Showing posts with label number talks. Show all posts
Showing posts with label number talks. Show all posts

Tuesday, November 17, 2015

Where was admin?


I had a beautiful conversation erupt during math time today.

Here was the problem:



They were solving with a partial products array (they're not quite ready for traditional or standard algorithms for multiplication) and a very loud, very passionate conversation erupted.  One student argued that having the "zero tens" row in the second factor (409) wasn't necessary.  Another passionately disagreed.  

Soon, I lost the whole class to this beautiful, loud conversation about if zero is a value or simply a place holder.  

Did it need to be represented? 

Could it be skipped? Always?

I reeled them back in after about five minutes of debate, much to the horror of the original instigators who hadn't successfully defended their perspectives.

What a beautiful, natural example of the math practices coming to life.



Now, where was admin?! That would have been a lovely example of math discourse in the classroom for my end of year evaluation.


Monday, August 3, 2015

Curriculum Must Haves! {Week 2}

I love reading Diane's blog posts on {Fifth in the Middle} and {Fancy Free in Fourth}.

This week's blog challenge is about curriculum must-haves. 



Our district, perhaps like most, is in a state of turmoil.  We've adopted the Common Core State Standards without curriculum to match, expect teachers to make due with out dated text books (seriously, the books are older than my students), and expect teachers to do more with less...including less money.  Yup, we took a pay cut and an insurance hike, so double whammy to the bank account!  To make matters worse, new to state teachers are given a several thousand dollar hiring bonus and to make up for the teacher shortage, retired teachers are invited back.  I have no issue with (qualified) retired teachers returning to the district, but I do have a problem that they receive both a salary and their retirement accounts.  Yup, they're allowed to double dip into funds, yet current teachers all took a pay cut.  

We also adopted the standards (which I have no problem with), but then rebranded them the Nevada Academic Content Standards (NVACS).  Why?  To deal with the critics who are outspoken against the Common Core.

From what I've read of the Common Core (which is not the whole thing, just the elementary portion), I don't really see a problem.  Are the standards perfect? No, of course not.  But the depth of what is expected of our students is much deeper then previous standards,  Seeing how Nevada is consistently at the bottom in terms of educational testing for a wide variety of reasons, I think challenging our students is a good thing.  When you're close to the bottom, you can only go up!

Long story short, we have no provided curriculum and have to rely on collaboration to create our lesson plans.  There are lots of inconsistencies across the district, but at least everyone in my grade level (and school) are pretty much on the same page.

So let's dive into this week's blog challenge and look at some curriculum must haves:





I can't say enough good things about this book.  We start each math lesson with a warm up that focuses on building number sense. 

We've tweaked it a little to roughly follow this format:

Mental Math Monday: The focus is on decomposing and composing numbers for computation.

Ten Minute Tuesday: The focus is on logic puzzles and brain teasers.

Word Problem Wednesday: The focus is on multi-step word problems and making sense of the problems.

Thinking Thursday: More logic puzzles and "tricky" problems.

Fast Facts Friday: Timed tests to focus on multiplication and division facts mastery.



Must haves:
Teachers pay Teachers products!

My novel guides are a life saver! I'm trying to keep track of several different novels at once with my small groups, so it's nice to have all my notes and homework questions in a nice, organized fashion.  

I've also founds tons of free stations that are great for independent and partner practice during RTI time!

As an added bonus, most stores are having their back to school sale right now! I know everything in my store is currently 20% off!  Go get inspired.



 

This book was truly a life saver.  I struggled with knowing how to teach phonics, phonemic awareness, and fluency.  I felt pretty good about my comprehension strategies but struggled with foundation skills.  This had great strategies and graphic organizers.  My copy is well loved:




Finally, one of my go to websites: FCRR (Florida Center for Reading Research)



This site has graphic organizers, centers, and games broken into grade level bands (K-1, 2-3, and 4-5).  They've recently added the Common Core State Standards to the center activities so it makes it even easier to find what your students need.

What would you add? Join the conversation!

Saturday, August 1, 2015

Book Blog Hop!



Diane from Fifth in the Middle (one of the blogs & TpT stores I follow) posted earlier about books that are being used in the beginning of the school year.  Obviously I love books and totally hopped on board with this book blog-a-thon!

I'll be using a few different picture books during the first week of school before starting our first novel, The Lightning Thief. 

