Rules of Sign Change

Zuger, Joel P. Chicago Metro High School

Objectives: 1. This is aimed at 7th and 8th grades as well as pre-algebra and
1st year algebra students.
2. Understand the operation of plus and minus signs during
arithmetic operations.

Apparatus Needed: 1. Number Line Materials 1.1 Number lines for each student printed across the whole paper. The lines must be spaced far enough apart so bingo markers cover only one line at a time. 1.2 Need translucent bingo markers, maybe 5-10 per student. 1.3 Need one acetate sheet with a number line to work with an overhead projector. 2. Function Machine 2.1 Cardboard or wood cutout representing a machine, titled "Function Machine". It can be as elaborate or as simple as you
wish to construct it.
2.2 Strips of cardboard or other material one of which will go into
the machine from the top the other will come out from the side.
2.3 Crank on the machine which is either functional (pulling through
the top strip and pushing out the bottom strip) or turned just
for show
3. Keep It or Give It Game 3.1 Two dice, each of a different color. 3.2 Sheet of equations, probably about 100 with positive and negative numbers with addition and multiplication operations. Recommended Strategy: 1. Number line strategy - shows positive and negative numbers as
directions on the line, negative left, positive right. Explain
the difference between negative numbers and subtraction, i.e. a
bill for $8.00 is a negative number, it is money owed and you
do not have; getting $10.00 and paying $8.00 to satisfy the bill is
subtraction, transferring money you have leaving yourself with
Experiment with the number line using an overhead (with the students
working on their own number line papers). I.e. move 10(right) move
-5(left) all should be on 5(positive side of the number line).
Continue with a few more examples to show direction, and how to use
it. Note: use a couple of examples of subtracting negative numbers,
using reversal of direction for subtraction, so negative numbers
subtracted will move in a positive direction.
Experiment with multiplication using the number line, also show a
consistent pattern on the board so two methods reinforce sign
Example: | 4.4=16|,
The products show a difference of 4 at | 3.4=12|,
each succeeding multiplication. | 2.4= 8|,
| 1.4= 4|,
| 0.4= 0|,
To show negative times negative is positive __________ use pattern of: | 3.(-4)=-12|,
use the number line using direction to | 2.(-4)= -8|,
show results. The reason for using more | 1.(-4)= -4|,
than one bingo marker is to show the | 0.(-4)= 0|,
pattern on the number line. |-1.(-4)= 4|,
|-2.(-4)= 8|;
______________ It is recommended the 1st number represent the multiple of the 2nd
number, i.e. 3x4 means 4+4+4 not 3+3+3+3. Even though
multiplication is commutative, it will be easier, in algebra,
to show that 5w is 5 times w, meaning w+w+w+w+w.
2. Function Machine - This is used as reinforcement to calculate with
both positive and negative numbers. A strip of cardboard is marked
off with ___________________________
| 1 | 2 | 3 | 4 | 5 | etc.| and this is fed into the input of
___________________________ the machine (which is cardboard or wood, etc. painted or marked to be a machine), the 1 being fed in first. There is a 2nd cardboard
which is the output for example;____________________________
| 2 | 4 | 6 | 8 | 10 | etc.|
which the students have to ____________________________ guess, after seeing one or two examples, at what the output will be and what function is making this output, this case is input times 2. Make different strips for input and output. The function can be as complicated as (input - 3) times -2. 3. Keep It or Give It Away Game - This is used as reinforcement for the
operations of positive and negative numbers. The class can be
divided into 6-groups. Each group starts off with 50-points. The
team reaching 100-points first wins. A paper with 100+ equations on
it, with the first 6 equations numbered 1-6. Teams go in order, team
number 1 starting. Two dice used, each of a different color. One
die determines what team will get the equation if the original team
gives it away. The other determines which equation is solved. After
an equation is used the next equation on the list (other than the
original 6) will replace used equation. The team tossing the dice
has 10-seconds to decide to keep the equation or give it away (teams
want positive results and give away negative results). The team
getting it has 30-seconds to give the correct answer. The evaluation
of the equation are the points involved, i.e. 8.(6-3).(-1), result is -24
points. If it was 4th on the list the next equation goes into the 4th slot,
etc. If the original team rolls 4 on the give dice then team 4 gets
the equation if the original team: 1) runs out of time, and result
is positive 2) wants to give it away; or 3) wants it but gives the
wrong evaluation and result is positive; else the original team gets
the points. Any other rules or changes can be made. Gear the rules
and the equations to the level of the class, it should be enjoyable
as well as educational.
Note: - The students should not be rushed to give instant answers.
Perhaps count 3-seconds before allowing any student to answer.
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