*great*question! It was an awesome formative assessment. As I listened to the conversations, I heard that some students immediately said 40, while other responses were all over the board (20, 100, 50, etc.). I reminded students that they needed to explain their answers, even when talking with a partner (

*“I think it’s 40 because…”*). My Tier III kiddos were not even in the ballpark, so I scaffolded…

[Putting out one ten-frame] *If I have one ten-frame, what’s the biggest number I could show?* (10)

[Adding a second ten-frame] *Okay, if I have two ten-frames, what’s the biggest number I could show? *(20)

At this point, I thought they would make the connection, so I asked them to look at their ten-frames, talk with their partner, and decide the biggest number they could show with four ten-frames. They *still *did not come up with 40. This was fascinating to me! Once again I repeated my questions about one and two ten-frames. I added a third empty ten-frame and asked what the largest number I could show would be (30). I then asked them the original question again (*“What is the largest number you could show with your four ten-frames?”*). They finally decided 40, but this just shows how much support our Tier III kiddos need!

Back to the planned lesson…I wrote the number 26 on my whiteboard and chose a student to read the number. I have learned not to assume students can read 2-digit numbers when they see them in isolation. Then I asked the students to work with their partner to build the number. While all the students successfully built the number, it was fascinating to see that most students were counting by ones as they put their counters on the ten-frames. After they had built the number, I asked them if they had to count by ones and reminded them that if the ten-frame was full, it was ten. We continued practicing this throughout the lesson (*“If it’s 26, how many filled ten-frames will you have? Which digit shows you how many filled ten-frames you will have?”*).

On my whiteboard, where I had written 26, I wrote the equation 26 = 20 + 6. I asked the students to talk to their partners about what this equation meant. They were able to tell me that the 20 was the two filled ten-frames and the 6 was the counters on the ten-frame that wasn’t full. It is not obvious to children that a filled ten-frame can be called a *ten*, and that when we have two filled ten-frames it is *two tens* but represents 20 counters. HUGE concept and hurdle in understanding.

Joanne Mitchell says

Thanks for sharing in great detail. I used your thoughts from a pervious post and spent loads of time on the topic. I kept telling my first graders how it important it is to know that 36 is 30+6. I think they are getting it….!

Donna Boucher says

It’s a toughie, right Joanne? I’ve got another blog post coming in the next day or two about our further adventures. Ha ha.

Em Hutchison says

Love love love!!! Already sent this to my partner for us to use in January! Thank you for the great conversation!

Donna Boucher says

My pleasure, Em! Happy holidays!

TheElementary MathManiac says

Love the details in this lesson! It sounds like you will be hard at work with place value ideas with these kiddos!

Tara

The Math Maniac

Donna Boucher says

Yep, we’ve still got a ways to go, Tara! 🙂

Martha Shelton says

The label, ‘ten’, above the 20 in 26=20+6 indicates there are 20 tens, when there are only 2 tens. An astute second grader caught that when I wrote a similarly labeled equation last week!

I love your place value questions, what a great peek into student thinking, thanks for the idea!

Donna Boucher says

Great observation, Martha! Actually, we talked about that being the value of the tens and the value of the ones. The kids have a really hard time recognizing that there are 2 tens, but there are 20 dots (on the two ten-frames). Very huge hurdle!

Beth says

Hello,

I have been a follower of your blog for a long time and have used many of your ideas in my classroom along the way! Thanks so much for all you do. I am looking for a comprehensive list of all the must know math facts (doubles, doubles +1, etc) and was wondering if you had any thing like that or knew where I might find one?

Thanks

Beth

thinkingofteaching@gmail.com

Thinking of Teaching

Donna Boucher says

Beth, my favorite resource for strategy-based fact instruction is the book

Mastering the Basic Math Facts in Addition and Subtraction: Strategies, Activities, and Interventions to Move Students Beyond Memorization