WEBVTT 00:00:00.046 --> 00:00:07.776 [Music] Welcome to Teaching Fractions in Grade 2. 00:00:09.066 --> 00:00:10.046 My name is Kathy Lembo. 00:00:10.046 --> 00:00:11.526 I am teaching second grade 00:00:11.526 --> 00:00:13.766 at Worthington Hooker School in New Haven, Connecticut. 00:00:13.766 --> 00:00:19.086 Second graders are introduced to fractions toward the end of the year. 00:00:19.236 --> 00:00:23.636 We move into multiplication first, and we cover twos, fives, and tens. 00:00:24.076 --> 00:00:27.836 We sequence, we break numbers apart, and so forth, and then we go into fractions 00:00:27.836 --> 00:00:30.746 for a very short period of time-- couple weeks, basically. 00:00:31.436 --> 00:00:33.686 They do add the numerators; 00:00:33.996 --> 00:00:36.296 they add some fractions with the same denominator. 00:00:36.666 --> 00:00:40.156 By the time they get to third grade, they will be adding 00:00:40.156 --> 00:00:45.536 and subtracting larger fractions with more value to the fractions, 00:00:45.536 --> 00:00:48.526 instead of a half, a fourth, so forth-- the easier ones-- a third. 00:00:49.106 --> 00:00:51.536 And they will get into decimals a little bit more, 00:00:51.596 --> 00:00:54.506 and they will represent the decimal equivalent 00:00:54.506 --> 00:00:55.866 to the fraction a little bit more than we were. 00:00:55.866 --> 00:00:57.296 We are just touching upon fractions. 00:00:57.296 --> 00:01:00.566 But a population like this, you have to expand a little bit. 00:01:00.566 --> 00:01:04.715 It's year's end, we have basically completed the curriculum. 00:01:04.715 --> 00:01:09.576 So at this point we are reviewing, and we zeroed in on fractions yesterday. 00:01:09.986 --> 00:01:14.446 What I had asked the kids to do was to define, just to explain the concept 00:01:14.446 --> 00:01:18.666 of fraction, and also to represent a fraction. 00:01:18.666 --> 00:01:22.416 We started with halves, we moved into fourths to represent a fraction 00:01:22.416 --> 00:01:25.626 in different ways, and we used life skills situations. 00:01:26.006 --> 00:01:30.396 For example, we talked about purchasing something on sale and we turn a half 00:01:30.396 --> 00:01:36.106 into 50 percent, what is 50 percent of $200, $300, and so forth. 00:01:37.686 --> 00:01:39.296 We moved into percentages. 00:01:39.296 --> 00:01:41.156 We moved into currency. 00:01:41.156 --> 00:01:45.646 We represented a half with 50 cents written with the cent sign. 00:01:45.646 --> 00:01:46.926 We used decimals. 00:01:47.246 --> 00:01:50.196 We were asking for representation in many different ways. 00:01:50.196 --> 00:01:52.466 That's what we do with mathematics. 00:01:52.466 --> 00:01:53.756 We look for perspectives. 00:01:53.756 --> 00:01:56.106 We look to problem solve from many different points of view. 00:01:58.156 --> 00:02:03.666 They were also given a handout, and in front of them they saw number strips. 00:02:04.126 --> 00:02:06.266 And one was presented as a whole, 00:02:06.266 --> 00:02:08.916 one was cut in half, one was cut into thirds. 00:02:09.316 --> 00:02:14.296 And they had to determine that all the strips were of the same length, 00:02:14.356 --> 00:02:17.996 and they also took a look at three-quarters and two- thirds, 00:02:18.226 --> 00:02:22.046 for example, and they had to tell which was longer. 00:02:22.396 --> 00:02:26.006 And they had to hold their finger at the end or use another piece of paper 00:02:26.006 --> 00:02:28.516 to determine, "Oh gee, this one's a little bit longer than the other," 00:02:28.516 --> 00:02:31.326 even though the numerator was so close to the denominator, 00:02:31.636 --> 00:02:33.866 one had more length than the other one. 00:02:33.866 --> 00:02:39.406 And in regard to area, the kids had graph paper in front of them, 00:02:39.406 --> 00:02:45.976 and I was asking them to show me four squares, and to show me one out of four, 00:02:45.976 --> 00:02:48.916 two out of four, and so forth, shaded or unshaded. 00:02:49.496 --> 00:02:52.046 We moved into other fractional amounts. 00:02:52.046 --> 00:02:58.786 I also asked the kids to show me the same area using eighths and sixteenths, 00:02:59.066 --> 00:03:02.356 so some of the kids at that point would cut one of the squares 00:03:02.356 --> 00:03:05.726 on the graph paper in half or into four parts. 00:03:06.126 --> 00:03:08.746 That wasn't something that everybody in the room could do, 00:03:08.746 --> 00:03:11.716 but it was fun for the kids to turn to their peers and say, 00:03:11.716 --> 00:03:13.236 "Let me explain this to you." 00:03:13.236 --> 00:03:17.026 I think they learn best from each other, so it's just an extension. 