math, Patterning & Algebra

Money (or “Learn to get along with your classmates!”)

This week we learned more about money.  We started “Trades, Jumps and Stops”, a Context for Learning unit and the first thing students do in that unit is count some money.  On the first day, I did a Number Talk, which was definitely not a Number String! I had 50 cents in my pocket and I told the class about the 50 cents.  Then I asked, “Can you tell me which coins I have?” We wrote down 5 or 6 different combinations of coins that are equal to 50 cents.  Then I told them I had 4 coins and they immediately knew which of the options they’d given was correct.  But by “them” and “they” I mean it was only about 3 or 4 students.  Granted, we had a lot of students away due to illness but it was clear that we needed some practice with counting money and making amounts in different ways, so we took a pause from the unit and did that for a couple of days.  By Friday we were using the piggy bank cards, which we need later in the unit, to count out coins, adding up two different amounts to get a total, and comparing them to our partner. This is a detour from the original content of the unit, but I didn’t feel like we could go forward successfully without solidifying this skill. Or set of skills I guess.

I am happy to report that everyone was counting by 5s and 10s, and many were adding up quarters too!  This is because we have progressed as mathematicians!  It is also because I only gave each group 5 pennies so they didn’t have the option of counting out a very big amount by ones.

This week I am also reflecting on how well we are collaborating when we need to.  For the last several years I have done a lot of work with intentional learning partners.  I assign my students to a triad and those people are their partners for the entire month whenever they need partners. In the beginning, I assign them to a partner, or I use a random system for matching students.  As the months go by, I start to ask for their input and ask them to do some self-assessment of their ability to be a good partner.  By the 5th month of school I would not be doing random assignments anymore.

This year is different. On Thursday I pulled out our partner matching cards and I immediately thought, “Why am I still using these?  Why don’t I have partner assignments ready to go?”  Intentional learning partners are meant to match students who will be able to actually help each other out and collaborate together.  Peter Liljedahl does the opposite and has students work with different students every day.  But his work is mostly focused on older students.  I believe that in the primary grades the students need different social things than they do in the higher grades.  For example, practice putting up with each other’s oddities in order to learn some tolerance, practice noticing someone else’s preferred work style and then trying out some tips from that person, and of course they need to learn how to take turns.  They also need to be matched with someone who is close in ability.  Maybe not the exact same ability, but in a split grade class I can’t have my most accomplished grade 3 matched with a grade 2 who is really struggling.  Or worse, a struggling grade 3 matched with a grade 2 who is sailing along! I take all of this into consideration when making matches.

So, why not this year? Well, I think there are a few reasons.  First, we have an attendance problem.  I don’t want to say too much about that, but some kids are away a lot. Second, we have a few kids who are really struggling with being told what to do.  I’m quite concerned that I will assign them to a partner and they will make such a fuss that it will ruin the class period/day/week/month.  Or worse, they will want to be partnered up with someone I do not want them to be partnered up with and I will not partner them up with that person because I am the adult and IT WILL NOT END WELL!  It all seems like a better idea to say, “Sorry, not my fault.  Talk to Fate! She’s the one who picked your partner.” or, “The cards decided, not me.” (which is what I am most likely to say.) We’re a little behind in some of our executive functioning skills and random partnerships let us work on some of those areas while avoiding some of the more volatile ones.  And as I’m writing this I feel like maybe I’m taking the easy way out because I’m exhausted from all the emotional stuff that goes with teaching.

And now I’m going to spend the day thinking about maybe putting some more time into developing the executive skills that will allow everyone to manage frustration in a way that does not make Mrs. Corbett want to cry every day on the way home from school.

But we can all count money, so HOORAY!

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This is the “cheat sheet” for the partner matching cards I use.  I got them from Teachers Pay Teachers.  There are individual cards which are handed out randomly and the students have to find their partner. I use the big heart as our “pick your own partner” card for the days when we have an odd number of students in the class.
math

Monday night and I just realized I never posted a reflection for last week! It was sort of normal, not very exciting week. I’m headed into a week of guided math in which I’ll be working with small groups to do sone learning about money (not very exciting) and everyone will be at other centres solidifying their math facts by playing math games.

