacation on his Dropping the S blog. So, if you'd like to see pictures and here about some of our adventures, check them out here.

How's the rest of my Summer List going?

SBG Skill List and Quizzes for Each Subject

Algebra 1 skill list is done, but I'm currently in the process of revamping it based on a presentation I attended at the Oklahoma Council of Teachers of Mathematics Summer Workshop. I still don't know what other classes I'm teaching...

No progress whatsoever on the quiz front.

I am happy to (finally) announce though, that my husband will be joining me as a math teacher at Drumright next year! This has been such a hard secret to keep!

Make a Planner for Next Year

DONE! I still need to blog about my planner, but here's a sneak peek:

Read More

In June, I read one novel and listened to three audiobooks. (I'm keeping track of my recent reads on this pinterest board if you want to follow along.) This isn't a lot compared to how much I used to read, but it's a definite improvement over how much I had become used to reading because of grad school. My favorite read (or listen) of the month was Made to Stick by Chip Heath and Dan Heath (affiliate link). Don't confuse this book with the much-loved by the MTBoS, Make It Stick: The Science of Successful Learning by Peter C. Brown (affiliate link).

The focus of this book was to determine what makes some ideas catch on and be remembered when plenty of others die. The book discussed the stickiness of ideas in the classroom which I found very interesting. After I finished listening to the book, I kept finding myself thinking things like "That's definitely adding to the stickiness of this idea." Then, I felt guilty about getting sidetracked from the point the pastor was trying to make on Sunday...

Here's a PDF overview of the 6 traits of sticky ideas. If you want a sneak peek, the Heath Brothers have posted Chapter 1 for free on their website. They have also posted a 13 page PDF extension of the book on their website titled, Teaching that Sticks. This shows how each of the principles shared in the book can be applied to the classroom.

If you're a fan of Malcolm Gladwell's books, I think you'll really enjoy this read!

Decorate my new classroom

My first task I attempted toward this was buying curtains for my new classroom. There is a huge window right behind my desk that I would like to cover up. Upon measuring the window, I found that it was approximately 90" high. The typical curtains that you buy at the store are 84-85" high. Looking at the curtains hung by other teachers, most of them have a 5-ish inch gap at the top or bottom of the window which I am trying to avoid. I found some 90" curtains on Amazon and ordered them. It was sold as a "pair" of curtain panels. A bunch of the reviews said that even though it was sold as a "pair" they only received a single curtain panel. However, plenty more reviews claimed to have received a "pair." I took a gamble and ordered them. What did I receive? A single curtain panel. I contacted Amazon, and they refunded my money with the instruction that I could keep the curtain panel I had received. Of course, I could order another one and have a "pair," but another review said they had done that and the dye lots had not matched. So now, I possess one curtain panel. That is the sum total of my progress on decorating. So much still to be done!

Compile a list of practice structures

Thank you all for helping me with this project! I have received some awesome submissions, but I am struggling to find a way to organize them that really makes me happy. I've tried several different formats and given up on all of them. Hmm...

Finish Changing My Name

I still need to work on this...

Keep Blogging Regularly

I feel like I was doing a good job of this BEFORE we went on vacation. Now that we're back, I need to work on this some more.

Exercise More

Shaun and I hiked a lot while we were on vacation. Now that we're back home, I need to find a way to find a way to fit fitness into our regular routine. Yesterday afternoon the weather was nice, so I convinced Shaun to join me for a short walk around our neighborhood. We made a loop that RunKeeper tells me is 0.51 miles. Part of my problem is it gets soooooo hot and muggy that I don't want to be outside at all.

Declutter the House

On Father's Day, we had lunch with my parents and grandparents. I was able to take the bags of clothes I had decluttered from my closet to my sister to see if there was anything she would like. Other than this, I haven't made much progress.

Try New Recipes

I haven't cooked much of late because of our vacation. But, I did make One Pot Roasted Red Pepper Pasta last month that turned out really well. On our last Aldi trip, I picked up a jar of pesto that I didn't really have any specific plans for. I used that to make some pesto pizza rolls with onions, mushrooms, black olives, and leftover roasted red peppers from the pasta experiment. Other than the fact that the wax paper wanted to stay stuck to the dough, they were so yummy!

