Monthly Archives: February 2013

Workshop Using Google Docs

I’m settling into a recipe for using Google Docs for my cooperative learning activities, and I wanted to share.  I am very pleased with myself for all but eliminating paper for those activities, and am hopeful I can reduce the paper usage even more.  Using Google Docs has also opened up interesting ways for the students to get engaged and collaborate, but as with anything, it introduces pitfalls too.

Pre-work:  Before class, I create the cooperative activity just as I normally would have made a worksheet.  I create it in Google Docs – sometimes as a document, sometimes as a spreadsheet, or whatever tool the activity calls for.  I share it with my entire class with “view-only” permissions.

A:  Log on and warm-up.  Our class netbooks take some time to fire up.  I give the kids their daily planner update / learning target / plan of the day, and then send them in small groups to get their netbooks and log on.  While the netbooks are doing their thing, kids answer warmup questions in their math journals and demo at the board.  We process the warmups.

B:  Opening and mini-lesson.  Kids are logged on at this point, and usually I have them lower the screen while we participate in the whole-class opening.  Here we pose some introductory questions that have to do with the lesson, and I model the thinking that we will be doing that day.

C:  Ready to work.  All activities are posted on my Blackboard website and coded for the date.  Inside the folder for today are these activities.  I bring them up on the board and label them.

My Blackboard links with instructions for the kids.

My Blackboard links with instructions for the kids.

D:  Work time.  Kids click the link to open the Google Doc.  One group member shares the document with their table group.  A leader is selected and that student keeps the rest of the group on the same problem, together.  My main role during this time is to question and guide their thinking.  Often, this is encouraging them to not go with the quick answer, but to carefully break down the problem.  Sometimes, of course, I police the teamwork. 🙂
In this case, I posted a little interactive activity to help them with the work.  Part of the document had spinners, and I had little moving spinners they could test if they got stuck.

Students analyze probability situations and write about their findings in the Google Doc.

Students analyze probability situations and write about their findings in the Google Doc.

E:  Reflection and summary.  On my Blackboard site, I place a link to a Google Form.  The forms are very easy to create, and all of the form responses go into a spreadsheet for easy access!  The kids click File –> Share and copy the link that shows up.  This link is pasted into the Google Form along with their reflections and any summary responses.

Sample form for collecting reflections.

Sample form for collecting reflections.


F:  Summarize and wrap-up.  We share any interesting answers and methods for solving the problems, and then log off the computers.  If it’s not the last class of the day, students stack the netbooks on a shelf instead of trying to cram them into the cart.  The last class of the day gets to put them into the cart.

G: My turn.  I read through the work I get from the groups.  I might decide to add feedback directly to the documents.  I let their work guide me in what we’re doing the next day.  I reflect on the mistakes and pitfalls and misconceptions and what could go better, and often there is quite a lot.

I’m still very, very new at doing cooperative learning in this way, so there are some problems that have come up, and also some incredible advantages.

Problems:  Breaches of etiquette in using information technology come up often.  When they started learning, I set (what I thought were) clear expectations, and then I reminded myself that they’re twelve and they think it’s funny to post “WAZZZZUP EVERY1” in the comments and highlight everything in red and add pictures of spiders.  I’ll be giving the kids feedback for quite some time on how to collaborate properly – and reminding them that the computers, and all information that passes through them, do not belong to the kids and must be treated professionally.  There are the usual problems of workload sharing, which are the same whether work is done on paper or electronically.

Advantages:  Everyone gets to see everyone’s thinking laid bare right there in the document. No straining over each other’s shoulders, and no “what’d you get? What’s the answer?”  Instead, the conversations turn to “how’d you get that?” and “It says explain. We should explain.” and “It’s not yellow, yellow. It’s yellow, green.”  I loved this.  The students also found it engaging and there really was less “policing” than usual.  It could be that we have settled in as a community of learners a little more, and that almost certainly played a part.  But the format made it much more possible for everyone to be part of the action.


Things to watch for:  The type of work has to be conducive to the format.  Hand computation isn’t a good fit.  Drill / practice is better suited for other media, not collaborative documents.  They have to be rich tasks that require a lot of thinking and writing and explaining.

