Addition and Subtraction of Signed Numbers
David Drymiller Morgan Park High School
10115 S. Oakley 1744 W. Pryor
Chicago IL 60643 Chicago IL 60643
312-233-7902 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 Berlin
are referred to in the Performance Assessment.
Materials needed:
For a class of 28: 3 paper lunchbags and 100 pennies
Strategy:
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 between
each 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.
Return to Mathematics Index