The Paper Clip Odyssey

 How far will a child go with a box of paper clips and an imagination?  The answer: Pretty far!  I was amazed that something as simple as a paper clip kept the interest of two children for over an hour!
 Saturday, November 24th, 2001, I had the privilege of teaching two children the basics of informal measurement.  And, I call this a privilege because not everybody has the chance to spend some quality time actually observing how children learn, through actions, words, and even each other.
 My adventure in teaching started Wednesday afternoon.  When first given this assignment, I was not sure who I would teach my lesson to, but after thinking about it for a while I knew exactly who I could teach my lesson to!  So, I marched around the block from my house, and I asked my neighbor if I could "borrow" her children and teach them a math lesson.  She immediately agreed to this, and she knew the children would be excited!  They are always looking for reasons to come over to my house, and this time, they already had one!  Anyway, we decided I would get no math action out of them that day, but we agreed Saturday would be perfect!  So, as the children came running out of the house to see me, I explained to them we would be doing a little math lesson together on Saturday, and I asked if that was okay.  They both jumped at the opportunity, and they were looking forward to it!  So, I set out to plan my lesson.
 Saturday morning came, and I set up my lesson.  Of course, I already had the plan written up, but I had to set up the materials, and have some sort of outline as to how I wanted things to go.
 The first activity I was going to have the children do was measuring their feet, and then additional body parts, with paper clips!  I set the paper clips out on the table, along with two index cards, the charts for them to fill in their information on, two pencils, and chairs for them to sit in.  I also laid out the other materials I needed for the following activity, and set them aside.
 I was all set for the children to come over, but I was a little nervous.  I was not sure how things would go because I am so used to being their neighbor, and their sister's friend, but not their teacher!  I figured I would talk to them like I usually do, ask them questions and just explain what it is they are helping me with, and then things would fall into place.
 Sure enough, about 10 minutes later, I heard two sets of footsteps running up the stairs!  The children knocked on the door, with their coats already flying off, and we greeted each other with smiles and "hellos."  I was glad to see them so motivated and anxious to get started, it was a relief.  Even though I knew they were excited to help out, I was still a little afraid they would not be as motivated or anxious as I had hoped.  But, I had nothing to worry about.  We were all ready to get started!
 To get started, I first explained that we were going to be doing a little measuring around the house.  They were really excited, and they told me how they help their mom measure things at their house.  So, I asked them if they knew what tools we normally use in order to measure things.  Immediately, they both said a ruler.  I encouraged them, and we took it a step further.  I asked them if they knew how people normally find out how big their foot is in order to buy shoes.  Mara spoke up, and she described the "metal thing with numbers on it, and it slides to where your toes are on it."  Though she had trouble getting her words out because she was excited to answer my question, I knew what she meant!  So, I came to the conclusion that we were ready to start the lesson.
 Through my lesson, I decided, though I knew I'd be observing many things, to come up with one main focus of my lesson, to keep in the back of my mind.  I was curious to see if the children would round the number of paper clips (and later on other measuring objects) they used to measure with, or if they would tell me the measurements in halves, quarters, and so on.  I did not put this in my lesson because I thought of it last minute, but I was really interested to see how they would handle when their objects did not measure exact.  So, the lesson began!
 The children looked at their worksheets I had set out at their seats, and first thing, they both put their names on the top.  I also had them put their grades on the top of the activity sheets.  Ryan, a second grader, and his sister Mara, a fourth grader, listened diligently as I explained what we were going to do.  I told them we were going to measure our feet using paper clips!  They looked at me with the biggest eyes, with an expression of astonishment!  Who measures their feet with paper clips?!
 So, they took off their shoes, and listened for other instructions.  I told them that they had to guess how many paper clips their foot was, and then actually measure it with the paper clips.  The shoes were off and the paper clips out!  Ryan guessed his foot would be four paper clips, and Mara guessed hers would be 5.  Ryan figured Mara's would be bigger than his because she is older, was he right?
 Well, Mara and Ryan set out to measure their left feet!  I was surprised at what I noticed about the way they both decided to measure.  Both children, without discussing it with each other first, hooked the estimated amount of paper clips together, measured, and then subtracted or added the number they needed to get the actual measurement.  I was impressed.  I was measuring my foot along with them (a little out of their way so they would not try and model me) and I attached each single paper clip until I reached my actual measurement.  It turns out, their way was actually less time consuming.  They usually only had to add or subtract a couple,  where I had to keep adding and adding to reach my measurement.  I was really surprised they thought to hook their paper clips together first.  I guess you never stop learning!
 After the children measured their foot, (Ryan's was eight paper clips, and Mara's was 9) I asked if they thought their right foot would be the same.  They both said yes, and justified it with the fact that their shoes would not fit their feet if they were different sizes!  Just to be sure though, they both measured their right feet, and came to the conclusion that they were the same size!
 Now, in just this one activity I noticed some things, besides the linking of the paper clips!  I noticed that Mara wrote her data in a complete sentence, where as Ryan wrote his in just numbers.  I think Mara was used to writing in sentences from school, and Ryan was just concentrating on writing his numbers, because that is what he knows how to do.
 In addition, I noticed that both Mara and Ryan rounded to the nearest whole paper clip.  They both ended up with whole numbers, when, in actuality, they both had only used a portion of their last paper clip.  Will this trend continue on?  I was able to find out in additional activities.
 Next, I had the children measure their body parts.  I gave them a chart with specified body parts to measure, and they did.  Again, they estimated their guess, linked the paper clips, and then added and subtracted how many they needed.