You have to have a good opening to scaffold the thinking.  You need to leave a lot of time at the end for summary and clean-up.  I am still struggling with this, because I see the kids doing good work and I’m hesitant to stop them.  But 8 minutes isn’t enough time to wrap up, reflect, summarize, and put everything away.

I plan to continue cooperative learning this way whenever I possibly can.  I love it and go home with a clean conscience from my reduced paper usage.  🙂

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Posted by on February 28, 2013 in Uncategorized


Google Docs and Interest

I am finishing up a unit on ratio, rate, and percent.  I am finally (finally!!) starting to get into the groove of using my class netbooks.  The first time we used Google Docs, it was just a disaster.  The whole class period was spent finding files and troubleshooting login problems.  I stayed away from Google Docs for quite a long time after that.  I created this lesson with an alternate plan for students who couldn’t get Google Docs to work, and I’m glad I did.

Standards for this lesson:
7th Grade Common Core: Use proportional relationships to solve multistep ratio and percent problems (7.RP.3)
Personal Financial Literacy: Solve problems involving percent of a number, discounts, taxes, simple interest, percent increase, and percent decrease (PFL)

Although the standard only mentions simple interest, I think it’s worthwhile to have the discussion about simple vs. compound interest.  The goals of the lesson were:

Describe simple vs. compound interest
Calculate simple interest if given the principal amount and the rate
Discuss how interest is part of saving for goals

I gave the students some notes on vocabulary terms yesterday. We reviewed them briefly today.


I told them that today, I wanted them to calculate how much money someone would have if they used simple interest versus compound interest for their savings account.  I wanted them to be able to compare simple versus compound interest, and which one would save you more money.  I pointed students to my Blackboard website and said we’d be working on spreadsheets to do our calculations.  I asked them to discuss the pros and cons of Excel versus Google Docs.  The students were very opinionated about it!
– Google Docs is convenient because you can get your files from home or school
– You can use Excel even if the internet is down
– Google Docs auto-saves whereas you need to remember to save Excel
– You can share Google Docs with someone to get help

Most students favor Google Docs.  However, not all students were able to view the file I shared, and I think it has to do with the settings for viewing their Google Drive… but I couldn’t troubleshoot it then and there.  I told students who couldn’t see my file to please open Excel. We spent some time just getting the files to open.

I guided them through making the calculations for Simple Interest, where you have $5000 in the bank and get paid 4% interest every year. Every year, someone would earn 4% of $5000 and still have $5000 in the bank.  The money was paid out directly and not put back into the principal.  The students decided that after the sixth full year (seven interest payments), the person would have earned $1400 in interest and still have $5000 in the bank, for a total of $6400.

I started them on the calculations for Compound Interest.  Students calculated 4% of the balance, added the interest to the beginning balance, and then this became the balance for the next year.  Next year, the bank account had more money and would earn 4% on that larger amount, and then that interest got added in, and so on.  I let the students finish with help from their friends.  A few students got stuck and stayed stuck, however most were quite persistent and sought help from friends to get the math done.  Some were really savvy about sharing their documents to troubleshoot together.  I felt good, as this was a great use of technology in the classroom and I think we are getting good bang-for-the-buck from the netbooks.

Some students were able to start on the second interest scenario, but many did not get there.  We discussed the differences between simple and compound interest, and we noted that compound interest earned more money over the years.  This was very easy to tell from the spreadsheet. Doing the calculation for each year was powerful.

I regret that I did have some students that stayed stuck on the task.  I will be targeting them over the next few lessons.

I enjoyed the task and I think the kids learned a lot from it.  I am attaching the blank spreadsheet, the key spreadsheet, and just for fun, my ticket-out-the-door responses (without names).  What do you think?  Did they get the idea behind the lesson?  Clearly I have some more spiraling to do on this topic, but for the first time they’ve calculated an interest scenario, I was pleased with the progress.

InterestLessonBlank  : Blank spreadsheet in Excel format

InterestLessonKey :  Filled-out spreadsheet

Ticket_no_names : My ticket-out-the-door responses.  I worded the first question badly.. we did the “analyzing discounts” lesson yesterday and I meant to say “calculate percent increases and decreases”.  But students responded as best as they could.  I did this with a Google Form and it worked beautifully.  Aren’t some of their answers awesome?


