In my book I talk a lot about how math exchanges must be ** both** contextually meaningful and mathematically significant. Many times “contextually meaningful” means relevant or useful to the life of the mathematician solving the problem. However, this year with my kindergarten class I’ve been exploring the role of mathematics in the imaginative play of the five year old mathematicians.

In Virginia the days are getting cooler and we’ve been taking fall walks to look for signs of seasonal changes. We’ve noticed lots of squirrel dreys (nests–I didn’t know this word before I came to kindergarten!) in trees, but we haven’t spotted a squirrel on our walks yet. (Perhaps the squirrels see the parade of curious five-year-olds and head for the hills!?) Yesterday we set up a squirrel feeder with corn and nuts in an attempt to attract squirrels, so these critters have been on our minds.

Today I introduced some little containers covered in fabric alongside some of the acorns we have collected on our walks. “We know squirrels collect acorns for the winter. We could do some pretending with these containers. They could be dreys or holes in the ground. I wonder how many acorns will fit in these different containers? You could try figuring that out today.”

“I’m a busy squirrel!” “These are my nuts. I’ve got to get a lot for winter. Maybe even more than 30!” “Hey, 33 nuts and 31 nuts are almost the same. They look the same, but 33 is two more.”

I try to find ways to invite curiosity, play, and imagination to mathematics. Is counting acorns contextually relevant for my students? I think so. Not in a solve a real problem kind of way (We work on lots of those kinds of problems too!), but certainly in a math is playful and creative way.

And let’s not forget that math exchanges must be mathematically significant! Context is important, but it is nothing if you’re not helping kids grapple with the big ideas of mathematics. Counting (1:1, number word sequence, cardinality, number identification and writing), estimation, and comparing numbers and quantities (Which container will hold the most? Why do you think that? If this container holds 30 nuts, how many will this bigger one hold?) are all ideas that are important for kindergartners to explore deeply. These imaginative math exchanges and contexts will lead into some story problems we’ll be working on in the next few days in which I’ll be taking a closer look at students’ strategies for various types of problems. (Stay tuned!)

So, how are you making your math exchanges both contextually meaningful and mathematically significant?