# Mini Review Units/ Integers

One of the things I have decided to do this year is to have mini review units in between each of my larger units.  So this year, I did a Rational Numbers unit, then an Expressions and Equations unit.  Now I am going to spend the next week reviewing rational numbers before going on a to a new unit.  After that unit, a rational numbers review week again, then an expressions and equations review week.  I am hoping that these mini units will keep students on top of the material we learned before and help them to realize that just because a unit is over doesn’t mean that they aren’t responsible for the material again.  On Friday, we did The Great Integer Race.  Each student got an addition or subtraction problem and they had to silently walk around the room and find the person with a problem that would result in the same answer.  But then, I added a next step.  We have been working on putting in Claims, Evidence, and Reasoning piece into our plans this year.  Once students found their matches, they had to write how they knew that their match was correct.  They switched their problems on the way back to their seats, then did the whole thing 4 more times.  It was pretty basic, but helped to review some skills they had learned in the past.

Activity

# Socratic Circle- Fundraisers

One of the high points of my year last year was when I did a Socratic Circle in my class.  We used a lesson from Robert Kaplinsky’s website– by the way, I am so happy to see that recently everyone seems to have found the awesomeness that he has on there, cause it is great!  We just completed another Circle this week, although we didn’t use one of his lessons, I’m planning on using a bunch of them during my next unit.

This time, we use a problem on fund raising from Math Gains.  I liked this problem to do early in the year because the math was pretty basic and there was no clear right or wrong answer.  Students were able to bring in many other considerations in addition to the math behind the fund raising to support their reasoning.

Yet again, this proved to be an amazing activity because it got the kids talking about math.  So many kids surprised me.  Students who have barely spoken in class were suddenly in the inner circle debating.  After day 1, I had a student who will barely lift a pencil in class yell “no!” when I said class was over and run up to me excitedly to tell me how great this activity was because it was a real world problem.

I’m trying Box instead of Scribd because apparently Scribd needs a password now.  If you need anything I have previously uploaded to Scribd, please ask.  I am happy to email you the documents.  Excuse the formatting if it is off, I used a fun font 🙂

Part 1

Part 2

# Keeping my mouth shut…

I posted last week about my success with my very first Socratic Circle.  It was so successful that I couldn’t just take one day for the discussion, we had to use the next day as well.  The lesson I used was from Robert Kaplinsky’s site which has some great real world problems that are engaging and thought provoking.  The problem we used was deciding between a 20% off coupon or a \$5 off \$15 or more purchase at Bed, Bath, and Beyond.  Wednesday I had the kids do Robert’s activity and prepare for the circle using the inner circle page.  Thursday we went over all of the answers to the problems and then started to discuss the big question- Which coupon is best?  By the end of the day on Thursday, I knew we were on to something good, we just weren’t quite there yet, so we continued on Friday.

The hardest part for me during this whole process was deciding how much I was supposed to/should say to get them started.  And this definitely depended on the class.  By Friday, my 3rd hour was almost to the end of their discussion.  About 15 minutes into class, they had clearly all reached the same (correct) conclusion and I presented them with a challenge problem to discuss.  My 5th hour needed some more direction.  There were a few students who presented some ideas and I used those ideas to ask a few guiding questions to get the students on track.  By the end of class, I felt good about how we left things, but would love to see them asking the questions in the future.

Enter my 6th hour.

I did my intro, this is where we left off, this is the big question… and asked who wanted to start.  Five students joined the inner circle and I told them to go.  So they had a general discussion that ended in the conclusion that the 20% off coupon was best for high prices and the \$5 off coupon was best for low prices.  Now the questions I want to ask are “What are high and low prices?” and “What about the \$5 not being used under \$15?”  But as I am getting to the point where the group is stalling and I am feeling like I need to get them on track, a 6th student from the outside circle stood up and walked to the center.  She sat down and said, “I am wondering what you mean by high and low?  Like can you be more specific?”  So I’m thinking, ok, great, that’s what we need!  So they discuss a little more, start to narrow down the ranges for when the coupons are best, and I switch out the center circle.  New 5 students.  Same situation.  They pick up from where the other group left off.  Again, they got to a point where I am just about to open my mouth… and a 6th student joins the group and asks exactly the right leading question.  Again, and again, and again.  Until it is now 45 minutes later and I have just watched in delight as they got closed in on exactly where they needed to be!  It was a thing of beauty.  Had I talked, I would have ruined it all!

# Socratic Circle

Today was just one of those days… that makes every single hard moment so so so worth it.

Is all because of the Socratic Circle.  This is a new thing going around that I have also seen called a Socratic Seminar.  We were introduced to this concept back near the beginning of the year and there are about five teachers from across the school (K-8) who have tried to do this.  The main example we saw was from a language arts classroom, and it seemed to work best with language arts or social studies where there could be two sides to an argument and the kids had to pick one of the sides.  But I was determined to find a way to make this work in my room.  Then I read Robert Kaplinsky’s post and checked out his amazing website.  Man, are there some awesome lessons on there!  I found this lesson and decided to try it for a Socratic Circle.  The basic idea of the lesson is to figure out which Bed, Bath, and Beyond coupon is best- 20% off one single item or \$5 off a \$15 purchase.