Picture Books:

I use Is a Blue Whale the Biggest Thing There Is? to start our math conversations.  



Before we go over Number Talks and math norms, we read this and start talking about the size of things in relation to another.  I think it's a great way to subtly introduce place value without mentioning those vocabulary words. 

I read Boris Ate a Thesaurus to start our conversations about word choice.



It's a silly book and they love it.

I also use My Mouth is a Volcano to talk about classroom norms.




It ties in well with listening and speaking norms, which we establish within the first few days of school.

I also leave out copies of Ms. Nelson is Missing, First Day Jitters, Unique Monique, and Thank You, Mr. Falker  for students to read during independent reading time.  


I also start the year with Rick Riordan's The Lightning Thief as our first novel.  It's great for seeing how the chapters build on one another because the author does an amazing job of foreshadowing.  Students (hopefully) were exposed to Greek Mythology in fourth grade, so it's nice to tie in with their background knowledge.




As an added bonus, the main character Percy, isn't a typical hero.  He struggles with dyslexia and ADHD (a side effect of being a demigod) and has trouble in school.  My students really get into the book and as an added bonus, there are many, many sequels!

Directly following The Lightning Thief is The Sea of Monsters, The Titan's Curse, The Battle of the Labryinth, and The Last Olympian. 

There is a Greek & Roman spin off series with The Lost Hero, the Son of Neptune, the Mark of Athena, the House of Hades, and the Blood of Olympus (which I'm finishing tonight!).  What is great about these books is the narrator flips every few chapters, so you get multiple perspectives.  This literary technique lends itself to some interesting discussions.

There is an Egyptian trio of books: The Red Pyramid, the Throne of Fire, and The Serpent's Shadow.  These also alternate narrators between Sadie and Carter Kane, two very different siblings.  Their sibling love-hate relationship is beautifully and subtly captured in the different ways the chapters are narrated.

Since Rick Riordan is determined to drain my bank account with his amazing books, I'm super excited about this new series:



It stars Annabeth's possible brother?! The last name can't be a coincidence.

What do you read with your munchkins?

Sunday, June 21, 2015

Book Reviews

Over the past few years, I've had the opportunity to participate in several book studies with the focus on improving my craft as an educator.  Here is a synopsis of those books:


Questions, Claims, and Evidence


This book really helped me shift perspectives for science instruction.  Essentially, this guided me through setting up my students for success and shifting away from teacher driven science experiments.  Instead, this is replaced with student created extension inquiry projects and helping them write about science.

Building Academic Vocabulary (Marzano)




Even after reading this, I struggle with vocabulary instruction.  It's the highest of the big five components of literacy (phonemic awareness, phonics, fluency, and comprehension being the other four).  It's crucial, especially for my ELL (English Language Learners).  I feel successful with teaching academic vocabulary when it's content specific (i.e. math, science, and social studies) but struggle when it comes to what words to teach whole group. I'm wary of just choosing a list and going from that.  I tend to teach words that are associated with the novels I'm using and more specific lists with my RTI group.  I want to empower my students to monitor their own vocabulary acquisition and give them the space to share these words with their peers. 

I haven't quite decided how this will look in my classroom, so stay tuned!


Waiting for Superman



I led this book study at my previous school...and it didn't go very well.  Part of it was because I was leading it, not an administrator.  Part of it was because I was still quite idealistic about how teaching should work because I had just finished my first year in the classroom and thought I knew everything.  This book, while an interesting read, doesn't give enough credit to the teachers who are working really hard to change the system.

Read, Write, Lead




I was really excited to read this book as part of a book study.  My group was assigned chapter five, which is all about principal leadership.  While I have no issues with my administrators popping in my classroom on a frequent basis, this was a cause of major concern for some of my colleagues.  The chapter also talked about celebrating teachers and students, which I don't think is done enough.  This was my big take away from this book is that while programs and standards may (and do) change, good teaching is consistent.  Good teachers are reflective, collaborative, innovative, and push one another to do better.  

Number Talks




This gem isn't really a book review but rather an opportunity to share that this is a wonderful book that should be used wherever possible!  While the first few weeks of number talks are rocky, especially if students aren't familiar with the format, the pay off, if done consistently, is amazing.  For the past few years, my students have left my classroom with a strong understanding of number sense and problem solving strategies.  This book is a large part of the reason why.  It's worth the money if your school district doesn't provide this resource. 

