“We are pretending today!” I begin. “See these little green counters?” I ask. “Well, they are going to be frogs today!” I declare. A couple of friends giggle. “Shall we ‘ribbit?,’ I continue. We practice our frog sounds, tapping in to a fun factor, because soon we will be mixing in some “big kid” number line addition.
I show part of our number line “pond” mat—the squares with the + and = signs, as well as the square for the sum. (I keep the number line covered up on purpose.) “We’ve had lots of practice with this!” I say.
“Let’s bring some frogs onto our square lily pads,” I suggest. I try to get the kids involved in the process as much as possible, right from the beginning. I ask the helper of the day, “2 frogs or 3 frogs to start?”
Our helper says “2!” and I move 2 little green counters into the square.
“Okay, now 1 or 2 frogs on the next lily pad?” I pick a student to supply a number for us.
“1,” he says, so I slide out 1 green circle onto the space.
Because we’ve been doing this awhile, I ask, “Okay, so what do I do with our frogs?” to which the kids respond, “Move them over to the altogether place,” and I affirm their suggestion and slide in the word “sum,” which only some of the kids even notice!
We say together, “2 + 1 = 3!” as I slide the counters to the right.
“Okay, we are really getting really good at adding with counters. Definitely. We are so good”, I say, “That I want to show how to a big kid tool that first graders and second and third graders use!” I say with excitement.
“On top of my square lily pads, I have… a NUMBER LINE, [I show number line on “big screen” in a Vanna White-like move] like the number line you used to find numbers yesterday. I bet you were wondering when we would start using our number line to add—I promised we would—and that day is TODAY!!!” (A couple kids cheer because we are 5, and things like “big kid number lines” are super cool. Ah, if only we could be 5 forever!)
“2 frogs in the square lily pad look like this, I say, directing attention to the big screen. You can show 2 on a number line like we did yesterday! Find the 2 and…”
“Circle it!” students respond.
“Yes! It looks like this,” I say, as I show the number line and I count out left to right to find the 2.
“Okay, I am circling my first number!” I say, verbalizing the process that the students will be doing.
“Hmm… that’s all we did yesterday. I need to show adding with the number line—the big kid stuff. So I’m at 2, the circled number. I will put a dot on the number line right above the 2 with the circle. Then, I’m going to jump to the right 1, to show 2 plus 1! See the frog hop?!” I demonstrate, with the kids looking at the big screen.
For my distractible goofballs, I will say excitedly, “See the frog hop, (and insert students’ names) to direct their attention and remind them that I am still watching them, even though I am filled with excitement for number line addition.
“The number where my hopping ends is the sum, the altogether number!” I say. “So let’s see, 2 + 1 equals….”
“3!” students announce. “That’s easy,” a little turkey adds.
“We will see, we will see!” I say with a smile. “Right… now! Let’s practice together!”
I pass out a laminated blue math mat for each student that is identical to my mat on "the big screen." At the same time, I pass out bins of green circle counter “frogs.” (I wait until the exact moment we need to use them before I pass them out.)
The kiddos go over the moon for plain, black dry erase markers and small, black felt pieces to erase the mats. Sure, I try to be fun and lively, adding little details like blue “water” colored background and pretend “frogs,” but the kindergartners get most excited about black dry erase markers! Someone calls the felt pieces “eraser blankies” and we all giggle.
I call a student up to circle our first number. I give a choice again—always a low number, like “2 or 3,” so they feel their ownership in the creation of our activities but I still keep the sums below 6.
As we practice together, students circle and dot their first addend, “hop” their frog counters and them hop their markers on the number line. I circulate through the room, providing specific reinforcement and encouragement. When it’s clear that a student is confused, I try to provide support and a strong model as quickly as possible so we don’t create bad habits. Is it sometimes hard to get to every kiddo? Definitely, but the effort pays off, and I get a little bit of a “How fast can you move around the classroom?” workout!
Now, the number line “ponds” are great, but our eraser blankies are busy at work, and I need to see for certain who is getting this idea and who is struggling. I need proof of learning. Furthermore, I want to know exactly when and where the struggles occur so I can provide the right support just when it is needed.
I switch out the blue “pond” mats for number line practice pages that can be turned in. (I make sure the pages are double-sided copies, so the students can get the most practice possible.) This is helpful for me, as I’m noticing that many students are confused when practicing independently. They all think they have this number line thing mastered, yet we are making mistakes like marking one addend, and then going back to zero to mark the second addend—never really combining the addends! I’m seeing it over and over again, so I swoop in and make our independent practice more of a whole group activity. We need it, I realize!
I am realizing as we practice that the counters aren’t just a “jumping off point,” but they really come in handy when students aren’t correctly adding the addends on the number line. I make sure the kiddos have the counters, and when I see number line errors, I will get the students to self-correct, (with lots of prompting, of course!) For instance, one little guy has 3 marked as his sum for “2 +3,” so I prompt him to count his “frogs.” He counts “5,” obviously, and I ask him about his number line. “Hmm…” I say, and we go through the steps of using the number line to add. “Oh, I know!!!” he exclaims, and he jumps forward from 2 to 5 correctly. I am hopeful (though not totally convinced, to be honest), that this realization will be a lasting reminder of how to add on the number line.
We scale back our practice to become a continuation of the whole group activity. After each step, whether it’s circling the first addend or moving left to right down the number line, I am cruising through the classroom to make sure students are practicing correctly. I am finding that at least one kiddo at each table is really confused, and I’m wishing I could split myself in two so I could help more students!
After a two-minute warning, I pick up supplies so students aren’t tempted to keep practicing during the closing.
“Well… how did adding on a number line go?” I ask, with my secret answer of “not so good!” tucked quietly in my head. Of course, the students say, “Good!”
I try to break down the steps, asking about all the things we have practiced. “How about circling the first number? Did you find that was helpful?” After students say “Yes,” I push even more. “Tell us about how it helps.”
I know that some kids are confused. We need more practice with this brand new concept, but I ask questions in the closing that some of the kids can answer. “How do you keep track of the two numbers that you’re adding together?” I ask.
A kiddo says, “Well, the first number is circled, and the second number is bumps.” “Yes! Bumps on the number line, like frogs hopping in a pond!” I affirm and clarify. “The bumps are the second number joining with the first number to get you to the sum, or the ‘altogether’ number!”
“How do you know you’re at the sum, the answer?” I ask. This gets a little tricky. I prompt, “When you are done hopping down the number line, the number where your bumps end is…”
“The answer!” one student exclaims. (We won’t mention that a few of our friends just “hopped” all the way to the end of the number line. They hopped and didn’t stop!)
“Yes, that is correct,” I say with a smile and a sigh.
I ask about what they liked about the lesson, and I’m not surprised. They like the number lines. They like the little green “frogs.” They like the dry erase markers and the eraser blankies. I think to myself, “I’m glad they like this number line addition, because we will be having lots more practice!”