(light-hearted music) (sparkling) (spring) (fart) (whistle) (glass squeak) - [Children] Math Mights.

- Welcome back 3rd graders!

My name is Mrs. Ignagni and I am so excited for another fun episode of Math Mights.

We have a great show for you today.

Let's take a look at that plan.

First, we're gonna get our math brains ready with a mystery math mistake then we are going to take a look at how to represent numbers in different ways.

Whoa!

What's going on?

All of their strategies are mixed up!

Is that DC holding Abracus's wand?

Here is how it works.

One of our Mathville characters is going to pose a problem for us that they have been having a difficult time solving.

We then need to act like little detectives with our magnifying glasses and take a close look at that problem to see how we can help and get them to the correct answer.

Let's see which Mathville character needs help today.

It looks like DC needs our help.

He is having a hard time with 76 + 97.

It looks like that DC decomposed that 97 into 5 and 92.

Here's what he did.

DC took 97 and he decomposed that into 5 and 92 to make that friendly number of 80.

He then added that 80 to the 92 to get 172.

What do you think about the way that DC solved that problem, boys and girls?

Do you see a mystery math mistake?

Did you see anything that he did wrong?

Let's see what the boys say.

Jameson said, "I think DC decomposed 97 correctly because 5+92=97, but something doesn't seem right."

I do see what Jameson is saying, and he's right.

Something doesn't seem right.

Do you notice anything?

I wonder what Josiah said.

Josiah said, "DC's answer is incorrect.

He should have decomposed 97 into 4 and 93."

So, let's take a look at what Josiah's saying.

Josiah said, "DC's answer is incorrect.

He should have decomposed 97 into 4 and 93."

Looking at our 97, you're right.

We could also decompose this into 4 and 93 to equal our 97.

And then 76 + 4 = 80 and we're actually just gonna cross this out.

We're gonna do 80 plus our 93, which equals 173.

Excellent work 3rd graders, I know DC would be so proud of the help that we gave him to solve that problem and figure out that math mystery.

Lets take a look at our "I Can" statement of the Day.

"I can represent numbers in different ways."

Take a look at A, B, C, and D, boys and girls.

Which one do you think doesn't belong?

It looks like we might be talking about place value today.

Lets see what the boys think.

Jameson said A doesn't belong because its not an expression.

Josiah said B doesn't belong because it isn't equal to 370.

Looking at A, I can see what Jameson is talking about because B, C, and D are written in expressions whereas A is dealing with those place value blocks.

Taking a closer look at Josiah's thinking when I look down at B, I can see 300 plus 70 plus 1 does equal 371.

But looking at our other choices, A, I see that I have 3 100 blocks for 300 and I have 7 10's which would equal 370.

For C here, I have 300 plus 60 plus 10 and I have again 370.

And then going to D, 400 minus 30, that as well is 370.

Josiah was correct, B is the only one that does not equal 370.

Let's see what else the boys say about which ones may not belong with C and D. Jameson said "C doesn't belong because the 10's aren't together".

Josiah says "D doesn't belong because it doesn't show addition".

Looking, I see that the 10's aren't together.

Like they are in A, B, and D. And when we are looking at Josiah's comments, D doesn't belong because it doesn't show addition, he is correct.

D is the only one that doesn't show or have you do an addition problem.

Great job looking at A, B, C, and D and finding out which one doesn't belong, but it makes me think boys and girls what do these have in common?

They look like their all dealing with expanded form.

That reminds me of our expanded form Mathville character Value Pak.

(music) Value Pak, remember, lives in Mathville and they come together as a family.

But when they separate, they show those values that they represent on their bellies.

So for example, separated our red character is going to have a 20 on his belly while our white character is going to have a 7 on his belly, marking their individual values.

If we look at that number we were dealing with, if we see it, we have 371 and if we use Value Pak's strategy we would separate these to 300 plus 70 plus 1 to get 300 70 1.

Putting those back together again, we see that value.

371.

That was a great example showing Value Pak's strategy and we're actually going to look a little bit more into this today.

We're going to do a card sort with Value Pak!

Here's how the game works.

We are going to make pairs by either looking at the expanded form, the standard form, the word form or matching it up to those place value blocks.

We're going to go ahead and get started with our first one.

329, now, I have to look closely at each one of these to see if they match.

Well, those are 200s, that does not match.

I have 300 here, but no, I need 2 10's and that definitely has more than 2 10's.

I have a 175, 300, 175, lets see.

300, 329, double checking my work, I have 329, 329.

We found a match boys and girls.

If I have 175, again looking at my choices to match.

I can see right here, J and C have 2 many hundreds.

