Math in a Box with Susan Johnsey

Need INSPIRATION for TEACHING~ create "BLUE SKY" in your classroom!

2012-01-31T00:18:00.000-06:00

Teaching students can be exhilarating or draining. If you are in need of some new motivation then read the book published just a few months ago by Walter Lewin (with Warren Goldstein): For the LOVE of PHYSICS. Lewin is the wonderfully inspiring MIT professor of PHYSICS. Watch his videos on YouTube; I guarantee that you will be inspired to improve your class presentations and enjoy them. You do not have to be a physics teacher.

One of the many hundreds of his activities for teaching is to create a "blue sky" and then "white clouds" inside his MIT classroom! Do you think his students will remember why our skies are blue and clouds are white?

Even Bill Gates has watched many of his YouTube videos.

Purchase the book at AMAZON or watch his videos at YouTube. See his enthusiasm in his writing and his classroom presentation.

Walter Lewin writes: "I've always tried to make physics come alive for my students. I believe it's much more important for them to remember the beauty of the discoveries than to focus on the complicated math. My goal is to impart enthusiasm to my students, to help them see the beauty of the world all around them in a NEW way. What counts, I found, is not what you cover, but what you uncover. Students love being apart of that discovery."


Math in a Box appreciates your support and comments.

Top 100 Tools for Learning

2011-12-31T13:53:00.001-06:00

Jane Hart offers valuable info for educators, students, and entrepreneurs with her top 100 Tools for Learning. At her web site she also gives the next top 50 - the 101st to 150th web software/apps/sites- that are quite helpful for learning, teaching, creating and communicating with your students or clients.

Most of the tools are free!

Find tools for quick communication or for producing your own movie or screen cast.
Geogebra will help you teach Geometry or Algebra online or in your classroom.
Free tools for drawing, painting, editing pics and docs.
Watch Science and Math videos.
Read research papers.
Build visual maps
Store your files in safe place with easy network or internet access
Create a Slidecast (narrated presentation)

And remember these are the top of the line software, apps and web sites. The offerings will produce quality goods for you or allow you to experience excellent goods. I use some of these in my work and will probably try some others in the new year.

Top 100 Tools for Learning 2011

View more presentations from Jane Hart

Free Web whiteboard - Tutor students online - includes audio

2011-11-07T10:45:00.003-06:00

Scribblar
Scribblar is a Flash-based hosted web site that is ideal for real-time tutoring and web collaboration. Built with simplicity in mind, Scribblar is

Easy to use – no training required
Browser based and cross-platform
Customizable and brandable to fit into your existing website

Try it now for free at Scribblar.com. The application requires no large downloads. It has a clear, user-friendly interface so it’s easy to get up and running quickly.

Send your students a link to your whiteboards and then they can join you. You can speak with them by turning on the microphone icon (one click), but of course, you must have a mic on you computer. If you do not have a mic then you can still chat with the student in the CHAT box beside the Whiteboard.

You can write, type, write math equations with LATEX, draw geometric shapes, use different colors for the text or background or shapes. You can even upload documents or pictures and edit these together. SAVE the EDITS or new Creations on the whiteboard and then send to your students
I have used this with several students.

Math and Tornadoes

2011-04-29T01:50:00.001-05:00

Scientists still do not understand the formations, movements and growth of tornadoes. Tornadoes strike sometimes before a tornado warning can even be issued.

Many warnings (sirens and radio-TV broadcasts) were issued and heeded by Alabama residents this week and lives were saved. Please pray for the citizens of my home state. At least 200 people lost their lives. Thousands have lost friends, family, pets, homes, businesses, and jobs.

Our state is blessed to have brilliant and compassionate weather forecasters and broadcasters, as well as, brave reporters. Many reporters were in the field chasing and sometimes running from the tornadoes in order to help the weather broadcasters better warn the people of our state.

So what about the math?    MORE is needed.    Numerical modeling has provided us with some insights as to how a tornado occurs. Video observations and numerical modeling has helped us discover and better understand the formations, movements and growth of tornadoes. The numerical modeling allows researchers to create computer simulations which can validate their ideas, as well as, uncover new information about tornadoes.

Can tornadoes be slowed down or detoured? Are you ready to study more math so you can help in future years?   Think about it, and please pray for guidance.

Quaternions: Are they from outer space, depths of the sea or are they surreal?

2011-04-20T00:02:00.014-05:00

Quaternions
Would you believe that they are NUMBERS, that is 4-dimensional numbers used to describe dynamics of motion in 3-D. Although created in 1800's they are today used for virtual reality games, robotics and geometry of space-time. Quaternions are implemented in flight software for the NASA Space Shuttles. If you have heard of complex numbers, a+bi where bi is the imaginary part, then think of quaternions as complex triple imaginary numbers. a+bi+cj+dk.

Irishman William Hamilton devoted his life to studying and teaching about his invention, quaternions. He founded a school of "quaternionists" and popularized them in several books. He was from Dublin and belong to the Irish Royal Academy.