It’ll be fine.

But last week I did notice how often our calendar is being accessed by kids. I saw a blog post this summer (I’ll try to find the link!) and decided I would display the whole calendar on our wall this year. I put up the 10 school months and then started the year, intending to find time to make it fancy.

One week in somebody added his birthday. Then we had to add everyone’s birthday. We added assemblies a field trips. During the first week of October somebody asked how many days until Halloween, so we added all of our major holidays, which lead to a lot of other holidays being added. There is a steady stream of people at the calendar counting how many days until this or that. The calendar has lead to many one-to-one conversations about time, counting forward and back, and important days for our classmates. (News flash: not everyone celebrates Christmas! This was news for many of my students.)

I’ve also been creating PicCollages of class photos to create a visual timeline. I need to get October printed! (Ugh!) it’s fun to look back at those memories too.

I haven’t done a class calendar in years. I thought it took too much time and space. But this very casual calendar, with no forced routine for its use, has been such a great addition to our class!

math, Mathematical Processes, Number Sense & Numeration

This week we did…something

It was a weird week for math. I spent some counting routine time counting backwards. They’re pretty good at it. I thought they could be independent as a small group while I worked with some people on something else. I was mistaken. We’ve still got some social collaboration and problem solving things to sort out. That’s the thing I’m reflecting on most as I move forward into next week. I know where I’m going lesson wise, but am still sorting through some of the mathematical process teaching I need to do.

Because of the work I’m doing to spiral in math this year I am feeling like I don’t have a lot of things to use for comments on progress reports. I’ve decided to focus my commenting on some of the mathematical process skills.

This week I’m realizing that so far I’m doing a lot of the selecting when it comes to the tools we use. I put a lot of work into making sure everyone knows how to use the tools properly. Now it’s time for me to talk about how the tools have specific purposes for which they are best suited. We can’t always choose the colour tiles because we like how they stack! It’s time to move along and choose based on what each tool helps us understand. I’m doing some guided math rotations this week, and want to come up with some opportunities for kids to articulate why they chose a certain tool.

That is going to lead us to some communication work. We’re doing okay with this when I am poking and prodding. Now it’s time for the students to think about being really clear with their communication. I’m going to jump in and set up a FlipGrid they can use to explain something they’ve done. They’ll have to think about how to make me understand their thinking when I watch the video at home (cause you know I’ll never find time or a quiet spot where I can view these at school!)

Finally…actually, I’m going to stop there. Don’t need to set too many goals at once, right? I’m also diving into “The T-shirt Factory” Context for Learning unit with my grade 3s and we’ll need to be focused on that math at the same time. Not totally sure what my grade 2s will do next week, but I’m sure I’ll get it sorted out.

It’s important to have a focus on teaching and doing math. But the seven processes are an important part of that we can’t neglect. In a problem solving based classroom students need to be able to do more than accurately find answers.

math, Number Sense & Numeration

I can’t sum up this week in a title

Classes reorganized this past week.  I had a new class list on Monday, and about 1/2 of  my class is new since the first day of school. The dynamic shifted.  Though it wasn’t exactly like starting over, it was enough like starting over that I didn’t feel like I could move forward as quickly as I wanted to.  I decided, therefore, to do activities that would sort of take us back in time to the first week while also moving us forward.

These are three of my first 2 weeks goals that I needed to accomplish in just this past week – the 3rd week:  really work on how to use the manipulatives without driving our teacher bonkers, work on what to do during Number Talk/Number Sting time, and practice working respectfully with a partner.  The friends who stayed with me had already practiced this for 2 weeks so I couldn’t simply start over.  And they didn’t need me to anyway. The friends who moved in had already practiced some of this with their “first 2 weeks” teacher, but we needed to do it the Room 16 way.  I realize that makes it sound like I have some control issues, but I assure you I do not.  Really.  I don’t. Please believe me!

