Counting Strategies: Circles

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SWBAT use a variety of strategies to count objects in a circle.

Big Idea

Kindergarteners often struggle with keeping track of objects while they count. This lesson shows kids different strategies to keep track of objects while they count.

Calendar & Daily Counting Practice

20 minutes

Each day we begin our math block with an interactive online calendar followed by counting songs and videos.

Calendar Time:

We do calendar on Starfall every afternoon.  This website has free reading and math resources for primary teachers. It also has a  “more” option that requires paying a yearly fee. The calendar use is free. A detailed description of Daily Calendar math is included in the resources.

Counting with online sources: Today we did counting practice to reinforce the counting skills. We watched two to three number recognition 0-10 videos (one to two minutes each) because some of my students students were still struggling with identifying numbers correctly in random order. We watched "Shawn the Train" and counted objects with him to refresh our memories on how to count objects to ten and to reinforce one to one counting. Since we have started the second quarter of the school year, we added to today's counting practice: counting to 20 forward and back, counting by tens to 100 and counting to 100 by ones to get a jump on our end of the year goals.

Direct Instruction

15 minutes

Keeping track of objects while counting is a challenge for kindergarteners. This lessons is part of a series that encourages the students to share their ideas of how to keep track of things while counting objects in different presentations.

I use a Powerpoint to teach this lesson on the ActivBoard. If you do not have ActiveBoard, you could use the PowerPoint presentation projected onto white butcher paper or use a doc cam using a printed version of the PowerPoint.

I first read a counting book (Every Buddy Counts from Envisions math kit) but any counting book to ten or twenty would work. We count the objects in the book together while I touch each object.

I tell the kids, "Today we are going to learn how keep track of objects that we are counting in a circle. We are going to share are ideas, or strategies, with all of our friends."

I open the Powerpoint and ask, "How could I count these objects without losing track of what I've counted or without counting an object twice?" The first set of objects are arranged in a circle.

Note: I want to expose the kids to all three  ways (array, circle, scattered) objects are arranged in each lesson so it's okay to use all three in the introduction along with the same Powerpoint. The images may be familiar to them, but the challenge still lies in the accurate counting.

I first choose a medium-high student to share their idea because I know they may be able to lead others to a clear understanding of the question and appropriate strategic thinking. I do not choose a high student first because they usually take the reigns and leave nothing for the other students to think about. I purposely want to leave room for probing questions and deeper thinking.

We count the objects together as the first student suggests and then discuss what we think of the strategy (MP3 & MP5).

I then ask the students if there is a another way I could keep track of what I am counting in an array.

Another student (randomly chosen from raised hands) makes a suggestion and we try that. I again ask the kids what they think of this strategy.  They agree that both strategies work well.

I show the next sets of objects which are done in scatters and ask how I can keep track of those objects as I count.

The kids have seen and counted these images before so I feel any of them should be able to contribute some thoughts to our conversation so I choose random students to answer by pulling names from a name stick can.

We continue this pattern throughout the rest of the Powerpoint. The same presentaton is used in the lessons for counting arrays and scatters.

Once we finish the Powerpoint, I take a box of counting cubes and grab a handful. I ask the kids how we could count how many blocks I have in my hands. A student suggests that I move them and set them on a table as I count them. (MP3 - Construct viable arguments and critique the reasoning of others) I demonstrate her thinking with her guidance.

I pull another handful and this time I arrange them in a circle. I choose a random student to guide us through how to accurately count those cubes.

I pull one last handful and I clearly and deliberately line them up in a need array. A student yells out that she likes that. I ask why and she says because it's clean. I ask her to explain what she means by clean and then I ask her if she would come up and show us how she would count these objects.

I ask the kids to share what they think of the way she counted them (as a class we have gone over that we do NOT like or dislike what each other has presented; we comment only on the mathematical reasoning). They were very positive about how she touched and wiggled each object while counting. She tells them they could slide them too. I was thrilled with the word slide! If I can get them to use that word while counting 3D objects, teaching them that 3Ds slide (except for spheres) would make teaching geometry that much easier!


10 minutes

I have my helper of the day pass out a counting sheet that has 5 to 10 objects arranged in circles in each square (see below). I tell the kids to use one of the strategies that we discussed to earlier to figure out how many objects are in each square.

I roam the room to check on the accuracy of counting. I carry a clipboard with an observational notes page on it to record any concerns I may see. For instance, one of my students was counting one to one "accurately" - one number for each object, but she was skipping numbers 13, 14 and 15 while counting. Later that day, I pull her into a small group with two other students to practice orally counting 0-20. Tomorrow, I will partner her with a strong counting student so she can see how to count objects using accurate sequencing of numbers.


5 minutes

We gather on the floor to discuss the strategies we have discussed for this lesson (they may be the same ones from yesterday, and that's okay!)

I ask the kids when and how they would use each strategy. I randomly choose some kids (name stick jar again) to come up and share their thinking on chart paper.

We discuss each strategy the kids demonstrate (I draw dots in random (circle, array, scatter) for them to count).

I take notes on any concerns I see on my observational notes sheet. Kids looking like they are in a fog or on another planet can be a concern! I revive those, but I also quickly meet with them one on one to make sure they have gained the learning they need.

Exit Ticket

5 minutes

This Exit Ticket is a close match to the activity! That makes is authentic and reliable. The objects have changed, but the mathematical reasoning and the format have remained the same.