AimeeM Posted January 17, 2015 Share Posted January 17, 2015 Is there a way to go over integers with c-rods? That is one topic not covered on education unboxed (that I could see). Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted January 17, 2015 Share Posted January 17, 2015 One method would be to use wet-erase markers to draw a line down the middle of one or two sides of each rod. Let dry, of course, and keep fingers dry while using. Let the marked sides represent negative numbers, the unmarked are positive. Negatives added together make longer and longer negatives, just like positives do with each other. But putting positives and negatives together, they cancel off parts of each other---like matter and antimatter---and all you have left is part of whichever rod is longest. When you get a positive and negative of the same number together, they obliterate each other entirely, leaving you with zero. Adding is easy to show: adding positive to positive or negative to negative just gives you more of the same. When you add a negative to a positive number, it dissolves away part of the rod and leaves you with a smaller positive number. Or, if the negative is the longer rod, the positive will dissolve away part of it and leave you with a "smaller" negative number. Of course, "smaller" negatives are actually greater (bigger, worth more, closer to zero) than "larger" negative, which is somewhat counter intuitive. Multiplying positive times negative isn't hard. Just put out that many of the negative rods. Subtracting is also fairly easy as long as you stay in all negatives or all positives (so you can subtract by taking away rods). Subtracting a negative number from a positive is tricky to model with manipulatives. You can do subtraction if you first teach that the same-size positive and negative together make zero, and you can always add zero to any number without changing your total amount of something. So here you have your positive rod, and you want to take away a negative, but you have no negative rod to take away. What can you do? Add in a zero, which doesn't change the total amount of your number, but make the zero by using the positive and negative of whatever size you are wanting to subtract. THEN you will have a negative rod to take away. Subtracting a positive number from a negative would use the same "add a zero" trick. The hardest calculation to model is negative times negative. Here is one method, which I think could be adapted to rods: Multiplying Negative Numbers with Rectangles Quote Link to comment Share on other sites More sharing options...
Farrar Posted January 18, 2015 Share Posted January 18, 2015 Oh, brilliant! We're to this topic now. I'm so going to use some of those ideas. Quote Link to comment Share on other sites More sharing options...
IsabelC Posted January 18, 2015 Share Posted January 18, 2015 Thanks for the ideas Denise (the site isn't letting me Like) I'm about to start on this with my eldest and interested to see how it will go. As a kid, I actually found the way negative numbers work to be intuitively obvious, so it hadn't really occurred to me until recently that it would be something I have to teach the kids. But it will be good to have a toolkit of strategies ready. Quote Link to comment Share on other sites More sharing options...
Alessandra Posted January 18, 2015 Share Posted January 18, 2015 <p> One method would be to use wet-erase markers to draw a line down the middle of one or two sides of each rod. Let dry, of course, and keep fingers dry while using. Let the marked sides represent negative numbers, the unmarked are positive. Negatives added together make longer and longer negatives, just like positives do with each other. But putting positives and negatives together, they cancel off parts of each other---like matter and antimatter---and all you have left is part of whichever rod is longest. When you get a positive and negative of the same number together, they obliterate each other entirely, leaving you with zero. Adding is easy to show: adding positive to positive or negative to negative just gives you more of the same. When you add a negative to a positive number, it dissolves away part of the rod and leaves you with a smaller positive number. Or, if the negative is the longer rod, the positive will dissolve away part of it and leave you with a "smaller" negative number. Of course, "smaller" negatives are actually greater (bigger, worth more, closer to zero) than "larger" negative, which is somewhat counter intuitive. Multiplying positive times negative isn't hard. Just put out that many of the negative rods. Subtracting is also fairly easy as long as you stay in all negatives or all positives (so you can subtract by taking away rods). Subtracting a negative number from a positive is tricky to model with manipulatives. You can do subtraction if you first teach that the same-size positive and negative together make zero, and you can always add zero to any number without changing your total amount of something. So here you have your positive rod, and you want to take away a negative, but you have no negative rod to take away. What can you do? Add in a zero, which doesn't change the total amount of your number, but make the zero by using the positive and negative of whatever size you are wanting to subtract. THEN you will have a negative rod to take away. Subtracting a positive number from a negative would use the same "add a zero" trick. The hardest calculation to model is negative times negative. Here is one method, which I think could be adapted to rods: Multiplying Negative Numbers with Rectangles Great post! (Can't seem to like on my phone) Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.