So…here’s what we did.

Guess my Number:  This is an activity from the Effective Guide to Instruction in Mathematics.  I displayed a hundred chart on the projector (This one, from Mathies.)  I had a number on a post-it note in my hand.  They had 20 guesses or questions to figure out my number.  At first, they were guessing one number at a time, but then one of them asked (I think it was accidentally, but I’m not sure) if it was one of the 10’s.  I turned over an entire column and a new strategy was born!  To make it a bit more fun, I was keeping score.  If they could get my number in 20 guesses or less they got a point and if not, I got a point.  By the second day we realized I had no chance of getting a point so we reduced the number of questions to 10, and they improved their strategy at the same time.  By week’s end the score was 6 to 2.  But their questioning strategy had improved so much that I’m not sure I’ll ever get another point. They are starting off every time with “Is it higher than 50?”  They can turn over half the board this way!  It’s a great first question.  Next, they start asking, “Is it in the 30’s?” or 20’s or 80’s or whatever they need to get a whole row turned over at once.  We had to talk about the word “teens” and “single digits”.  And we talked about being a gracious loser.  Or rather, I modelled being a gracious loser.  And they practiced not rubbing it in when they won.  Sort of.  And we practiced not shouting out but raising our thumb to indicate, “I want a turn.” We also talked about tally marks. I kept score with tally marks, which I discussed on the 3rd day, and a student used tally marks to keep track of how many questions had been asked.

Find it on the 100 chart: I gave them hundred charts, in groups of two.  I gave them containers full of counters.  I called out clues, from “Find it on the 100 chart”  by Marcie Cook which I have owned for approximately 100 years.  I called out clues, they had to cover the number I clued and in the end the manipulatives would have built a picture.  They had to cooperate with their partner and share turns.  They had to clean everything up, even off the floor, when we finished, and put it all away.

Counting Necklaces:  You’d think they’d be getting tired of this by now.  But they are not.  Not even close.  I’ve written about it before here, so I’m just going to say that we ended our math class with this all week and by the end of the week nobody was getting too upset about not getting a necklace because they realized there would be more turns on another day. Once again we had many opportunities to talk about what patterns we were seeing, and what happens to the pattern if someone leaves the circle to use the washroom or if someone moves to another spot.

Usually by this time on a Saturday morning I have a goal for the following week. In fact, I always start writing my lesson plans by writing my math plans for the week.  I’m not ready today.  We accomplished some good goals for the week, but we needed more repetition to get there.  That means I am not where I wanted to be on my curriculum map.  I’m generally okay with that, but I also think there might be a way to still get there by next Friday as planned.  I’m following the TIPS spiralled math document and even though I know I need to be flexible with the timing, I also want to try to trust the timing.  We’ll come back to all of our content again. I don’t need to teach to mastery the first time for every skill.  I think I’ll move forward with our 100/200 chart puzzles.  I think we’ll move forward with the estimation and counting jars/bags.  I think it’s a 4 day week with no other interruptions so we should be able to do that.  Maybe I am more ready to write my plan than I thought.

 

Data Management, math, Number Talks

Sorting and organizing

I am using the spiralling document found on EduGains to work through my math program this year. The first week is meant to be devoted to sorting and organizing skills from the Data Management strand of our math curriculum. I decided to get started on Monday even though we were, ironically, waiting for information about re-organizing classes because of our enrolment numbers.  Because I will be coming back to sorting and organizing many times, I didn’t worry about doing this without a few students who will be joining our class on Monday.

I started with some “Guess My Rule” slides I made on PowerPoint. I had enough to do 3-4 each day this week.  As we discussed them, everyone tried to “guess my rule” and we discovered that there could be 5 or 6 different guesses and all could be correct.  What mattered here was the ability to justify one’s “guess” about my rule. This is a really important skill that everyone needs early on!

