# 2nd Grade Counting,Unitizing, & Combining

The other day, I began writing up my lesson plan for a second grade class I was teaching today. I drafted the lesson, got feedback, revised and ended with this plan, around the 5 Practices, going into the classroom today.

I started the lesson, as I planned, with the students on the carpet like they typically are for a Number Talk. I wrote the sentence “There are 12 people in the park.” on the board and asked them to give me a thumbs up if they could give me a math question I could ask and solve from that statement. A couple students shared after a bit of wait time and I was getting a lot of even/odd talk or questions that involved adding more information to my original sentence. I asked them to turn and talk and one little girl next to me said they could find the number of legs. When I called the group back together I asked her to share her conversation with her partner and after that, hands shot up like crazy. It ended with a board that looked like this…

I asked them if we could think about any of these in the same way? I tried to underline the “same thoughts” in the same color, but they started making connections that is got a bit mixed. A lot of there conversation turned to numbers and so I started a new slide and asked what numbers they thought of when they read those problems and why. I recorded what they were thinking…

I really liked this opening talk (15ish minutes) and really didn’t want to let them go when it was time for their recess break in the middle of math class. So, they lined up and left for 30 minutes.

When they got back, we recapped the numbers and then I gave two groups question #1 and the other two groups question #2. They had individual time to get started and then they worked as a group to share their thinking. Knowing that I was going to be trading seats at groups for them to share their problem with another table, I was walking around looking for varying strategies so I didn’t trade seats and have a whole table who solved it all the same way.

They did a beautiful job working in their original group. I saw students who had different answers for the same problem talking out their strategies and arriving at a common answer. I saw students practicing how they were going to explain it to the new table they visited. I saw students who were stuck working through the problem with their tablemates. I can tell there is such a safe culture established by Lauren, the homeroom teacher. They trade seats, shared their problem and then I had to readjust my plans.

At this point, I wanted the tables talking about what was the same and/or different about the two problems but I was running out of time. In order to pick up with that conversation tomorrow, I decided to have them come to the carpet and I chose two papers (of the same problem) that had the same answer but different strategies. I asked the students privately if they would want to share and they were both excited so I put them both under the document camera and had them explain their work. I thought they was similar enough for students to easily see they both drew the figures out but as I walked around I heard the 1st student counting each one by ones and the 2nd student counting by twos after he wrote the equation. I had them explain their work and asked the class to think about what was the same and what was different and we discussed it. Here are the two I chose:

They pointed out all of the similar things such as feet, people, two’s (but were counted differently), and the same answer. The difference was the equation which was an important thing to come up. I saw quite a few students with the correct answer but incorrect equation. A lot arrived at 22 by counting by wrote 7+2 as their equation so that was an important thing that a student pointed out.

I only had 5 minutes left, so I decided to collect their papers and pick up with the sequencing and connections tomorrow. Which I kind of love because it gives me time to be more thoughtful about how they should share them and also time to talk to their teacher about what I saw today.

So, from my previous plan, I am picking up here:

Practice 4: Sequencing

In the share, after each group has presented to the other groups, we will come to the carpet for a share. The sharing will be sequenced in the way I discussed in the Selecting part, asking students during each student work sample how it is similar and different than the ones we previously shared.

Practice 5: Connecting

The connecting I see happening through my questioning as we share strategies. I am still working on writing this part out and looking for the connections that can be made, aside from the picture to number representation connections.

The connections I would love to see students making throughout the work and sharing, is how we can combine equal groups. For example I would like the student who is drawing ones and counting them all to move to seeing those ones grouped as a 2 or a 5 depending on the context. I would love the student who is seeing the five 1’s as one group of 5 to now see that if they have 2 of them it will make a 10 and if we have 4 of them we would have 20 and really start looking at different ways to combine those groups.

The problem I am seeing in this plan is the differences in the two problems. As I sit here with the papers all over the table, I am struggling to make a sequence involving both problems. So, do I sequence a set for each problem and give each 1/2 of the class time to talk about the similarities and differences? or just choose one problem and go with that?

For problem 1, I like this sequence in moving from counting by 1’s to grouping them and then to the finding half of 34.

For question 2, I see this sequence from pictures to grouping them by people and dogs, the third shows the 8 composed but broken apart on the number line and the paper before it, and the last one starting at 14.

I collected their papers and asked them, in their journals, think about how many people and dogs there could be in the park if I just told them there were 28 legs. I thought that after their share tomorrow of this problem it would lead them into a nice problem from which some great patterns could arise. Here were a few I grabbed before I left:

and this last one was getting at some really great stuff as she got stuck at 9 people and couldn’t figure out the number of dogs. I asked her to write what she was telling me!

Looking back, I would have probably chosen just one problem to work with to make it more manageable in sequencing and making connections during the share. Having two problems was nice as far as having them explain it to others, so I like that, but I am wondering if we did #1 through this process and then split for questions for #2 and #3.

I look forward to hearing how it goes tomorrow!

~kristin

## 8 thoughts on “2nd Grade Counting,Unitizing, & Combining”

1. Simon Gregg

Thanks Kristin for documenting this lesson and its genesis so thoroughly for us! I really get a sense of how it went and what the students were understanding. Their written work helps immensely.

I love that last one too, and that she writes down what is puzzling her, noticing that it only works for even numbers of people!

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1. Simon Gregg

Oh, and among so many other great things about this lesson, that it worked just writing the sentence at the start, and getting questions. It’s such a good way this, isn’t it, to help students to be question-askers, rather than passively receiving the question!

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2. Denise

I love how you chose to start the lesson. What a great way to build a reference point where you could have went in so many different directions! It is fun to see the student work too. I look forward to hearing how the rest of the lesson plays out.

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3. Maya Quinn

In case you are building towards the pre-algebra problems in which one is given (for example) the number of heads and legs, and asked to figure out the number of people and dogs, there are some interesting arithmetical ways to approach these problems.

One example often used is of the following structure:
I counted tricycles and bicycles in the shop.
I counted a total of 27 wheels and 22 pedals.
How many tricycles were there?

This is sometimes solved quite a few years later by setting up two equations with two unknowns.

Here is another way:
Consider taking the number of wheels, 27, and subtracting the number of pedals, 22.
Each tricycle has 3 wheels and 2 pedals, so you will have 1 left over for each of them after subtraction.
Each bicycle has 2 wheels and 2 pedals, so you will have 0 left over for each of them after subtraction.
In other words, 27-22 = 5 is the number of tricycles.
(Illustrations may help!)

One way to apply this to (for example) the heads and legs problem with people and dogs:
Consider how many left legs there are.
Each dog has 2 left legs and 1 head.
Each person has 1 left leg and 1 head.
And so the subtraction here, # of left legs – # of heads, will give the number of dogs.

So if you are given the # of legs at the start, then you can divide it by 2 to get the # of left legs. Then you can proceed as described.

Just some thoughts that might be of use (maybe to teachers, maybe to students, maybe to both!).

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