Lola, age 4, and her mom are volunteers in a research project investigating everyday family interactions. The setting is a preschool that Lola attends.
Lola and Mom, who is mostly out of the camera’s view, are seated when the researcher arrives to explain the activity. The researcher says, “This is for your mom to teach you how to organize a party and set the table,” and then goes on to show Lola some of the materials that she can use.
Lola is very excited—she can hardly sit still—as she sees the tablecloth, napkins of different colors, party hats, cake, treats, teacups, small and big plates, forks, and two large stuffed animals that will attend the picnic as guests. Lola is especially animated (and Mom is, too) at the mention of the cake. Just to be sure, Lola asks the researcher to confirm that there really is cake in the picnic basket (there is!). As she leaves, the researcher explains that Mom and Lola can organize and set up the pretend party any way they want: “There is no right or wrong way to do it.”
Here’s something about the party that may surprise you: Lola and Mom use a lot of everyday math as they set the table. What is everyday math and why do you need it to set a table? Read on.
After the researcher leaves, Mom starts out by asking, “What do think you have to do first?”
Mom’s question suggests that setting the table should be done in a sensible sequence—a useful order. Something has to come first, then second, third, and so on. Parents use these mathematical terms all the time to help organize everyday behavior like getting ready for school. For example, “First put on your coat and then put on your backpack.” This is everyday math talk.
Lola then states what she thinks should be done first, namely: “First I want to do the cake.” Mom rejects Lola’s plan: “No. We have to set it up first. What would be first?” Mom is firm about not starting with the cake but encourages Lola to come up with her own ideas about the proper sequence.
Lola then selects a bag containing the tablecloth and some napkins. She and Mom spread it out on the floor and Lola suggests that next they should put the food on it. Mom explains that you need something before the food but does not say what is needed. Again, she asks Lola to come up with a suggestion. Asking children for their ideas is part of good teaching.
Next Mom helps Lola put out the right number of napkins for the partygoers.
Mom asks, “How many people are going to eat?” Lola looks quickly at the stuffed animals and says that there are two. She didn’t count them before responding; she saw that there were two. This is very typical of young children. Sometimes 4-year-olds can even see—without counting—that there are three or four things. Seeing how many is convenient because it eliminates the need for counting.
Mom then asks, “And who else? Me and you.” Mom is suggesting that the two of them (Mom and Lola) also need to be included in the guest count. Mom repeats, “So, how many people?” and immediately suggests how to find out, namely by counting.
You can think of this as a simple, everyday addition problem. We started with two and now need to add two more. Lola points to Mom, laughs a little as she points to the camera operator, and then goes on to count the two animals and finally herself. Lola is a careful counter; she points to each person as she says the numbers one through five. Each number gets paired with a person so that each person is counted once and only once. The last number counted gives the total number of people.
Mom then asks how many napkins are needed and Lola says, “four.” Why four if she already said that there were five people? I think that Lola knew that the camera operator didn’t belong in the party. That’s why she laughed as she counted her—it was a counting joke. Lola then immediately subtracted one from five to get the total, four, in the party. Sorry, camera operator!
But that’s not the most interesting thing she did. Remember that Lola counted the people and noted correctly that there were four altogether. She did not count any napkins. Instead, she reasoned that if each person gets one napkin, and if there are four people, then there must be four napkins. This is just like pairing each number word with each person. Here each person is paired with one napkin. This important mathematical idea is called one-to-one correspondence.
Space and Place
As Lola and Mom continue to set the table, they place different colored napkins in each corner of the tablecloth and also put out the same number of cups. Next, they see the teapot.
Mom asks what it is and says that they should put it, “in the middle, for later.” There are two math concepts in her statement: location and sequence. As we’ve already seen, Mom and Lola can think about a sequence of events. Mostly they have referred to “first”, but here Mom introduces a new concept related to sequence—getting thirsty Iater.
At home (and everywhere else, too!), children and parents often have to refer to location: “Put your hat on your head,” or “Put the fork next to the spoon.” In our example, Mom’s focus is on “in the middle.” But finding that location is not so easy in this case. You have to make sure that the teapot is the same distance from each of the four corners of the tablecloth. Mom didn’t measure to get the exact middle. She estimated and seemed to do a pretty good job. Congratulations, Mom.
Notice, too, that the napkins and the teacups are all placed roughly at the four corners. We don’t know whether Lola understands the word “corner,” but she can certainly see the corners and she knows that they differ from “in the middle.”
Knowing the location of things and location words is really important for young children. Before school, they develop an informal math understanding of space and place. Later in school, they will study location as spatial relations, which is part of geometry. Ideally, their school learning about the math concept builds on what they have already learned at home.
Mom and Lola continue to set the table.
Mom asks how many plates are needed, but Lola is more concerned with size. She wants to put out the small plates first and Mom lets her do that. Lola puts the small yellow plate with the yellow teacup, the small green plate with the green teacup, and so on, until each plate is with the same color teacup. Again, this is a one-to-one matching of plates with cups of the same color.
Mom then asks Lola to put out the big plates for the cake. At first, Lola can’t find them, but eventually she does and places the large yellow plate with the small yellow plate and yellow teacup. She continues until all the plates and teacups are on the table in their proper positions.
The story does not end here. Lola then puts out all of the utensils, sorted by color. She puts the green fork, knife, and spoon with the green teacup and the small and large green plates. She continues this with the red, blue, and yellow utensils, teacups, and plates. Lots of sorting and matching!
Where Does the Cake Go?
Finally, we come to what Lola has been waiting for—the cake! She knows exactly where to put it.
The More of This, the More of That
It turns out that there are other pastries to share, too. Lola distributes them and then turns her attention back to the cake.
She distributes the pieces of cake in a clear order: one for Mom, one for herself, “one for the animals,” and the last piece for the animal with no name.
Notice what Lola has constructed. Everything is sorted by color (except for the poor napkins that all came in blue). Moreover, the small cups are placed on the small plates, and the large plates are full up with the cake and pastries. This is like the story of the three bears: large Papa Bear gets the big bowl of porridge and little Baby Bear gets the small bowl. In Lola’s party, the bigger the plate, the more you can put on it. This is another important mathematical idea: the more of this, the more of that. The more cake you eat, the fuller you get (unless the cake is a fantasy).
During the party, Lola engaged in a lot of informal mathematical thinking, all of which took place within 8 and a half minutes. That’s pretty impressive. Cheers to Mom and Lola for their wonderful party!
What You Can Do at Home to Support Early Math Learning
You can do similar activities and have conversations about math as you set the table at home:
- How many napkins do we need? How do you know?
- Where should we put the bowl of beans?
- Do we eat the ice cream first or the hamburger?
- Do you have as much as I do? Is it fair?
- Do we need a big dish for the fish or a little dish?
- Please get me three small dishes and two big glasses.
Also, if you have paper or plastic plates, cups, utensils, some of each can be put aside to be used for your child’s independent play. Your child can create their own parties, and maybe, if you are good, they will invite you.