 While they were doing this activity, they noticed their estimations were getting closer, and even exact, to their actual measurements as they got nearer to the end of the chart.  I asked them why they thought this was happening, and Ryan said it was because the body parts they were measuring were smaller than the ones in the beginning of the chart, therefore, it was easier to see how many paper clips would be needed to reach the actual measurement.  Again, I was impressed with his answer.  I figured Mara would get it, but seeing as Ryan is only in second grade, I was not sure if he would understand my point, but he did!  This was definitely a confidence booster for me!
 Now that they had completed that activity, I allowed them to pick from a variety of objects to use as their measuring devices, and they got to choose five household objects to measure.  I let them do this completely on their own, just to see exactly how much they really understood (in my lesson, this is my for of assessment, and an additional assignment for homework).  Mara chose to use Q-Tips as her measuring device, and Ryan stuck with the paper clips.  I think he did this because he was comfortable with the paper clips.  I didn't ask him, but I was wondering if he stayed with the paper clips because he was afraid changing his measuring object would change the way the activity worked. Anyway, the two set off on a household adventure, and the discovered quite a bit!
 Mara, still writing all of her answers in words, chose to measure fairly small objects with her Q-Tips.  She measured candles, a camera, and the height of the television.  Now, she did discover that certain objects were needed "halves" and "quarters" added to their measurements, so she broke the Q-Tips in half and measured that way.  I think it was easier for her to see this with the paper clips because they were bigger than the paper clips she used before.  She wrote the actual fraction on her paper, and she then realized she could use ‘halves" in her estimated measurements too!
 As for Ryan, he took a more challenging route.  He decided to measure the height of a living room chair, the length of the curved brim of his hat, and a credit card!  When he first started out with the credit card, it was easy for him because it was small, but the jump he made to the chair, now that was interesting!
 Ryan decided to measure the height of the chair, but thought he had to go all the way up, over the cushion, and to the back of the chair.  So, I sat with him for a minute and we looked at the chair.  I explained he could measure the chair that way, but I asked him if he could see an easier way to measure the chair from top to bottom.  He looked for a minute and realized he could measure the back, flat part of the chair from top to bottom.  And so he did!  But, he had reached another problem.  He guessed the chair would be 100 paper clips tall, and he did not want to string all 100 clips!  So, I asked him how else he could string the clips.  He thought about it, but he was not sure.  So, I offered him a little suggestion.  I told him he could start with a smaller number of clips, and add more if he needed to.  He thought that was a great idea, and he wondered why he did not think of that!  So, that is what he did!  And the journey continued for the both of them!
 As I was watching both children, I noticed they were both basing their estimated guesses on how big their measuring objects were.  They both measured those with their fingers and then held their fingers up to the object being measured and guessed that way.  That is how they were making their estimates.
 After they had finished measuring their objects, I asked the children to glue the amount of paper clips or Q-Tips it took for them to measure each object to paper.  So, Mara glued all of her Q-Tips to a piece of paper, writing the measurement next to the Q-Tips, and Ryan did the same.  He had a little trouble understanding what to do, so he looked to Mara's paper for some assistance, and then he got the idea.  They both glued their objects, and then handed me their papers!  They were finished with their math lesson, and so was I!
 I talked ot them for a minute about what they learned, and mara said that she learned she couldmeasure wiht anything,as long as she kept it the measuring device the same size the whole time.  Ryan said he learneded that there are easier ways tomeasure a chair!  I smiled and wrapped upmy lesson.  I explained that Mara was right, as long as the same sized object was used, that could be the unit of measurement.  I asked if they thought this was a good way to use all the time, and Mara said no.  Ryan joined in and said he would not want to go to the shoe store and measure his foot with paper clips every time he needed shoes!  I agreed it was not always the most convenient way to measure things, but it was good to know!
 So, they both put their shoes on, and I brought out their candy tin that I leave for them while I am at school.  They took a few extra pieces because they worked so hard!  They thanked me, and I thanked them for helping me out.  They said any time I needed their help they would love to come over!  I smiled as they walked down the stairs, and then I reflected on my lesson.
 All in all, my lesson was a success.  They understood and applied what they learned to everyday activities and objects, as well as relating the lesson to measuring with actual rulers.  I kept hearing Mara say inches and centimeters while she was measuring, so I knew she understood the difference between sizes of inches and centimeters.
 I also liked how the two worked together.  If either of them needed help with something, the other one was always there to offer assistance.  They did not do the same work as each other, and they knew that just because they had different objects, the concept was still the same, and they could help each other out.  At first, like mentioned, I was afraid Ryan didn't think the concept was the same if he was using an object other than paper clips to measure with, but after watching him more closely, I think he just wanted to use the paper clips!
 At the end, Mara told me she thought her objects would have higher measurements than what they did, but she soon realized it was because the Q-Tips were so big, her measurements were smaller.  She knew her estimates were not exact, and, at one point, Ryan said he got a smaller measurement than Mara, and they measured the same object.  I stepped in and explained that is because measurement is never exact, it is always a pretty close measurement, but sometimes people measure a bit differently, causing the numbers to be different.
 I asked if they had any questions, and neither of them did.  At first I was a little concerned, but I realized we had been asking each other questions throughout the activities, so then I was not as worried!
 I am glad I had this experience.  It was fun teaching a lesson I had planned.  Though I had done so at Lime Hollow, this one was actually with children I knew, I was by myself, and I only had the one shot at it!  But, my feelings are still the same: I absolutely love teaching children!