Rows of Carts
When I was out running errands the other morning, one of my stops was Target. We love TARGET. I had finished shopping and was heading out of the store, and came around the corner to the exit doors, and encountered … CARTS, lots of red CARTS. I stopped short, as the guy who was in charge of wrangling the carts was moving a long line of carts into rows in their designated space between the automatic doors of the entrance and the exit.
Did I say…lots of carts?
Since I was stopped next to the guy, I said, “Lots of carts.” (Not the most original conversation opener–but it seemed to work–he acknowledged my statement.) He was super polite, and just smiled. I then asked, “How many carts are there?” He shrugged, “Maybe 50?”
I started counting the row closest to us–and got 14. He said, “Well, maybe there’s 60.” (So wanted to ask him a string of questions like: why that was his second guess, what information did he consider when he revised his guess, how many carts does he usually put in a row–you know, the usual questions you ask in a conversation about carts in Target.)
But, what I did was that usual thing that happens with estimation, once an idea is put out there, most of us model our guess after the estimate that is offered first. I moved my guess into alignment with his and figured about 75–about 5 rows of 15ish. This is exactly why in a class you use the estimation 180 method–a guess that is too high, a guess that is too low, and then your guess. And then, everyone shares out–after there has been enough time for everyone to consider all that needs to be considered.
So, I counted the next row, and got 23 carts, and because I could see that each of the next two rows were the same length, and there is a nice constant with the cart length, I knew there were 46 carts combined for rows #2 and #3: 2 x 23. Now we were up to 46 + 14. That left the last 2 rows. My co-cart conspirator counted the 4th row and found that there were 20–and then he stepped away, added more carts to the last row to make it the same length as the row he just counted (row #4)–doubles strategy. Voila! We had our final count: 14 (from row #1) + 46 (rows #2 and #3) + 2 rows of 20.
We smiled and nodded–I snapped a couple of quick photos–and we went on our separate ways.
1. Drat. Didn’t want there to be 100 carts if I was going to use this for an estimation task. Too many kids guess 100, not because of number sense–but because they like the number 100. It feels big to them–and that could be anything from a set of 50ish on up. However, not sure that it is just kids who like the number 100…
2. Cool guy at Target–super fabulous of him to play along and help me out.
3. Doubles strategy. We used it a few times: once to count rows #2 and #3, and again, to even out the last two rows so as to make that nice round set of 100.
4. And now we have a fun context for a great number exploration or a number talk and an estimation 180 all rolled into 1 to use to answer the question: How many carts are there?
46 + 14 + 2 rows of 20
Can’t you imagine the big white boards or big pieces of sticky back chart paper and markers out on the tables for kids to use and off they go to find a bunch of different way to figure out how many carts were at Target the other morning?
What strategies might we see the kids using?
My predictions: doubles, make ten, break apart by place value, adding up in chunks, open number lines, adding on…so many options and this makes for great conversations and discourse.
5. A warm up for a percent lesson I saw in a class I was working in last week–need to still get permission to use the teacher’s idea. The work was focused on percents, and since we have 100 carts, we should be able to do construct a problem sequence that offers great opportunities for interesting conversations, conjectures, and discussion.
6. Finally,…a place to fit in the post about arrays that I have been thinking about so that it wouldn’t be so random.