Next, out came our math tools.  Everyone worked on sorting the tool of their choice.  I haven’t started with a “guess my rule” game before and I was pleasantly surprised to find that my students did not focus on sorting by colour.  This is often a problem.  I have to spend a lot of time getting them to think about other attributes.  I feel like the “guess my rule” activity set them up for success because they were already trying to be very clever and “trick” their friends.  Nobody is tricked by colour, so we (most of us) tried to think more deeply about our tools.  Those who needed prompting quickly moved on past colours. The work we did last week on how to use the math tools properly also paid off!

Some of the tools I chose for them to use included the necklaces, coloured glass marbles from the dollar store, attribute blocks, and base ten blocks.

The necklaces were sorted by colour, but also by bead type.

Attribute blocks were sorted by colour, shape and thickness.

These glass beads are the best money I’ve ever spent at the dollar store.  They are very versatile: bingo chips, counters, sorting tool, and some kids just love playing with them for no reason at all!  They can only be sorted by colour…or so I thought!  Turns out they are not all exactly the same size.  The  new ones I bought this summer, 10 years newer than most of the others, are slightly larger and a slightly different shade of blue and green.  I’ve lost a whole bag worth of red over time.  They are very popular!

We did this sorting activity for 2 days because we had some other interruptions that shortened our math class.  On the third day, I asked them to use any material in the room to create their own “Guess My Rule” page.  Here are a few.  Can you guess the rule?  Once again, there were many possibilities guessed, so I know students were looking at many attributes of the materials they chose.

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Bright colours vs. dark colours

 

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None of us got this one! “I will not buy containers without matching lids!”
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Some guesses: flexible and not flexible, longer than a metre & shorter than a metre, colourful & wooden, inches and centimetres & only centimetres.

This activity was a lot of fun.  We had a field trip on Thursday, so we were doing math in the real world instead of in the classroom.  On Friday, the students had all been re-sorted into the class they will have for the rest of the year.  I elected not to do the math I had planned because I want to do it with my “new” class (about 1/3 are new to me since the first day.) So here I am, going into the 4th week of school and already “behind” where I thought I’d be.  Typical!  But I am not worried because I will come back to those activities later when sorting comes up again.

Next week:  Counting! This is where I would typically start.  I’m glad I started somewhere else because I have seen everyone as mathematicians aside from their ability to count. I need to start my math interviews as well, so some of the centres I had created for organizing will work as activities  to keep people productively engaged while I am doing individual assessments.

math, Number Strings

Minus/Subtraction/Take-Away

Minus…subtraction…take-away.  Do these all mean the same thing?  They are certainly all represented by the same symbol.

Last week the math coordinator was in  my class for a few days.  (Here name is Melissa and she blogs here!)  After watching me do a number string related to subtraction, she encouraged me to always say “subtract” when I am reading the problem to the class, rather than “take-away.”  Some kids will actually do some adding to solve these types of problems, and by always saying “take-away” I would be restricting their thinking and maybe even imply that they need to use a certain strategy, namely that they need to remove.

I know that there are different ways to solve a subtraction problem:  add on, count back, think of it as a part of a fact family and figure out the addition problem.  But I hadn’t really been intentional about my language when discussing subtraction with the class.  I was more focused on the answer!  (I’m hanging my head in shame!) (not really…but you know what I mean!)

