Line Plots & Benchmarks: A resource guide for plotting benchmark fractions.
Tapping on Prior Knowledge: I asked students how we plot data so that it is easier to read? I had put my graph samples in a large manilla envelope.(See resources from A Graph Party: Looking at different graphs and writing about them.) I offered the envelope to a student and asked her to pull one of the samples out. She pulled out a bar graph. We discussed how common they are and that they compare data very easily and are visually great to use. She held up her choie so we could discuss the title and labels and talk about how important these components are. I had another student draw out another graph. This time it was a pictograph. Students immediately shouted out what it was. It was important to keep drawing out different graphs and talking about each one so that students would grasp the concept that line plots are also ways of graphing comparisons. We finished our discussion by looking at pie charts and line graphs, talking about the meaning and purpose of each.
I asked if they knew any other way of graphing data and comparing data? It got silent, so I turned to the white board and drew a line plot numbering it 0-4 and placing x's randomly along the line. One student shouted, "Line plot.!" I took a survey with hands to see how many students had heard of a line plot. There were more hands down than up. This standard from third grade needed to be mastered first before we could move on to mastering adding and subtracting fractions using a line plot! ( I address this further in my reflection.)
Create a Line Plot Together: I titled my line plot: Dogs Owned. I continued by asking what they thought the x's stood for? Could we tell from my graph? I asked this in my questioning to get them to think about prior knowledge that all graphs need labels and possibly a key. One student offered up that the x's stood for the dogs.
To reinforce their thinking more deeply, asked what the 0-4 stood for? Another student suggested that the 0-4 stood for houses. But then, he realized that you can't really have 0 houses and have a dog. I asked: How many of you have no dog's at home? I drew a key and labeled x= 1 dog. I should have re- written, x= students who own dogs.
I re-wrote the title: Dogs in Mrs. K's 4th Grade. Four stood up as I was writing and I placed the x's on the 0 on the line plot. I asked a student from the "no dog" group to come up and plot x's for me as I continued: How many have one dog? ( and so forth until we got to four. I asked if there were any people who had more than four?) Suddenly they could see what a line plot was about because we talked about comparing. We talked about how one half of the class had one dog and almost half had none. Only two people had 3 & 4 dogs.
Connection to Rulers: I asked them if they knew that a ruler was a number line? I asked them to get out their rulers and take a look. I brought up the SB file with a numberline drawn with benchmark fractions and substituted the data of our dogs to the ruler labeling the x=1 dog. I placed 11 x's on 1/2 mark symbolizing that about 1/2 of the class had 1 dog each. I explained that we had to note the amount of people in the whole class to give the reader an understanding of how many were in the whole. I explained that this was showing a part to a whole 1/2 of 21 is, and therefore making a comparison. Next, I talked about how a ruler is divided into fractions and that there were benchmark fractions that helped us as markers. I gave an example that if we were actually measuring objects to make a set of data.
I turned to the third page of the SB file revealing the ruler. I labeled the ruler with the benchmark fractions. I explained that a line plot could be used another way to show benchmark fractions. Connection to Rounding: They were not able to reason that the benchmark meant that it was a guidepost or marker. So I had to tell them. I knew it was important at this point to show them why. I wrote 2 5/8 on the board next to the ruler. I asked what benchmark fraction would be the closest? They all said 2 3/4. I told them it was sort of like rounding in this case. I told them that eventually, they will be able to visualize what one half or three quarters looks like in our mind's eye. These visual benchmarks are used in every day life.
Making the Transfer: I explained that the line plot could also be used to plot measurement data. We charted the data about leaf measurements together to work on satisfying the standard.
I decided to reinforce the third grade standard based on my understanding of my students, and had some students watch a Learnzillion Lesson to review how to make a line plot on their iPads, while I instructed other students who I thought probably had mastered understanding in our warm up, about measuring and plotting fractions on a line plot.
Students were given a large cup full of old crayons from my "dejected and lost crayon box" and the work sheet, Introduction to Creating a Line Plot Using Benchmark Fractions. I got this group of students started by showing an example of how to measure the crayon, figure out the closest benchmark and plotting on the line plot after they entered it in the chart. By the time students were finished with their video, the other students were busy measuring crayons and plotting their chart and line plot.
The students who watched the video joined me at the back table for a review of what they just saw. We worked together to create a line plot using a worksheet from American System - Line Plot Worsheets from www.commoncoresheets.com/LinePlots.php. We discussed how to make benchmark fractions on their little paper rulers that are included in the resource. I chose to use the flash drive worksheet because I liked it. It's relevant. They used the paper rulers to measure each one and we plotted the charts together. Then, I noticed one student Lining up tools to compare. He realized that he could see how the lines in the regular ruler worked through lining up the paper one with his ruler. It was awesome to see him think like that! When I thought they had a grasp on the plotting, I got up and roved the classroom to see the progress with other students.
One common mistake I could see was that if students had two crayons measuring the same, they thought they didn't need to plot it. They didn't understand the concept of the set. One more student thought that a crayon was 4 and 4/4". He realized that he didn't start at zero but started at one.
Students plotted and finished quickly. I checked their sheets and sent those who finished early and correctly out to help anyone who was struggling.
I asked students to stop and talk about any 'aha" moments they had. One girl spoke up about how she finally learned to measure using a ruler. She said the benchmark fractions and drawing it on the paper ruler helped her. Writing the benchmarks on the tool: The boy who realized that he needed to start measuring from zero talked about having to adjust his chart and fix his line plot. He said that the clue was when I said, " I haven't ever seen a 4 inch long crayon before. Are you sure you are right?"
I asked, "can any of you describe a benchmark fraction in your own words?" One of the boys said: "Benchmark fractions are markers to help you see the fraction in your mind." I was pleased that he realized that he could envision the fraction. I hope this conceptual understanding of benchmark fractions continues to help them envision parts to a whole better.
Finally, I concluded; "Well, with that remark, I guess you understand how a benchmark fraction works and that it can be used just like whole numbers are on a line plot." I had them stick their hands out, reach around and pat themselves on the back and say " Good job, Me!"
I assigned IXL.com Level F J.6 and J.7 Each student had to do 20 or more problems from each section. If one section was mastered, they could move onto the next section. For advanced students, I moved them up to Level G S.10 or S.11.