Also of note, I made my first loaf of bread in the bread maker. Since the bread maker was Shaun's birthday present from his family, he read the manual and has been the bread machine expert. After we got back from vacation, I decided to bake a loaf of bread by myself while he was mowing the lawn. I'm happy to report that it was a success!

I also made a new-to-me dish (as in I knew it existed as a dish but I'd never made it before) without a recipe the other day. I made vegetarian chili in my cast-iron skillet and topped it with cheesy-corn-and-jalapeno cornbread. Shaun declared it a very American dish!

Come Up with a Housework System

I downloaded a "Habits" App to my phone that I've been using to try and build habits. I've been tracking things like making the bed, doing a daily load of laundry, washing the dishes, flossing, taking my multi-vitamin and pro-biotic, sweeping the kitchen, swishing and swiping the bathroom, and reading my Bible. I wasn't sure how motivated I would be by the check mark system, but I think it's definitely working!

I've gone from being a person who regularly thought "I should floss. Oh, I'll do it tomorrow." to a person who has flossed 22 days in a row. Of course, it's not magical. My "best streak" for doing the dishes is 2 days in a row. And, my daily goal of sweeping the kitchen has occurred a grand total of 4 times. But, progress is being made!

Oh, and one other exciting thing happened in June:

My diploma for my master's degree showed up in the mail!

Yesterday, I mentioned that I had recently read Elizabeth Cohen's Designing Group Work: Strategies for the Heterogeneous Classroom (affiliate link to 2nd Edition / 3rd Edition).

I absolutely loved this book, and I think it's one of the most practical, applicable education books I've ever read. I know this is going to be a book I reference over and over and over as I seek to engage my students in productive group work this year.

Here was the blog comment that led me to buy the book:

Having now read the book, I completely concur!

A few years ago, I made these classroom/group work norms posters to hang up in my classroom.

I guess I thought that hanging posters up on the wall would magically convince my students that this was how they should work together. They would point to one of the posters every once in a while and make a comment, but other than that they didn't really do much to change the culture of my classroom.

Now that I've read Cohen's Designing Groupwork, I realize that norms are something that must be taught and practiced and reinforced and reinforced and reinforced if you want your classroom to be characterized by them. Thankfully, the book provides concrete activities you can do with your students to illustrate the importance of these norms.

This year, we will be starting school on a Monday instead of our normal Thursday. In the past, we've always started on a Thursday which meant we could do fun, getting-to-know-you activities the first two days of school. Then, we'd have a weekend to recuperate and be able to hit the ground running on Monday. Because our students' schedules change so much in the first couple of days of school, I don't want to jump straight into content. So, my current plan is to spend the first week of school teaching my students how to work in a group. We'll work through a series of activities suggested by Cohen to build/reinforce norms. Cohen claims that time spent reinforcing norms is time well-spent because it allows future groupwork to proceed much more efficiently.

The first activity that really caught my eye in Designing Groupwork was Broken Circles.

Cohen notes that Broken Circles was developed by Nancy and Ted Graves. And, this activity is based on an activity known as Broken Squares that was invented by Dr. Alex Bavelas.

Students are placed in groups of 3-6. Each student is given an envelope that contains 2-3 puzzle pieces. The objective of the activity is for students to put their pieces together in such a way that each student has a complete circle.

There are some very specific rules that must be followed, though.

1. No talking. I think this will be the hardest rule for my students to follow.

2. No point or hand signals may be used at any time. This will also be very tricky for my students. As soon as they realize they can't talk, this will be the next thing they want to do.

3. Each player must put together his or her own circle. No one may show another player how to put together his or her circle or do it for him or her.

4. Students may not take pieces from another student. However, they may give one or more of their pieces to another student. They may not put the piece in another person's puzzle. Instead, they must hand it to the other person or lay it down on their desk.

Here's a task card I typed up to laminate and give to each group:

So, what do the pieces look like?

The book came with an image of how to make the puzzle by cutting up pieces of card board. I instantly turned to google with the hopes that someone had made the puzzle into a pdf I could just print out. I thought I had lucked out when I found this Word Document on Stanford's website. I printed out the pieces to play around with them, but the angles were not accurately drawn. Three pieces that were supposed to fit together and make a perfect circle just didn't. [NOTE: This file does have the full text description of the activity as found in Cohen's book in case you want to read about the activity in more authoritative detail!]

