Combining Like Terms Sorting Cards

It's time to share another resource.  This card sort was modeled off of one that Sarah Carter shared on her blog here for solving equations with variables on both sides.  I had been looking for an activity to have my students practice combining like terms, but a lot of what I was finding was very simple expressions like 2n + 3n.  I created this card sort so that students would get practice combining like terms with expressions that have different variables and exponents.

This card sort contains 12 cards.  Students sort the cards into 3 groups of 4 cards so that all four cards in each group simplify to the same expression.  An answer key is included.

View/Download: Combining Like Terms Sorting Cards

My Favorite Review Activity

Alright, last post for the year.  I've been much less active here and on Twitter lately after kind of just going all in last year.  Nevertheless, I still have things I want to share and reflect on, so this post is about an activity that I have used several times now as review before a quiz.

Okay, so here it is.  Currently my favorite review activity is a cross between this 1-100 Grid I first heard about on Twitter from Julie Morgan (@fractionfanatic) and this Ghosts in the Graveyard activity from Sarah Carter (@mathequalslove).  The idea behind the 1-100 Grid is that for every question students (or pairs) answer correctly, they choose a number on a hundreds chart.  Once a number is claimed, no other students can pick that number.  At the end of the activity, I use a random number generator to select a winning number from 1 to 100.  The more questions students answer correctly, the more numbers they get to pick on the hundreds chart increasing their chances of winning.

A chart typically looks like this by the end of a class period.

One thing Julie points out in her post about the game is that it works well for smaller classes as it can get quite hectic.  TRUTH!  My classes are slightly smaller this year, but still, it can be challenging with 25+ students in class.  Here are the ways I altered this activity to work with my classes of up to 30 students.

1. I used the idea of challenge cards from Sarah's Ghosts in the Graveyard activity.  Instead of letting students pick a number for every single question they answered correctly, they chose a challenge card with 3-5 questions that all had to be answered correctly before they could pick a number.
2. I set up an answer checking station.  Once the activity started, I sat at this station and DID NOT GET UP FOR ANY REASON (except the time there was a fire drill of course).  If students needed help, they had to come see me.  If they needed an answer checked, they had to come see me.  If they needed the hundreds chart to pick a number, they had to come see me.  If they needed a new challenge card, they had to come see me.  The first time I ran this activity this year, I forgot that this was how I had done it last year.  So instead of staying in one place and having students come to me, I was flying around the room trying to check answers, help students, and pass around the hundreds chart all at once.  It was pure chaos on my part (although students still seemed to be working just fine).
3. I only let students work on one challenge card at a time - there is no hoarding challenge cards.  In order to get a new challenge card, they had to get their old card checked by me.  Because I was not circling the room as they were working, I still needed a way to check their progress and be sure they weren't practicing something entirely wrong for the whole class period.  This also helped me in the preparation stage because I only needed to have a handful of copies of each challenge card since students could work on challenges in any order.
4. I gave students a recording sheet.  It's mostly a blank piece of paper for them to show their work and answer the challenge questions, but it also had space for me to sign off on which challenges they had completed.  The very first time I ran this activity, students kept asking me which challenges they had already done when they were picking a new card.  It was a nightmare for me to try to keep track on an attendance sheet (once students start getting answers checked, this gets very fast-paced and students really do race to complete as many challenges as they can).  Having this designated recording sheet also gave students something to hand in at the end of class - do your students also feel like they always have to pass something in?

I allow students to work in pairs or individually when I do this activity, but I definitely encourage pairs so that they have someone to go to if they get stuck.  I remind them that if they have to come to me for help, they may be waiting in a line of people getting their answers checked.

Every time I do this activity, I am amazed by how much practice my students are able to get in one class period.  Even students who are typically less engaged in class rush to complete as many challenges as they can!  In fact, the last time we did this activity, I had only planned on doing it for half the class and then taking a quiz the second half of class.  But students were so engaged and working so hard to finish every challenge before the quiz, that I decided to let them keep working all class period.  You could tell every time they came up to get their answers checked that they were more confident with the material and for some students, they were getting more practice in that class period than they previously had during the unit.

I've used this activity to review rational numbers, properties of exponents, and rate of change & functions, and at some point I may share my files with the challenge questions and recording sheet, but for now, it's New Year's Eve!

