SWBAT use linking cubes and a recording sheet to show all the number combinations to make a sum of 8.

Decomposing big numbers is a complicated process. This systematic activity focuses on the the process and makes decomposing large numbers accessible for all.

5 minutes

For some reason, my students are fascinated to hear stories about my sons. I think it may have to do with the fact that we spend all of our time together at school—and a lot of time, in our full-day K, thank goodness! It’s that same phenomenon when they run into me at the supermarket or Wal Mart and they act like they’ve seen a movie star. So funny! I get to meet family members and wave “hi” and “bye” numerous times, and then, the next time (or few times) I see that student at school, I will hear, “I saw you at Wal Mart!” For some reason, they get immense joy from seeing a teacher at a non-teacher place. I think the same is true about hearing that a teacher has a family, or any sort of life beyond the excitement of the classroom!

So I start off the lesson talking about my 3 year-old Jake*. “Hey friends, you know how Jake really likes monster trucks?”* I begin.

One particularly talkative turkey reports, “Yes, and your bigger son plays soccer.”

*“Mmm Hmm,”* I agree, continuing on with the Jake story. * “Jake, you could say, collects monster trucks. He has a bunch of them, and he loves them all. Lately, he’s been having fun making parking lots with his monster trucks, lining them up in rows.” *I continue. They’re fascinated. Oh my goodness, only in kindergarten!

*“Well, over break,”* I say, *“Jake didn’t want to pick up his parking lot. He was so pleased with his line of monster trucks that he left them out in the living room, just like this,”* I say, as I show a picture of Jake’s trucks. A few boys announce that they have some of the same monster trucks, with infinite pride. So silly!

*“I decided to do an experiment,”* I continue, with a devious smile. *“I took a monster truck off the end, and I hid it!”*

“Miss Ovelli! That’s not nice!” a student protests.

I smile and agree. “*I know! I just wanted to see if he’d notice, and guess what! He noticed right away! First thing the next morning, he woke up, went straight to his parking lot, rubbed his eye and asked where his blue monster truck was!”*

The kids giggle.

*“So later on,”* I continue, “*I moved his trucks around in his parking lot, and do you know what?!” *I ask, tapping in to their interest*, “As long as all of his spaces were filled with a monster truck, he didn’t mind where they were in his parking lot!”*

*“Today,” *I say with extra excitement, getting a little quieter, *“We are going to make 8 in different ways, and the same sort of “rule” will apply! We will have to keep the spaces full to make 8 in our row, but as long as we always have 8, like Jake always had all his trucks, we will be A-OK! In fact, we will have a way to show all the ways to make 8, which is really big kid stuff!”*

*“Are you ready to get started?”* I ask, to total excitement.

“Yes!” the students declare.

30 minutes

Before we begin with our group practice, I show an old Decomposing 4 page, with the chubby 2-colored circles. *“Do you remember this?”* I ask, to a bunch of affirmative nods and “Yes”es.

“Well, we’re doing the same type of thing, but 8 is such a really big number, there’s no way I could fit 8 of these big old circles across a page and up and down. We will use these cubes—we can pretend they’re cars in a parking lot if you’d like—to show our 8’s,” I explain, showing a row of Unifix or counting cubes.

My student of the day helps me pass out a recording sheet to every student. I take rows of Unifix cubes and remove the last 2 cubes, reducing each row to 8.

*“Now, girls and boys,” *I begin, “*You will need to have one row of cubes sitting all together on your top row, like this,”* as I project an image of my row of intact cubes up on “the big screen.” *“The other cubes,*” I continue, *“Need to be pulled apart and placed down by your tummies. Those are your fill-in cubes, because like Jake’s parking lot, we have to have 8!”*

Students giggle.

I walk around to see that we are all in a good place to begin. Students look ready, and we begin the process of coloring our squares to show the exact number of cubes that we have. This is where our former graphing practice comes in handy—I remind the kids that just like we made our little reminder marks in the exact squares that we color on a graph, we make those same marks to show exactly where to color on our rows of 8.

This is where I have a heart attack moment, I am embarrassed to admit. We count 8 together, across the top row, or so I think. As we count and get all the way to 8, I realize that we have AN EXTRA RECTANGLE on the recording sheet! (Since I make all of this stuff from scratch, I made the 9 page at the same time I made the 8 page we’re using today. Somehow, I thought I took off a space, but I apparently just shrunk the rows of 9—which remained 9 on our 8 page! Oh no!!! This is a great moment to explain that “nobody’s perfect,” and we all make X’s down the side of our paper. (This horrendous mistake has been corrected before adding the resource to this lesson. I just wanted to explain why we all have a bunch of X’s.)