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Posted by on February 8, 2013 in Uncategorized


Magic! Help me do it again.

I had a wonderful day today.  Classroom magic happened.  It is so rare and beautiful that I didn’t know what it was at first.  I processed with a colleague afterward, and he asked what I put in place that made the magic happen.  I had a tough time with this question.  I always think I put my best effort into a lesson, but something happened with it during period 7 today that made the whole classroom do mathematics together.  So here’s how it went down.  What do I need to be sure to do tomorrow to re-create magic?

We started the lesson yesterday.  We did whole-class questions on percent of a number and percent discounts, and had volunteers solve the problems in different ways on the board.  Kids demonstrated benchmark percents, multiplying by decimal equivalents, converting to fractions, and hybrid strategies.  I told the kids to get their netbooks and log on while I gave them instructions for the group work time.

In their groups of 3 or 4, I asked for one person to create a new Word document while the other group members downloaded the activity .pdf file.  Their learning target was to compute and analyze discounts to find the best deal.

I got the activity from the Financial Fitness for Life book that I picked up at a recent training.  I originally had in mind that the learning target would be to compute percent discounts, but I liked that this activity had different kinds of discounts, not just percents, so kids really had to read the word problems carefully and not just apply an algorithm to get the cost.  It also spiraled back to rates and unit pricing, which I liked.  I will attach one page of the activity so you can see what it’s like, but you should get the book.  It’s wonderful.


While the kids were logging on to the netbooks and downloading the file, I asked for a little multitasking attention and modeled an example problem for them.  At MexiFiesta, I have two coupons:  One that is “buy three, get one free” and one that is for 15% off my total bill.  I planned to buy 3 burritos at $6.00 each and one kids’ meal at $3.50.  I thought out loud and analyzed the two discounts I would get, determining that the first coupon would save me $3.50 while the second coupon would save me $3.23, so the first coupon was a better deal.

I told them they would be seeing ten problems, each with 2 possible coupons to use.  They would have to analyze the discounts with their teammates and calculate the better deal.  The teammate with the Word document would capture their complete-sentence responses and submit the team’s answers and reflection.

They started, but most teams only got 1 or 2 problems in before the period ended.  So we continued the next day.


Day 2!

I asked the students to log on to their netbooks and open the Coupon activity or Word document, whichever they were working on yesterday.  While they logged on, they worked on warmup problems on computing percent of a number.  Randomly selected students showed their work on the board.

I pointed out one tricky problem in the problem set, in which students paid different prices for peanut butter but got different amounts of peanut butter.  I demonstrated how someone could organize the information: dollars, ounces, dollars, ounces… and suggested maybe unit rates would help, but they ought to consider whether dollars per ounce or ounces per dollar made more sense.

I told them to share their thinking with each other and reminded them to capture complete-sentence responses in the Word document.

And then magic happened!!!

I circulated, waiting for a group to need reminding to get on task.  Waiting for a group to say “I don’t get this problem.”  They never did.  The room was filled with the sound of debate and discussion and “I think I figured it out” and “My answer is different” and “How’d you get that” and “We got done 5 problems, let’s do the next one.”  They made mistakes, but they worked them out as a team instead of summoning me over.  After the first 10 minutes, a student said “We’re all doing math. This is weird. This isn’t like our class.”  EVERY kid was doing math and even doing hand computation just to prove they could.  No one asked to use the restroom or sharpen a pencil.  Anything I said would have been an interruption to their work.  There was noise in the room, but it was a busy working noise.  Amazing.

They were excited to share their answers and write their reflection statements.  They put the netbooks away neatly and got out their journals to capture vocabulary for the next lesson.  I was sad to see the class end when it did.

I think I organized the lesson the same for period 5 and also period 1, but it was in that last class of the day that every kid on the room decided to be a mathematician.  There are probably other factors I haven’t thought about.

Period 7 is smaller than my other classes, with 20 students instead of 30.
I really can’t think of any other factors that would have played a role. The demographics of each class are really similar as far as the mix of partially proficient, proficient, and advanced students.  And to be fair, the other classes did a good job.  I just had to do a little policing as well and in each class, there were one or two groups that had a tough time getting things going.  Not so in that last class.

