cheesemonkey wonders

cheesemonkey wonders

Wednesday, August 29, 2012

INBs Day 2: the Test & the Announcement of the INB Beauty Pageant on Friday

Students did pretty well on today's "Parts of the INB test." The lowest grades were low As, which made me very happy. I gave them five minutes before the test to quiz each other, and it was great to see how engaged and involved they were with their foldables. They are starting to really "get" the idea of the parts, the idea of the date stamp, and the Table of Contents. Today I gave our first Daily Date Stamps, and several students had to quickly fix mistakes they had made, such as taping page 2 of their TOC to page 3 (a LHS page) rather than to page 2 (a RHS page).

Not only does this process give students practice in following instructions (which middle schoolers sometimes have trouble with), it also gives them a chance to settle into the aggressive pace I am setting for the year. It also creates a culture of intrinsic motivation, with an emphasis on autonomy, even though they are following general instructions and interacting with their notes far more than they generally do. The amount of energy expended in handling their materials is really new for them, and nobody complains about writing brief reflections on a LHS page or redoing their table of contents.

So it was predictable that when I announced we would be having an INB Beauty Pageant on Friday with awards in a wide range of yet-to-be-determined categories, my students would completely flip their lids.

The time has been flying by, both for students and for me. It's a really lovely way to begin the year.

Tuesday, August 28, 2012

Day 1: INBs and foldables and tests, oh my!

Introducing the Interactive Notebooks (INBs) on Day 1 of school worked ALMOST PERFECTLY!

You should have seen the scissors and tape flying in there. :-)

I introduced the concept to my class of 7th graders very briefly, then quickly got them  busy DOING things -- getting handouts, making a foldable on the parts of the INB, filling it in, and setting up their table of contents pages. The homework tonight is to finish setting up the TOC pages and study the foldable on the parts of the INB in preparation for tomorrow's test. Yes, a test! On Day 2! I must be a maniac!

I did the same with my mostly 8th grade class, though we didn't get through quite as much as the earlier class. In their defense, they do have Algebra right after lunch and frankly, after all the rules and responsibilities reviews all morning, nobody is at their best right after lunch on the first day.

The funny thing, though, was that the activity instantly got everybody engaged in what was going on. Because no one had ever done it before, no one was at a particular advantage or disadvantage. They've all been cutting and pasting since pre-school, but never in the service of their more recent learning.

I used the document camera to model what we were doing and I found that the kinesthetic aspect added an extra dimension of interest to the activities. The foldable was on yellow paper, and my scissors have bright orange handles, and I was showing them where and how to fold and cut and snip. There were some misfires during the cutting process (which I had anticipated there might be), but I told these students to simply recycle the spoiled handout and get a new one from the hanging file because in mathematics making mistakes is a normal part of the learning process and we simply regroup and keep going.

I got the impression that no one had ever normalized the mistake-making process, and that made me even more eager to play The Mistake Game with our giant group whiteboards.

At the end of each class, I took a brief, unscientific poll and discovered that nobody in either class had ever done a foldable in class before! Egad! And they all really seemed to like the tangible nature of managing the learning of abstract procedures.

I'm excited to see what happens on Day 2. Stay tuned for more!

Monday, August 13, 2012

Life on the Number Line - board game for real numbers #made4math

UPDATE: Here is a working link to the zip file:

Last year I blogged about my work on a Number Sense Boot Camp, so I won't rehash all of that here. This year I want to give the follow-up on how I used it last year, what I learned, and how I'm going to use it this year in Algebra 1.

This was my breakthrough unit last year with my students. It anchored our entire Chapter 2 - Real Numbers unit and really solidified both conceptual understanding and procedural fluency in working with real numbers, the real number line, operations on real numbers, and both talking and writing about working with real numbers. We named it Life on the Number Line.

Here's how the actual gameboards, cards, and blank worksheets looks in action (sans students):

I sure hope I didn't make a bonehead mistake in my example problem!

The most effective thing about this activity was that it compressed a great deal of different dimensions of learning into the same activity, requiring learners to work simultaneously with the same material in multiple dimensions. So for example, they had to think about positive and negative numbers directionally in addition to using them computationally. They had to translate from words into math and then calculate (and sometimes reason) their way to a conclusion. They had to represent ideas in visual, verbal, and oral ways. And they had to check their own work to confirm whether or not they could move on, as no external answer key was provided.

Since they played Life on the Number Line for multiple days in groups of three or four players comprising a team who were "competing" in our class standings, learners felt that the game gave them an enormous amount of practice in a very short amount of time. Students also said afterwards that they had liked this activity because it helped them feel very confident about working with the number line and with negative numbers in different contexts.

