## #WODB

I wrote back in August about a great book I wanted to use during the first two weeks of school.  It’s called “Which One Doesn’t Belong” and is written by Christopher Danielson.  (You can read about that here.)

Today was an inclement weather day, meaning the busses were all cancelled.  It was our second in a row, and we have actually had a lot this winter now that I am thinking about it.  I needed to spend about an hour doing an activity with a bunch of kids (grades 1, 2 and 3), over half of whom are not in my class on a regular day. Actually, probably 3/4 of them aren’t in my regular class. I decided to pull this book back off the shelf.

I explained the concept and read the first few pages.  I made sure that every child knew that on every page there would be 4 things, and they could think of at least one reason why three of those things would go to together, but one wouldn’t belong. I explained that there is not one right answer for each page, but what matters is justifying your own thinking so others can at least see what you mean, if not actually change their own mind.  It’s great math!  And it is also so interesting to see how children think.  I have been through this book a few times now, and I am always amazed at how they come up with answers and justifications that I haven’t noticed.

After, I challenged them to create their own using LEGO, two colour counters, attribute blocks, colour tiles, and poker chips (I got them cheap – over 1000 in lots of different sizes and colours at Value Village.  Best investment ever!)  Here are a few:

I took photos and we projected them on the whiteboard so we could share our thinking.  They LOVED it.   This one with the dominos really intrigued me.  I immediately saw kids doing some counting, but nobody used the counting in their answers.  I decided to take that one a bit further.  I wrote the totals on the board beneath each domino.

Several thought the 13 does not belong because they are all in descending order, but it is out of place.  Some thought the 12’s do not belong because they each have a twin and none of the others do.  Finally, several thought 9 does not belong because it is a single digit number (they actually said because it is less than 10 and the others are over, so I pointed out the single/double digit difference.)

It was a fun activity, and I think all of the students learned something!

## They heard me. They really did!

Last week, I was ending the week feeling like I may have spent a few days talking to the walls. (You can read about it here.)   This weekend, I feel much better.

We spent the week working on building an understanding of number lines. After making a measuring strips, in groups of 5’s and 10’s, and measuring some things, we needed to start thinking about how a person could skip around on that number line and use it for adding.  When I taped a 100 strip to the board and started asking kids to tell me the number of a certain cube on that number line, it was like a miracle had occurred.  Because nobody could reach the number line to touch each square, and because we’d talked a lot in our math congresses about how we could use the 5 and 10 structure of the paper number line to skip count, they started actually using the number line tool and the skip counting strategy to find the answers I was seeking.  THEY ACTUALLY DID!

Oh, and no big deal, but they were finally counting on from a known number instead of starting back at zero every time.  Seriously.  I’m not even exaggerating to make myself look/feel better.

Here’s the lesson for me:

1. Trust Cathy Fosnot.
2. Sometimes moving forward helps some kids who appeared to not be ready to move on.  I thought I would do a quick number string, sort out who needed some more help with skip counting and counting on, and then make up some Math Workshop groups.  But, low and behold, some of the kids who haven’t been counting on started counting on!  And many who had been fully committed to counting by ones were using the 5s and 10s.

So there you have it:  Valentine’s Day, Winter Electives, and a field trip, all in the same week, and we still moved around on the Landscape of Learning!

## Use the 5’s and 10’s, PLEASE! I’m Begging You!

This week I started a new Context for Learning unit with my grade 2/3 class.  Prior to this unit, we have completed the “Collecting and Organizing” unit, which encourages the use of the 5 and 10 structure to organize and then count large groups of items.  We counted books in our classroom because that was a meaningful thing for my class.  The parent council had recently offered up money to buy more books, so I tied that all together. After that, we completed the “Double Decker Bus” unit, again using 5’s and 10’s and thinking about adding and subtracting.  Simultaneously, my grade 3’s – who were already doing well with the models and strategies taught in the bus unit – were working on “The T-Shirt Factory” unit.

Measuring for the Art show comes next on the recommended order list.  I should be starting “Grocery Stores, Stamps, and Measuring Strips” with the grade 3’s.  However, I really want to solidify this number line business, so I am not going to go forward with that unit for another week…maybe two. I am going to extend the numbers well past 100 in this unit so the grade 3’s are still challenged. Picking the numbers is my job this weekend.

