Notes to InstructorsSection I - Whole Numbers There are many excellent adult education books that cover addition, subtraction, multiplication and division of whole numbers. Because this project's purpose was to develop supplemental material to support the adult basic education basic curriculum and not to redevelop material already in common use, there is no new curriculum to support this section. Area II uses Contemporary's Number Power I with excellent results. Section II - Addition and Subtraction of Decimals There are many excellent adult education books that cover addition and subtraction of decimals. Area II uses selected sections of Contemporary's Number Power II with excellent results. Area II employees report a workplace need for instruction in addition and subtraction of decimals. They report using shop decimals numbers ( the decimal form of shop fractions) for most workplace applications. They do not indicate any workplace applications for entry level workers in multiplication or division of decimals. The curriculum uses shop decimals and only covers addition and subtraction. Section III - Addition and Subtraction of Shop Fractions Area II employees report a workplace need for instruction in addition and subtraction of shop fractions including halves, fourths, eighths, sixteenths and thirty-seconds. They do not indicate any workplace applications for entry level workers in multiplication or division of fractions. The curriculum uses shop fractions and only covers addition and subtraction. Area II uses measurement tools to teach shop fractions because measurement is the most common workplace application of fractions. Instead of extensively using mathematical terms such as numerator and denominator, fractions are demonstrated and explained using a ruler . For example, a ruler is an effective, concrete example of the meaning of the terms numerator and denominator. Students are able to see what a fraction means in a workplace related example. If an inch is divided into two equal parts, one of those equal parts is ½ inch. The bottom number tells a student into how many equal part an inch is divided and the top number tells the student how many of those equal parts you are using.
¾ inch means that an inch was divided into 4 equal parts and you are thinking about 3 of those parts. This understanding of fractions in terms of measurement forms the basis for instruction on borrowing and carrying with fractions. It is important for students to be taught to read a ruler and to understand what the divisions mean. Instructors point out that the inch line is the longest, the ½ inch measurement is next in length and so on down to the shortest line on the ruler representing either sixteenths or thirty-seconds. It may be helpful to spend additional time identifying just the denominator of shop fractions on the ruler - though it is not necessary to use the mathematical term. Draw lines of varying lengths and ask students to identify only the lower half of the fraction (denominator) of the fractional length. To prepare for instruction on borrowing and carrying with shop fractions, students need to understand equivalent fractions. One way to demonstrate this is to use a ruler to show a student that one- fourth inch is the same length as two-eighths inch or four-sixteenths inch. The students may draw lines that are one-fourth inch, two-eighths inch and four-sixteenths inch and compare the lengths. Another way to demonstrate equivalent shop fractions is to have a student draw a line that is 1_ inches long. Then have a student count eleven eighths and draw a line that is 11/8 inches long. The lines will be the same length because the measurements are the same. Section IV - Scale Drawings The local employers in Area II report a workplace need for understanding simple scale drawings. Employees are expected to calculate missing lengths and basic area or perimeter from a scale drawing. Section V - Metric Conversion The local employers in Area II report an increasing need to convert measurements to metric. Parts are often purchased from foreign catalogues that use metric units to size items. It is necessary to convert measurements to metric units in order to order the correct size. The curriculum is limited to conversion from inches to centimeters and millimeters because that is the need identified by local employers. The curriculum may be easily converted to other metric measurements as needed.
Introduce Conversion Table I and conversion between units - This table helps students know how to move the decimal point when converting from one metric unit to another. For example, student write the first letter of each unit (using one of the memory techniques if they wish). K H D U. D C M To convert centimeters to millimeters, the decimal point must be moved one place to the right - from the "C" above to the "M"above. (24 cm = 240 mm) (62.3 cm = 623 mm) To convert millimeters to meters, the decimal point must be moved 3 places to the left. ( 60 mm = .06 meters) (9.3 mm = .0093 m )
NOTE: Master to make multiple job aid copies is included.
Section VI - Ranking Decimals and Fractions Manufacturing equipment such as drill bits and manufacturing materials such as conduit and wire are sized using decimals and/or inches. Employees need to be able to rank order decimals and/or fractions in order to select the next larger or smaller size as appropriate. A ruler provides a good visual when teaching students how to change shop fractions to a common denominator. Section VII - Measurement Measurement skills are both difficult for students and important to employers in Area II. Much of the fraction material will need to be repeated as part of the measurement instruction. An effective way to start measurement instruction is to "build" an oversized ruler on the chalkboard. First indicate the markings that represent inches. As a group, measure lines drawn on the board to the nearest inch. Then add the markings that represent one-half inch intervals and measure lines drawn on the board to the nearest one-half inch. Continue this process with quarter inch, eighth inch, sixteenth inch and perhaps thirty-seconds inch. | |||||||||||||||||||