Sharing comes up a lot at our house.
Whatever it is, one kid always wants what the other one has…it’s a given; sharing snacks and toys is an everyday thing. But did you know that the act of sharing snacks and toys is a perfectly, wonderful way that your preschooler, and even your toddler, is exposed to the basics of division?
The act of divvying up items between children is a great way to introduce the concept of sharing tasks, or forming fair shares. Sharing tasks are an important basis for learning about division and fractional parts of a whole.
So many adults grow up with a fear of math. Where does this fear originate? Could it be the way we present the ideas of math to young children? Do we presume that math is too difficult to explore with preschoolers? Toddlers? Babies?
Math is everywhere; it’s all around us. Imagine…It’s a hot day. You have two popsicles. You have two children. Even the youngest children are able to grasp that this means that each child gets one popsicle.
The simple experience of sharing two popsicles between two children is division. 2 popsicles divided by 2 children = 1 popsicle each. Your children are doing division, and you had no idea!
And they may not know it either, until you begin verbalizing what is happening.
By talking about math in a normal and fluid manner as children encounter it, children have the opportunity to become aware of naturally occurring math experiences in their everyday lives.
So how can you verbalize math experiences to encourage your child’s understanding of naturally occurring math problems? Try this. Get three pieces of candy to split between three people (or two if is just the two of you at your house).
Before it is snatched out of your hands and devoured (my son can eat candy faster than anyone I have ever met), go over how many pieces of candy you have. Narrate the experience to your children: Okay, how many pieces of licorice do we have? Three? How can we split the candy up so that everyone gets a piece? Three pieces of candy and we each get one. One for me. One for you. One for brother. We had three and we divided it by the three of us and we each got one!
That’s it. There is no need for fancy language and you don’t need to write it down. It may sound overly basic or common sense knowledge, but this is the kind of talk that gets little ones thinking about the role of numbers in their lives (number awareness) and gives them a sense of math problem solving.
Preschoolers who are ready can begin experimenting with dividing numbers other than one. For instance, the other day we were playing with our counting bears. If we have three bears, it is obvious to my preschooler that we each get one. But what if we had twelve colored bears to share between the three of us? How do we share the bears so that we all get the same amount?
My preschooler began by just randomly guessing how many would go on each plate. He would put some bears on a plate, count them, and shift them around. He was determined and eventually came to a point where he had four on each plate, but it took him awhile.
We talked about different ways we could organize the bears to figure out how we could split them up evenly. We tried a method of counting each bear out one by one and found this was the quickest way. We then tried this technique with fifteen bears.
Next, we experimented with an amount that does not divide evenly: ten bears. He was a pro at counting the bears out one by one by this time. As he finished counting them out, he gave me a puzzled look when we had a leftover bear and began recounting, assuming that he miscounted at first. I told him that he was indeed correct the first time, but that maybe ten is a number that does not divide by three evenly. We talked about how this tiny little bear was our remainder. (10 divided by 3 = 3 remainder 1.) What could we do with this extra bear? Should we try and cut it up (fractions) and split up the pieces? Finally he suggested that we give Daddy the extra bear when he gets home later.
Children are typically taught early math concepts with manipulatives, such as the colored, counting bears that we use (bears, vehicles, people oh my!) Snacks work great for manipulatives! Think goldfish, popcorn, pretzels; cheese or other soft items that can be cut up into fractions when there is a remainder. We also often explore division concepts using play money.
Him: I have a one hundred dollar bill (his favorite bill!), how many toys can I buy?
Me: Well, if Hot Wheels are $1 how many could you buy? Or if your princess dolls are $20, how many could you buy?
We then work to gather the toys and start counting them out. (And yes we have a ridiculous amount of Hot Wheels).
While most children benefit from these type of concrete learning experiences, some children will prefer just (or also) working with the numbers. My preschooler has a well-worn hundreds chart that he refers to often when we encounter numbers throughout the day, and it helps him to have it available as we explore ideas like division. Seeing the numbers displayed like this helps him to understand their relationship to each other in a way that using the manipulatives does not.
At snack time, test your preschooler’s division knowledge when it comes time to decide how many of each item each person should get. Talk with them about what they are doing. Verbalizing sharing tasks at home is a great way to connect a child’s basic thinking with early mathematical concepts, such as division. It is not important to implement fraction language or introduce preschoolers to fraction symbols this early, though if they are ready for it give it a go! The goal of early math isn’t to overwhelm young children, but to give them a sense of familiarity with number and number problems as they arise in their daily lives.