Ok, really, stop judging me. I brought home my Investigations book, ready to dig in to whatever lesson my team said we were going to do. It was about even and odd numbers and making groups of 2s, 5s and 10s. We were working on it last week, too. So I had some idea of what we were going to do. I also knew that Kristin's (@mathminds) 2nd grade teachers were working on the same thing, because yes, I shamelessly stalk her on Twitter. So when I saw a blog post that she was planning some 2nd grade content, I knew I was in for a treat.
The lesson she was planning was about counting collections of objects which I find students just love to do. (I'll admit, I also love to organize and count the coins in my piggy bank!). You can find her prep for the lesson here https://mathmindsblog.wordpress.com/2015/12/06/planning-k-5-literally/ and her reflection after the lesson here https://mathmindsblog.wordpress.com/2015/12/08/2nd-grade-even-and-odd/. In all honesty I haven't read her reflection post yet since I wanted to get my ideas down first.
So, Monday morning I get my collections of items and find pairs for my students based on ability. I don't often do this, but today wanted my students to work with a math peer rather than just someone with whom they feel comfortable. I didn't give too much direction to my students, just that they needed to tell how many of the item they have. I did tell them that they were going to be required to share their ideas on Seesaw so the expectation was that they could take a picture of something.
I set them to work. One of my favorite parts of a super engaging lesson is that immediately students find a private corner of the room and the noise level is at a relative minimum. Students are engaged with what they are doing and therefore not distracted by whatever else typically distracts them. There is something special about Monday morning and just taking a moment to realize that students love math. I even have students writing poems about math! But I digress.
Walking around the room, I saw a variety of different strategies. This partnership decided to organize by color. When they finished, they had a fairly nice looking array, but when I asked how many tiles they had, they didn't know. They eventually decided to do the second picture below. Still organized by color, but at least now in groups of 10. 
Another partnership chose to organize by color also, but immediately knew that they were going to put them into groups of 10. This partnership was of two students who rarely feel confident in math. I wanted them to productively struggle together. Well, from what I could see, they were just productive, without the struggle! This was great for this particular team because they needed some confidence. Here they are organizing and getting ready to group by 10s. Even the fact that they had their sticks organized into arrays, but not yet by 10s, as you can see in this photo, is total progress.
I also of course had students who decided to group by 5s or 10s immediately, and some even organized the groups into arrays.
The group with the pennies knew to put them into groups of 10, but then realized that they had so many groups that it was going to be hard to count all of them and not lose track of which ones were already counted. They ended up using Seesaw to help. Talk about perseverance!
As an extension for many students, I asked them to count their items in a different way. Everyone had a less efficient way and told me so, meaning the first way they did it was most efficient. Gets me thinking-did I actually ask them an extension?
After everyone finished, we made a list of the different ways that students decided to organize and count. The students who organized first by color realized that it was not the most efficient way, and we agreed that groups of 10 was usually the most efficient grouping.
I then gave them a totally different bag of items and asked them to make 2 equal teams. Was it possible? When I asked the question, I got an immediate "huh" from many of them, and reminded them of SMP 1-make sense of the question and persevere in solving it. Off they went and again I had a variety of strategies. My favorite is that my partnership of low confidence math students immediately knew what to do. One student called me over (for help, I incorrectly assumed!) to show me that they were finished. I saw 2 groups of 16 pencils. Based on their explanation from Seesaw, it sounds like they counted by 10s and put 10 into each group, then by 1s, and put 6 in each group. For these two students, this is a total success to be celebrated! (They even took a video of their work to explain it!)
For other students, this work was not as intuitive. I had several groups who still didn't understand what I was asking them to do. Relating it to soccer, they knew their two groups were not the same, and therefore the teams were not equal. Some groups had trouble figuring out how to make them equal once they figured out what the problem was asking.
One group knew they had 71 items (I'm not sure how they figured it out), but then were trying to separate their items into two groups. When I pushed their thinking into even and odd numbers, they were able to realize that it was an odd number, and just like with the number 5, they would not be able to decompose the number into even groups. (Sounds like a great opportunity for A/S/N!).
I had another student who approximated 2 equal groups, then counted each and moved some of his items from one group to the other to make them even. Turns out he had an odd number.
I also had a group (the same one with the colorful array above) who had no idea where to start, according to my TA. I did not have a chance to work with these two, but my amazing TA alerted me to the need to check in further with them.
All this great thinking and problem solving is happening, but of course it's time for recess. I ring the chime to clean up and hear an immediate "awwww" because they want to keep working. That truly is music to my ears at 8:30 Monday morning!
I may not have had my lesson planned days in advance like my coworkers, but I walked quickly back to my classroom to get started after our Monday morning assembly while I saw some slowly moving feet from others. My enthusiasm is certainly contagious to my students.
Content Standards addressed:
CCSS.MATH.CONTENT.2.OA.C.3
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
CCSS.MATH.CONTENT.2.NBT.A.1
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
CCSS.MATH.CONTENT.2.NBT.A.2
Count within 1000; skip-count by 5s, 10s, and 100s.
Count within 1000; skip-count by 5s, 10s, and 100s.
*****I'm seeing ways to extend this lesson to even more content standards!
And just as importantly, the SMPs utilized:
Standard 1: Make Sense of Problems and Persevere in Solving Them
Standard 3: Construct Viable Arguments and Critique the Reasoning of Others
Standard 5: Use Appropriate Tools Strategically
Standard 6: Attend to Precision
Standard 7: Look for and Make Use of Structure
Standard 6: Attend to Precision
Standard 7: Look for and Make Use of Structure
Takeaways:
-I am long winded. Boy can I write! Cheers to anyone still reading!
-So important to engage with other teachers at your grade level.
-Seesaw is amazing to document student work.
-I do a lot of reflecting after lessons, I want students to do that, too. Seesaw or their math journals are a good medium for this. I wish I had more math time!
-I need to be better at looking at all this wonderful data (yeah it's data, even though it's not a paper/pencil test) and deciding next steps.
-Kristin has amazing ideas.
-I need to plan more in advance to anticipate student answers and misconceptions.
-Most students have mastered efficient ways to count. Next time I work on this with students who only looked at color, I would probably give them a set of items with only one color to see what happens.
-Giving students a context for a new task I am giving them is helpful (2 teams like in soccer)
-Not a new idea, but low entry, high ceiling tasks are the best! Naturally differentiate without having to plan different lessons for different students and keep track of it all!
-I just realized the standard only requires students to determine odd or even of up to 20 items. All students were working with bigger numbers. Did I push their thinking or did I go out of my lane?! Maybe it's a standard we are ready to move on from?
Im open to any and all feedback, I'm certainly here trying to grow and learn.
And I'm doing this on my iPad, so the formatting may not be nice and fancy.
