Preserving Food by Drying: a Math-Science Teaching Manual (Peace Corps, 1980, 218 p.) Appendices Appendix A. Materials cross-reference list Appendix B. How to make a round hole in a tin Appendix C. Conversions between metric British and American weights and measures Appendix D. Differences between British and American terminology Appendix E. Detecting changes in temperature without a thermometer Appendix E. Making an equal arm balance Appendix G. Making a set of weight's Appendix H. A heating stand made from a tin

Preserving Food by Drying: a Math-Science Teaching Manual (Peace Corps, 1980, 218 p.)

Appendices

Appendix A. Materials cross-reference list

A list of all the equipment and materials needed to do the activities in "Preserving Food by Drying" is presented here. The list is divided into categories intended to assist you in the practical tasks of locating and storing these things. The categories are as follows:

Items used without modification which can be obtained free or purchased locally.

Items cut from a larger piece, or that need to be modified slightly, and which can be obtained free or purchased locally.

Items made from easily available materials that need some effort or skill to build.

Consumable items obtainable locally.

Consumable items obtained from specialized sources.

Equipment obtained from specialized sources.

Available resources.

Colored materials.

Heat sources using fuel.

Where appropriate, the items in a category are divided according to whether or not they require special care in storing. Items in each list are in the order of their first use in the book. Next to each item are listed all of the activities throughout the book where it is needed. By looking through this list, you can see what materials and equipment are frequently needed, what is needed occasionally, and what is needed only once or twice. Thus, you can make decisions about what items to accumulate, what items to borrow when needed, and what activities you may have to modify or omit due to lack of materials or equipment.

Alternatives are suggested for many of the items. Any of the alternatives should work in all of the activities listed for the particular item. Many of the materials can be collected by your students. Involving your students finding materials has value because they learn what materials are available locally, and their resourcefulness and problem solving abilities increase as they learn to substitute other materials for those suggested here. We are anxious to know about any successful materials substitutions you and your students make. Returning PCV's are urged to write Program Designs for Educators at: Chevrons and PDE, P.O. Box 235, Jamaica Plain, Boston, Massachusetts 02130, U.S.A.

Most of the activities do not require tools, but as the students make the transition from learning how dryers work to designing and building them (Activities I-llB and II-2), the importance of having tools suddenly increases. We recommend making your own tools. As part of the framework of this manual, "How to Make Tools" was created by Per Christiansen and Bernard Zubrowski as a companion piece.

Items used without modification which can be obtained free or purchased locally

Items used without modification which can be obtained free or purchased locally (cont’d.)

Items cut from a larger piece, or that need to be modified slightly, and which can be obtained free or purchased locally

Items cut from a larger piece, or that need to be modified slightly, and which can be obtained free or purchased locally (cont’d.)

Items made from easily available materials that require some effort or skill to build

Consumable items obtained locally

Consumable items obtained from specialized sources

Note: Most of these items are likely to be available at pharmacies, hospital laboratories, health centers and secondary schools.

Equipment obtained from specialized sources

Colored materials

Heat sources using fuel

Appendix B. How to make a round hole in a tin

In cases where one wants to insert a tube into a tin tightly so that there is no leakage between the tube and the hole it fits into, it is necessary to make a round hole in the tin. If the hole is large enough to be able to fit the case of a Bic pen into (or a very small hollow bamboo branch) use the following method. First, make a tiny hole with a nail having a length of 5 centimeters. Then enlarge the hole with a 6(1/2) cm nail, followed by a 10 cm nail, and lastly by a 15 cm nail. It is important that these four nails be used in this way. If only the largest nail is used, it will make a square hole because the point of the nail has four sides.

Appendix C. Conversions between metric British and American weights and measures

These conversions have been rounded to produce values that are easy to work with and to remember. However, they are all within 2 percent of the exact values.

LENGTH

Metric	British and American
1 centimeter	= 4/10 inch
1 decimeter	= 4 inches
1 meter	= 40 inches
1 kilometer	= 5/8 mile
British and American	Metric
1 inch	= 2.5 centimeters
1 foot	= 3 decimeters
1 yard	= 9/10 meter
1 mile	= 1.6 kilometer

AREA

Metric	British and American
1 square decimeter	= 15.5 square inches
1 square meter	= 10.8 square feet
1 square meter	= 1.2 square yards
1 hectare	= 2.5 acres
British and American	Metric
1 square inch	= 6.5 square centimeters
1 square foot	= 9.3 square decimeters
1 square yard	= 5/6 square meter
1 acre	= 4/10 hectare

VOLUME

Metric	British	American
100 milliliters	= 3.5 ounces	= 3.4 ounces
500 milliliters	= 17.5 ounces	= 17.0 ounces
1 liter	= 0.88 quart	= 1.06 quart
5 liters	= 1.1 gallons	= 1.3 gallons

