Fun and Games

It’s not really all fun and games, but I have found math games to be a life saver for us this year. All of the math that happens during a game seems to be secondary to the learning that comes from actually participating in a game with a group of ones peers: sharing, turning taking, good sportsmanship and gracious losing.

One of our favourite games as been played with dice and a giant pop-it board. I bought a few of these and we’ve definitely gotten my money’s worth.

The kids take turns rolling dice, adding up the totals and then popping that many pop-its. Nothing like jumping on a trend! They love this. I’m already seeing many more kids subitizing, counting on instead of counting every dot, and doing the addition from memory.

We have also played a card matching game. We removed the face cards and tens. The remaining cards are layed out in an array. Kids turn over two at a time and try to make a match. A match is any two cards that add up to ten. We still need some help with this game. Mostly we need help remembering what makes a match instead of just trying to find two of the same number.

Picture this:

Me: No. 4+4 isn’t a match. A match is two cards that add up to 10 and 4+4=8.

Them: But that’s hard!

Me: But it won’t stay hard if you keep practicing.

Them: *dramatic sigh*

We’ll keep working on this game.

This past week I introduced a new game. This game is all over the Internet and is typically called “Shut the Box”. I have no idea why it earns this name because the boxes are usually laid out in a straight line. It should be called something like “Fill the Line”. For now I’m calling it, “This cool new game I think you’ll like.” I’ve got until Monday to come up with a better name.

For this game they need a game board (one each) and a pair of dice. On their turn they roll the dice twice, then try to figure out which of the numbers on the game board can be covered with a counter of some sort. They can add or subtract the numbers on the dice. I made my own game boards and printed them on 8.5 x 11 paper.

This game was a big hit with everyone, especially the kids who got The Tricky Version.

I didn’t have enough ten-sided dice, so the groups playing this version used virtual dice on Toy Theater. They were especially excited to find that I’d made a mistake! In my haste to completed my planning and creating, I neglected to notice that the 10 sided dice here have the numbers 0-9, not 1-10 as I had assumed. On Monday I am going to have them help me figure out which numbers I need to add or take away on the game board.

I’ve also created a game board we didn’t use yet. It uses the “count by tens” dice on Toy Theater. I’ve decided the 00 side will count as 100.

One of the really interesting things about my class this year is that they have such a wide range of abilities. It’s a 2/3 split, but in math they are more like a k-4 split. Some of the students will stick with the first game board for a while, while others will be creating their own game boards using the fancy dice on Toy Theater. I’m glad for games that can be adapted to meet a wide range of needs. I’m also glad for games that can be played independently. We’ll be using this, the pop-it game and the card game all month while I am doing Guided Math. I’ve always talked myself out of Guided Math, but I can’t this year. There’s no other way to meet the needs of all the people in the room. I’m teaching two different Fosnot units (Double Decker Bus and The T-Shirt Factory) at the same time and I really need to be with everyone while they work. The group that is not with me can play a game or work on Dreambox.

You can get a copy of the game boards I created here.

Math Workshop Thoughts

I’ve been learning from Cathy Fosnot for many years.  I first started using her Context for Learning Math Units about 15 years ago.  I’ve read her books, even the newest conferring book.  I’ve attended in-person workshops with her.  I listened to every episode, sometimes more than once, of her podcasts on VoicEd Radio. (Go here if you want to listen!)

You might think I didn’t need to go to a 2 day workshop to learn some more from her, but HOLY COW I learned so much in the last days.

Both days we focused on using Number Strings to promote the development of numeracy.  I wrote in my notes:  We do STRINGS to promote a development of NUMERACY – a deep understanding of number and operation. We want to eliminate as much working memory stress as possible. We want SO MANY things to become automatic and known so they (students) don’t have to work every piece out.  

After spending a few days working through Number Strings with Cathy and many of my colleagues, I have come up with a few things for me to work on adding to or refining in my teaching practice.

1.  Cathy had all the problems in the string listed on the side of the board.  She added her models and numeric representations on the side.  Some of these were erased as they got messy or as she ran out of room, but the equations in the string stayed up during the whole conversation.  This will help students have the answers from previous questions, and helps them see the patterns in the questions, which will hopefully help them see the patterns in the solutions that can help them learn how to solve equations.
2. Cathy talked a lot about using multiple representations for a single strategy.  This helps children who understand one begin to understand another.  This is also because if they don’t understand the first they have a chance of understanding the second. Overtime they can develop some fluency and flexibility and choose for themselves which strategy or representation makes the most sense. In my notes I wrote: “DIFFERENT REPRESENTATIONS DEVELOP DIFFERENT THINKING! Choose the model carefully. Go back and forth between representations so that they can constantly see the connections.” This is also something Monica Neagoy really stressed in “Unpacking Fractions” (Summer book club, which I just realized I never blogged about!)  Showing things with many different models helps kids understand the math instead of just understanding the model.
3. I have been modelling decomposing using carrots, and Cathy was modelling them using parentheses/brackets.  She admitted this is new thinking for her.  I learned about the carrots from her!  I’m going to use the brackets from now on.  The carrots do make it messier. I also think that going straight to the brackets, using associative property and commutative property from the start, even in primary grades, is going to remove an attitudinal barrier that exists for students who think they are starting to learn algebra for the first time in grade 5 or 6.  I think this makes it so obvious that algebra is taught all along!

Those are 3 pretty good goals, I think.

I am excited and mostly ready to go back to school. Workshops like this, at the end of August, help me get even more excited about starting with a group of children and helping them grow as mathematicians (and readers and writers, and humans.)  I’m also looking forward to more podcasts with Cathy Fosnot on VoicEd starting at the end of September.  I feel like I STILL have a lot to learn from her.

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.

WWCFD: 3

I already blogged earlier today, (here) but I want to talk about another amazing math moment, so here I am again.

A few weeks ago when I went to a Cathy Fosnot learning session, someone new to her Number Strings called her work magic.  Specifically, seeing how one problem helped solve the next problem and the next seemed like magic.  He said something like,  “Now that I see what your doing with your magic, I can figure out this problem.”  She countered by explaining that it isn’t magic, it’s math!

Problems don’t exist in isolation.  The connections we find in math  help us solve problems. We can use familiar and known problems to solve unknown problems.

Because I am just like Cathy Fosnot, I had a similar moment this week.

We (me and the grade 3’s) started with 3+6 = 9.  You can see where we went from there!

See that note on the side?  After 56+43, One of the students said, “That’s (pointing to 3+6=9) spoiling this answer. It has 6+3 in it!”  I got to say, in my best Cathy Fosnot impression, “I’m not spoiling it!  That’s math!  Math is all connected and knowing how to do one problem helps you with so many other problems!”  And then we talked about a bunch of other answers, and made some connections and found out that math is actually kind of magical.

A few years ago, long story short, I figured out that my students were not making connections in math.  They were thinking about each unit, each skill, each day in isolation.  I started to explicitly talk about connections between big ideas, strategies, models, numbers, etc.  I feel like it really pays off and helps to build understanding.