Solving problems is not doing math.
Hi, I’m Sarah.
I’ve been a math and science teacher for 20 years,
and I’m here to make math engaging and fun.
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There’s so many different ways that you can teach
the relationship between integers.
And again, if a student doesn’t have a solid foundation with this,
it’s going to be really hard for them to go through algebra,
because there’s so much that we talk about that is like,
where we talk about, like,
canceling out and getting rid of these things, right?
Keeping it in balance. So ultimately,
you’ve got to understand that, like,
if I have a positive five on here,
I can’t just take away that positive five, right?
I need to put a negative five there so they cancel out,
but I also have to put the negative five over here. Okay?
So those are things that you’ve got to really understand.
So we’ve got the positives.
I know this is trying to make all of these say one
so we don’t get too confused.
The blues are the positives and the reds are the negatives.
So you can honestly use any sort of manipulatives.
You know, I’ve got some discs in my.
In my room that are like two sided little counter tokens, right?
You can use anything. You can use coins,
you can use, like,
flash cards, post it, whatever.
But ultimately, the big thing to Understand?
Is that one negative, one positive?
That’s zero 0 pairs. So I could put as many here as I want to.
Right, but that’s zero because you have plus one minus 1 0 pairs.
If I give you a dollar, and then I take that dollar away,
you’re still at 0 0 pairs.
So let’s just start with 2 – 3.
Now, also,
when you’re. When you’re doing this,
you would look at, like,
you know, what are these different numbers? Right?
So if I had. I know I’m kind of jumping all over the place,
but. So if I had this here,
what number would this represent?
Well, I’ve got two positives,
but I’ve got four negatives,
so these are going to cancel out.
I’m just left with negative two.
So if I have positive two and I need to take away three,
so what I need to do is I don’t have three pots.
So there’s two different ways you can go over this,
but we’ll. We’ll do both ways. Right,
but if I’m just gonna take away three. Hmm?
I don’t have three to take away.
But if I put in these zero pairs,
now I have three to take away,
and I look at those two canceling out,
and what I’m left with is one negative.
So it’s negative one. So that’s one way to show it.
Another way that you could show it is, oh,
if you start with two, you can just put In one of those zero pairs.
Cause now you have three positives to take away,
you’re left with negative one.
You can also explain that this is the same thing,
and this is sometimes, sometimes a jump that they’re.
That they’re ready to make,
but sometimes they’re not.
And you can just show that to them,
and if you see that look on their face and you go,
never mind, let’s try another one. Right?
So if you have that minus 3,
you can say, well,
it’s also the same thing as just adding negative three,
because, look,
I’m still left with the same thing.
I’m still left with that negative one.
So now if we have that two minus negative three,
okay, so I’m still starting with positive two.
Now I need to take away negative three.
So it’s the same thing, right?
When we’re taking away, we need to start adding in those zero pairs,
right? So we’re gonna take away negative three.
So I can’t just add in three negatives to take away, right?
But what I can add in are 3:00 pairs.
So if I put in 3:00 pairs like this,
that’s still positive too.
I haven’t changed anything about it.
That’s still positive two.
But now I have three negatives to take away,
so that’s positive five. If you do this a few times with students,
they will usually make that jump to be like,
oh, wait,
so it’s the same thing as adding there It is.
That’s it. Two minus negative three.
It’s less negative, which means it’s positive,
which means you’re adding.
It’s helping them realize that
there are so many different ways to look at something.
And if you put emphasis on them just memorizing the algorithm,
the algorithm will work.
But they may struggle to understand how to apply it in a new context,
meaning they may not realize that it still applies to fractions
or decimals or things like that.
When they start kind of, you know,
when they. When they just memorize it,
they’re like, oh,
You just put the two lines,
you take the two lines and you make them into a plus,
and it’s ad done. But it.
The concept isn’t there. They just know how to solve that problem.
They’re not doing math right,
and that’s a big difference. It’s math.