Did I just get lucky, or what other factors make magic happen in a classroom?

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Posted by on February 7, 2013 in Lesson Reflections


Every Choice Has a Cost

I attended some personal financial literacy training last weekend, presented by the Colorado Council for Economic Education.  In Colorado, we’ve adopted the Common Core State Standards (CCSS) mostly, but with added standards for Personal Financial Literacy… which show up in our standards tagged with (PFL).  A couple of co-workers and I thought the training would be a good introduction to what we need to teach in the new standards, and we weren’t disappointed!

If there’s one enduring understanding I could take away from personal financial literacy, it’s that “every choice has a cost”.  The ability to analyze and make informed judgments on the costs of your choices could make a big impact on your future success.

In sixth grade, the standards include saving for goals, using percents to solve saving and investing problems, and explaining the difference between saving and investing.

In seventh grade, we move on to understanding taxes – computing taxes, describing the role of taxes in society, and demonstrating the impact of taxes on your income and spending.  In addition, students should be able to compute interest and use unit rates to make purchasing decisions.

In eighth grade, students should understand how credit and debt impact their life goals, and describe the components of credit history.

There is a lot there, and we don’t tend to cover financial literacy well now.  However, it helped me to think of the big understanding, that the thread woven through many units of study must be helping students to analyze the cost of choices and make good judgments based on that analysis.

I want to put in a plug for the Council for Economic Education and the Financial Fitness for Life books.  The books have kid-friendly resources that cover finance problems, and put them in context of analyzing choices.  You can view some activities on the companion web site for the middle school books – click on a lesson and get to some information about the lesson and web resources.

I’m working on adding this analysis to the conversation as we work on our units on percents, probability, and linear algebra.


Rate Activities


We are working in a unit on rates and ratios, and I wanted students to be able to understand different applications of rates, such as area.  In one workshop, I introduced some warmup questions and then a mini-lesson on unit rates, followed by some work time on some more complicated area questions.  These are just old CSAP/TCAP released items, but they’re great problems that can be solved a number of different ways.  The kids worked hard and came up with some clever solutions.  Some pitfalls came up – some obvious, others not so.  I’ll put a link to the whole activity below.  It was exported from the SMART board software.

Area and Unit Rates
Misconceptions & pitfalls:

Moving right into calculating the time to plow the field, without calculating the “square feet per minute” rate first.
Calculating “feet per minute”, or the length of the field that can be plowed in one minute, instead of area.
Dropping zeroes when multiplying, making the field an order of magnitude smaller.
Not converting minutes to hours, or converting incorrectly (for example, 240 minutes equals 2 hours, 40 minutes)

I really encouraged students to think about the reasonableness of their answers, knowing any of the above mistakes would give them answers that should raise flags.  All in all, it was a good activity and I was pleased with how well the students worked together and struggled with the problems.  Some groups moved on to the food court problem, but many groups did not get there yet, and we haven’t summarized that part.


We have 3 teachers on the seventh-grade team at our school, so we often have flexible grouping days.  We use these days to split the kids into “support”, “target”, and “enrichment” groups.  We work with the kids on remediation of some concepts they are not secure with, or extension and depth if they’re ready.  Since the topic of study this week was unit rates, we gave the kids a pre-assessment and then grouped them into three groups.

Support:  These kids struggled with the idea of a unit rate, and correctly labeling which unit rate they calculated (such as misunderstanding ounces per dollar, versus dollars per ounce).  We gave them this activity.  unit_rate_flex_group

Target:  These kids seemed to understand some concepts of unit rates, but struggled some with how to find the correct unit rate to make a valid comparison.  We wanted them to work with ideas around comparing and scaling rates, using this activity.  Making Comparisons of Two or More Rates

Enrichment:  These students understood the how and why of calculating and comparing rates.  With these kids, we dug deeper and used technology so they could understand table/graph/equation relationships.  Comparing Water Usage Investigation

My team felt this was a pretty successful day of flexible grouping, where all groups of kids made some growth toward their targets.  Another big success was that we went paperless!  With class sets of netbooks in every classroom, we posted our activities on our websites and had students access them online, edit, save, and submit.  We hope to do this more and more!