In the 1900's the MATHEMATICS of quaternions was replaced with VECTOR analysis. Who would have thought that 100 years later they would be revived for NASA and for virtual reality games of the 21st century.

Super Egg in Geometry!

2011-04-15T17:23:00.003-05:00

Super Egg -
The upright egg was created in 1965 by a Dane, Piet Hein.
The 3-D shape is a superellipse defined by the graph of the relation:

The ellipse is then revolved about the z-axis. In most super eggs that you see a/b = 4/3 ! Or have you not seen one yet!.

Hein's super eggs were popular as toys in the 1960's. The world's largest super egg can be seen outside Kelvin Hall in Glascow, Scotland, UK. The super egg with a/b= 6/5 was used as a round-about road in Stockholm, Sweden. Traffic flowed more fluidly with the super egg design.

You can purchase a set of super eggs on Amazon! They were designed by Hein as salt and pepper shakers. They will wobble a bit but do not fall over!

I gleaned this from a book you may want to consider reading at your public library.
The Math Book : from Pythagoras to the 57th dimension, 250 milestones in the history of mathematics by Clifford A. Pickover.

Need more information about the SUPER ELLIPSE?

Learn to create your own here:

Math World at Wolfram

iPad 2 and its Classroom possibilities

2011-04-15T16:27:00.002-05:00

Do you enjoy learning the newest technology? Have you tried out the new iPad 2?

Houghton Mifflin this month, April 2011, introduced new apps for their Algebra 1 curriculum.

Houghton Mifflin Harcourt, a Boston company known for such educational products as textbooks, said it is launching HMH Fuse: Algebra 1, the first core K-12 education solution developed exclusively for the iPad.

"The portability of a complete Algebra 1 course on an iPad enables students to learn in the classroom, on the bus, or at home — anytime, anywhere," the company said.

These are current prices, updated each day:

With iPad, the classroom is always at your fingertips.

At the iTunes App Store, there are thousands of apps available to download.
Apple’s iTunes U is home to more than 350,000 free lectures, videos, readings, and podcasts. Universities such as Yale, Stanford, UC Berkeley, Oxford, Cambridge, MIT, Beijing Open University and The University of Tokyo, as well as broadcasters such as PBS, offer free content on iTunes U.

Graph Sine and Cosine using GEOGEBRA

2011-02-17T23:17:00.008-06:00

You should print this worksheet, see below, or you can make up your own functions to study.
Then click link to go to the Graphing ACTIVITY.

Click here for the Geogebra activity: Graphing Sine and Cosine Functions with Variations

Worksheet for Graphing Sine and Cosine:
Use pencil and paper to copy each of these graphs that Geogebra will create for you.
You should have 12 separate graphs.
Can you predict the graph changes?
Try some yourself.     If you use y=2sin(x) what graph will you have?
Change the 2 to 3 or -3, what happens to the graph. The amplitude changes.
Try other combinations.     y=sin(2x). This 2 will affect the period of the function rather than the amplitude.

1. SINE function
A. period=2pi amplitude = 3 Equation_________
B. period=2pi amplitude = 3 up 3 Equation_________
C. period=2pi amplitude = 3 up 3 left pi/4 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.
Does your graph match the info I gave you for C? I hope so HOW can you know for sure?
2. SINE function
A. period=pi amplitude = 3 Equation_________
B. period=pi amplitude = 3 down 1 Equation_________
C. period=pi amplitude = 3 down 1 right pi/2 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.
3. COSINE function
A. period=2pi amplitude = -2 Equation_________
B. period=2pi amplitude = -2 up 1 Equation_________
C. period=2pi amplitude = -2 up 1 right pi/4 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.
4. COSINE function
A. period= 4pi amplitude = 3 Equation_________
B. period=4pi amplitude = 3 down 2 Equation_________
C. period=4pi amplitude = 3 down 2 right pi/3 Equation_________
D. Complete each graph and also state the "5 points" for B. and C. on the graph.

Let me know if you need help.       If you need the equations then email me. Be specific in you request as I have many online students studying different topics.
Susan Johnsey sjohnsey at bellsouth dot net

Email request for solving linear equations

2011-02-06T17:25:00.000-06:00

Hi   johnsey, I have a hard time figuring out solving 2 math problems.
Here they are:
5y - 3 = 8 + 4(y - 2) and   if 7x + 3 = 5x - 5, evaluate 2x - 1.

+++++++++++++++++++++++++++++++++++++++
5y - 3 = 8 + 4(y - 2) Multiply on right side and add LIKE terms then solve.
5y-3 = 8+4y-8       the 8-8 is 0 so we get
5y-3 =4y      Since the only number term, the -3, is on the left side I will move the y-terms to the right.   Subtract 5y from both sides.
5y-3 -5y =4y -5y

-3 = -y   Now we want to finish with y or +1y so divide both sides by -1.
-3/-1 = -y/-1   thus we get y = 3.