I also introduced the idea of working toward extra credit as a form of "self-investment" with this game. For each team that completed and checked some large number of problems, I allowed them to earn five extra-credit points that they could "bank" toward the upcoming chapter test. Everyone had to work every problem, and I collected worksheets each day to confirm the work done and the class standings.

What I loved about this idea was that students won either way — either they had the security blanket of knowing they could screw up a test question without it signifying the end of the world, or they got so much practice during class activities that they didn't end up actually needing the five extra credit points!

Students reported that they felt this system gave them an added incentive to find their own intrinsic motivation in playing the game at each new level because it gave them feelings of autonomy, mastery, and purpose in their practice work.

The game boards were beautifully laminated by our fabulous office aide but do not have to be mounted or laminated. The generic/blank worksheets gave students (and me) a clear way of tracking and analyzing their work. And the game cards progressed each day to present a new set of tasks and challenges.

All of these materials are now also posted on the Math Teacher Wiki.

Let me know how these work for you!

UPDATE 10/27/2016: Here is a working link to a zip file of all the components for this:


  1. Am I missing something? I don't see what the rules of the game are. Maybe I have it. They roll one number die and two +- dice. They record the +- rolls first and then the number, so that they get (as in the worksheet shown) something like 0 (old position) + -5. Then they take a card (in this case an 'odd # task'), figure it out, and do what?

    This sounds great. I'd like to ask kids at my son's school if they'd like to play test it.
  2. I just just discovered the msmathwiki and in turn your blog. I love everything you have written. I have been teaching for 14 years, but this is the first time I've taught Algebra. I love playing games and am so excited I don't have to create them all from scratch. I will excitedly be checking your blog daily to see what other awesome activities you post. Thank you!!!! 


    1. Thank you! I'm glad these are helpful to you.
  3. Thanks for the feedback! In answer to Sue's question, the rules are, everyone works every problem. Each player starts at the origin, rolls the three dice, and moves where they indicate. Choose an even, odd, or zero problem card. Everybody works the problem and checks answers, then the next player rolls.

    It's only a game structure. I keep "score" by confirming how many problems each team has completed and checked each day.

    Hope this helps.
  4. I'll tell you how this goes when you send me a beautifully LAMINATED class set of these made by the lovely office ladies, okay?! C'mon now, sharing is caring. I wanna do this, but it's too much work to make. #cryingwahwah #stopthewhining
  5. Hi, I loved your idea. I am trying it over the summer. I have a question about some of the answers to the cards. On the 2-1 green and yellow cards, you have a few fill in the blank cards. What was your answer for them? For instance, one of the cards says "To avoid getting confused, we read the expression -w as _" The one that has been stumping me is, "The absolute value of ANY number is always _, which means that it is always also_"
    I know it is positive but what is the other blank?



    1. Sorry about that! I forgot that you weren't there in class when I was drumming these ideas into our collective consciousness.

      With regard to the first card, when we start out in Algebra 1, I always have students read "–w" as "the opposite of w" or as "opposite w" rather than as "negative w." This helps ground them in what a signed VARIABLE means, as opposed to a signed NUMBER. If the value of w happens to be (–2), then –w is opposite-w which is –(–2) which is going to be a positive. Because they ground themselves in thinking about the opposite sign of the VARIABLE (rather than as a negative number), they get less confused as they evaluate expressions using different values for "w."

      With regard to the second card you mentioned, I also have students actively use the definitions of positive and negative — i.e., a positive number is defined as being greater than zero while a negative number is defined as being less than zero. So in the case of that card, I would hope they would say that "The absolute value of ANY number is always positive, which means that it is always greater than zero."

      Since definitions are our bedrock for the axiomatic aspects of algebra, this practice grounds them in thinking about whether a number lives to the left of zero (in the world of negative values) or to the right of zero (in positive territory).

      Hope this is helpful. Let me know if there are any blanks I can fill in!

      - Elizabeth
    2. Thanks! This helps a lot! I came up with numerous possible answers but I couldn't sleep without knowing your right answer! lol

      Thanks again!
  6. In the example you showed, did they just chose whether to go to positive or negative 5?


    1. Chelsea — They rolled three dice: two + / – dice and one six-sided number die. If they roll + — 5, they move 5 in the NEGATIVE direction (i.e., to the LEFT of zero). If they were to roll a + + 5, then they would move 5 spaces in the positive direction.

      Hope this helps!

