Return to Mathematics IndexRules of Sign Change

Zuger, Joel P. Chicago Metro High School

280-2020

Objectives:1. This is aimed at 7^{th}and 8^{th}grades as well as pre-algebra and

1^{st}year algebra students.

2. Understand the operation of plus and minus signs during

arithmetic operations.

Apparatus Needed:1.Number Line Materials1.1 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 Machine2.1 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 Game3.1 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

$2.00.

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

rules.

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|,

|-1^{.}4=-4|,

|-2^{.}4=-8|;

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 1^{st}number represent the multiple of the 2^{nd}

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 2^{nd}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 4^{th}on the list the next equation goes into the 4^{th}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.