# Circle, Circle, Square Addition Mats

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## Objective

SWBAT use an addition mat and similarly formatted practice sheet to develop an understanding of joining sums together and representing with numerals.

#### Big Idea

Addends are placed in circles and then joined in square-shaped sum areas, and then recorded with numerals.

## Attention Grabber/Introduction

10 minutes

“Hello, friends!” I begin, as students come in from lunch.  “We practiced adding with our pumpkins, and it was fun, but I thought we needed a little more practice. We sent our pumpkins from the pumpkin patch home.  Does anybody have any ideas for what we can use for pumpkins?” I ask, as students sit down in our meeting spot.

“We could draw pumpkins,” one thoughtful student suggests.

Oh, yes, that’s a good idea…” I ponder, as I lift a bag of pumpkin crème candy (like candy corn).  ‘What about… PUMPKIN CANDY!?!?” I suggest while students cheer. [I used pumpkin candy because we introduced addition to 5 in October, but any sort of seasonal candy or inexpensive items could work, like Christmas candy or wagon wheel “snowflake” pasta—anything small, fun, and easy to count could work.]

“Now, I have to be able to trust you,” I begin.  “We’re not just having an after lunch snack—we are doing math here!  Can I count on you to do your math and practice self-control?  We cannot eat our yummy counters…”

One student who could easily have a career as a lawyer or some sort of professional negotiator ahead of him raises his hand.  “Could we do math with the pumpkin candies and then eat them for a snack?” he suggests with an ingenious compromise.

“Hmm… I think something could be arranged,” I say, but I quickly reiterate, “You have to promise to use them for math first.  Can you do that?”

I look out to a sea of nodding heads and murmurs of “Yes.”

“Great!” I exclaim.  “We are ready to get started!”

I show my addition math mat on the document camera.  I point out that there are circles on the left hand side by the plus sign, and then a square on the other side of the equal sign.  (I actually ask buddies who need practice recognizing circles and squares to point out the shapes, but having kiddos say shape names is completely optional!)

“Hmm… The circles are the groups that I will put together, the addends,” I say, not so much stressing the term “addends” but throwing it out because it’s proper math terminology and 1 or 2 kiddos will actually pick it up just by my casual suggestions.  “So the circles hold the groups that will be joined together to get that “all together” total in the square.  Let’s practice,” I continue.

I ask the student of the day to select “1 or 2” pumpkins for our first group.

She quickly responds, “2.”

We all count out “1-2” pumpkins as I place them in the left circle, projected with the document camera on “the big screen.”

I ask a slightly squirrely boy, “1 or 2?” for the second circle, and he quickly replies, “I!”

I am not proud to admit this but, a day or two ago, if I were to say, “2 + 1 equals…” a good number of exuberant, happy little beginning adders would holler, “1!” Ugh.  We need this high interest visual.  We need it bad.

With pumpkin candies in the circles and my hands pointing away, I say, “So, friends, let’s see how 2 + 1 really does join together to make a different total.  2 pumpkins,” I say, gesturing sort of like a model on an old game show, “Plus 1 pumpkin,” I continue, moving to the middle circle, “Equals…” I say with suspense as I slide the pumpkins into the square on the right, “1-2-3!  Let’s say it together:  2 + 1 equals 3!”

“I can write numbers to record my addition problem,” I continue.  “On my record sheet here, I can write numbers for the candies that I just moved.  First I started with…”

“2!” students respond.

“Yes, that’s right, and to that, I added…”

“1!” other students state.

I have written a “2” in the small circle on the left and a 1 in the middle circle.  “We just counted pumpkins to get the sum or the total of them all together.  Let’s remember, ‘2 + 1 equals… ‘3!’” we say together.

“Are you ready to practice our pumpkin candy addition with our math mats and recording sheets?”

“Yes!!!” students declare.

## Guided Practice

25 minutes

I make sure the addition math mats and recording sheets are passed out to every student as the students are dismissed by work group to the tables.

I actually count out 5 pumpkins—quickly—to each kiddo.  It’s not super efficient, but there are turkeys in my class who would eat a pumpkin candy in 2.3 seconds or try to sneak an extra candy.  We even count our 5 pumpkins together after all candies are distributed. “1-2-3-4-5” we say, getting a little 1:1 correspondence in as we confirm that we all have the correct amount of pumpkins.

I continue the procedure of calling on kiddos to choose one of two numbers that could be joined for a sum of 5, but I mix up the process slightly.  When a kiddo says “1” for the first addend, for instance, I move one pumpkin candy into the left circle, and then I immediately write a number 1 on the corresponding smaller circle on the record sheet.  (I really want the kids to see the link between the physical objects and the numerical representation!)

As we get a little practice under our belts, I start asking the kiddos to tell me, “What do we do next?”

We practice this way for our entire practice time.  As I move on out to watch kiddos practice, I see enough students really struggling that I know we are not quite ready to practice fully independently.  Fewer of us are impulsively writing “1 + 1 = 1!” as we did the first time we attempted to add, but the process of joining groups is not yet… solid, for several students, I’m observing.  Independent practice for all but a handful of my turkeys could be a descent into total confusion.

(If your students are more “ready”—or if better yet, you’re getting a later start in the school year to addition—you could easily program in some addends on one side of the recording sheet for independent practice.  I am a huge fan of having students roll or spin to get their addends when practicing addition—it makes it more like a game—but it’s just too many steps too early in the process of learning how to add.  If we keep the focus on the groups that are combined and the numbers representing those groups, we have a better chance of paving a strong addition foundation.)

## Closing

5 minutes

As our practice time winds down, I give students the option to eat their sum once they have been accurately moved and recorded.  For instance, one problem might be “1 + 2 = 3” and then the following problem is “1 + 1 = 2” to get all of the pumpkins potentially eaten.  Some kids will want to save them to eat later, and I give them the option to either zip them into their backpacks or place them in the back of their cubbies—no pockets for snacking during class, though!

As we get to our “wrap up,” I ask the kiddos how they felt about math today.

“Adding is awesome!” one student declares.  I ask what helped today, honestly thinking someone might refer to the circles and square on the mat, but the kindergartners—several—declare, “The pumpkins!”

Yes, my buddies are 5 and 6.  Of course candy helped.  So I keep fishing… “The pumpkins were put on math mats that had…”

I keep on working to get our closing, (even though my buddies are most excited about doing math with pumpkin candies, I know.)  “So we get the groups of pumpkins on the…”

“Circles!” the kids announce.  This is promising…

“We write the numbers that go with the groups we’re adding together in…”

“Circles on the paper!” a student blurts.  Sure, I’ll work with that response!

“When we join the groups together, where do they go?” I ask.

I call on a kiddo who says, “In the square!”  Another student—one of the four kiddos who could’ve practiced independently interjects, “The sum.”

“Yes, the all together total is called the sum!” I reinforce.  I want to develop the concept, and it’s good to have proper math terms in the conversation.

“We are really beginning to get the hang of this very, very important process,”  I state.  “We will practice some more, until we get really good!”

“More candy!” one of my turkeys declares.  We will see, we will see… (But it’s not likely!)