(soft music) - [Kids] Math Mights!

- Well, hello there, third graders.

My name is Mrs. Ignagni, and I am ready for an exciting episode of Math Mights.

Are you?

Let's take a look at our plan for today.

First, we are gonna get our brains ready with a mystery math mistake.

Then we are gonna take a close look at the traditional algorithm to add within 1,000.

That is a jam-packed show, but first, what's happened to our friends in Mathville?

Oh no, boys and girls, all of our friends have their strategies mixed up.

In fact, is that T-Pops holding D.C.'s mallet?

Here is how it works.

What's gonna happen is one of our math friends is going to share with us a problem that they are having a difficult time solving.

It is our job to look closely at that problem, like little detectives, and see if we can figure out where they went wrong, and then help them to solve it correctly.

It looks like Value Pak is all upside down, and needs our help.

Value Pak is trying to add 245 plus 362, but looking at some of that math, let's take a closer look at what Value Pak did.

If I have 245 plus 362, Value Pak told me that they decomposed this number by place value, and got 200, 40, and five.

Then using that same strategy, decomposed our second addend by place value, and we've got 362, breaking that into 300, 60, and two.

Then using the strategy of partial sums, adding those together, we have 200 and 300, Value Pak got 500.

40, and 60, 100, and then looking at our five and our two, got seven.

Adding those all together, Value Pak got 670.

Hm, boys and girls.

What do you think about that?

Could you find a mystery math mistake in the way that Value Pak solved that problem?

Let's see if the girls see anything wrong with this.

Sunshine said, it looks like Value Pak decomposed both addends by place value correctly, but something doesn't seem right.

Looking closely at the work that Value Pak did, I do see how this is correct.

200, 40, five, and then I have 300, 60, and two equals my 362.

So I agree with Sunshine.

Value Pak did decompose both of those addends correctly, but something still doesn't look right.

Let's see what Mirah has to say about it.

Mirah said Value Pak added incorrectly.

500 plus 100 plus seven equals 607, not 670.

Looking at our addition over here, I brought that down, and she's right.

500 plus 100 plus seven does not equal 670.

This actually equals 607.

Excellent work, third graders.

I know that Value Pak would be thrilled with the way you used their strategy to solve that equation.

And remember, when you are decomposing by place value, it's very important that you pay close attention to those numbers, so you're using the correct place values.

Let's take a look at our I Can statement of the day, I can use the traditional algorithm in more than one way to add within 1,000.

Hm, when I see that word traditional, that actually makes me think of the oldest citizen in our Mathville, T-Pops.

(soft music) T-Pops, our oldest citizen in Mathville, carries a cane, wears glasses, is balding, and wears these cute little bunny slippers.

Now T-Pops used to believe that his traditional method was the way to go.

But when he started spending all of his time with those new age characters in Mathville, we realized that maybe those strategies are better to learn first before working with his strategy.

Let's see what T-Pops has in store for us today.

How can we solve 362 plus 354?

Taking a look at the boys' strategies, they each solved it a different way.

Tyler used base 10 blocks.

Lin used some non-proportional counters, and then Hans went ahead, and used T-Pop's traditional method.

Let's go ahead and take a closer look at each one of these boys' method, starting with Tyler's.

You may remember these base 10 blocks from second grade.

So if we have our two addends counted out, we have our 362 and our 354.

I'm gonna go ahead and add my ones.

If I have four, five, and six, and then counting my 10s, I have 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, I'm actually gonna pause there for a second, third graders, because I'm going to exchange those 10 10s to bring in a 100 block.

So I'm gonna go ahead and rename these with my 100 block.

So now I know that I have one 10 listed there, and I can now add my 100 blocks together.

I have 100, 200, 300, 400, 500, 600, 700.

So putting this all together, I know that I have 716 as the answer to that problem, just like Tyler showed.

Tyler gave us an excellent example of how he would have completed that problem, and now let's take a look at what Lin decided to do.

What do you think, boys and girls, have you ever seen those disks before?

It might be something that you used in second grade too, but having that out here, I have Lin's non-proportional discs, and I actually showed the difference with Tyler's way.

Now with the base 10 blocks, each one of those squares actually equals one, so that it's a proportional tool that you're using.

However, with Lin's tool, he's using a non-proportional tool.

What that means is that his disks all look the same, but you have to pay close attention to what is written on them, because their values are different.

And that's the difference between proportional tools versus non-proportional tools.

So taking a closer look at the non-proportional tool that Lin used, I still see that my equation is still the same, I still have my 362 plus my 354, but you'll notice that using those non-proportional tools actually makes for a more efficient cleaner look, and is easier to maneuver.

So adding this together, I still start with my ones, my two and my four equals six, and then counting up my 10s, I have 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Again, I'm gonna stop there, boys and girls, and I'm actually gonna take those 10 10s, and regroup, and rename them 100.

