A parent writes:
I would like to continue the discussion about how parents can help and ask for advice.
Before I became more involved in my kids’ math education, I did not know how hard it would be for me with my standard math background to explain algebra to a child with an “Investigations” math background.
I never heard complaints from my daughter about math being hard or from the school about my daughter not being able to understand math. When she went to middle school, I finally saw that the pace at which kids are instructed in elementary schools is not acceptable. I believe that my kid deserves higher education; it should not be only for the elite. That is why I began to give her extra help and extra assignments.
I am explaining new material to her both ways: standard and graphically. I had to do that, because she was solving equations with one unknown using a graph. That was not a problem for me. I figured that it is too late to change her vision of math completely right now. However, when I explained multiplication of real numbers I had a problem explaining graphically the multiplication of two negative numbers. I was using position of a number on number line. Apparently, my math is not as strong as I hoped for. Can someone help me with it? Who knows how to use a number line to explain the multiplication of two negative real numbers?
Thank you.
I can relate to the challenges of communicating across the Investigations gap, as well as the dust and cobwebs in ‘math-related details’ brain cells
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Alas, I can’t think of a good graphical way to explain this (there may NOT be one?), and I’m not sure how I’d use a number line, other than to show the relationship between numbers (+, -, and 0). Perhaps focusing on the basics: each integer has both a sign (+ or -) and a value. These signed numbers or integers have certain rules that go with them that kids can readily learn and apply in order to find the sign of the answer to multiplication or division problems: 1) if the signs of the two numbers that are multiplied or divided are the same, the answer is positive; 2) If the signs of the two numbers are different, the answer is negative.
Another approach would be to use the signs of the factors and multiply the absolute values. The pattern becomes clear if you write out several examples. ++ or — signs of the factors give a positive product; -+ or +- signs give a negative product.
It’s a little analogous to having double negatives in language. If you’re not tall, you’re short. If you’re not not tall, you ARE tall. Kids might get that logic?
Finally, you might also find Math on Call (Houghton-Mifflin, ISBN-13: 978-0-669-50819-2) a helpful resource to have in your family’s math toolkit. It distills the essential aspects of math down, provides clear definitions and examples, and glossaries of math terms and formulas.
Hope that helps a little, and keep up the good work at home with your kid(s)!
This _is_ a hard thing to explain. Here’s a good explanation from a math website for parents who homeschool:
http://www.homeschoolmath.net/teaching/integers.php
Funny that we were just discussing this a couple of nights ago at home. I was not able to give a satisfactory ‘real life’ situation . (Probably some math ideas are not really related to everyday money situation?) However, my 6th grade daughter came up with one argument. She said, if -2 times 3 is -6, then -2 time -3 can not be -6 again, so it must be 6.
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