Up next?  I'll be diving into Love and Logic for some new strategies to use with my whole class.  I also borrowed The Tough Kid Tool Kit to gain some new tips and tricks for dealing with difficult students.  I had a particularly troubled one last year that gave my whole school lots of headaches, but I'm glad next year that kiddo will get the services that are needed.  

What books would you recommend?  Which ones were educational game changers?

Wednesday, August 27, 2014

Year Six, Day 2

Day Two

With no duty to be had and the kinks from yesterday all worked out, the morning ran much smoother.

We started our day with this meme:



Before I showed them the wordle from their first day feelings exit tickets:



I was pleased many of them wrote in complete sentences.  My favorite may have been the child that just wrote "I'm satisfied."  I still have a few that are nervous, but that's to be expected. 

We went over more classroom procedures, did our number talk (which lead to some awesome discourse about making sense of problems!), made our class norms with a gallery walk, and did another read aloud:



This mentor text focuses on life skills and provides strategies on not erupting (interrupting).  Again, most of them had never heard this book so I'm on a roll!

Can't wait to read this gem on day 3!


I did make my first student cry.  Yes, we made it through a day and a half of fifth grade before there were tears.

He had his phone out and in his words, was just looking at the time.  Since his back was to the wall, I chose to believe him.  We had a conversation in the hallway because it's not a conversation for the whole class.  He apologized, we talked through strategies (look at the clock, keep phone in backpack), and I moved him seats so he would face the clock.  I gave him his phone back at the end of the day, but there were still tears. 

I guess the honeymoon is over?

Day three is a weird day.  We'll tackle second prep and our first assembly.  Fingers crossed!

Tuesday, August 26, 2014

Year Six, Day 1

The weekend before school started, I was a wreck.  I worked Friday night on various small tasks for my classroom, took all of Saturday off to spend with friends, and worked for a little bit Sunday morning before heading to B's family's BBQ.  Sleep did not come easily Sunday night and nightmares of past students and worst case scenarios flooded my mind.

I got to work about seven am on Monday.  Our start time is 8:26. My first task was hanging our classroom pom-poms:



 I had duty (bummer) and I struggled with undoing the folding gate.  See, the gate was run over by a (rude) parent, so it's bent in a strategic way.  This means it doesn't fold up nicely and has quickly become my new Monday/Friday morning nemesis. 

Luckily a parent helped me wrestle the gate.  I was also burdened with both a stop sign and radio, so next time I'll not carry those.  Or wear open toed shoes.

My other job at duty was to help direct drop-off traffic.  We have a lot of red curbs in front of our school and I had the unfortunate job of trying to tell parents not to park.  These parents were obviously very excited for the first day and taking pictures of their kiddos in front of the school.  I had to be the bad guy and ask them to not capture this precious moment.

I went to the wrong spot to find my class and our line got bisected when we were entering the building.  I forgot to collect lunch money and we were a few minutes late to specials, after I tried to take them down the wrong way.

Thank goodness for first prep!  I took a few deep breaths, calmed myself, and proceeded to tackle my to do list.

The rest of the day was smooth sailing :)

I had 27 students show up and they were talkative from the first moment.  They're responding really well to my positive classroom vibe, which is good.  Considering how frustrating last year was, I'm determined to stay positive.  I want my room to be a joyous place.



I didn't spend hours on procedures.  I gave them a first day treat.  We covered a lot (norms for read alouds and number talks), learned some procedures, and practiced structures like Kagan pair up and share.

We read First Day Jitters, which many of them had never heard before.



It's a cute picture book with a fun twist at the end. (Spoiler--the teacher doesn't want to go to school!)

Prior to reading, we went over read aloud norms:



I was a little worried about some of their initial responses.  I asked what my job was during a read aloud and the first response I got was "to grade papers." 

Um...no.

I clarified that during a read aloud, I was the one reading.  They were dumbfounded by this notion and asked when I would grade.  I told them they wouldn't see me grade in the classroom unless it was a one on one assessment (Aimsweb, Core phonics, etc).  They were bewildered and asked when I would get their stuff done.  I said at home, in front of the TV, or while they're at specials.  This seemed to satisfy most of them, but that does worry me...

A teacher shouldn't be known for spending hours of in class time grading.  Yes, it happens.  But that shouldn't be what your students expect you to do.

