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.