We began in class yesterday.  I had the kids do some review on how to find a percent discount of a number.  This is when I started to really regret my choice to do this.  While the basic idea of a discount was no problem, they couldn’t round to save their lives, they asked me a million times why we rounded to two decimal places, they tried to round every single problem to a whole number… After the review I had them do Robert’s activity.  I really hung back and did not answer a lot of questions, because I wanted the Socratic Circle to help iron out any problems.  This is when I found huge problem #2… or 3 or 4 or 5.  I was very frustrated at this point.  They were so good at finding the percent discount after our review that they wrote a percent sign after the \$5 and treated it just a like a percent.  Sigh.  I left with a blog post written in my head entitled “Stupid Questions?” about why America’s children lack common sense and where we failed them along the line.  But I was busy last night, so you don’t get that downer post, you get this one!

Today I came in super nervous and convinced that I was going to spend my 75 minute classes having the kids stare at each other in misery all having no clue what the purpose of the activity was.  In walks my first class…

So now a basic overview of what happens during a Socratic Circle.  Preparation is done by the teacher and kids before hand.  I only needed one day, but it could also be an end of unit assessment type of thing.  There needs to be a big question that the kids have to write an answer to at the end of the activity.  The kids should come to the Circle with their opinion in their minds as well as reasons to support that opinion.  In class, 6 desks are put in a group in the center and everyone else is in a large circle around the outside.  5 kids sit in the inner circle, leaving the 6th desk open for someone who has something they want to say to jump in.  We walk through the questions that they have answered the day before.  Everyone in the outer circle should be taking notes and writing down points they want to bring up, but they aren’t allowed to comment outloud.  Every few questions, the inner circle people go to the outer circle and new students go in.  At the end, students have to write an essay answering the big question.  Our language arts teacher will be using the essay for an ELA grade as well.

So here is my first class, we are all set up and ready and I begin with the first questions on the page… Question 1- What is the price with the 20% off coupon.  I ask it, one kid answers it, all kids in the class look at me like, “Really?  You set all of this up for THIS??” And I start to get nervous.  So we trudge on through the first several questions, switching inner circle kids every once in a while and suffering.  Then we get to the big question- What is the best coupon?  A student says “20% off is always best”.  They all nod and stare at me again.  So I say, “Always?” and slowly an outer circle kid stands up and takes the 6th seat.  And away we went!

From then on, they were fighting to get to the 6th seat, proposing situations where 20% would be best, would be worst, begging me to switch inner circle kids so they can get in.  And then I found myself one minute before the end of the hour and I just couldn’t bring myself to stop them.  So I told them we would continue tomorrow and to think of what other points they wanted to bring up for tomorrow’s discussion.  Then I walked into the hall to overhear them talking about it, bring up points, using our respectful disagreement phrases…  Sigh of relief…

Same in my next two classes.  Up until the very last minute, groaning and yelling NOOOOOO! When I had them clean up and hurry to their next class.  I even had one girl clearly use a phrase that our ELA teacher uses with them as she asked a classmate to “formulate a bold thesis statement with supporting evidence”.

So while today went amazing, I do feel like the beginning math stuff made this Circle different than ELA/Social Studies ones since I wanted to clarify the math answers first, so I may have to think about how to change this in the future.  And it clearly can’t be done with a topic where there is one single clear answer, but this activity worked perfectly.  I did feel like I had to cut them off in the middle of the good stuff, and I definitely don’t feel like they could write the essay at this point, we still have work to do tomorrow, but it was so great to hear them discussing math!  They posed questions, they argued respectfully, they fought to participate.  And all I did was ask a few leading questions when they needed to get started.  I feel like this could only get better since they haven’t done anything like this before.

I will post the files I used, but I left my flash drive at school and I just had to blog about this tonight!

# Combining Like Terms/Whiteboards

This week, we continued with our fast food theme and I used the same hamburgers, fries, and pop pictures to create a combining like terms activity.

I really think the best feeling ever is teaching a lesson where students have always struggled when I have taught it in the past, and then a new idea suddenly makes it make sense to them.  I heard one of my kids say quietly, “This is awesome.”  WOW.  That’s a good feeling.

We also have used whiteboards a lot this week, and they have been amazing.  There is something magic about kids being able to write on whiteboards that seems to motivate even the most stubborn students.  I can also monitor so much better when I sit in the front of the room and I can easily see everyone’s work and answers and make any corrections that I need to.  I am also easily able to differentiate this way, because I can see which kids are moving fast and doing well and then assign them harder problems while I work with students who are struggling.  Yay!