Here's what the Stanford template looked like. If you look closely at the A wedges in the first three triangles, you'll see the issue I ran into.

Shaun suggested that I could easily make perfect circles using the degree measures from the template in GeoGebra. (Of course, he had to walk me through making them step-by-step. GeoGebra and I are only casual acquaintances.) This also helped solve another problem. The above circles are designed for groups of 6 students. I wanted to be able to use this with my groups of 4 and possibly a group of 5 or 6 if necessary. Making my own templates would make this much easier.

The Stanford file had larger versions of the circles that printed 1 to a page. I cut out a version of these, but I decided that this seemed like a waste of paper to me. For my version below, each group's circles will print on a single page. This makes me feel a lot more like laminating them and cutting them out!

Here are the circle templates for a group of 6 students. All the pieces with the same letter go in a single envelope.

To make the activity work for a group of 5, the last circle is deleted. And, the remaining F piece is redistributed to make up for the piece that was taken from the D envelope.

I repeated the process for group sizes of 4 and 3.

So, I still haven't shared the part about this activity that makes me the most excited to use it in my classroom on the first day of school: It's not as easy as it looks!

Of course, the no talking, no pointing, no touching other people's pieces rules will make it tricky. What makes it super-tricky is that the person with the A envelope is going to set the tone of the game and they don't even know it.

Take a moment to look at the three A pieces above. Notice anything? If I did my GeoGebra-ing correctly, each of the A wedges should measure 120 degrees. What happens when you have three 120 degree pieces? Yup. They make a circle.

Now, take a look at the pieces for the other letters. They will most definitely not make a circle when put together. What I'm expecting to happen is this: the person with the "A" envelope will get very excited and put their circle together. The rest of the students will struggle and struggle and struggle. The group will not be able to make any headway until the person with the circle made of A's decides to pay attention to what the other group members need. Even though all of A's pieces will make a circle, this circle is not part of the final solution.

To succeed in this activity, students must pay attention to what their group members need. This is not something my students are accustomed to, and I'm hoping it will be a powerful lesson for them.

Here are the two norms that this activity is meant to reinforce:

1. Pay attention to what other group member's need.

2. No one is done until everyone is done.

After groups finish, I plan to give them this reflection sheet. Each person in the group will be responsible for filling out a different box on the sheet.

Then, we'll wrap-up the activity with a class discussion about what we learned about being effective group members.

I'm super-excited to try this activity on the first day. I'm not sure exactly how long it will take, but I think the activity + reflection time + discussion + other first day of school importantness like taking roll and telling students what supplies they need should fill the 50-minute class period.

Of course, I'll make sure to have a back-up activity in case we fly through this waaaaaaaaaaaaay faster than I expect us to.

Are you as excited about this activity as I am???

I've uploaded the files I created here. You'll need to download these free fonts if you plan to edit the Publisher files; HVD Comic Serif Pro and Open Sans. If you download the PDF files, the fonts will be embedded, but the files will not be able to be edited.

If squares are more your thing, here's a link to a Broken Squares activity I found.

twitter.com/theshauncarter

My planner for the new school year has done for a while. Now, it's time to finally share it with you. (Thanks Shelli for the push to get around to blogging about this!)

For my planner this year, I'm using the Arc System by Staples. In the past, I've purchased a planner, but I hated that I couldn't customize it. This discbound system lets me change things to my heart's content. Shaun is also using the arc system for his planner, so we felt like we could justify buying the fancy punch.

Note: I've already blogged about most of the pages below and included links to download them. You can find that post here. The calendar pages (which I haven't blogged about before) can be downloaded here. If you download the editable version, you'll need to also download the free fonts Ostrich Sans Heavy and HVD Comic Serif Pro or substitute your own favorite fonts.

Since I was planning on designing my own inside pages, I just bought a pretty cover and a set of pink discs to get my planner started.

Inside, I have a clear zippered poly pocket that holds post-it notes, stickers, etc.

I also invested in a set of 8 dividers for my notebook to keep things more organized. I bought these from the Martha Stewart line at Staples because they were cheaper than the Arc brand. Plus, I got a set of 8 dividers instead of 5.

I still haven't decided if I'm perfectly happy with the way I have stuff ordered in my notebook yet. But, that's okay since I can easily reorder the pages.

My plan at the moment is to have the first tab contain my to-do list and info on current projects.