British	Metric
1 cubic inch	= 16.4 milliliters
1 ounce	= 28.0 milliliters
5 ounces (1/4 pint)	= 140.0 milliliters
10 ounces (1/2 pint)	= 280.0 milliliters
1 pint (20 ounces)	= 560.0 milliliters
1 quart (40 ounces)	= 1.1 liters
1 gallon (4 quarts)	= 4.5 liters
American	Metric
1 cubic inch	= 16.4 ml
1 ounce	= 30.0 ml
4 ounces (1/2 cup)	= 120.0 ml
8 ounces (1 cup)	= 240.0 ml
1 pint (15 ounces)	= 480.0 ml
1 quart (32 ounces)	= 960.0 ml
1 gallon (4 quarts)	= 3.8 l
Miscellaneous	Metric
1 bottletop (Coca-Cola, etc.)	= 3.5 milliliters
1 usual teaspoon	= 4 to 5 milliliters
1 measuring teaspoon	= 5 milliliters
1 tablespoon, eating	= 8 to 10 milliliters
1 tablespoon, serving	= 14 to 16 milliliters
1 measuring tablespoon	= 15 milliliters

Note: 40 British ounces - 1 British (Imperial) quart, and 32 American ounces = 1 American quart. The unces are almost the same size but this relationship creates a difference of about 20 percent in the else of pints, quarts and gallons between British and American measurement of volume.

WEIGHT

Metric	British and American
10 grams	= 7120 ounce
100 grams	= 3.5 ounces
1 kilogram	= 2.2 pounds
British and American	Metric
1 ounce	= 28 grams
1 pound	= 450 grams
10 pounds	= 4.5 kilograms

Note: The British and American units of weight shown above are the ones in common use, the "Avoirdupois" system, which hoe 16 ounces in a pound. Another system exists in both Britain and America, the "apothecary" or "troy" system. Its pound, which equals about 370 grams, contains 12 ounces. This system is only used in certain specialties.

TEMPERATURE

See page 122 for a conversion chart between the Fahrenheit and Centigrade temperature scales.

Appendix D. Differences between British and American terminology

British English	= American English
Cement	= Glue
Common pins	= Pins or straight pine
Edible oil	= Cooking oil
Muriatic acid	= Hydrochloric acid
Paraffin	= Kerosine, charcoal lighting fluid
Pasteboard	= Cardboard
to revise a lesson	= to review a lesson
Spirit	= Alcohol
Tin	= Can

Appendix E. Detecting changes in temperature without a thermometer

In a number of the activities where an increase of temperature takes place, it can be felt with your hand. These are Activities I-3B, I-4C, I-4C Further Study, I-5A and I-10.

In several other activities, the increases in temperature can be noted the same way, but it would be desirable to improve both measuring skills and understanding of the situations by making a somewhat more quantitative measurement. The approaches suggested here apply to these activities: I-5B, I-7, I-7 Further Study, I-8B, I-llA, I-llB and II-2.

In the Further Study following Activity I-3A, a laboratory thermometer which can measure temperatures up to 100 C is needed. This is a difficult requirement to meet with improvised temperature measuring devices, but perhaps you can invent one or locate an existing design that is easy to make and works well. If you do, please communicate it to the Information Collection and Exchange office. Also, please let us know about your successful or unsuccessful attempts to measure temperature in any of the lessons.

In many industrial applications, temperatures are measured using pieces of material that melt at known temperatures. For example, in Activity I-7, three tiles are placed in the sun. They are all horizontal. One is black, one is earth colored, and the other one is white. On each tile, you could put a piece of margarine and a piece of wax. Whether both of these melt on each tile, and how long it takes could be noted. Maybe in your locality, both of these melt too easily. Can you find another material that melts at a higher temperature?

The following device can measure small and medium changes of temperature.

Figure

The air trapped in the tube expands as the temperature rises. Experiment with the size of the air space. A small air space gives less sensitivity, but a higher temperature can be measured without the water spilling out the end of the tube. The range has an upper limit near the boiling point of water because too much water vapor forms in the air space. Positions along the tube can be marked, or it can be glued to a piece of paper, pasteboard, plastic or wood, and that can be marked.

The following device is useful for measuring relatively small changes in temperature. Air in the body of the pen expands to move the colored water. Air must be free to leave or enter the tip. Water getting in it will impair its operation.

Figure

All connections must be sealed, including the small hole on the side of the pen. When the air is warmed and expands, it pushes the colored water. It must not escape elsewhere. The whole device is sensitive to change of temperature. Either the whole thing should be put in the place where temperature is being measured, or the same length must be used for all measurements which are to be compared. It also responds to your warm fingers, and thus must be held some other way.

As you can see, these devices have some merit, and we are anxious to hear of your efforts to use them. However, they also have limitations. Perhaps they can be adapted in some way to become better.

The conditions of measurement in the various activities are as follows

Appendix E. Making an equal arm balance

Many science lessons can be improved by having weighing equipment available for the students to use. Often there is only one triple arm balance or weighing scale in the science room, and the teacher is apprehensive that it may become broken if students are allowed to use it.

Simple designs for equal arm balances that can be made from easily available materials are shown here.

Several details of design affect how sensitive a balance is:

1. Friction at the center point.
2. Whether the center hole is placed above or below the end holes.
3. The weight of the beam and where the center of gravity of the beam is located compared to the center hole.

