My favorite math game for young children

My favorite math activity for young children

 Experience has taught me that there are many parents of young children who are already worried about SAT scores and college admissions. Some of you may find you way to this blog. This post is for you. I originally wrote it in response to a question on Quora. I decided to be lazy and let it do double duty. :)

My favorite math activity is “The Chips Game”.  I didn’t invent it; I read about it somewhere – I wish I could remember where - and have since adapted it to suit many purposes.

To play the chips game you need 3 colors of poker chips and dice.  One color of chip is worth one point, a second color is worth ten points and the third color is worth one hundred points. Roll the dice. The number you roll is the number of chips you earn. You earn one-point chips. Once you have 10 you can trade them for a ten-point chip. The goal is to trade in 10 ten-point chips for a hundred-point chip. Notice that place value and “regrouping” are intrinsic to the game.

It sounds too simple to be either fun or educational, but the game is highly adaptable and the real value lies in the modeling and conversation that happen when you play. For example, when you play with your three-year-old (which I’ve done) you can emphasize the counting. If you roll a 12, then at first you would count out 12 chips and then trade 10 of them, but eventually you should model taking a ten-point chip and two one-point chips. Allow your child to do what feels comfortable, but when it’s your turn model the next step up. When you play with a fourth grade student (which I’ve also done) you can multiply the dice and talk about probability: “What must I roll to catch up with you? Am I likely to roll at least that?”

You can start with one six-sided die and then add another six-sided die so that the child must add the numbers on the dice. You can use dice with more than six sides. You can have a die that represents the number of chips you earn and a second or third die that represents the number of chips you LOSE, which introduces subtraction with regrouping and negative numbers as well as making probability conversations more interesting.

Note that whether or not you win is completely based on luck. There is no skill involved. Very young children may not understand that and they find games that they win more often than not to be more fun, so when you play with your three-year-old for the first time, cheat so that s/he wins. Also if you feel his or her attention start to wane before anyone earns a hundred-point chip, then either quit while your child is ahead, or add more dice to get there faster.

A fun way to boost your vocabulary!

A fun way to boost your vocabulary!

Generally, one of the best ways to boost your vocabulary is to read. There can be two problems with this method:  First, you must read text that includes words you do not already know; rereading the Hunger Games series for the third time isn’t going to cut it. It can be hard to find reading material that has advanced vocabulary but is also enjoyable. Second, this method works best when practiced over a long period of time. What if the test is just around the corner?

Clearly what you need are fun books that are dense with polysyllabic words but that are also quick to read. Try Calvin and Hobbes. Calvin and Hobbes was a comic strip drawn by Bill Watterson in the 1980’s and1990’s. The strips were collected into books that are still available from Amazon or Barnes and Noble. You might even find them at your local library.

It was my children who first alerted me to the comic’s usefulness as a vocabulary builder. We own over a dozen of the books and both boys grew up reading them. My oldest remarked that he had learned more new vocabulary from Calvin and Hobbes than from his English class assignments. Consider this sentence from a strip in The Indispensable Calvin and Hobbes:  “Poised precariously over a percolating pit of putrid pasta, Spaceman Spiff is held prisoner.” Or, “With stupendous powers of reasoning, the caped combatant concludes there’s no need for homework if there’s no school tomorrow!”

With a few Calvin and Hobbes books, you can build your vocabulary without feeling as if you spent your holiday break studying!

Don't dismiss the shortest answer!

Don't dismiss the shortest answer without a reason!

On the writing sections of college entrance exams, any form of wordiness or redundancy is considered an error. Therefore, shorter answers are somewhat more likely to be correct. If you have the choices narrowed down to two and you can't choose between them, pick the shorter answer.

Length Matters!

Length Matters!

Studies show that there is a strong correlation between your ACT or SAT essay score and the length of your essay. Make sure your essay is as long as possible. College admission officers can read your essay online, so make sure it is well-written, but if you are choosing between verbose and succinct, go with verbose.

The Problem With Exercises

The Problem With Exercises

I was working with a trigonometry student on trigonometric identities. He was expecting his teacher to announce a test or a quiz soon, and he was still uncomfortable with the topic.  “I just don’t feel like I know the steps,” he told me. I’m afraid he found my response unsatisfactory:  “There aren’t any steps. You just have to play with it. You’ll have to come to terms with that.”

When I’m tutoring and a student pulls out a question, I usually know the steps. However, occasionally I have to say, “I don’t immediately see how to do this one. Give me a minute and let me play with it.” I have come to realize that letting them watch me solve a problem while I think out loud (formally known as “modeling problem-solving behavior”) is actually more educational than teaching them steps. They would not agree. They want a recipe, dang it, and any delay in getting there is just wasting time.

I recently learned that in Russia as early as 1^st grade (or rather the Russian equivalent of 1^st grade) the schools distinguish between “problems” and “exercises.” An exercise is a question that one answers using an algorithm. The question was usually assigned specifically to allow the student to practice a particular algorithm. A problem, on the other hand, is a question that one does not initially know how to approach. What may be a problem for some students may be an exercise for older, more experienced students.

I have decided to begin distinguishing between problems and exercises when I talk about them. Old habits die hard and I imagine I will need to correct myself often at first. However, the trouble with schooling is that there are too many exercises and not enough problems. I think the first step towards addressing this issue is to point out the difference.