We practice the process of carefully marking the spaces, then recording the numbers, and removing one cube off the end at a time. When students are inclined to leave a block off the end, I remind them, “Remember the parking lot? We need to keep the spaces full!”

I keep looking for that moment where I can step back and make this an independent practice activity, but to be perfectly honest, it never happens. At each one of our 4 heterogeneous tables, there are at least 2 students who are not “solid” on the process at all. Sure, there are 4, possibly 5 kiddos in the class who can complete this activity with no further input from me, but they seem happy to be staying with the group. So group work continues. Perfect practice makes perfect. Confused practice makes… confusion!

Each time we take off one cube, we fill it in with our “fill in” cubes from the bottom. Everything about this activity focuses on the process, and each time we complete a new row—I make sure we emphasize the fact that 6 and 2 is 8, but 4 and 4 is also 8! We go on and on about the different combinations, and this is where the little guys who really “get” this concept are shining. By the end of the activity, I have those kiddos explaining the combinations, and they are telling me how “Yes, Ms. Novelli, it’s still making 8…” This is fun!

When our parking lot is completely full of “fill in” cars, I start walking—without writing the numbers on “the big screen” to match the number combination. I know that if a student really understands this process, the first blank will have a 0 and the second will have “8.” Hmm. It’s not looking too good. I’m reassured that the entirely guided lesson was necessary.

8 minutes

As we wrap up our lesson, we put all of our cubes together in rows. (For little guys who make their cube rows into drum sticks, the cubes are quietly removed!)

*“Let’s sit back and admire our great work,”* I begin, and I show my work on the big screen while the kiddos look at their pages.

I love to talk about mathematical thinking, to put words to thought processes and to draw student attention to concepts that will help them grow as young mathematicians. So I start talking, directing their attention. “*Hmm… my row was all red to start, and then there’s this line that splits right down the middle—a diagonal line—and before I know it, at the bottom of my page, everything is blue, and there’s no red left at all! Look at your pages. Do you have that too?!” *

Some of the turkeys note that their colors were not red and blue—their colors are different—but the color switch is the same! Wow!

Then, we talk about the first row of numbers, and we count down the line. I’m pointing on the “big screen” as we count. “8,7,6,5,4,3,2,1,0!” A couple kids add “Blast off!” Hehe!

“Now, let’s talk about the other side,” I continue. “From the top, there’s 0,1,2,3,4,5,6,7,8!” Hey! What can you say about this!”

Students say some good stuff, like “The numbers keep changing!” Yes. “They go in order, like counting!” Yep. “When one goes down, the other one goes up!” Awesome.

I ask about their favorite parts of the lesson. They like coloring. One little guy likes the X’s, with no sarcasm or bad feeling at all. *“Glad I could help,” *I say with a smile. Of course, they like Jake and his trucks, and ask if I can bring them to school. Aw, I love my turkeys!

In classic kindergarten fashion, when asking about tricky parts of the lesson, the initial response is the same as usual, “It wasn’t tricky. It’s easy.” So I start pulling it out of them. *“Hmm… what about keeping track of the colors? Didn’t you have to color over a section with another color, at least once in awhile?”* I pry. One of my turkeys blurts, “She did!” pointing to her neighbor.

I remind them, *“I’m not asking you to think about your neighbor’s math, this is sharing what you think about your math!”*

A few kids start to share that knowing where to put numbers on the number side was tricky, and I agree. We talk about paying attention to order and the places where things belong is so important. I take this moment to tell them that this habit of being precise and putting things in just the right place and using our routines just right will be important throughout math and science and in other classes too! I remind them it’s good that we’re already getting such good practice with this. They smile.

Back to pep rally mode for me. *“Did we find lots of way to make 8?!” *I ask/holler.

“Yes!” students respond.

*“Tell me some!”* I yell, while picking students. (For every eager kid that I “call on,” I select someone else who is not raising a hand, just to keep things lively and the engagement high.)

“8 + 0!” “4 + 4!” “2 + 6!” I’m hearing. I add *“Equals 8”* to the number combinations, but it’s great to hear them coming up with number