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ATTENTION

The QUEST Board is now fully functional in Kankakee.

     Jack and I traveled up to Kankakee Monday, February, 25th, to help Helen Dewitt tie up the loose ends on her board in Kennedy Upper Grade school. The trip was very successful. We, with the help of Scott, were able to hook up the modem and communication package. After some diligent work and messing around everything snapped into place. We sent messages to the main board at UIUC and also used the software program Talk is Cheap for a backup, to reach the UIUC boards.

     As of March 1, we have received questions and have already answered them. So, please continue sending them in.

     I certainly hope you will get on the computer and browse around to see all the new things. All you need to do is type NEW were it says Name: answer all the questions and in a few days you will be logged into the system. Then you can send messages to the UIUC Quest board. Helen can do the same thing on the Kankakee Board. She is the system operator (sysop).

     Now our trip to Clarendon Hills. Jack and I also went further north into the suburbs and visited Prospect school. We talked and worked with Carol Haynes and showed her the Quest board. We also found some questions that were sent to the wrong address. Jack and I personally answered the questions (they are printed later in the newsletter). The same goes with the teachers at Prospect. You can either use Carol Haynes logon or type NEW and answer the questions and you too will be updated on the system. Please do this so we can receive many questions. -- TN

     Judy Sohn and I have been continuing our work with big numbers in her first grade class. The children remain very interested, but a few continue not to catch on to the place value system perfectly

     We made orange paper scrolls, based on a third-grade Japanese Association of Mathematical Instruction (AMI) text, to represent a thousand tiles. Each scroll was carefully measured out to be 10 inches wide and 100 inches long. Each one was divided into ten ten-by-ten inch squares, which fit the 100-sheets of tiles we have been adding and subtracting since the first of school. They decided to make 20 scrolls, one for each pupil, and they are all rolled up with a rubber band around them. With the aid of those scrolls, we measured the area of the carpet on which we work, by covering it with unrolled scrolls. It took 16 scrolls, and there was still a little bit of carpet showing, so we stopped at the answer: somewhere between 16,000 and 17,000 inch squares.

     Judy received an astronomy box as a part of the new hands-on science curriculum and I found in The Science Network a list of questions and answers a number for the stars in the Milky Way galaxy, 100,000,000,000. Using a chart, Judy had prepared and put up on the board giving the number of zeroes in each power of ten to a billion, the children figured out different names for this large number. A hundred, thousand, million, a hundred billion, a hundred million thousand, and more. There were just a few off-beat names suggested, like a hundred thousand, four thousand and two! However, most children, working in pairs, could dispense with such names without offense, and stick more closely to the chart, adding up 11 zeroes by making combinations of the various numbers of zeros in the chart.
 

one  ten  hundred  thousand  ten thousand  hundred thousand  million  ten million  hundred million  billion

1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 1,000,000,000

no zeroes  one zero  two zeroes  three zeroes  four zeroes  five zeroes  six zeroes  seven zeroes  eight zeroes  nine zeroes

    As far as treatment of off-beat ideas by the teachers, we tried to get the children who gave them to explain them to the others just as we did with the correct answers. The idea is that whatever it is that leads a child to such answers might mislead others on some occasion, and discovering what is wrong with them is important for many pupils.

     This exercise turned into a useful review of addition facts, ways to make eleven. And, we hope, it will familiarize children with the idea of place value much better than tens and ones, which must seem dumb to children who can count to a hundred without ever thinking of how many tens and ones there are.

     A set of "flash cards" (see figure I ) was prepared and used in the following way: The chosen card was held up and those who had an answer were instructed to raise their hand but say nothing. Then those who could not think of any answer were asked to raise their hands. If there was anyone who didn't know any answer, which was almost always true, one of those who did was asked to explain, reading the exercise out loud and using the scrolls and tiles, if possible, to demonstrate how to work it out.

     Sometimes these demonstrations and the resulting answers were incorrect (e.g., 250 + 250 = 401), but that judgment was left to frequent polls of the entire class with little or no teacher input.

Anyone who was stuck was invited to ask someone else to come up in the center of the carpet and help them. Sometimes, when I was leading, the two people (explainer and chosen helper) got into an argument about the problem, and occasionally the audience then lost interest. It seemed important to keep moving fairly quickly and not to allow anyone to take too long. Talking it over cooperatively in pairs was occasionally helpful. (See article entitled, Dialogue and Conceptual Splatter in Mathematics Classes, by Easley, Taylor and Taylor in the March, 1990, issue of The Arithmetic Teacher, p. 34-37, It gives

two examples of first grade dialogues.) In keeping with all the expert panels on revision of the elementary math curriculum (NCTM, AAAS, NAS, etc), we are not trying to teach one algorithm for each operation, +, -, x, -, but to encourage children to invent their own ways of doing the first 3, at least. Today, one first grader asked what 4 + 40 was? Was it ten? I asked him what 40 + 4 was! Ten, he said. Then I said, what's 2 + 4? -2, he said. I said, "If you had two apples and four people had to share it, how much would each get? 1/2, he said, Not, -2, I said! And he agreed. I'm usually not so directive on +, -, and x, but I felt he could handle being proved wrong -- he's often too gleeful in proving other pupils wrong. --JE

Q1. Why do they call it cottage cheese and what does cottage have to do with cheese?

A1. In early days before machines and electricity, cheese was made by hand and not by specialized equipment. The people would take the milk from the cow and add rennen to curdle the milk, causing the milk to bunch together making curds. The liquid left was the weigh. Remember Little Miss Muffet, she was eating her curds and weigh. She was actually eating cottage cheese. Back to the point, the curds and weigh would then be put into a press. The press was lined with a tightly woven cloth. The liquid could be squeezed through the cloth. The press would be closed and the liquid would be forced out. This leftover liquid would be fed to the young cattle. This was how cheese was made.