I have 371, that does not make sense.

I see, oh, 175.

Looks like we made another match boys and girls.

Putting those together, double checking my work, 175, 175.

Matching those and moving them to the side.

Next, I'm going to try my place value blocks.

So if I have 200s plus 1, 2, 3, 4, 5, 6, 7, 8, 9, 9 10's and I have 2, 4, 6, 8, 9 1's I can see that those place value blocks represent 299.

Now I have to find that match.

If I have 299, looking over here, I see that's not going to work.

371.

813.

Oh, look, I have 299.

Looks like we found another match, boys and girls, good work.

Lets now pull our expanded form.

If I have 800 plus 10 plus 3.

I know that equals 813.

Lets see if we can find our match.

So I'm looking at my place value blocks and I see 300s.

That's not going to work.

I see that I have 371, that's not going to work.

We don't have enough hundreds in that particular answer.

But I do see in our standard form, 813.

Look at that.

We have another match.

8 plus 10 plus 3 equals 813.

Nice work.

Now boys and girls, we only have 2 choices left.

And I know what you're thinking.

They must match.

But really good mathematicians and 3rd graders that really want to make sure that they're actually getting the right answers always want to double check that last one, just in case.

Looking at C, I see that I have 300s, 7 10's and 1 to get 371.

Now looking at my final match choice, I do notice that yes, in standard form, it is 371 as well.

So now I know for sure I've double checked my work, that those 2 match.

Excellent work 3rd graders, let's see if we can challenge ourselves though.

Lets take a look at a number like 385 and see if we can write this number in different forms.

Lets even go further and see if we can show it in 4 different ways.

If I see this example, and I have 385, I see one way of writing it is 300 plus 80 plus 5.

Another way to write out this number, is 300 plus 70 plus 15.

And to take it one more level, if you see the final example, 200 plus 180 plus 5.

Let's see if we can challenge ourselves with our own number.

If I have the number 485, I see that I can break that apart and I can have 400 plus 80 plus 5.

And then together again, I have that 485.

Lets go ahead and record that example as one of the ways that we decomposed 485.

So I can have 400 plus 80 plus 5.

Now that we decomposed 485 into 400 plus 80 plus 5, lets see if we can decompose it in another way.

Looking here, I see that I have my base 10 blocks.

So if I have 400s, as you can see, I have 1, 2, 3, and 4 hundreds.

And then I have 2, 4, 6, 8, 8 10's and 5 1's, I know that if I wanted to take one of these 10's and cash it in, it would be equal to 10 1's.

So I'm going to cash that in, and I'm going to bring over my 10 1's.

Do you think boys and girls, that this still equals 485?

Lets write it out and find out.

If I have my 400 plus now, my 7 10's, which is 70, plus my 15 1's... yup!

Looks like we still have 485.

Except this time, we've decomposed it in a different way.

Now remember, we're trying to challenge ourselves.

Do you think there's a fourth way to decompose 485?

Lets try it!

So, I have my 485, but we already shown it that way, so boys and girls, what do you think, how else can we decompose 485?

Looking at my 100s, I wonder if I take one away, and I now have 3 100s, and exchange it over here, and I have 300, plus 100, and then I have my 1, 2, 3, 4, 5, 6, 7, 8 10's with my 5 1's, do I still have 485 as my total?

Lets write it out.

If I have 300, so I have my 300 written down but I'm wondering what am I going to write for my second number.

Lets look back at that.

If I have 100, and then I add my 10s, I have 100, 110, 120, 130, 140, 150, 160, 170, 180, so I am going to write 180.

So I have 300, plus 180, I can't forget my 1's.

I have 5 1's.

So I ask you boys and girls, does that still equal 485?

You bet it does.

300 plus 180 plus 5 still equals 485.

Fantastic job 3rd graders.

I have taken a number and I have decomposed it by place value in two different ways.

We're going to see if those two different ways actual equal the same number.

So if I have 600 plus 90 plus 5, that together makes 695.

Nice work.

But I wonder now does my second, um, expanded form equal the same?

Here I have 500 plus 180 plus 15.

Now will that equal 695?

Well I know that if I add 500 plus 100, I do get 600.

And now if I have 80 plus 10 I do get 90.

Now all that's left is my 1's and there are 5 of them.

So yes, it did show that both of those expanded forms did actually represent the same value.

Now its your turn to play Card Sort with Value Pak.

Don't forget all of that learning we did today to help you with this game.

Nice job, boys and girls, we had a great time today showing how we can actually represent numbers in different ways.

I can't wait for our next episode of Math Mights, but until then, bye!

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