My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?
As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have a cookie and I give you two more cookies, how many cookies will you have then?”
The fastest way to a child’s mind is through the taste buds. Children can easily visualize their favorite foods, so we use mainly edible stories at first. Then we expand our range, adding stories about other familiar things: toys, pets, trains.
Math That Is Social
“Panther the barn cat went hunting in the field and caught two mice every day. How many mice did he catch in four days?”
Don’t limit your story problems to the child’s grade level. If she can make a picture in her mind, she will be able to work with it. You may encourage your child to count on her fingers: one finger for each mouse. Using fingers as symbols is a step into abstraction, paving the way for later algebra. If you do not believe in finger-counting, then teach your child to count on blocks or craft sticks, or make her a counting rope for working with bigger numbers than she can handle mentally.
“Panther went out to the woods and met a gray cat named Shadow. He invited her to come back to our barn and chase pigeons. There were 15 pigeons in the barn, and Panther chased six of them. He let Shadow have the rest. How many pigeons did Shadow chase?”
As you both get used to the game, occasionally throw in something harder: fractions, division with a remainder, an answer that comes out negative. See what your student can do with a tough problem. You might be pleasantly surprised — even a toddler has ideas about how to split three hot dogs between two people.
If your son is stumped, try not to give away the “right” answer. Instead, ask him to explain the problem back to you. As he puts the problem in his own words, he will often see a solution. Pretend to be Socrates, asking questions that guide him toward the answer.
“After Shadow came to live in the barn, we had two cats, and half of them were girls. But then Shadow had four kittens, and now 2/3 of our barn cats are girls. How many of the kittens were girl cats?”
There’s Only One Rule
Here is the most important rule — in fact, the only rule — of the oral story problem game:
- Take turns.
If I ask my daughter a story problem, she gets to give me one. And I have to try to solve it, even if she uses made-up numbers like 80-hundred or a gazillion. This is playtime, not an oral quiz.
As you are solving your child’s problem, think out loud. Model mathematical problem-solving by talking about how you figured it out — and if you got stumped, that’s even better! Model stuckness: how to recognize what you don’t know, how to mentally regroup and look for an alternate approach.
Things to Consider in Creating Story Problems
- Some quantities are discrete and countable, such as marbles or dinosaurs. Other quantities are continuous, like a pitcher of juice or a length of rope. Use both types in your problems.
- Addition and subtraction are often thought of as putting-together or taking-away sets of discrete items. But they can also be represented in stories by growth or comparison (how much more or less) or by classification of parts (separating sheep from goats).
- Multiplication and division are often thought of as counting or sharing out groups of items. But they may also be represented by growth or shrinkage (how many times as much) or by rates and ratios (cookies per child, hot dogs per package).
- Division of continuous quantities may lead naturally to fractions (sharing candy bars, or cutting pieces from a spool of ribbon).
- Money provides an excellent way for children to begin thinking about decimal numbers.
Oral story problems are not just for young children. Students of all ages benefit from the practice of working math in their heads. As your children grow, let the stories grow with them: soccer games, horse stories, or space adventures will keep middle-school students figuring.
Make oral story problems a part of your daily bedtime routine with Bedtime Math. This website publishes a daily math problem (with answers) at three levels of difficulty: Wee ones, Little kids, and Big kids — approximately preschool to upper-elementary level.
For more information, here’s an interview with Laura Overdeck: Turn Your Child’s Bed Time into Fun Math Time.
I think the best starting point is to look at your favorite objects and activities, and your kids’ favorites. Anything that involves quantities is an opportunity to count: Lego blocks, stuffed animals, candy. Anything that involves motion is a chance to measure time, distance and speed.
And absolutely any object can be measured with a ruler, or weighed on a scale. It’s mind-blowing to find out what some things actually weigh: a cubic foot of wet sand weighs 100 pounds! (I didn’t believe it till I weighed it myself).
Numbers are everywhere, and favorite objects are a great jumping-off point.
Edited to add: This post is an excerpt from my book Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It!