     Small unkept or unfinished buildings which were built on the outskirts of town were referred to as "cottages." Similarly cheese that wasn't totally finished got the name cottage cheese. Some other names for this type of cheese are: Dutch cheese, pot cheese, or smearcase,
 
     Cottage has nothing to do with cheese other than this type of chunky, runny cheese (unfinished).

Q2.  How do they keep the water out of the tunnel when they are digging it?

A2. The Channel Tunnel is being dug through a kind of soft rock(chalk Marl) that is ideal for keeping water out. That is, they dig a few feet and put in concrete linings which have been made in advance just to fit inside the tunnel hole. A small hole is drilled ahead of the large tunnel to test for the strength of the rock and hold up long enough to get the linings in. However, there are various techniques that can be used in troublesome spots like that. One of them is to use steel linings that come in various sizes and another is to use shotcrete, a soft liquid concrete that hardens quickly. It is sprayed on the loose rocks as the tunnel is dug. We'll keep looking for more details - -JE

       Making a scale model of the Solar System seems to be an appealing idea, and it has been done before. The pictures in many attractive books about the Solar System give one the impression that the planets are so large that they could be placed close together around the Sun. However, in Miss Henderson's fourth grade class at Bottenfield School in Champaign, we set out to make such a model and encountered a great surprise. We chose a scale of one inch for the diameter of the Earth, so I inch represents 8,000 miles. The diameter of the Sun, then, had to be 109 inches in our model, representing its size of 865,000 miles in diameter, which was quite surprising, since none of the picture books showed these two objects so different in size. Jupiter and Saturn were several inches across, which looked better.

       When we had finished cutting out circles of construction paper for nine planets, the Sun, and the Earth's moon, mounted them on a bulletin board in the classroom, and started working on the rings and satellites of other planets, we finally came to consider where we would mount the solar system for display. Some children figured out that the angle the Sun formed at the Earth was huge, compared with the relatively small size of the Sun in the sky. Someone else knew from library research, that the Sun is 93,000,000 miles from the Earth. On the scale of our models, 1 inch for 8,000 miles, that meant the Earth would have to be 11,600 inches from the Sun, or nearly 1,000 feet. We measured the length of the hall outside the classroom and found it to be 240 feet long. That would not be nearly long enough to have both the Sun and the Earth in it. Taking the other corridor and adding on the community room (lunch room and gym), it still was too short to contain our model Sun and Earth, not to mention all the other planets farther away still.

       Several people in the class said, we had to have two scales: one for sizes and one for distance span. For, if we shrank the models much more, the satellites and Pluto, would become almost invisible. One of our astronomy books gave the distance from the Sun to the planets in terms of the Earth's distance. When we decided Pluto should fit in the same hall as the Sun and other planets, we hit on a suitable scale for distance span. Pluto, 40 times further from the Sun than the Earth, would be 200 feet from the Sun. Neptune was 30 times the Earth’s distance, so it would be 150 feet away. Uranus, 20 times the Earth's distance, would be 100 feet away, and Saturn, 10 times the Earth's distance, would be 50 feet away. Our scale was 5 ft. for the Earth's distance of 92,000,000 miles. It was interesting that these planets came out in such even spacing. " A pattern of halves," the students said.

       However, someone noticed that, on our model, the Earth was barely going to be outside the Sun. It would be even closer than we had had it on the bulletin board. Mercury and Venus would be inside the Sun. Their distances from the center of the Sun were 2/5 of the Earth’s distance or 2 feet, for Mercury, and 3/4 of the Earth's distance or 3 and 3/4 feet for Venus. Mars would be I and 1/2 times the Earth's distance or 7 and a half feet away from the Sun.

       We decided to hang the Sun from the ceiling when we found out that it was too big to put on a wall. The hall had a lower ceiling than the classroom. When we got it put up, with a cardboard ring around it, and lots of string holding it up, the big orange paper Sun blotted out the light in the ceiling, and made the hall darker. "How come it's darker when the Sun is up?" someone wanted to know. The next day someone brought a floodlight to shine on the Sun and brighten up the hall. Then we put the planets along the wall, measuring: carefully from a piece of tape marking the center of the Sun. So Mercury and Venus weren't actually touching the Sun, after all, but sort of under it.

       We learned a lot of things about measurement and scales. We also learned that the Solar system is really big, not shrunken together like the pictures in the books, or in our model. If we had put the Earth outdoors, nearly 1,000 feet from the Sun, then Pluto would have had to be nearly 40,000 feet away. A mile is 5,280 feet long, and dividing that into 40,000 on our calculator, gives 7.5757575 miles. 7 miles is nearly that far, and nobody going to our school lives that far away. So Pluto would have to be farther away from the school where the Sun is than anybody in school lives. And Pluto is only 3/8 inch across on our model. So it could get lost very easily if we put it out on a highway or in some corn field.

How did anybody ever find little Pluto so far away in the sky in the first place?

       Planetary portrait gallery. Voyager 1 celebrated Valentine's Day by taking an unprecedented set of pictures of most of the planets in the solar system. The rectangles represent areas to be photographed by the spacecraft's wide-angle cameras. The images will be made from a position 32 degrees above the ecliptic plane in which the planets orbit the sun. Launched in 1977 Voyager is 'now about 6 billion kilometers from Earth. Figure below (This article is possibly from the latest Science. Feb. 17, 1990, but I don't know for sure).
 

 
Please submit questions or comments by FrEdMail to either:
JEASLEY@UIUCEDE TNEAL@UIUCEDE

either enter them in the QUEST board @UIUCEDII or send them to US by mail to:
CIRCE, 270 EDUCATION
1310 S. SIXTH ST.