WEBVTT
00:00:04.046 --> 00:00:06.566
(Bret Mosley): My name is Bret Mosley.
00:00:06.736 --> 00:00:12.996
I am a fifth-grade teacher at Eliza Hart Spalding School of Math and Technology in Boise,
00:00:12.996 --> 00:00:14.826
Idaho, in Meridian School District.
00:00:15.106 --> 00:00:22.236
The lesson today started off with a contextual problem of asking the kids to divide 20
00:00:22.236 --> 00:00:26.606
and one-half by one and three-quarters of an inch.
00:00:26.716 --> 00:00:30.166
The importance of a context problem to me is huge.
00:00:30.316 --> 00:00:33.456
Numbers are numbers to kids, but when you put them
00:00:33.456 --> 00:00:35.736
in the meaning they see them a little bit different.
00:00:36.286 --> 00:00:41.306
And being able to understand what you are asking is huge for kids.
00:00:41.736 --> 00:00:47.096
Putting them in context for kids makes them vested in what they are looking at.
00:00:47.206 --> 00:00:48.946
(Student): Shane and I were playing in the garage,
00:00:48.946 --> 00:00:51.826
and he wanted to be just like Spiderman, big shock.
00:00:52.316 --> 00:00:55.736
He asked if we can make him a web shooter out of the rope that he found.
00:00:56.806 --> 00:01:04.536
To make each web shot, it takes one and three-quarters of an inch of rope and if he found 20
00:01:04.536 --> 00:01:08.346
and a half inches of rope, how many web shots can we make for my Spiderman?
00:01:09.546 --> 00:01:11.026
What is the mathematical sentence?
00:01:11.956 --> 00:01:12.536
Then solve.
00:01:12.896 --> 00:01:17.766
(Mosley): B says once you figure your answer for A, how much rope is left over?
00:01:19.936 --> 00:01:23.566
C says how much more rope is needed to make another web shot?
00:01:25.036 --> 00:01:30.916
And D, which I think might be the most challenging, is what would your mathematical model look
00:01:30.916 --> 00:01:32.616
like for the way you solve the problem.
00:01:32.616 --> 00:01:36.296
(Mosley): We had measuring tapes, yards sticks, or meter sticks.
00:01:36.466 --> 00:01:39.896
We had yarn that was precut at 20 and a half inches.
00:01:39.896 --> 00:01:43.566
They also had Cuisenaire rods, and whatever manipulatives they wanted to use.
00:01:44.346 --> 00:01:46.806
I would recommend that you work out our problem before you give it
00:01:46.806 --> 00:01:49.526
to the students because the numbers are huge.
00:01:49.576 --> 00:01:54.206
I wanted to make numbers that were easy to work with but were also problematic,
00:01:54.206 --> 00:01:57.276
so they had to find the equivalent fractions of halves
00:01:57.276 --> 00:01:59.546
and fourths to be able to solve this problem.
00:02:00.076 --> 00:02:07.136
So making it problematic, but doable, as well as working out the problem to see what kind
00:02:07.136 --> 00:02:12.076
of answers you could get from students, so you are prepared as an educator to be able
00:02:12.076 --> 00:02:14.236
to answer the questions and know where to go.
00:02:14.236 --> 00:02:18.726
(Student): I drew up big long number line from zero to 20 and a half.
00:02:20.316 --> 00:02:24.806
First, I went up to the first one and three-fourths and that would be one.
00:02:24.876 --> 00:02:26.066
Then second, two.
00:02:26.066 --> 00:02:33.466
I just kept doing that continually until I got to 20.
00:02:33.466 --> 00:02:38.096
Right there I could do another one, so that leaves me with a half.
00:02:38.656 --> 00:02:46.206
So my answer was 11 remainder one, remainder one-half,
00:02:47.816 --> 00:02:52.406
but since a half wouldn't count as a shot, it was 11 shots.
00:02:53.176 --> 00:03:00.436
(Mosley): So that top row here represents the total length of string.
00:03:01.206 --> 00:03:04.386
What does the bottom represent in his case?
00:03:04.746 --> 00:03:08.196
What does your bottom numbers represent, the one, the two, the three,
00:03:08.196 --> 00:03:09.946
the four, the five, all the way to 11?