Instead of me giving a tour of the classroom, I sent them on a scavenger hunt:


It's way more fun when they investigate!  Plus it gets their bodies up and active, which is crucial.

I went over the hand procedures for number talks and then made an anchor chart about the strategies they used:



After we did our number talk, I had them create their fractional me sheets:



They had forms for homework and left with smiles on their faces.

The hardest part of day one?  Well, besides the rough start?

Wearing shoes the whole day!

Wednesday, August 13, 2014

Math training, days 2 & 3

After tackling my homework for math training, grocery shopping, and spending several hours leveling my library (such a daunting task), I didn't have the energy left to process what I'd learned.  

However, today I was home much earlier so I could reflect on yesterday and today's math trainings.

Days 2 & 3:

We talked about multiplication.  We talked about it...a lot.  Perhaps it's because I teach fifth grade and have taught inclusion, but none of the strategies mentioned were new information.  I grasped the concept right away and helped my neighbor make the same mathematical discoveries.

However, I did learn a few new things over the past few days.  Here are my "ah ha" moments:

The minuend is the first number in a subtraction problem and represents the amount you start with.  The subtrahend is the amount that is being removed or subtracted.  

This discovery raised an interesting question within our group.  Why is it that other math vocabulary terms (addend, sum, factor, product, quotient, etc) are well-known but minuend and subtrahend aren't?  Why can teachers (and hopefully their students) use the correct vocabulary for the other operations, but stumble on subtraction terms?  I know I'll be incorporating these terms into my math instruction!

"Give One, get one, move on" strategy

The page is divided into four sections.  Students solve the problem in the first quadrant, which is labeled "give".  After time to process the problem, students then will stand up and find three other people to "get" strategies from.  The students will work in pairs to explain their strategies to one another.  Not only does this allow for movement, but students can explain their thoughts to one another.  During this time, the teacher is monitoring as an informal assessment to see what students are grasping the content and which ones still need a little more practice time.

The next classroom tweak deals with these manipulatives:
Found in almost every elementary classroom, I always called these "ones", "tens", "hundreds" and so on.  Most teachers do.

However, in doing so, you're limiting students' understanding of the relationship (powers of ten) between the manipulatives.  

These will henceforth be referred at as units (smallest), rods (long ones), flats, and cubes.

By doing so, a teacher is able to stress the relationship between a value being ten times larger or smaller than the value next to it on a place value chart.  

Referring to these as units, rods, flats, and cubes also allows for the manipulation in upper elementary.  If my "one" is now the cube, I can use these manipulatives to represent a tenth (flat), a hundredth (rod), and thousandth (unit).  I can also regard the unit as a thousand, then have students prove the other values. (Rod would be 10,000, flat 100,000, cube 1,000,000).  

Finally, we played close to 100 (from Investigations).  While this game was not new to me, I did appreciate the discussion about its importance in the classroom.  In playing this math game (and others), students are provided the opportunity to practice many math skills such as estimation, reasoning, critiquing the reasoning of others, operations, and place value.  These games take minutes to learn, can be a good task for students if they finish early with an activity, and can be used as homework.  I know my students would much rather go home and play a math game as their homework then fill out a worksheet.  

Close to 100 also reminded me of another quick math activity:




What an easy way to get their brains working during the first few moments of the day!

Stay tuned for a recap of days 4 and 5!

Monday, August 11, 2014

Math training, day 1

First, it was difficult to get up at 5:30 this morning.  Second, I didn't factor in nearby construction, so I just barely made it to my 7 am training.  I wasn't late, I just wasn't my normal five to ten minutes early.  Because I was late by my own standards, I had one of the last choices in seating which meant I was stuck in a set facing the back of the room.  I've got a bit of a neck cramp from turning my head around all day.  All those minor factors aside, I shook off my frustration and settled in for six hours of learning.

That's when I learned this training is five days, not four.  I had planned to go into my new school Friday to start setting up my classroom.  There's also a school tour and it sounds like that's the day my administration is going over all of the details about our school.  Good thing I have two close friends also starting at my school so I can get the info :)

I like the ladies I'm sitting with and the instructors are friendly and knowledgeable.  Two of the other ladies at my training are at my former coach's school so I shared how lucky they are to have her guidance.  