      Elizabeth (@cheesemonkeysf)
  7. Greetings everyone,
    Enjoy the shared learning and knowledge.
    I am interested in using this to model rational addition and subtraction - i.e. -2.45 + 3.6 or -3 and 1/4 + 2 and 7/10
    How would you incorporate this in to the game?

Monday, August 6, 2012

WEEK 1: 'Words into Math' Block Game | #made4math

In keeping with my Week 1 emphasis in Algebra 1 on activating prior knowledge of how to translate words into mathematical expressions, equations, or inequalities (or at least gelling some of it back into place), I've also created a "Block" game for practicing 'Words into Math' in my Algebra 1 classes. There are two levels of game cards that correspond to Lessons 1.3 and 1.4 in McDougall Littell Algebra 1 California edition (for those of you playing along at home).

This is a variation on Maria Anderson's wonderful, tic-tac-toe-style "blocking games" (Antiderivative Block, Factor Pair Block, and Exponent Block — using her generic gameboard, rules, and my own game cards for each of these first three games of hers on her web site).

The game can be played in any number of ways — either competitive or collaborative. Students can compete against each other — tic-tac-toe style — to get four of their counters in a row. Or they can simply take turns choosing the problem and working on solving each problem on the whole board.

I've created two levels of "Words into Math Block": Level 1 (purple problem cards) and Level 2 (green problem cards). I use Maria's generic PDF gameboard and print or copy them on colored cardstock or paper. I have learned the hard way to give each level its own color ID as soon as I create the game cards so I can easily recreate the card sets later whenever I need to.

I allow students to use whatever resources they need to during practice activities, so I expect to see those nifty Troublesome Phrase Translator slider sleeves flying during these two days. :-)

All of my materials, plus the photo above (in case you need a model) are on the Math Teacher Wiki.

Students really love these block games! I have a bunch of different "counters" that they can use as their game board markers: little stars (Woodsies from Michael's), circles, and hearts, colorful foam planet/star clusters, and various kinds of beans.

I'm hoping to get my students to be less flummoxed by mathematical language by giving them practice in using it early and often. Enjoy!

Starting the New Year Right — Buckle Up for Week 1 #made4math

This is my second year at my new school, which I guess technically makes it no longer my 'new school,' huh. *facepalm*

This matters because Year 1 in a new place is always a time of establishing a reputation, but my reputation got totally screwed up last year because this year I am being positioned by the kids as cool flavor-of-the-month "nice teacher" everybody wants to have.

So to protect my street cred, I need to ruin my reputation at the start of the school year — and fast.

"INB Overview" foldable glued into my sample INB
I'm introducing Interactive Notebooks this year in my math classes, so everything during my Week 1 this year is going to revolve around that.*  Day 1 will be my "Introduction to the INB," including The Ceremonial Decorating and Labeling of the INB Cover, The Death-Defying Gluing-In of the Table of Contents (TOC) and other general reference pages, and most importantly, The Making and Filling-In of the "Rules & Parts of the INB" Foldable (photo at right).

This is the most important thing on Day 1 because I am giving a test on the INB Set-Up and Use bright and early on Day 2.

The test covers the six key things about INBs that I want students to have down cold from the start: the TOC, LHS and RHS pages (plus the LHS and RHS acronyms, which will be useful in working with equations and inequalities), The Rule of the Page (i.e., the fact that everybody stays on the same page), The Rule of Attachment (the fact that nobody leaves until (a) everything is glued into INBs and (b) INBs have been put into their zipper bags and hanging files), and finally, the purpose and importance of the Daily Date Stamp.

The message I want to send here is that, in Dan Meyer's words, "We use time well in this class." I also want to communicate that I am a badass unicorn who gives a test on Day 2 on actual material that is vital to your survival in my class and isn't that totally unfair and OMG. So let the word go forth — stay on your toes in my class and do not be fooled into complacency by my seeming niceness or my obviously wrongheaded reputation.

Using the set-up and use of the INB as my core "Day 1 Lesson" also allows me to teach classroom procedures through a foldable, which means that students learn how to use and study from a foldable right away. It also gets everybody onto the same page and creates that sense of shared suffering at the hands of a crazy teacher that is so vital to classroom community-building. ;-)

It also lets me put some teeth into the bellringer activity on Day 2. The test will be time-limited, so there will be no time for screwing around at the start of class.

The test will be a "trade and grade" affair, so that all I have to do is enter the scores into Power School and hand them back. While someone collects the tests, everybody will glue their INB Overview foldable onto page 7 of their INB.

Then I'll stamp page 7 of their INB and we will move on to creating some Chapter 1 pages and getting down to the business of Chapter 1.