So…here we are, measuring for a fictitious art show, and also thinking that we will run this year’s school art show.

I gave groups of children baskets of cubes in 2 colours and set them the task of using the blocks to measure the papers.

As you can see, there was some great measuring going on!  We even agreed on the measurements!

Despite all the work we have done with counting things in groups of 5’s and 10’s, some of my little friends really can’t stop counting by ones.  I asked myself, “WWCFD?” (What Would Cathy Fosnot Do?) I finally had a serious talk with them about it.  “WHY?????”  I screamed. But out-loud I said, “I know you guys can count by 5’s and 10’s, but you keep counting by 1’s even when we have a lot of things to count.  What’s up with that?”  They gave me the blank stare.  “Here’s what I think,”  I continued.  “I think you know how to count by 2’s, 5’s and 10’s, but you’re not sure you are getting the right answer so you always count by 1’s because you are sure that will give you the right answer. Am I right?”  There was a lot of vigorous nodding.  “What I want you to do is keep counting by 1’s.  But do it after you count by 5’s or 10’s. Do it to double check your work.  But challenge yourself to grow your brain and do it the harder way.  I know this is going to help you feel more confident!” So now we are doing that, except a lot of them quickly realized they were getting the right answers the first time, and it was a lot more efficient to skip count.

After 2 days of this, including a congress when we had the above conversation, I asked them to help me make a number line, organizing the cubes into groups of 5.  Believe it or not, there was magic!  As soon as I had a long string of cubes up on the board, out of everyone’s reach, 15 out of 18 immediately saw the value of using the 5s and 10s.  We worked on related Number Strings for 2 days, and then I asked them to make a number line like I had been making using their own cubes and a piece of adding machine tape.

The group pictured on the left kept counting  by 5s, but when they got to the mis-matched groups of 5, they realized that maybe I am a genius after-all and they should have listened when I said, “Make all 5 the same colour!”

So everyone make beautiful number lines, with mostly iterated units.  We put the cubes away and I didn’t get them back out. When I asked them, the following day, to figure out where numbers like 13, 23, and 33, should go, they did a great job of reasoning their way through the problem.  I can look at these and see some immediate needs I need to address on Monday or Tuesday.  But I feel like we are on our way!

In a VoicEd.ca radio broadcast (You can listen here!) , Cathy Fosnot said she hoped that teachers who were listening would stay curious and keep wondering about the things their students are doing.   For me this is some of her most valuable advice.  Being curious about why my students are doing something, especially if it is something that makes no sense to me, has paid off so many times.

So…there you go, Cathy Fosnot.  You were right again.

## Slice of (Cooking) Life

I couldn’t help myself.  I mean, it IS cooking, and people can’t cook without doing math.  So even though I had signed up to lead a cooking elective group, and even though the 14 children who signed up to be in the group were expecting cooking, we were actually mathematizing as much as we were cooking.

There was all the standard math you are expecting, like measuring and running the timer.  But at one point in the lesson, after the first batch of cookies had come out of the oven, it came time to see if we were going to have enough.  Plans were being made to take some home, of course.  “Wait,”  I said. “If you want 2 cookies each to make your ice cream sandwich, we have to make sure we have enough for that before you start making plans to take some home.  So..do we have enough for that?”  And I walked away.  Everyone, grade 1-6, started counting each other and counting cookies. A few kids jumped up and ran over to the oven to see how many cookies were in the oven.  A few others were checking the bowls to see if we had enough dough for  more cookies.

“Well,” I asked again, “do we have enough cookies so that everyone can make an ice cream sandwich?”  They agreed we did, and several spoke over the top of each other because they were so excited to justify their answers.  These aren’t my regular students, so I have no idea what sort of work they usually do.  However, their explanations were great!  And I loved that some were counting by 1s and some by 2s and some counted all of the m by 1s or 2s but then said, “We have 14 here, and 13 in the oven, so we need 1 more cookie from the next batch before we have enough for each of us to make a sandwich.”

Next week we’re making pizza.  I don’t really intend to turn this into a math club, but we’re probably going to have lots of chances to talk about fractions. Hearing all of the awesome mathematizing was almost as great as my oatmeal cookie + homemade ice cream sandwich!  Almost.