Then the math activities started.  Now, I've been to a lot of trainings over the past five years.  I like learning and new strategies.  90% of what was covered today I've heard before.  Now I could be grumpy about this, or I could be fortunate that I've had some great mentor teachers and coaches who've already shared this information.  I'm choosing the second option and going to focus on the new information I learned today.

One of the videos we watched was a middle school Number Talk.  Most of the time the videos are focused on elementary, so it was nice to see a change.  The teacher set the norms for the problem: (123-76)

1. Don't solve traditional algorithm
2. You may write down numbers, but you need to try this in your head
3. Thumbs up when you've got the answer (standard Number Talks procedure)

The teacher then allowed for think time.  Instead of asking for the answer, he asked what is know about the answer.  I'd never heard this question phrased and I will definitely be using it in my classroom.

The students responded that the answer was positive and less than 100.  Another student estimated the answer to be close to fifty based on his rounding (125-75).  

From there, the teacher asked for strategies for solving and answers.

I loved how this simply question gives students a daily opportunity to practice estimating and reasonableness. I like that this wording helps them think critically about the problem but I'm not the one telling them what to think.

I'm embracing the mindset of being their math coach, not their math teacher


I want them to make mistakes. I want them to make their own discoveries.

Now, it's time for homework before day 2 tomorrow!






 

Wednesday, February 12, 2014

Word Problem Wednesday

For our number talks, we switch up the focus each day.  Today's was a word problem:


We are working on critical thinking.  I let them use dry erase markers on their desks to solve the problem:


 

And they loved it!  I liked that I saw a variety of strategies being used (pictures, numbers, etc).  They really enjoyed writing on their desks! (My little rebels)

Monday, January 20, 2014

Change can be a good thing

I'm halfway through year five of teaching and my oh my have things changed.

For the most part, I see the changes as a good thing.  I know to truly see a program or strategy's effectiveness, it should be consistent within a school for several years to be able to accurately measure growth.  That's something we're working on at our school.

When I started teaching, we followed a scripted reading program with weekly spelling tests and a story of the week.  I taught comprehension strategies, sort of, but we were expected to abide by the book.  I thought I was doing pretty well following the structure and doing the same things as the other teachers in my grade level.

This blind, naive attitude only lasted a few months and (with administrative approval), I'd completely abandoned the scripted program by my second year. I don't do well with scripted programs anyway.

I brought additional challenges upon myself by having to find meaningful content, but at least during my second year I was teaching standards and not just a story.  My students were becoming more engaged and I was enjoying teaching more.

By year three, I was feeling more confident in the classroom.  I'd finished my masters degree and my Teach for America obligation. I had taken a lot of district trainings and was on a task force to unwrap the (at the time, new) Common Core State Standards.  There were still lots of extra demands on me to find the materials I needed to teach with and lots of long weekends preparing.  I was also in conflict with veteran teachers in my grade level who were unwilling to try new strategies and envied my successes in the classroom.

Year four brought more confidence and a partner.  I was no longer pitted me against the grade level, but rather me and my ally against the veteran teachers.  Slowly but surely, our students rose to our high expectations and outperformed the others simply because we weren't teaching a bland, scripted program.  We were teaching (and reteaching) the standards with a variety of strategies.  Not all of them worked, but our students were rarely bored.  Their high levels of engagement translated into higher test scores due to what I believe was their interest in learning. 




Year five: my dream team.  I work with three other fifth grade teachers and my special education co-teacher.  We are on the same page 95% of the time and always supporting one another.  None of us follow a scripted reading program with a new story a week.  No one gives a spelling test with 20 words that students had to memorize over the week and regurgitate on Friday.

No no, I think we do something much, much better.  




We teach a weekly, grade-level phonics skill with explicit phonics.  We teach the patterns, practice sorting by sounds, encode and decode with text, then on Friday give them a quick formative assessment with five words to see if they can apply the skill.  I don't want to see if they can memorize basic facts, I want to see if they an apply their knowledge of word parts to spelling unfamiliar words because that's a much more true assessment of whether or not they got the skill.

For math, we are using the Investigations program which is far superior to what we previously used.  Based on over eighty years of research and partnership with NCTM, the program has students discovering math concepts through manipulation and discourse, which provides for a more meaningful understanding of mathematics.  They are constantly building their number sense through Number Talks and math games that rely on critical thinking.