The next section contains my calendar pages. My husband made this version of our school calendar for us both to include in our planners. Have I mentioned that I'm super excited about getting to work in the same building as my husband next year?!?

For my planner pages, my goal was to have a way to keep track of several things:

School Stuff - Faculty meetings, meetings with parents, deadlines for submitting things, student council meetings, days when various student organizations will be absent, school sporting events, etc. Having this all written on my calendar helps me figure out what days to not schedule a test or what days are open to schedule a student council event.

Personal Stuff - Doctor and dentist appointments, birthdays, reminders to do things like pay the rent, etc.

Good Things - I love reading the One Good Thing blog. The teachers who participate in this blog commit to blog each day about something good that happened during their day. Sometimes it's something big. Other times, it's a small thing that would often go unnoticed. But, it's always good. If you haven't subscribed to this blog, you are definitely missing out! The posts there never fail to put a smile on my face. While I don't have the commitment necessary to write a daily blog post, I do want to build a habit of recognizing the good in every day. I started doing this at the end of last school year in my planner, and it was definitely my favorite thing to look back at every day. So, I want to include a space to record something good about each day.

Meal Planning - Being married means I have to do a lot more thinking about meal planning than I ever did when I was single. I'm not a serious meal planner. This will probably be used more in retrospect to record what we eat to help us come up with ideas later on. Or, if I really get on top of things, maybe I will start planning ahead.

What you WON'T find in this planner is my plans on what to teach on what day. I plan to keep these in a google document. I've never been required to turn in my lesson plans, so I've never been good at writing down and recording my plans to look back at later. I've tried to do so many, many, many times, but I always get frustrated when plans change. It seems like I never get everything done in a class period that I thought I could get done. I'm thinking that having them in a google document will let me copy and paste them to the appropriate day which should lessen the sting a bit... When I get a lesson planning document I'm happy with, I'll be sure sure to blog about that, too!

Okay. Enough talking about what I want it to contain. Let's look at pictures. :)

(Notice how June 10th is filled in below? That was the day I actually took the pictures for this blog post...)

For these calendar pages, I created a basic weekly template. Then, I typed in all of the dates in an excel file and used mail merge to put together my planner pages. This was so much faster than trying to type directly on the pages. I've included the mail merge file with the dates in case you want to edit my template to fit your needs. (Remember: files can be downloaded here!)

I only made my planner pages go through June 2017 because I figure by next summer I'll be itching to try out a new planner page design. To keep track of dates that don't fall in my planner's range, I included a section for future dates.

And, I also made a section to record birthdays. Now, I need to actually get busy and record some birthdays...

I like that my dividers are slightly see-through because I can see the header page for the next section through it.

This next section is to record notes from meetings at school. My new principal says he rarely calls a faculty meeting. My previous principal believed in weekly faculty meetings. We'll see how much use this section gets. If I don't end up using it, I can always just pull these pages out.

A big goal of mine this year is to do a better job of keeping in contact with parents AND recording that contact. I'm hoping these planner pages help with that.

My next divider contains information for my role as student council adviser. Right now, it just has templates I made to record notes from our student council meetings.

Since I'm terrible at remembering passwords, I created a passwords section for my planner. Now, this isn't the place for super sensitive passwords like my online banking or credit card. This is more for things like "What's the password to see my evaluation online?" or "What's the password to update my page on the school website?"

My school pays me to do after school tutoring IF I keep a detailed log. I've never been good at this, so I usually end up doing lots of tutoring without any compensation from the school. I know, not smart. This year, I have a log to keep me organized and compensated. :D

The next pages are for me to record things I have loaned to others and things I have borrowed from others. This will hopefully deter students from borrowing things and never bringing them back. It will also help me to track down those that forget since I'm the one that forgets who I loaned stuff to all the time.

My school provides all students with calculators while they are at school. When students take the ACT, they need to borrow a school calculator to do so. This sheet is to help me keep track of these loaned calculators.

This next section has nothing to do with school. I just want to keep a log of my recently read books.

The last section of my planner is my address book. This is where I go when I need to send a thank you note to my great-aunt or send a birthday card to my sister (why can't I ever remember her zip code???).

Having these all in one place means I can finally throw away all those corners of envelopes I've torn off over the years with people's addresses on them. Yay for decluttering!