Counting Strategies: Arrays

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SWBAT use a variety of strategies to count objects in an array.

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

10 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 can 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 an array (arranged in rows and/or columns). 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.

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 circles 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.


10 minutes

I have the kids go to their tables and practice counting objects in arrays and recording the numbers in the box with each set of objects. My daily helper passes the page (two-sided) out to the kids.

I roam the room to monitor behavior, participation and accuracy in counting. I pull kids into a small group if I see them struggling with keeping track of objects while they count.

If the kids are pulled into the small group, I guide them in crossing off the objects as they count them. After a couple of rounds, I have them show me how they keep track of the objects.


5 minutes

I have the kids gather together on the floor to talk about what we learned to day. I keep the focus on the counting. The kids like to veer off topic and talk about the objects they counted because some of the pictures are cute.

I ask two open-ended questions so the kids have to explain their thinking, not just give single word answers. This makes the kids verbalize their thinking, which solidifies their understanding and their learning.

1) What did you learn today?

2) Why is what you learned important and how can you use this learning in your life (making it personal)?

Exit Ticket

5 minutes

The Exit Ticket replicates the activity. It just has stars instead of a variety of objects. This makes the work product authentic and fair.

I have my helper of the day pass out the exit ticket and the kids get right to counting and recording. Use privacy offices if necessary. I didn't for this one for the sake of time. We had to get to our special area quickly. They only had five minutes to complete the exit ticket.

As I collect the completed forms, I place them in two piles - okay and needs help. If a student has miscounted more than once, I place their paper in the needs help pile and I meet with them in a small group later in the day or the next morning. It's important to provide safety nets as soon as possible.

When I meet with the kids in the small group, I have them demonstrate their counting strategy for me. I check to see if it is actually miscounting or if it's a case of writing the incorrect number because they are confused with number ID.