For reading, we're loosely following another school district's pacing guide because it draws heavily from mentor text that is rigorous, engaging and within an appropriate lexile level.  Before choosing to go with their plans as our backbone, we read through their plans, double checked that all standards were covered and added in our own notes.  I think it's going fairly well.

We don't give a weekly reading test (thank goodness!).  Instead, we give a monthly one with longer reading passages (to build their stamina) with questions that cover several standards.  I'm not testing how much they remember of a story we'd read together and discussed in class five times (because at that point, it was regurgitation, not knowledge).  We're testing how well they can independently apply the skills we've been working on in whole and small groups to the unfamiliar passage.

I look back at my first year in the classroom and have the overwhelming urge to apologize to that group of students. 

 I did the best I could with what I had, but I would never go back to that way of teaching.  I would never rely on worksheets and a story of the week.  That's not what helps students learn.

As an educator, I'm constantly trying to learn new strategies and implement them in my classroom.  While this highly reflective process can be a tad frustrating when things don't go as planned, I think that learning and trying new things is far better than repeating the same thing over and over again.

In the past five years, I've implemented interactive notebooks and Number Talks.  I do explicit phonics three times a day (whole group and both small groups).  I have students interact with technology rather than me being the sole one to create things.  I have centers and literature circles with novels, something I didn't even attempt until my second year.  I've learned how to do the CORE phonics assessment to see where students break down phonetically and the DRA to determine their reading levels. (Although it's time consuming, I much prefer it to the old diagnostic tests I had to give!).  We're using mentor text for reading and writing, doing mini-lessons and having students publish drafts both on the computers and the iPads.  It's been a tough, uphill battle and I'm proud of the new things I've learned.  I'm appreciative of the trainings I received at my school, from my district and from outside educational entities.

I'm saddened by teachers who are scared or unwilling to try new strategies.  I don't have the same bunch of kids I did when I first started five years ago, so why should I teach the same lesson the same way?


(Poor Harry Potter, subjected to the old ways of teaching)

Change can mean better instruction for students.  Change can mean more engaging, thoughtful, purposeful, driven lessons.  Change can mean teachers have more flexibility and students have more opportunities to collaborate with their peers on projects and activities, rather than just sitting quietly and working independently. Change can bring joy back into the classroom.  I'm not saying every aspect of education needs to change nor that all change should be blindly accepted because that's no good either.  However, if change brings about higher student performance and helps create more critical, thoughtful, passionate young scholars, why not give it a try?




Change can be a good thing.  

Thursday, January 2, 2014

Real World Math

While we do number talks to start our math block, I like the idea of this type of problem as an additional warm up or closure:


Umm...close?  But last time I checked, that wasn't how much I'd save!

It's important for students to be able to analyze the mistakes of others and critique their reasoning (math practice #3).  Plus this provides a great "teachable moment" on the importance of checking your work and how math truly is all around us.

Thursday, September 26, 2013

Terrific Thinking Thursday

Our school is using Number Talks for math to boost our students' number sense, working understanding of mathematical concepts and critical thinking.  The philosophy behind Number Talks aligns perfectly with Investigations, which we are using as a tool to guide our standards-based instruction and assessment.  Through hands-on learning and discourse, our students are learning how to interact with math rather than memorize and regurgitate information.

Our grade level has tweaked our number talks:

Monday: This is our traditional number talk.  A problem is displayed on the board, students solve mentally then raise their hands to share their answers.  Emphasis is given to strategies and explaining their thinking.

Tuesday: Ten minute math from Investigations.  We are starting with quick images where students are looking for patterns, which is supporting the 8 math practices.

Wednesday: Word problem Wednesdays.  We are moving away from the traditional circling of the number and choosing an operation robotic routine.  Instead, we are focusing on criticial thinking and strategies.

Thursday: Terrific Thinking Thursdays!  We display a deceptively simple problem and let students solve individually before sharing out whole group.  

Fridays: Fast Facts Fridays.  Students are working on their individual goals for fact fluency (multiplication and division) in a fun, game-like way with their shoulder or face partner.

Since it's Thursday, here is an example of today's problem:

The problem states "You have $2.75.  What coins could make this amount?"


None of my students gave me an answer invoving dollar bills.  There were actually more answers they came up with later and I was impressed they used half dollar coins in their answers.  Not bad for eight am :)