## #mathematizethis: fractions

Wednesday is pizza day at our school.  As I prepared to hand pizza out to my student, a little voice whispered: “#mathematizethis!”  So of course I took a picture before passing it around.  (To clarify, taking pictures of food is not a thing I usually do!)

Just for good measure, I took this picture too, and I was glad for it.

Today, Thursday, I used these pictures for a Number Talk.  I put up the pizza picture and said, “What do you see?”

Pizza:

• There are 2 pieces of pizza missing.  (This might not seem like a big deal, but it showed me that they could extrapolate the information by comparing the 2 pizzas.  This came about as people said, “There is one whole pizza and one part of a pizza.”  And “There are 10 pieces in a whole pizza.” And “I can see 5 cheese, and 3 ham, so two must be missing because we need 10 for a whole pizza.”
• At first, they were all about the counting.  (We have done only 1 other fraction Number Talk.) One girl said “I saw 1,2,3,4,5 on one half, so that means 5 on the other half, then 5 on the other half, so that’s 15.  Then 3 more, so there are 18 pieces of pizza.” UNITIZING!!!  AND SUBITIZING!!!
• Soon after that, the fractions started rolling in.
• 3/18 are ham
• 15/18 are cheese
• 2/18 are missing. (We talked about how it was really 2/20 missing.)
• I asked, “What fraction of the pizza would a person have if they only had 1 piece?”  I  am super excited that 1 person said 1/10 since we’d established that 10/10 is a whole pizza.  Nobody argued for 1/18, and nobody looked confused, so I call that a win.

Milk:

• There is one milk missing.  9 can fit in the box.
• 1/8 of the milk are plain.  7/8 are chocolate. They went to fractions much quicker the second time.

I asked what they would do if a class ordered more than 9 milks.  Most agreed you could stack the milk on top, but some thought a second box would be required.

Overall, I am super-nerdy excited about how this went.  It’s a contextualized problem, and one that they will encounter again because pizza comes every week.  I am also thinking this could be a Guided Math centre question at the beginning of every month.  The number of children who order pizza tends to change a bit every month.  AND, we could take pictures of the pizza in other classes.

I am going to teach fractions earlier next year just so I can do this!  And then I am going to teach graphing so we can graph our results. I just decided that right now, so if you don’t see this reflected in my long range plans, please hold me to it!

## Guided Math: Where to start

I’m going to write tonight about September.  In part because my brain is already thinking about how I will do this whole teaching thing better next year (I think that every year.) and in part because I don’t want to share too many more things that will alert everyone to the fact that I kind of got hung up on a few concepts earlier this term, leaving us scrambling to finish a few things at the end of May. *sigh* (This happens every year, and every year I think, “I will not let that happen again!” but then we get waist deep into learning something that I think is really important for us to learn really well and I keep saying, “I’m just going to do this for one more week.” and then at the end of May I am covering something like probability by teaching math all day every day for a while and…well…you’ve probably done it too.) (But, honestly, when we spend a whole day on a certain concept, the learning can be pretty magical too.  And something like probability is fun to do that with.)

But…back to where I wanted to start.

Guided Math.

After doing this for one week in my class, you may recall that I thought I’d try it for another.  However, as I sat down to plan out that week, I realized there were way too many things that I needed to put into place to make it successful.  See, I will be teaching many of my grade 2s as grade 3s next year.  I felt/feel that if I go about it all haphazardly I might be setting us all up for some trouble in the new year.

I had a table set up where the students were to take a survey and create a graph.  We have done this so many times over the course of the year, I assumed they could do it independently over the course of a few days.  I gave them the topic: favourite holiday.  I gave them the paper and graph templates they would need.  I asked for their completed graphs on Friday.  Now, I feel I should say that I was monitoring what was happening at that table.  I really was!  So I know some surveys were taken and some graphs were made.  Here’s an estimation question for you:  Approximately how many students do you think actually had a graph to hand in to me on Friday morning?  If your answer is near 2, or roughly 10% of my class, then you are correct.  They had parts and they had papers and they had apologies and excuses.

Every student already has a 2-pocket folder for their writing.  I laminated them last June in preparation for this school year, and they have lasted the school year.  (Hooray!)  ON the back, every child has a personal word wall.  I have labeled the pockets “drafts and ideas” and “work in progress”.  It’s a good system, if I do say so myself.  This June when I am making my red writing folders (because I love how it sounds close to “Red Riding” haha) I am also going to make some math folders.  I think that I will keep the word wall, and use it exclusively for math words.  Actually, it is highly likely I will do that.  (see…probability…it’s everywhere!)