Friction at the center point can be kept very low as long as the pivot uses rolling instead of sliding friction. Using a nail that rolls on the edges of tins is one effective way to keep friction at the pivot from being a problem, and is the method used in the diagrams that follow.

Figure

To investigate the effect of having the end holes

a. below the center hole, and

b. in line with the center hole, make the holes shown in the following diagram in a wooden ruler.

Put a nail in the center hole, which is approximately at the center of gravity of the ruler. Then hang a hook or lightweight container from the lower holes at each end of the ruler. Get many small objects that all have the same weight. These could be common pins, paper clips or staples. One of these object should be enough to unbalance the ruler. (If the ruler does not hang level at first, put an elastic band around the portion of it that is higher, and use its position to adjust the ruler so it is level.)

Then put five pins on each side.. Add a sixth to one side. Does the ruler move? Add five more pins to each side, so you have ten on each side. Add an eleventh to one side. Does the ruler move? Continue this procedure for fifteen and twenty pins.

Now hang your hook or light weight container from the upper holes at each end of the ruler. Do the same thing, testing the sensitivity to detect the weight of one pin when there are zero, five, ten, fifteen and twenty other pins already in each container.

You will find that in one case, the sensitivity decreased greatly when many pins were already on each container. This characteristic is useful when you want students to quickly compare objects that are approximately the same weight with other objects that are very different in weight, such as being only half as heavy. Too much sensitivity might make every object seem different in weight from every other object, and the students would get bogged down. Measuring the potato cubes in Part I of Preserving Food by Drying is an activity where the balances purposefully should not be very sensitive.

Now make one more hole in the center of the ruler, so it looks as follows:

In this explanation, the weight of the beam is staying the same it is the weight of a ruler. If you need to make an extremely sensitive balance, the same principles described here can be used with a light weight beam made from thin cardboard. Similarly, if a more rugged balance is needed for heavier weights, a design using parts of a tree could be made, similar to the diagram at the end of this explanation.

Now put the nail in the new hole you have made near the edge of the ruler. First put it on the pivot with the hole near the lower edge of the ruler. You will see that it does not balance when it is used this way. This is because the center of gravity of the ruler is above the pivot. The ruler tries to fall to a position where its center of gravity is below the pivot.

Now put the ruler on the pivot so the new hole (with a nail through it that rests on the edges of the tins) is near the top edge of the ruler. Repeat the same procedure of testing the sensitivity of the balance by putting one pin on one side, when you have zero, five, ten, fifteen and twenty pins already in the containers at each end of the beam.

You now have seen how the sensitivity varies according to where you make the holes at each end, and the hole in the center that the pivoting nail goes in. Now you will be able to make a balance where you can design what the sensitivity will be, even if you use materials such as shown in the following diagram:

Figure

Appendix G. Making a set of weight's

Without a set of weights, an equal arm balance can be used to see whether various objects are equal in weight or not. This is done in Activity I-6, where the equal arm balance shows that if one of the cubes is cut into several pieces, the pieces still weigh the same as the other cube that was not cut.

If the objects are to be weighed with the equal arm balance, a set of weights is needed. This is necessary where the weight of a piece of fresh food is to be compared with the weight of the same piece of food after it has been dried. The equal arm balance can be used for weighing by putting the piece of food on one side of the balance and by putting enough weights on the other side to balance the food.

The set of weights should be based on some easily available objects that all weigh about the same. In Appendix S, things like staples, common pins, and paper clips are suggested for testing the sensitivity of the balance. However, these are too light to be useful for weighing the food pieces. They also have the disadvantage that unless they are all bought from the same source, they may not all have the same weight. Washers also do not make suitable weights, because they are made from scrap pieces of sheet metal, and although the diameter may be the same, the thickness varies tremendously.

Bottletops from Coca-Cola, Fanta and beer bottles are quite uniform in weight. These are probably the best things on which to base your set of weights. They have the added advantage of being obtainable for free.

The set of weights can consist only of bottletops. For example, a piece of food might weigh 130 bottletops fresh and 47 bottletops after being dried. This gets to be a lot of bottletops to pile on the balance, however.

Somewhat heavier objects that are quite uniform are batteries of the kind used in flashlights and radios. The weights may vary between batteries from different makers, but all batteries of a certain type made by the same company should weigh about the same. Consider that you have some small batteries that each weigh 14 bottletops, and some large batteries that each weigh 55 bottletops. To weigh the fresh food in the example, two large batteries would equal 110 bottletops, one small battery would add 14, and 6 bottletops would add the rest, to reach the total of 130 bottletops of weight. To weigh the dried fruit, three small batteries would equal 42 bottletops, and 5 bottletops would be added to balance the food's weight of 47 bottletops.

Objects such as these can be used to make sets of weights suitable for all the food drying activities in this book.

Table

Appendix H. A heating stand made from a tin

Using one of the methods of cutting a tin shown previously, you can make heating stands while you obtain rectangular pieces of metal to use for other purposes.

Figure