00:03:10.316 --> 00:03:11.226
What does it represent?
00:03:11.226 --> 00:03:11.806
(Student): The shots.
00:03:12.346 --> 00:03:14.296
(Mosley): The number of shots.
00:03:15.446 --> 00:03:20.566
(Student): I got one and three-fourths equals one of the ...
00:03:21.796 --> 00:03:28.126
and if you times that by two, it will equal three and a half.
00:03:28.696 --> 00:03:32.086
And I did the same thing with my three.
00:03:32.086 --> 00:03:40.576
I did 3 x 2 = 6 and then 1/2 x 2 = 1, 6 plus 1 = 7.
00:03:40.576 --> 00:03:48.876
And then I did 7 x 2 = 14, and I kind of tie in to14 again, so that would equal 16,
00:03:49.356 --> 00:03:57.266
and that would equal 28, so I couldn't do 16, so I did 19.
00:03:57.266 --> 00:04:12.206
So I did, so I added 1 3/4 to 14 to equal 15 and 3/4, and I added 1 3/4 to 15 to get 17 1/4,
00:04:12.856 --> 00:04:16.296
and then did the same thing with that and got 19.
00:04:16.416 --> 00:04:18.546
(Mosley): What does that represent?
00:04:18.766 --> 00:04:21.086
(Student): Rope shots.
(Mosley): Okay, web shots.
00:04:21.086 --> 00:04:24.436
So one web shot gives you that.
So what does this represent?
00:04:24.436 --> 00:04:29.566
(Student): How much the length of the rope.
(Mosley): Thank you.
00:04:29.566 --> 00:04:43.086
(Student): I multiplied 1 3/4 x 6 and that got me 10 1/2, so 10 1/2 - 20 1/2 would equal 10.
00:04:44.056 --> 00:04:51.266
So I was thinking that I could do six one more time, but I couldn't because it's a half over,
00:04:51.696 --> 00:05:02.166
so I went down to five, and I multiplied 1 3/4 x 5 and that got me 8 3/4.
00:05:02.906 --> 00:05:08.606
And then 10 - 8 3/4 would be 1 1/4.
00:05:09.886 --> 00:05:17.046
So 6 plus 5 = 11, and 1 1/4 is the remainder.
00:05:17.326 --> 00:05:24.456
(Mosley): I want you to show me your six on your partial quotient is ten and a half.
00:05:24.456 --> 00:05:28.746
Where is that represented in Kyle's?
00:05:29.296 --> 00:05:34.106
(Student): Yeah two-fourths is the same as one-half, two-fourths.
00:05:34.106 --> 00:05:37.036
(Mosley): So what are they?
(Student): Fourths.
00:05:37.286 --> 00:05:38.946
(Mosley): Okay. So they are dealing with fourths.
00:05:39.026 --> 00:05:42.536
(Student): Yeah, but I just put a half because it's the same thing.
00:05:42.536 --> 00:05:48.736
(Mosley): We go up to the board often with usually several different strategies up there,
00:05:49.186 --> 00:05:53.496
so the kids gets comfortable with seeing different strategies and solving it different ways.
00:05:53.496 --> 00:05:57.016
A lot of times I will ask for multiple ways of solving it,
00:05:57.016 --> 00:05:59.956
so it gets them different ways of thinking.
00:05:59.956 --> 00:06:01.726
So they can check their answer.
00:06:01.926 --> 00:06:05.766
They are always asked a couple of questions like "Will it work all the time?"
00:06:05.766 --> 00:06:09.456
because some tricks work every once in a while, but they won't work all the time.
00:06:09.456 --> 00:06:14.306
And that's where multiple strategies come in because a kid could get a wrong answer one place
00:06:14.546 --> 00:06:18.556
and get another answer, but the ability to see different strategies
00:06:18.556 --> 00:06:23.946
and talk through those strategies with their peers is huge because I think kids,
00:06:24.246 --> 00:06:27.226
when they talk about their strategies with other classmates,
00:06:27.746 --> 00:06:31.076
defines their own understanding as well as helps others.
00:06:31.316 --> 00:06:35.426
So those multiple strategies are huge in math.