In my last post I explored how to add and subtract negative numbers on the number line. I got to a place where I think I can teach that to my students, but it still feels cumbersome--maybe because I can see on a number line that subtracting a negative is the same as adding it, but I still don't understand why.
As I was scrolling through the lessons with my good friends over at the Khan Academy, I found the Negative Numbers and Coordinate Plane section. Sounds promising. . . .
Oh my gosh they have a whole practice section on section on negative numbers on the number line! Let me click through that right quick . . .
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| Question 1 |
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Etc etc etc. . . . These are not what I need, although I do like how they do the number lines both horizontally and vertically which may give students the chance to conceptualize numerical order slightly differently.
Let's see what else they have. . . . A-HA! Here's an introductory video on negative numbers. This might be just my speed:
The most helpful explanation of the concept of negative numbers starts for me around 2:10: the higher the negative number, the smaller it is. He says it this way:
"Negative 100 is a lot less than negative 1."
He adds that we can think about this idea as a negative being a lack of something. So if I lose $100 from my bank account, I have way less money than if I lose $1 from my bank account. I might say it this way:
"How not-much of something do I have? If I have 100 not-muches of something, and you have 10 not-muches of something, who has less?" (Now that I see that all typed out, it could be even more confusing. But who knows? Maybe it unlocks something for someone. . . .)
I can also connect this concept to my last post about the number line: When I subtract, I go to the left--and when I go to the left, the numbers get smaller. So anytime a student is confused by this concept, she can simply draw a number line--all she has to do is memorize what the number line looks like, i.e., that the numbers immediately to the left of the 0 start at -1. So which number is smaller, -10 or -30? And she will see that the answer is -30, because she has to go to the left of -10 to get to it:
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| Gotcha. |
I'm really starting to see how grasping the concept of negative numbers--especially adding and subtracting them!--can be very confusing for students. After all, I'm a student, and I'm confused myself!
Next time let's look in more depth at adding and subtracting negative numbers. Thanks for stopping by!
Hey, Erin! For me is the same confusing how the higher number can be smaller, such as -10 is higher than -30, but I should always remember that it is negative number. I think for children is not really easy to get it the same way, but an example with the bank account where to lose $100 and $1 makes a difference! :))
ReplyDeleteI try to recall my school math experience and I can't remember that we used a number line concept. I feel it is a good way to explain subtraction and addition. We used to calculate only by columns, and we didn't know any other ways to do it. I feel like I so behind from new math concepts... even though I need to make subtraction my brain tends to operate in frames of old school experience and it's hard for me to shift myself to do calculations by new innovated approaches.I am working on it :))
Thank you Erin for sharing this with us!
Great feedback Tatiana.
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