Everyone Loves Exploring – Whether your ideal place to explore is a deep dark jungle, a long, sandy deserted beach or a marketplace in a distant, exotic land, we all have an idyllic place that we could spend hours and hours exploring and making wonderful discoveries.
Children are certainly keen explorers too, perhaps even keener than adults. Children still have a natural curiosity and an unending desire to explore and discover. So let’s look at how that natural curiosity can be used to advance math skills.
We know that children love to explore and discover so how can we harness this to help them with math. The answer is simple – let them explore and discover in math. Give them numbers to play with, let them explore patterns, let them discover properties of numbers and shapes and measurements.
Best of all, when they learn this way they also develop a real understanding of these concepts because they haven’t just been told that this is the way it is, they have discovered it for themselves.
Math games are a great way to explore in math. When children play with numbers they learn about numbers. They discover patterns. They discover properties of numbers. They discover relationships between numbers. They discover number concepts.
Best of all, when they learn this way they also develop a real understanding of these concepts because they haven’t just been told that this is the way it is, they have discovered it for themselves.
Let’s do some exploring of our own now and look at a few games we can use to explore math concepts.
Higher or Lower is a great game for exploring number order and place value.
To begin select the upper and lower number limits, e.g. between 10 and 100.
One player selects a number and records it on a piece of paper.
The other player/s guesses what they think the number might be. For each guess the first player tells if the chosen number is higher or lower. Play continues until the number is guessed. A more challenging game would be to explore larger numbers or decimal numbers. This game is always a favorite no matter what age group I am teaching. I just adjust the size of the numbers to the ability of the students.
Grab and Group is a great way to explore division. Players take turns to grab a group of items (marbles, toothpicks, counters or even pens). They then attempt to make groups of 2’s with no remainders, then 3’s, 4’s, 5’s and 6’s. Players score points for each of the groups they can make, e.g. a player who grabs 9 can only make 3’s so they score 3 points. A player who grabs 12 would score 2+3+4+6=15 points as they could make groups of 2’s, 3’s, 4’s and 6’s. This game is also easily adjusted to the abilities of the students. Younger students will manipulate the items to see if the number is divisible by the given number. Older children will simply count the items then mentally calculate what the number is divisible by.
You can also have children explore properties of numbers by posing a question for them to answer.
- How many prime numbers are there between two given numbers, e.g. 1 and 100 or 200 and 300?
- How many times do you write the digit 7 when you write all of the numbers between two given numbers, e.g. 1 and 100 or 500 and 700?
For more games to get your kids or your students exploring math you could try a number version of Hangman using a complete computation.
Tic Tac Toe can also be played in number versions, e.g. use the numbers 1-9 to fill the grid. The first player to create a line that totals 15 is the winner.
There are many other math games that are ideal for exploring in math. Playing games in math offers so much more than just a bit of fun. These games also help to develop a deep understanding of math concepts and a positive attitude towards a sometimes unpopular subject. Don’t be surprised when you even hear, ‘Gee that was fun! Can we do it again?’
By: Teresa Evans
Posts Tagged ‘Discover’
Let’s Be Math Explorers
April 28th, 2010Learning How to Think Again
October 9th, 2009A couple of months ago, I read in the newspapers about how this woman in her late fifties, with heavy make-up, colored hair and the trendiest clothes had been denied entry in one of the hippest clubs in town. She and her friends were eventually allowed in but the club denied them free complimentary drinks on “Ladies Night”. The free drinks on Ladies Night was meant to attract much younger ladies to the club which would in turn entice men to come patronize the club. That article set forth some rather heated debates on local forum websites with some netizens suggesting that she and her older friends should patronize other community clubs meant for older folks. I for one did not understand why a person at her age would put herself through such an embarrassing episode. Then a few days ago, a picture of her appeared in the newspapers again. Apparently she had died of cancer and she had been fighting for her right to party and have a good time before the curtains came down for her. And because of her and the publicity generated, the club eventually set up a separate section where people of all ages could have a good time drinking and dancing on the club premises.
The example I cited above demonstrates how our narrow thinking can be if we set ourselves up into believing what seems to be the obvious. If we look beyond the obvious and ask ourselves “what if” questions, we may be surprised to discover that there can be many interesting answers and solutions to any problems. Life can be like a big noisy party. With music blaring in the background, people laughing and shouting and glasses clinking. But even with all these going on, it’s still possible for you to understand the person across from you. Or even one from twenty feet away. That’s because our attention is selective and we can tune out certain things and tune in to the things we want to focus on.
You can test this for yourself. From where you are seated, find five things that have “red” in them. Suddenly your mind starts to focus and things with red starts jumping out around you. With your “red” mindset, you see red on a book, red on a cup or red on a picture and so on. Likewise, whenever you learn a new word or phrase, you suddenly hear it being used around you. Or after you bought a new blouse, shirt or skirt, you might start seeing it around town. That’s because people find what they’re looking for. If you’re looking for beauty, you’ll find beauty. If you’re looking for conspiracies, you’ll find it. It’s all a matter of tuning your mental channel to find what you’re looking for.
We learnt how to set our mental channels from our formal education. Other important sources comes from our family and friends we hang around with. Through the years, you learn what is appropriate and what is not. Through this, you learn many of the questions you use to find out about your environment. You learn how to probe and search for information, which ideas to pay heed to and how to think about these ideas. Your educational background gives you many of the concepts to understand and put order to the world around you.
For example, if you were taught the right memory techniques to train your memory, you’ll discover you can suddenly memorize long chains of numbers like credit card numbers or telephone numbers. As a student, your study skills will improve and you will experience accelerated learning. You’ll remember complicated road directions easily and can memorize long grocery lists. As you progress with your memory training over the years, sometimes even unknowingly, your friends may even accuse you of cheating in poker games or bridge. This is because you can remember the card sequences and what hands are being played. People with memory training are also protected against Alzheimer’s disease or dementia much more longer than people who don’t have mental skills.
Much of our educational system work against the nurture of creative thinking. For example, in school, our teachers have always taught us how to find the “right answer”. However, memory training and creative thinking is all about using our imagination to “think out of the box”. By the time the average person finishes college, he or she will have taken over 2,000 tests, quizzes and exams, all gearing us to coming up with the “right answers”. The “right” answer approach becomes deeply ingrained in our thinking. This may be true for some mathematical problems where there is in fact only one right answer. The problem is that most of life isn’t this way. Life is ambiguous and there are many right answers. It all depends on what you have been looking for. But if you think there is only one right answer, then you’ll stop looking as soon as you find one.
When I was in college, one of my teachers put a small chalk dot on the black board. He then asked the class what it was. After a few seconds of awkward silence, we were all relieved when someone blurted out what seemed like the obvious, “A chalk dot on the blackboard!”. The teacher glanced at the ceiling and said, “I’m surprised at all of you”. He told the class, “when I did the same exercise a year back with some kindergarten kids, they thought of twenty things it could be, a puppy’s eye, a stone, the top of a can of can, a jelly bean, top of an orange, a crumpled piece of candy wrapper, a Christmas tree ornament, a bug and so on. They were letting their imagination run wild !”. In the decade or more between kindergarten and college, not only had we learned how to find the right answers, we had lost the ability to look for more than one right answer.
By: Martin Mak