(air whooshing) - All aboard.

(train horn blowing) It's time for another math expedition and I'm so glad you are joining me today as we solve problems together.

And so thank you for being here.

Have you ever played that game where you try and guess how many objects are in a jar?

Maybe it was Skittles, or jelly beans, or whatever it might be, but all these objects are in there.

Now, I have different little stones, little jewels inside of this container and I wanna know how many are in there.

And I can guess, right?

That's called estimation.

Right?

We're estimating, we're guessing how many things are in a certain container.

And so that's really fun.

What if I did this, though?

What if I said, you know what?

I'm gonna take some out, reach in there, and I grab some and I say, all right, I took four of these out, can you now know how many are inside of the jar?

Well, I don't know how many there were to begin with, right?

So we couldn't know exactly how many there were, but what if we did know how many there were?

I bet you could solve that problem, and that's what we're doing today.

So let's look at this.

Inside of my secret treasure box, we have some ping-pong balls.

And I'll tell you, we have exactly 10 ping-pong balls inside of the box, all right?

So now that you know how many we're starting with, what happens if I take some out?

Can you figure out how many are left inside without looking?

I bet you can.

I'm just gonna reach, I'm not gonna look either, so that we can solve it together, all right?

Okay, look, I've got three.

Now, I'm gonna set that down.

And I've got three ping-pong balls here.

So, now remember, we said we started with 10, so there was 10 inside and now I've taken out three.

How many are remaining in that box?

Let's see if you can solve this along with me.

One of the ways we could solve it is we could say, hey, we could use a 10 frame, right?

Because there were 10 objects to begin with in our box.

And so if we draw out the 10 frame and each one of these little circles represents one of those ping-pong balls.

Now, we took three away.

Remember that taking away or removing them away is the same thing as subtraction.

That's the operation we wanna use when we're writing this out, okay?

So if I take three away from the 10 we started with, on our 10 frame, we can just mark those out and say, you know what?

I have one, two, three in my hand, so they're no longer in that box.

Well, how many are still remaining?

And because we have this visual representation, we can just count up how many we have.

I know there's five along that top row, right?

And let's keep counting from there.

Six, seven.

That must mean that there's seven inside of our box.

So 10 minus, how many did we take out?

We took out three.

So we can write this as an equation, right?

10 minus three equals, we're saying that there must be seven inside.

You know what?

I think we should check.

Let's see if we were right.

So if I set these over here, now we're gonna pull them out.

You ready?

All right, one, two, three, four, there's still some more, five, six, and seven.

There were seven.

We were right.

You solved the problem.

Great job, everybody.

All right.

Guess what?

I think we can do one more.

Now, we solved that one using subtraction.

Do you think we could solve it in another way?

I think we could solve it using addition.

Let's try.

Okay, so I put all the ping-pong balls back inside our box, all right?

And I'm gonna reach in, I'm gonna grab some out, and this time we're gonna try and solve it a little bit differently, all right?

Now, I'm still not gonna look.

I'm not gonna look.

I'm gonna use two hands.

Let's see if we can do this.

All right, we have one, two, three, four, and five.

We have five ping-pong balls here.

So how many must still be inside?

I'm gonna set these down and let's see if we can solve this in a different way, all right?

So we have a 10 frame again, but this time, instead of subtracting from 10, because we know we started with 10, let's see if we can actually solve it with addition.

Okay, so we have that 10 frame.

How many are we starting with?

How many did I have in my hands?

We had five, right?

Okay, so we could fill in that 10 frame with five circles, saying, hey, these are the five that we have in our hand.

How many do we have to add on to five to make 10?

'Cause we know that we had 10 in that box to start with.

So that's what we're trying to get to, right?

It's supposed to equal 10.

Well, we can write this either with that 10 frame, or with an equation and say five plus, if we add five more onto it, we know we're going to get to 10.

Five plus five equals 10.

So we solved it one time with subtraction.

We solved it a second time with addition.

See, there's different ways of solving problems, and you guys are doing awesome.

I'm so proud of your work today.

So as you do this at home, you can create your own box.

You could have a plastic sack that you could use, just fill in objects.

You don't even have to use 10.

It could be a different number.

But keep learning and keep problem solving, and we'll see you again real soon.