Question Stack: Rational Number Conversions 2

It's been forever again since I've posted.  I have a bunch of drafts of things from last year I've wanted to share, but for today I'm sharing something new - an updated question stack for rational number conversions.

I originally shared a question stack for fraction and decimal conversions in this post.  This year I made an updated version which includes fractions that can be simplified first to make the long division easier and improper fractions.  I've tried to stress to always simplify your fractions before working with them, so I like that this updated version gives students a chance to practice that.  I also like that in this version, students have to pay attention to which number is the dividend and which is the divisor.  Even in eighth grade, I still see students mix up the numerator and denominator when dividing; because this version includes proper and improper fractions, students cannot just go on autopilot and always do the smaller number divided by the bigger number or vice versa.

Fraction Side

Decimal Side

View/Download: Rational Number Conversions Question Stack 2

I'm Only On Page Seven...

I just started reading Daniel T. Willingham's Why Don't Students Like School.  I am only on page seven and already I made a strong enough connection with the text that I felt compelled to stop reading and write about it!  To be honest, I don't know yet how important this idea is to the subject of the book as a whole - I'm only on page seven, remember?! - but I can say that being able to relate what I'm reading to some of my own experiences makes me excited to read more.

Willingham describes how tasks that require you to think can become automatic with repetition.  He gives the example of learning to drive a car - all the minor bits that go into it like how much pressure to put on the pedals, how far to turn the steering wheel - and how in the beginning, new drivers may not even listen to the radio, but with time they are talking, eating, and pointing out landmarks all at once.

I immediately thought of my first retail job when they started me on register.  I was shy and timid and outgoing Val was my trainer.  I still recall some of my first transactions with customers.  Val greeted each customer while I smiled politely.  Val took clothes off the hangers, hung the hangers in an organized fashion on the rack behind us (shirt hangers on the top row, pant hangers on the middle row, swan hangers and kids hangers on the bottom row), and handed me the item to be scanned with the tag upright.  I scanned the item.  By that point, Val had already removed the hangers from several more items of clothing, organized the hangers on the rack, and lay the clothes neatly on the counter with the tags exposed for me to scan - all while talking with the customer.  I scanned the next items.  When it came time to pay, Val kept an eye on me, ready to give me reminders as needed, all while maintaining her conversation with the customer.  I pressed the right buttons in the right order.  Phew!  As the receipt printed, I realized that at some point Val had neatly folded and bagged all of the customer's items.  Here's my actual journal entry about this day.

So, working the register was fun, but I was shocked how much there is to do!  I mean, Val was moving my hangers out of the way, bagging for me, and talking to the customer!  All I had to do was scan things in and type the discount and I was barely handling that!  I'll get the hang of it soon enough though.

And I did get the hang of it.  Quiet little me learned to make small talk with the customers while quickly processing their items and keeping my work space organized.  I could even do all that while answering the phone, which was maybe not the best customer service practice but hey, you do what you gotta do when the store's busy, and I was a multitasking machine!  I learned to do all those things without thinking about them.  With repetition, they became automatic.

My Reflection on PBL101

I tend to be what you might call an "on my own" PD person.  I am the webinar-podcast-book-article person, not the attend-this-collaborative-hands-on-training kind of person.  That's not to say I don't do both kinds, but when I have the choice, I tend to choose options where I am learning on my own.  Funny how that's the exact opposite of what I hope to see in my classroom.

I just finished a 3-day workshop on Project Based Learning from the Buck Institute.  It was great because not only did I learn a lot about designing Gold Standard projects, but I also was reminded of what it's like to be a student.  Long story short, I had moments (more than a few) where I was so overwhelmed with the task of creating my own project that I just sat and stared at my computer screen for longer chunks of time than I'd care to admit.  I needed more time to process everything I had learned before I felt ready to implement it and design my own project.  Besides learning about PBL, the goal was to leave the training with a ready-to-go project that we could do with our classes in the fall.  I wish I could say that I accomplished that goal and left the training with my PBL unit complete.  What I can say is that I left the training feeling inspired and excited to create my own PBL projects.

One of the hardest things for me while designing my PBL unit was keeping it authentic and open-ended.  I realized that I'm maybe not as flexible as I thought.  We have this driving question that is supposed to guide our inquiry, but I still want there to be a right answer at the end of this.  How else will I know if my students "got it?"  And if I'm so focused on the end, is this really a PBL project that I'm designing or is it a "dessert" project where you show what you know at the end of a unit?  I mean, PBL should be about the journey, right?  The ongoing learning that takes place throughout the unit?  I'm having a hard time finding the balance.

