`Addition and Subtraction of Signed NumbersDavid Drymiller                Morgan Park High School                               1744 W. Pryor                               Chicago IL 60643                               312-535-2550   Objective(s):    To master the addition and subtraction of signed numbers.    To recognize linear equations of the form x + a = b and their solutions.Multicultural aspects:    Cities of the world including London, Peking, Moscow, Cairo, and Berlinare referred to in the Performance Assessment. Materials needed:         For a class of 28:   3 paper lunchbags and 100 penniesStrategy:     Ask the students to bring some pennies (no more than 10) with them to class the next day.  Number the bags 1, 2 and 3 then place in each bag 18, 21 and 23 pennies respectively.  In 3 groups (2 rows per group) have 1/2 the students  place pennies into the group's bag and 1/2 take out pennies from their group's bag.  (Make sure the amounts put in and taken out vary.)  Have the students  record the number of pennies they put in or took out.       Questions for the group to answer within the next 10 minutes:  Are there  more or less pennies in the bag?  How many more or less?  Next have each group count the number of pennies in their bag and answer the question.  How many pennies were placed in the bag before class began?            Have a member from each group explain how they got their answers to the class while you point out that putting in pennies equals a POSITIVE number and taking out pennies  equals a NEGATIVE number.  Explain that they had to add or subtract positive and negative numbers to answer the questions.  Also the number of pennies placed in the paper bag before class began served as the variable X, and they had to solve a simple linear equation to get the last answer.     The above activity leads to the following examples:         put in 8         and      put in 5          equals        put in 13             8             +           5               =              13         put in 7         and    take out 9          equals      take out  2             7             +          -9               =              -2       take out 4         and    take out 7          equals      take out 11            -4             +          -7               =             -11       take out 8         and    put in 11           equals        put in  3            -8             +          11               =               3    At this point a discussion of simplification of signs is needed.           5 = +5   the + sign is superfluous, so discard it.          - - = +,            - - - = + - = -,            - - - - = + + = +,    This may be visualized by using construction paper strips 1" by 6" as negative signs; join 2 negative signs together with a paper clip to make a positive sign.      For any addition or subtraction problem only one sign is necessary betweeneach number in order to know what to do.               +8 + - 7 -(-9) - +5 =                                                         8  -  7  + 9   - 5    Now the class is ready to do problems in class and for homework in order to master the addition and subtraction of signed numbers. Performance Assessment:    In the game of Civilization the population of a city must be content or happy in order to produce any goods.  Given the facts that                A HAPPY   PERSON   is worth  +7 points.               A CONTENT PERSON              0 points.                AN ANGRY  PERSON             -4 points.               A HOSTILE PERSON            -10 points.                 Given a city with 30 persons determine if the city is producing any goods.If the city is not producing, how many more happy persons does the city need to start producing?  If producing, how many more angry or hostile persons will stop the city from producing? Note:  A city is represented by 30 circle faces on one sheet each drawn to show the 4 possible attitudes of its citizens. Conclusions:     Positive and Negative Numbers are appropriate in any situation where opposites are present. Evaluation:    A simple quiz with 9 nine-point problems with the above Performance Assessment for nineteen points. Rubric:  19 points   Correct answer and notices and uses the multiplication                     of signed numbers.         16 points   Correct answer presented clearly in complete sentences.         13 points   Correct answer use of repeated addition and subtraction                     work shown neatly .         10 points   Incorrect answer, correct method shown but error in                      addition or subtraction.          5 points   Incorrect method or no method shown but correct answer                     without supporting arguments.          0 points   Incorrect answer - No answer - and invalid arguments.`