On Thursday and Friday we had bus cancellations, so I didn’t really get a chance to try this out until today.  We were working a Number String from Cathy Fosnot’s mini-lesson book.  We talked about 14+1, then 14-1 (Did you read that 14 subtract 1? or 14 minus 1?)   Then I gave them 14-13.  You can’t see them in this picture, but I had the maths.ca relational rods going in the background, and had build 14+1, and 14-1, and those were still visible to the students. I saw lots of kids with their fingers out counting back.  It’s an okay way to get  correct answer, but very inefficient.  However, I then asked my favourite student (my daughter!!)  to tell me how she solved it.  I’d seen her working away on those fingers, and I know that if she spent a tiny bit of time thinking before she started that, the answer would have been obvious to her.  Knowing this, I had to ask her about her strategy.  “Well, I thought about having 14 cookies, and then I ate 13 of them, so yeah…one is left.”  This is not totally unreasonable for her (don’t judge my parenting!) especially if they are Viva Puffs!   I annotated her thinking like this:

I pointed out to everyone that CC was thinking of subtraction as “taking away” something.  And then asked others what they thought about when they saw a subtraction sign.  Someone else said, “Well, I knew you would only need one more to get from 13 to 14, so I knew it would be 1.”  I talked about how that child was thinking about the difference between 14 and 13, which was different from CC’s but they both still got the same answer.  Then we did 2 more problems from the string, and talked about the “take-away” strategy and the “find the difference” strategy.

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Someone even mentioned that they thought about 9+2=11, which is a great connection to some work we did a week or so ago, so that was awesome too.

It’s funny how being intentional about how I was reading that symbol to the class changed the strategies they used.  This wasn’t truly the goal of the Number String, but “m delighted by the results.  I am hoping the forecasted 25-35 cm of snow (and 80 Km/h winds!) hold off until late on Tuesday so we can work on this again tomorrow.  I feel like we are developing a really big understanding about subtraction!

math, Number Talks

Collaboration

We’ve taken a little break from partner work in our class.  Increasingly our struggles with problem solving were getting all tangled up.  Instead of feeling frustrated because working with partners is hard, I felt too many of the students were starting to blame math for the problem and I didn’t want that feeling to perpetuate.  We took some time to do some worksheets *GASP* alone – mostly because I needed a bit more data to feel confident about assigning letter grades on report cards.  Geometry has been the focus of these.  We also took some time to loop back to patterning because this seems to be an area where lots of people hadn’t made a connection between patterning and using an open number line to add numbers.  I think we are there now!

Before we dive into our next unit (Trades, Jumps and Stops from the Context for Learning kits by Cathy Fosnot), I’m going to take some time next week to do some work on the collaboration part.  I have been assigning partners all year.  We’ve talked a lot about why I am choosing those particular partners for everyone.  Now it is time for them to make some choices of their own and I will also be asking them to justify those choices and articulate what makes a good partners.

Once partnerships are established, partnerships last for a month.  They stick together for every part of our day when they might need a partner – writing, reading, science, math and anything else. We will be working on building our collaboration skills all day long.  Specifically in math, I am going to ask everyone to do a “turn and talk” with their partner during each Number Talk.  Usually we do what I think most people do:  I put up a problem, kids work them out alone, then we discuss them together.  I think the turn and talk time will help them practice actually talking to their partner about how to solve the problems.  They will be empty handed, so they can focus on talking about the math instead of arguing about who will be using the marker to write it down.

The second thing I am going to do is create some problems for everyone to solve.  Today we are going to do an activity from The Super Source where partners work together on some describing and listening skills.  One builds a design using no more than pattern blocks. The second partner is not allowed to see this.  The first partner describes the design that was built so the second partner can recreate it.  It’s a tricky exercise for 7 year olds, believe it or not.  Positional language,  attributes of geometric shapes, and expanding on one’s own words are all practiced.  I find that the person describing often reverts to giving directions such as “get a triangle and put it on top of the square…no that way…no that way…no down…YES!”    The other problems are going to involve some addition, maybe some subtraction and will be put in a context they can work with.

The final thing I really need to work on is how to respectfully disagree, and how to accept that “No, I don’t think so” isn’t the same as “I hate your guts and will never speak to you again!”  It’s a hard one, but necessary.

I had initially planned for next week to be the start of my next unit.  But I’m feeling better about this plan of action.  It’s going to help us have a smoother run through the unit, and it is going too help me set up the Math Workshop groups we’ll need during the unit.