One of my questions going into the training was "What is the difference between a project and a task?"  I was thinking about Dan Meyer's 3-Act Tasks and wondering if those were mini PBLs.  Did I ask my question?  Nope.  Why not?  Honestly, I don't know.  We had opportunities to ask questions anonymously and I still didn't speak up.  So here I am after the training, working on my PBL unit alone, still unsure of that distinction and starting to question whether the distinction is even important.

Okay, when I say "alone," I am reminded that I'm not really alone.  Being on Twitter has been so great for me, the I'll-just-hole-up-in-my-room-and-watch-this-webinar-by-myself type of person.  I can reach out to all these other teachers and learners.  I even did just that during the workshop despite the fact that I was surrounded by other teachers from my district.  With Twitter, I get the community without the anxiety.

Despite some of these frustrations, I meant it when I said I'm feeling inspired and excited.  Our presenter's enthusiasm was contagious and the knowledge and experiences he shared could convince even the most resistant that PBL is the way to go.  This is the first time since I started teaching that I am not teaching summer school and I'm feeling really motivated to work on my PBL unit this summer. 

Clearing Fractions from Equations Notes

When I jumped into blogging and the world of Twitter at the beginning of this school year, I couldn't imagine how much these two outlets would help me grow.  I love learning from other teachers' experiences, and I love being able to share my resources with other teachers as well.  As I find myself feeling too busy to blog some days (or, let's be real, some weeks...okay, maybe months...), #teach180 reminds me that while reflecting on lessons and my teaching practices is helpful for me, sometimes simply sharing my daily resources (and using resources and activities that other teachers have shared) can be even more beneficial to the community as a whole.

With that said, today I am sharing notes that I used with my students in our multi-step equations unit.  I don't have much to say about these notes other than feel free to use them if you teach students how to solve equations containing fractions by clearing the fractions and solving an equivalent equation with integers.  The notes are available to download as a PDF or an editable Publisher file.

Additionally, I'm sharing this homework assignment that I used with students before we completed the notes above.  This assignment was used to prepare them for clearing fractions from equations.  It gives students a chance to find the LCM and LCD, multiply fractions by whole numbers, and use the distributive property with fractions.

View/Download: Clearing Fractions from Equations Notes and Preparing for Clearing Fractions Assignment

First 1000 Digits of Pi Posters

Earlier this month I put up these digits of pi posters in the hallway outside my classroom.

They sparked a lot of great questions and conversations with my students, other students, and other teachers in the building.  I blogged about some of these conversations here.

In case anyone may be interested, I thought I'd share the file I used.  To create the posters, all I did was google the first 1,000 digits of pi, which I copied and pasted into a Word document.  I enlarged them until each digit filled a page and I added the ellipsis at the end of the document.

After determining that I could fit a 7 by 14 array of digits on the wall, I needed to print the first 97 pages of the document, plus page 1,003 for the ellipsis.  I knew that I wanted each digit to be a different color, so I arranged my colored paper on the floor like this.

I used my Word document of poster pages to determine the pattern of numbers where I would stop - so I looked at pages 93-97 to know that I was ending with the digits 3, 4, 2, 1, 1.  Then I went back to the webpage showing the digits of pi (rather than clicking through each page of my document) to start arranging the colored papers in order.  I inserted white pages for the decimal point and the ellipsis.  By having the colored paper in order of the digits of pi, I was able to simply put that stack of paper in the printer and print pages 1-97 and page 1,003 of my document.

Here are a few more printing tips:

• Make sure you're set to print single-sided.
• Print a custom selection of pages using the hyphen to include the pages of digits you want to print and a comma to also list the ellipsis page (p. 1003).
• Be sure that you know if your printer starts printing with the first page of a selection and prints forward through the selection or if your printer starts with the last page of a selection and moves backward through the selection (if you don't know, print a short selection on scrap paper to find out).

You'll need the free font Comic Zine for the Word document to display correctly (or feel free to change the font to something else - you may also have to adjust the page margins and font size if you do that).

View/Download: First 1000 Digits of Pi Posters