The kids were intrigued by a contest at the drop-in care at the gym*, one of those ones where you estimate the number of candies in a jar and whoever is closest wins. They carefully wrote out their names and guesses (Anya said 101, Alex said 100 right after- he's almost got the Price Is Right strategy down. So close and yet so far.) and dropped them in the box.
This seemed like the perfect chance to get them interested in the idea of estimating, especially since the most frequent question I get is, "How could you know?" They are both eager for learning new tools to understand the world and predict how it will work.
I took four identical mason jars and put miniature marshmallows in each- five, ten, twenty and one hundred.
Then I made up quick sheets for the kids to fill out- a dotted line on top for their names, then four rows, each with a sketch of a jar and a box.
I asked them to tell me what an estimate is ("A guess!"), then talked to them about the difference between a guess and an educated guess. I tried to emphasize that an estimate involved using your senses and mindfulness/"using your head" since they are always interested in the body and we are struggling with both of them not thinking about what they are doing, from rushing to put on clothes and doing it backward to tenaciously clinging to every conclusion they jump to, no matter how much that conclusion flies in the face of their experience of the world. I asked them to tell me times that people used estimates, and they mentioned counting stars, contests (Thank You, Curious George!) and when prompted about things I do in the house, they mentioned that when I am cooking I estimate ingredients, but that they still have to measure.
I had them each take a jar, and encouraged them to pick it up, turn it around, look at the marshmallows from all different sides, feel if there was any difference in weight (could really do a lot more with this using lighter jars and heavier counting objects). We put the jars in ascending and descending order based on how much each looked to be filled.
Once they had explored them for a bit, I asked them to draw a picture of what the marshmallows looked like in the jar, then write the number of marshmallows that they estimated was in each next to the picture. I wanted to encourage them to really look at the different volume that each number took up, rather than just focus on trying to count.
It was really cool to see them working up from being able to simply count the marshmallows to actually having to work out a way to estimate. As I suspected, both of them had an immediate inclination to count, even when it was impossible. When they got stymied by that I encouraged them to look at the jars, compare them with the jars they had already done, and make their estimates from that. I started to talk about the amount of marshmallows doubling, but while Anya especially has been very interested in proto-multiplication (3 sets of 2 makes 6, take a away 2 and 2 sets of 2 makes 4), the abstract idea of doubling was a little more than they could do right now.
In the end, we went through and talked about each of their estimates while looking at the jars together, then counted each jar to see how close they got. Then I let them eat the marshmallows. Math = Fun, guys! Remember that (not the obscene number of marshmallows)! Now let's go run around the yard for an hour!
* I recently conquered my fear of going to the gym, which has allowed me to restart the Couch to 5K program (because it turns out that running outside in Wisconsin is not for the out of shape and feint of heart). It's a post for another day, but running again has made me feel like a new woman. I did not realize just how much of my energy was being burned up simply by trying to stay afloat rather than get pulled down by the dark undertow of depression. I am extremely thankful to Luke, for keeping my gym membership alive even when I didn't use it for so long, and to my friend Jenny who inspired me to get back to running. I am also thankful that my kids will finally allow themselves to be left at the drop-in care, so that I no longer have to push 90+lbs of kid-and-stroller in order to run. Seriously, this is the best development in my life since finishing nursing school!