DAYS 3, 4, and 5
The Day 2 Test will be taped into the INB first thing after the bellringer on Day 3. Taped in and date-stamped. No monkey business.

These days will cover Lessons 1.1, 1.2, and 1.3, complete with in-class activities and homework. It's important to establish our routine right away so I can jump on any students (and parents) who need a nudge to get with the program. By the time we have our Back to School Night, I expect parents to have seen, signed, and checked a number of activities and documents that will become part of their student's INB.

My thinking about homework is to deal with it separately. I'm going to set up a file box for each class with a hanging file folder for each student. Since INBs will live in the classroom and can only be brought home to study for a test, the hanging file will provide a home for each student's INB Ziploc bag as well as their archived loose HW papers.

To carry materials back and forth between home and school, students will use a two-pocket folder that contains their current chapter HW assignments as well as a stash of binder paper. I want to use the LHS pages for higher-level processing work rather than simply pasting in HW.

That also allows me to use bellringer time for students to do active processing of the previous day's material on their LHS pages. I'll keep you posted on how well this works, and I'll be curious to hear how others deal with the LHS pages.

By the time we reach Day 4, we'll be deep into mathematics. That is the best way I know to communicate my in-class goals and values to students.

More on the opening lessons and materials in my next post.

*I use the acronym INB rather than the more common IN or ISN because my school is acronym-heavy and both of those acronyms already stand for other things at our school. For once, I'm not intentionally trying to be a cheesehead.

Friday, August 3, 2012

#made4math | Words into Math - Taming Troublesome Phrases with an interactive foldable translator

It's been busy here in the Intergalactic Cheesemonkeysf R&D Laboratories
(see trusty assistant hard at work, right). Ever since Twitter Math Camp 12, I've been working on implementing all the lessons and activities I learned about in person from my fabulous math teacher tweeps!

I'm using the Interactive Notebook structure that Megan Golding-Hayes showed us, and I'm also incorporating a lot of Julie Reulbach's foldables. The most helpful insight (out of many) I received from Julie was the idea of using a foldable as a way of getting kids to SLOW DOWN and trust the steps of the process as they're working on word problems. So I've made a nifty little foldable like hers that will go into an INB pocket the first week and will be usable on all quizzes and tests.

One of the reasons I like having students develop tools they can use on tests is that many of the discouraged math learners just don't trust their own learning. They have a habit of "collapsing" when they encounter a first speed bump. So from the perspective of encouraging students' courage in problem-solving, it is good to allow them to have tools they can use, even if the tools are sometimes nothing more than a security blanket — a talisman or a good-luck charm they can touch as a tangible reminder of their own courage and resourcefulness. So a four-step problem-solving foldable serves double duty: it acts both as a checklist (as in Atul Gawande's New Yorker piece and book) and as a reminder to have courage and perseverance in working through problems.

However many students have a habit of either not using the tools or finding the tools too complicated or frustrating. Nowhere has this been more evident than when I've given them approved lists of words and phrases they should stop, consider, and look up if need be. The charts and lists seem to turn into giant floating word clouds that signify nothing. So I wanted to come up with a slightly more interactive than usual foldable that students could use as a way of isolating and decoding some of the most troublesome words and phrases they get hung up on. Not only does it slow them down, it gives them a focal task that redirects an anxious mind.

After a lot of research on both blogs and on Pinterest ("PINTEREST!" #drinkinggame), I came up with the idea of a folded sleeve with a sliding chart insert, containing the phrases that often confuse kids or cause them to second-guess their translations from words into math. Here's what the finished product looks like:

Here is a close-up:

I used OmniGraffle to make the sleeve template and I used Pages, Preview, and Adobe Acrobat to make the insert. I'm linking to the Troublesome Phrase Translator sleeve, a generic sleeve you can customize for your own fiendish purposes, and a PDF of my exact insert (Troublesome Phrase Translator INSERT). 

If you want to make your own inserts, you'll need to set up your own table (Word, Pages, Excel, etc) making sure that your row height is exactly 1/4 inch. Your LHS cells should be 1 9/16" wide and your RHS cells should be 1/2 inch wide. You can have about 19 or 20 rows, depending on what you put in them.

Sometimes a little magical thinking is just the thing to displace a discouraged learner's anxiety (or freaked-out-ness) for that extra second it might take to recommit to the process of solving a problem. If that helps me hang onto just one extra student a day, it's a win. But usually I find that a tool like this will encourage multiple students to encourage each other's confidence as well, which is an even bigger win in my book!