1 system, used 2 different ways will = success!  I am sure of it.  I think a way to keep track of their papers from day to day will really help them start and finish something, and give them something they can turn in at the end of the week (accountability).

I am going to borrow another writing-related idea.  I think that at the end of each week I’d like my students to write a reflection about their learning.  I am going to give them a math journal….let me just stop there.  I have seriously tried this before and hated it. But I am thinking that I have evolved a bit.  I think the written reflections will be useful in helping them consolidate their thinking.  I also like a written record they can refer to and see growth.  AND it will give me some interesting anecdotal comments when it comes to report card time.

In the book “Making Thinking Visible” by by Morrison, Church and Richart, there is a thinking routine called “connect, extend, challenge”.  I used it a lot in math last year with my grade 3/4 class, and have used it somewhat with my grade 2/3 class this year.  I discovered that having students find the connections between math ideas, and within math ideas, was really valuable.  So, if I teach them this routine early on and have them use it to write in a journal, I think we’ll get some interesting stuff.  Basically, they need to thinking about how the learning they have done connects to other things they have learned, then try to extend that learning, and finally talk about what is still challenging them.  Here’s how it might look. Pretend I am 7 and we have been making graphs all week.

Connect:  This is like when we took surveys about things people like last year in my other class.

Extend:  I could use it to find out what people want to play at my birthday party.

Challenge: I want to know how to organize my work better.

The challenge part is a big challenge for the little people, so we might not add that in until after Christmas.

And that will be easy to do because I am going to be completely on track and following my long range plans perfectly.

That’s where I am now with Guided Math.  I have other thoughts too, but I am not ready to write them down yet.  I need to keep exploring this idea.

Guided Math

## Guided Math: #2

I started out last week with a plan to do Guided Math for one week.  I KNEW I would hate it, but that I might be on my way to hating it less.  So, really I should be proud because MISSION ACCOMPLISHED!

We made it through the week, with just one interruption. Junior track and field events on Friday left us with some extra students for the day.  They were grade 3 students from a 3/4 split. (Primary track and field is another day.)  Because of this, our routine was quite out of whack.  Friday was supposed to be the day that my class and I sat down to go over, in a congress-y kind of way, the math that we did this week.  I will have to do this on Monday.  I think that my class actually liked the Guided Math activities, but I am anxious to hear their thoughts and ideas.

Highlights:

• I had 10-15 minute rotations going, with one grade staying with me for about 40 minutes while the other grade rotated through 3 activities. I think the timing was right.  Keep in mind that I have a grade 2/3 split, so though our stamina would probably allow for them to stay with the activities longer, our wiggly butts were happy to move along after 10 minutes.
• If I were to start this in September, I think a math folder would be necessary.  I had them putting away work in their cubbies at the end of the rotation, but a folder would have kept it all more organized and easier to find the next day.
• If I spent September training the class, as I did during our literacy block, they would know that they need to work quietly and not interrupt the group meeting with me.
• I met this week based on skills I wanted to teach. Grade 3s needed to work on multiplication, and I wanted my grade 2s doing some more addition/subtraction work.  I had different curriculum expectations to focus on.  This week, however, I am going to be teaching fractions to everyone, and I think my groups will be divided based on abilities rather than grade assignment.
• Yes, you read that right. I am going to give it another go this week.

When my current school board started pushing people to use Guided Reading (that’s about the year I started here), there were many people who resisted this style of teaching.  They didn’t know what to do with the rest of the class.  They didn’t really know what to do in meetings with small groups.  They weren’t sure they had the resources they needed to really teach the program.   I spent a lot of time trying to use my zeal in my role as a literacy coach, hoping to convert as many people as I could to Guided Reading.

Now I am faced with some zealots who believe in Guided Math.  I have concerns:  What does the rest of the class do?  Do I have the right resources at my disposal, or will I be up until midnight every Sunday night inventing the wheel?  What am I supposed to do, exactly, with my small groups?  (Sound familiar?)

