Yet, when presented with a number line, BatBoy can find the midway point between 7600 and 7700, and then deduce that 7651 is, in fact, closer to 7700. But we need to draw this diagram over and over again.
Monday, October 28, 2013
Zooming the Number Line
Presented with a problem of rounding in Museum of Mysteries, by David Glover, BatBoy makes a very common mistake: He wants to round 7651 to 7600. At least I know he is not just memorizing the answers (or at least it is very clear when he has just memorized an answer) because he makes this same mistake every time he comes to this point in the story. 7651 seems to be closer to 7600 than to 7700 because there appear to be more similarities between 7651 and 7600.
Yet, when presented with a number line, BatBoy can find the midway point between 7600 and 7700, and then deduce that 7651 is, in fact, closer to 7700. But we need to draw this diagram over and over again.
Yet, when presented with a number line, BatBoy can find the midway point between 7600 and 7700, and then deduce that 7651 is, in fact, closer to 7700. But we need to draw this diagram over and over again.
Sunday, October 13, 2013
Creating a Culture of Math: Books
Children love books. Books are a window to the world greater than their own. Within books, children can play with personas, meet friends, explore ideas, discover people different from themselves, and have great adventures. Books can be either informative or fantastical. Either type can be a good way to ensure math is included in your family culture.
For the youngest children, we have counting books and shape books readily available. One of our favourites is The Very Hungry Caterpillar, by Eric Carle. I also recommend Math Fables and Math Fables Too, by Greg Tang . They are everywhere you can find books. Pick one or two that your child enjoys and put it on your bookshelves, or borrow them from your local library. Read them with your child; enjoy the story and count the pictures together.
After counting, math books seem to vanish from the bookstore shelves. We need to look a litte harder to find them. After counting, children like to see numbers in use. Some they might like include
For the youngest children, we have counting books and shape books readily available. One of our favourites is The Very Hungry Caterpillar, by Eric Carle. I also recommend Math Fables and Math Fables Too, by Greg Tang . They are everywhere you can find books. Pick one or two that your child enjoys and put it on your bookshelves, or borrow them from your local library. Read them with your child; enjoy the story and count the pictures together.
After counting, math books seem to vanish from the bookstore shelves. We need to look a litte harder to find them. After counting, children like to see numbers in use. Some they might like include
Saturday, October 12, 2013
Operations in Fractions
BatBoy understands fractions in the concrete sense, as equal parts of a whole. We haven't really touched on concepts like finding common denominators or multiplying fractions. Instead, he has spent time and energy really getting to know a few basic fractions and how they "work together." As he has learned to add and subtract, and then multiply and divide, he has been able to apply these operations to these basic fractions (halves, thirds, quarters, eighths, and occassionally, sixths). Using his visual understanding, he has solved problems involving adding or subtracting fractions of the same "family" (halves, quarters, and eighths; or thirds and sixths) including their mixed numeral relatives. He is able to find answers with negative values, such as the solution to 1/8 - 1/4. Today, he was playing with the sequence of dividing numbers by two. Beginning with 8, he divided by 2, again and again, until he got to 1/16 and couldn't (his words) "multiply 16 by 2" without paper.
SpiderGirl plays with concepts less and so, seems less drawn to mathematics than BatBoy. But given problems, she solves them quickly. She gets mental blocks when she is anxious. If she thinks that there is a "right" way to solve a problem (a way that she is less than confident with), or that I expect a particular answer, solved in a particular way, she freezes and claims she has no idea. But, if the problem is presented in a low pressure environment, she can shine brightly indeed. SpiderGirl understands fractions visually. Even when fractions are not of the same "family," she can puzzle it out using manipulatives. She used manipulatives to figure out to find common denominators in order to add or subtract. When she gets more comfortable with multiplication, factors, and multiples, I have every confidence she will gain a more methodical way of finding common denominators. When manipulatives are not available, SpiderGirl is also to present reasonable guesses to problems involving fractions, decimals (to hundredths), and percents. And she is learning that there is value in her ability to estimate.
SpiderGirl plays with concepts less and so, seems less drawn to mathematics than BatBoy. But given problems, she solves them quickly. She gets mental blocks when she is anxious. If she thinks that there is a "right" way to solve a problem (a way that she is less than confident with), or that I expect a particular answer, solved in a particular way, she freezes and claims she has no idea. But, if the problem is presented in a low pressure environment, she can shine brightly indeed. SpiderGirl understands fractions visually. Even when fractions are not of the same "family," she can puzzle it out using manipulatives. She used manipulatives to figure out to find common denominators in order to add or subtract. When she gets more comfortable with multiplication, factors, and multiples, I have every confidence she will gain a more methodical way of finding common denominators. When manipulatives are not available, SpiderGirl is also to present reasonable guesses to problems involving fractions, decimals (to hundredths), and percents. And she is learning that there is value in her ability to estimate.
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