# Distributive Property

I saw this idea on Sarah’s Math = Love blog.  She actually got the idea from Adventures in Teaching.  So the idea is to teach the distributive property using combo meals.  I created this activity for the kids to do.

I feel like this was the first time I taught the distributive property where the kids were all talking about how easy it was and how it made so much sense- such a great feeling for a teacher!  I am going to do the same thing for combining like terms tomorrow, so I hope the success continues!

The distributive property

# Solving Equations

This week we worked on solving equations using the AIMS Equality in the Balance activity.

Using a scale isn’t a brand new idea for solving equations, but this activity is pretty cool.  The idea is that there are packets of pennies and individual pennies on either side of the scale.  You have to solve the equation to figure out what is in the packet.

I found that this activity was awesome for the kids because:

1. They could visualize figuring out how much was in a packet of pennies vs solving for some random letter.

2. They could physically cross off pennies from either side of the scale to make them balance- this helped them understand the reason we have to do the same operation to both sides of the equation.

3. To divide up pennies between packets, students could circle the pennies to create the groups.

I also told the kids that instead of writing the word “packets” every time, we were just going to abbreviate the word as “p”.  Again, this helped them put meaning to the variable rather than it being a random letter.

# Variability

In the past, my data standards always consisted of teaching the students how to make graphs.  While there were a few graphs they weren’t familiar with, many of them seemed very repetitive.  These kids have been making line and bar graphs since first grade.  The new common core standards change things drastically.  It is all about sampling and variability now.

On Tuesday I started with an AIMS activity from the Statistics and Probability book.  The activity had the students comparing synonyms for blue, yellow, and red to see the different lengths of the words.  I added a component where the students would have to find the interquartile range and mean absolute deviation, two things that they weren’t familiar with at all until now.

Then today, we did another activity, Counting Characters, from the same book.  For this one, the students had to find a random sample by throwing squares of paper at a sheet of newspaper, then they counted the characters in each of these squares.  Students used that data to estimate how many characters would be on the entire page.  From there, I had the students find the mean absolute deviation of their data and we compared these numbers to the rest of the groups to see which group had data with the highest variability.

I think both of these activities went pretty well.  I was quite shocked at a few of the things that happened during the random sampling for the counting characters activity.  First of all, I had the students cut out squares to throw on the newspaper.  I had a few groups that didn’t cut on the lines for the squares.  They simply cut between the lines on the paper.  Really???  I really just didn’t think this would be something I would have to say specifically.  I also had students toss the squares at the newspaper, lean down and straighten the square so it was nice and neat on the paper, then throw the next one.  Not a random sample then, guys!  And then, again, the cutting out of the squares from the newspaper was appalling.  How do you get jagged edges?  How do you have pieces that are drastically different sizes?  All I kept thinking of was the common core standard for mathematical practice “Attend to Precision”.  While I don’t think that cutting newspaper squares was exactly what they were thinking of when they wrote this standard, it certainly fits the bill.  How can we expect our kids to do higher level precision when cutting carefully isn’t even on their radar?

# Slicing 3D Figures

One of the very first blog posts I came upon this summer when my blogging journey began was Julie’s Volume of 3D Shapes with Play-doh.  I have been so excited to do something like this since I read this post and since I found little tubs of play doh at the \$1 spot at Target.

Instead of finding the volume, we used the play doh to do one of 7th grade’s new 7th grade stadards, slicing 3D figures.

Each of the kids was given a container of play doh and a plastic knife.  We formed 3D shapes and then made parallel and perpendicular cuts and examined the cross sections.  This was one of my favorite things we have done this year, and I am pretty sure the kids agreed!  They really seemed to get what we were doing and had a little fun, too!

The other awesome part was the kids were over the top impressed with my amazing sculpting skills.  And I do not have amazing sculpting skills.  But every single class was in awe of my shapes and how quickly I made them.  Great ego booster.

# Floor Plan

This past week, we have been working on a version of Sarah’s Apartment Remodel Project.  We did not do all of her amazing flooring stuff, we just stuck to finding the basic area and perimeter of rooms.  I did change some things a bit.

Sarah posted a picture of the floor plan she used, but she said she didn’t have the file anymore.  I ended up creating my own that is pretty much the same exact thing as hers without the detail.  I also changed some of the measurements.

Here is the space I gave them to work in.

Sarah had them draw all of the rooms on graph paper, then use that paper to find the area.  I started off with this as my plan, but then decided that was not necessary since they had the measurements.  Big mistake.  While I think this activity had the potential to be great, the amount of rooms that I gave them (since I also added outside stuff), along with no graph paper was way overwhelming and too much.  I will for sure do this again, I think it was a great way to have them figure out missing measurements and find the area of irregular figures.  But I for sure will have them do it on graph paper!  This will make the concept of area so much easier to understand and help them to visualize the area much better.