And all of those are legitimate concerns, I think.  BUT – I don’t want to be the teacher who is still teaching a “Mrs. Frisby and the Rats of Nimh” novel study every October to my 5th graders because when I was hired in 1999 that’s what they told me to do with 5th graders in October.  So, do I want to keep excusing myself from trying Guided Math because I am satisfied with the way I do math now?  Well….kind of I do. Change is hard!  But I can do hard things, right?  (I’m asking…please reassure me!)

This is how the math block looked last week, basically, and I am going to try it for another week.

M/W:  Grade 2 students at activities.  Grade 3 with me working on multiplication.

T/TH: Grade 3 students at activities.  Grade 2 with me working on adding and subtraction (skip counting on the 100 chart and number lines by 10s.  I think they all have it this time around!)

Friday:  The circus came to town.

Activities:  Students had 3 –  Take a survey and make a graph about favourite holidays, Dreambox on the class iPads, play a game to practice adding up amounts of money.

Number Talks:  Getting ready for EQAO!!!  (I know, so exciting!!!)  so our Number Talks this week were really reviews of math skills.  I pulled out the EQAO from a few years ago and picked out a question on 3 days.  We reviewed patterning, telling time, and I forget what else.  A few times I did this at the end of the math block for about 10 minutes.  Typically I start math with Number Talks, so this was different.  It was a good way to settle the class at the end I think.  Usually I use a Number Talk as a warm-up. However, last week I was using the first few minutes of class to explain the centres, and to remind everyone to just please, if they had any compassion for me at all, to work quietly at the activities, and solve their own blasted pencil problems on their own!

This week:

Activities:  Reflections/Rotations/slides, graphing, and Dreambox.  Monday well will talk about last week, and I will read them a book and do a quick activity that sets them up to do the reflection/rotation/slide work.

Lessons:  Fractions.  I did a quick assessment in gym the other day when I asked them to walk/run a fraction of the distance between walls.  Interesting results! So I know a few of them, not necessarily all in the same grade, are going to need more support at the beginning level, while others are ready to try working through an investigation of some sort.  We need to work on naming fractions of a set, and fractions of a whole.

Which I better go plan right now. 🙂

## Guided Math: #1

I first heard of guided math too long ago to have a story to go with it.

I have resisted this classroom management strategy in all it’s forms.  Like guided reading, there is a lot of “behind the scenes” organizing that has to take place.  In reality, I felt like have done a fine job of differentiating the work we do in math class, so this strategy for further differentiating has seemed very overwhelming to me.  I’m already teaching 2 grades, so there is a multitude of curriculum expectations that I need to be looking at (sometimes they criss-cross, but not always) and then there is the range of differences in ability that needs to be covered.

I use Writer’s Workshop, and mostly Reader’s Workshop/Guided Reading.  I don’t do centres or stations in literacy  because I want my students to have authentic reading and writing opportunities.  And I want to be available to work with them, not managing the “job’s board” or the Station Rotation. This prejudice has also stopped me for doing guided math. I can only be in one place at a time, right? I tried Daily 5 a few different years and always felt like it was going to push me over the edge into a yawning, black abyss.

But….suddenly the idea of guided math seems to be haunting my subconscious.  I keep hearing about it.  Last year the range of ability in my classroom was especially wide, and this year it’s even bigger.  And I am not talking about the few outliers that are always at either end.  I’m talking about a full range and it’s WIDE!

In the collaborative inquiry I have been participating in, guided math keeps coming up.  All my usual reasons have been checked off my list every time we have talked about it:  I am not doing it because it is:

a) overwhelming

b) hard work

c) a time sucker

d) all of the above.

Except…for the second year in a row I am sort of realizing that even without doing guided math, I am feeling overwhelmed, and over worked and out of time.  I’ve started to consider that guided math might be a solution to some problems, instead of something that will exacerbate the problem.

So this week I am trying it.  Not for just one day, but for the whole week. I’m going to report back on Friday.  We did some GM on Monday, and I will reluctantly admit it was ok. And I have started to think about not needing 40 different games and activities to use during “stations” (or whatever I decide to call them) and maybe only needing a few that we can circle back to throughout the year.

That’s where I am with it right now.  And it helps that a few other people in my building are trying it out and talking about how it will look and how we can make it work and how we can support each other. I think the reason the literacy stuff is so successful is because we have so many similar management systems in place throughout the school.  Maybe this could happen in math too.

I’ll be back on Friday with a report on the week.