So I'm gonna go ahead, and pull those away, and I am going to go ahead and add my 100, and then I have my one 10 left.

So now counting up those 100s, I have 100, 200, 300, 400, 500, 600, 700, to make, again, that total 716.

So boys and girls, you can see that even though Lin used a different tool than Tyler, they still actually came up with the same correct answer.

And it just goes to show, third graders, how you're able to use different strategies to come up with the same answer for those math problems.

But let's take a closer look at Han's strategy, because this might not look as familiar to you.

So for Han's way, he did a show all approach, which really emphasizes, and shows that you understand the value of each one of those places.

Let's take a look.

Looking at Han's way with his show all totals, using our place value, we're gonna go ahead and start in our ones with two plus four equaling six.

Now the next step is pretty critical, third graders, because sometimes in my class, my third graders do this wrong.

They take a look at six plus five, and they just say that it's 11, but when we're actually using this strategy correctly, we don't, we're not actually dealing with six plus five.

We're dealing with 60 plus 50, which is actually 110.

So if we have six 10s plus five 10s, it's actually gonna be 11 10s.

So incorrect there.

And we're gonna go ahead and show that we have 11 10s, or 110.

Now we can't stop there, because we still have our 100s to add.

And again, looking here, kids might say three plus three equals six, but when we're looking at place value, and representing it accurately, it's not three plus three equals six, it's 300 plus 300 equals 600.

So I'm gonna go ahead and write that down.

Now it's time to add all of these place values together, and we have six in our ones, we have our 10, and then we have 700.

Our correct answer then, Han has showed us, is 716.

This is so interesting, boys and girls.

Are you understanding all of these different strategies?

I hope you are, because you definitely want to cement these strategies down before you move to T-Pop's traditional method.

Let's have some more fun working with these different strategies.

Taking a look at the problem that T-Pops wants us to solve today, 475 plus 231, he wants us to use his T-Pop's place value mat.

With the T-Pops place value mat, you'll see that we have it set up, so not only can we use our counters, but we also have space here to write out our problem.

Now, when we're putting our non-proportional counters on there, sometimes I'll have students that want to label each one of those columns to keep it in order.

So for example, they'll want to say ones, 10s, and 100s.

However, that actually is not a very accurate way to use this chart, because if you look here, if I have these two 10s, it's actually showing 20 10s, which isn't correct.

Now with some of our beginner maths.

I know that T-Pops understands if you need those labels, but as we're working our way through third grade, our hope is that you don't have to use those labels anymore.

Now that my mat is ready to go, first, I'm gonna go ahead and set up that first addend.

So I have four 100s, then I'm gonna go ahead and place on my mat, four hundreds.

Next, I see that I have seven 10s.

So I'm gonna go ahead and fill up, and place out my seven 10s, or 70.

And then finally, looking at my ones, I see in this number, I need five ones.

Now, once I have this complete with my first addend, I like to go ahead and grab my second addend of 231, and sort of put it down here at the bottom where I can sort of stack them like coins, so that I can show how I'm actually going to be adding those up onto the original addend that I have up there.

So looking at my five ones, if I want to add a one, I'm gonna go ahead and add that there.

And now I have six, five plus one is six.

Having my three 10s down here, I need to go ahead and add that to my seven 10s.

So I'm gonna pop them on my place value chart, and look at that.

If we have 10 10s, boys and girls, we know that we can actually rename that whole group, and it actually becomes 100.

So I'm gonna go ahead and I'm gonna clear my 10s, and I'm going to regroup, and I'm going to add my 100 over here to my 100s board.

Now we've made a change on our board, T-Pops always likes to remind us that we need to show that change in our algorithm.

So coming over here, if I have my seven 10s plus my three 10s, that actually gets regrouped into 11 10s.

Now some like to put their regrouping mark at the top.

However, I like to put my regrouping at the bottom, so I don't forget what I've actually done.

I'm actually gonna go ahead, and take that away to show the true value of what I have done.

I actually now, adding those together, have zero 10s, but one 100.

Now it's time to add my 100s together.

Now I'm gonna go ahead, and add my two 100s to my board.

I can easily see that I have 700.

So adding that to my algorithm, I have 706.

That was really great.

I know T-Pops would be so excited that you're using his strategy, even though I know that it can be a little bit tricky.

Now it's your turn to solve addition problems with T-Pops.

Great work, third graders.

We started off our show today working with Value Pak, and figuring out that mystery math mistake.

Then we learned that there is many ways that we can use that traditional algorithm to solve within 1,000.

I had so much fun with you today.

This was an excellent show.

I can't wait for next time, but until then, bye.

(soft music) - [Kid] Sis4teachers.org.

- [Girl] Changing the way you think about math.

- [Narrator] The Michigan Learning Channel is made possible with funding from the Michigan Department of Education, the state of Michigan, and by viewers like you.

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