00:03:17.026 --> 00:03:20.086 Some of the kids in the room would really need to work 00:03:20.086 --> 00:03:24.376 with me separately later on, and that's where I model and then bring 00:03:24.376 --> 00:03:26.346 in the peers later on with the manipulatives. 00:03:26.346 --> 00:03:33.616 Through this review we attempted to revisit the concept of fractions. 00:03:34.036 --> 00:03:35.046 We used rulers. 00:03:35.046 --> 00:03:36.216 We used handouts. 00:03:36.566 --> 00:03:39.916 We used clocks, yardsticks. 00:03:39.916 --> 00:03:41.756 We also used Unifix cubes. 00:03:42.136 --> 00:03:46.766 The kids turned to each other and asked that they separate the cubes. 00:03:47.196 --> 00:03:50.336 For example, one child would ask, "Would you place three-tenths"-- 00:03:50.396 --> 00:03:53.566 they were given ten cubes-- "would you place three-tenths at the top 00:03:53.566 --> 00:03:55.716 of the desk and stand up seven- tenths?" 00:03:55.896 --> 00:03:59.606 We used any medium we could find in the room-- anything around us at the time-- 00:03:59.606 --> 00:04:04.216 just to discuss the concept of fractions from many different perspectives. 00:04:04.566 --> 00:04:11.176 At the end of the lesson, I stood before them with a play clock and yardstick, 00:04:11.176 --> 00:04:14.076 and I asked, "What do these things have to do with fractions?" 00:04:14.506 --> 00:04:19.156 And the kids jumped right into, "Oh, quarter after, half past, 00:04:19.156 --> 00:04:21.526 quarter of, o'clock, 60 minutes." 00:04:21.716 --> 00:04:25.116 We are breaking them into 15-minute sections. 00:04:25.516 --> 00:04:29.116 Oh yeah, the ruler, well, let's see: from zero to one if we are looking 00:04:29.116 --> 00:04:33.206 at the yardstick and we are thinking linear, there are 16 little sections 00:04:33.206 --> 00:04:35.596 between the zero and one, for example. 00:04:35.596 --> 00:04:39.226 They also have a little metric ruler in front of them in the paper form. 00:04:39.226 --> 00:04:42.696 And they noticed that, again, they were thinking, "Oh, we are talking tenths, 00:04:42.696 --> 00:04:44.466 hundredths here, we are not talking twelfths, 00:04:44.466 --> 00:04:45.826 twenty-fourths, thirty-sixths." 00:04:46.106 --> 00:04:51.206 And these from the zero to the one, we seemed to be separating in half, 00:04:51.366 --> 00:04:52.876 maybe quarters, that's about it-- 00:04:52.926 --> 00:04:55.586 separated a little differently on the linear side. 00:04:55.586 --> 00:04:59.496 These skills are important to all of us as human beings. 00:04:59.496 --> 00:05:02.696 I think we live with-- everything is fractional when you think about it. 00:05:03.126 --> 00:05:07.036 We don't need to talk about squares, for example, on graph paper. 00:05:07.036 --> 00:05:11.386 We can be talking about human beings-- as equal human beings-- 00:05:11.386 --> 00:05:14.336 even though we don't all look the same, we are 24 in number 00:05:14.336 --> 00:05:16.036 and we are in four groups of six. 00:05:16.786 --> 00:05:20.216 The concept of a part, or a piece especially, an equal part, 00:05:20.216 --> 00:05:22.216 comes up in every part of the curriculum, 00:05:22.216 --> 00:05:26.556 especially when we are counting money, graphing, making tables and so forth, 00:05:26.556 --> 00:05:28.716 the fraction always comes up. 00:05:29.066 --> 00:05:33.046 To determine whether a child really understands a given concept, 00:05:33.266 --> 00:05:39.006 we usually ask that the child explain a solution for many different points 00:05:39.006 --> 00:05:42.806 of view, and by that I mean the child could verbalize, 00:05:42.806 --> 00:05:48.026 the child can enact something, present something to the class, write about it. 00:05:48.296 --> 00:05:50.636 There are so many different ways, and that's what we are expecting 00:05:50.636 --> 00:05:52.786 and we also base lot of things on speed: 00:05:52.786 --> 00:05:55.726 How would you do that many different ways? 00:05:55.726 --> 00:05:58.316 How quickly can you tell the class, "Oh, I would do it this way, 00:05:58.316 --> 00:05:59.446 that way, and the other way"? 00:05:59.736 --> 00:06:03.306 We are not looking for one solution to any problem. 00:06:03.996 --> 00:06:07.626 At year's end, I have at least attempted, and was successful 00:06:07.626 --> 00:06:11.566 in some degree, to empower them with the strategies 00:06:11.566 --> 00:06:12.976 that they can use to problem solve. 00:06:14.046 --> 00:06:18.186 To learn more about teaching fractions, please see the additional materials 00:06:18.186 --> 00:06:21.806 on the Doing What Works website.