+++++++++++++++++++++++++++++++++++++

If 7x + 3 = 5x - 5, evaluate 2x - 1.

Solve for x first then we evaluate.
7x + 3 = 5x - 5 I will move the variable terms to the left side and the number terms to the right.
subtract 5x from both sides.
7x + 3 -5x = 5x - 5 -5x

2x+3 = -5   Now subtract 3 from both sides.
2x+3-3 = -5-3
2x=-8   so x = - 4.

now evaluate 2x - 1. let x=-4 we get 2(-4) -1 -8-1 = -9.   The -9 is the answer.

Geometry SSS of congruent triangles Illustration

2011-01-28T12:47:00.000-06:00

Here is an illustration for explaining congruent triangles when we know the lengths of the sides of the triangles. I would suggest using pipe cleaners, or strips of paper to make this a hands-on activity.

The Twelve Days of a Large Family Christmas

2011-01-17T23:10:00.001-06:00

I know this is a bit late, but you will enjoy.
Counting to 12!

Exponents and the Order of Operations

2011-01-14T14:09:00.005-06:00

Exponents are a shorthand for writing a multiply that uses only one number several times.

5² is 5 with an exponent of 2 means 5 times 5 = 25

6 with an exponent of 3 or 6³ means 6 times 6 times 6 = 216. I wrote the 6 down three times.

But notice the differences:

-6² = -36, but (-6)²= +36 and (-6²)= -36 One of these is tricky!!

The parenthesis around the -6 tells me the -6 is squared (another word for exponent of 2). We write the 6 down 2 times and then we multiply.

SEE:

(-6)²= (-6)(-6) = +36 .We write the -6 down two times and multiply. Recall two negatives multiplied yields a positive answer.

Without the parenthesis only the 6 is squared. We write the 6 down two times and multiply.

- 6²= - (6)(6) = - 36.

With the parenthesis BUT the 2 is inside: (-6²) = - 36 This is really the same as -6². tricky one!!

Do you see that the exponent 2 is inside the parenthesis?

That means only the 6 is squared not the whole parenthesis, not the -6.

Thus the -6² and the (-6²) are really the same. They equal - 36.
And (- 6)²is +36.

Write these down on a note card or place a sticky note.

You will see this on the QUIZ below. .

We have studied the FOUR operations of math:

addition, subtraction, multiplication and division.

And, you have studied exponents.

You know how to do each of these, but can you do them if I mix 3 or 4 of them together?

Study these carefully.

A. -60 divided by 10 * 2

B. -60 divided by 5 * 4

C. 60 divided by (-5 * 4)

D. -60 divided by 2 divided by 5 * 2

Which of the above means - 3, and which means -12?

Which one has another number for its answer?

You must understand the above problems and these below about exponents before leaving this lesson.

Do not jump into these without studying the rules.

Most people remember this somewhat, but there are pitfalls that many always seem to fall into.

When the operations and exponents are MIXED together which do we do first?

THE ORDER is important. An agreement has been made.

All calculators and teachers and computers know it.

It is time for you to learn it too.

The Order of Operations AGREEMENT:

You must follow the order.

Step 1 requires you to SEARCH for the grouping symbols and then complete the work INSIDE them.

Grouping symbols are the parenthesis ( ), brackets[ ], bars| |, braces{ } and even the long fraction bar. While working "inside" you follow these 4 steps.

Step 2 requires you to SEARCH for the exponents in the expression and evaluate them.

Step 3 states that you are to do the multiply and the divides but not necessarily in that order. Many students think that you do the multiplies and then do the divides. That is WRONG.

You do NOT search for the multiplies and then search for the divides!!!!! They MUST be worked from left to right. Before beginning step 3 be sure you have returned to the left side of the problem. Then do the divide or multiply as you move across the problem going toward the right. If the divide is left most then divide first, but if the multiply is left most then you multiply first.

Step 4 states that you are to do the add and subtracts, but not necessarily in that order.

You do NOT search for the adds and then search for the subtracts!!!!! Many students think that you do the adds and then do the subtracts. That is WRONG. They MUST be worked from left to right. Before beginning step 4 be sure you have returned to the left side of the problem. Then do the subtracts or adds as you move across the problem going toward the right.

ORDER of OPERATIONS EXAMPLES

Example 1 :
- 3 + 36 ÷ (3)( 2) = There are no grouping symbols nor exponents.

Do we do the division or the multiply first? WRITE these on your paper going down the page as I have done.

You MUST learn to write them this way. Otherwise you will only be able to do the simple ones.

- 3 + 36 ÷ (3)( 2) =

-3 + 12( 2) =

-3 + 24=21

I started with step 3 since there are no grouping symbols and no exponents. Begin on the left and do multiply or divide as you come to them. Many people will do the (3)( 2) before the divide; that is wrong.

But you must begin on the left.

Multiply is done before division only if it is left most.

Then begin again on the left and do add or subtract as you come to them.

Try this problem:

Example 2:
45 divided by (3)( 6 - 3) =

we have 45 ÷ (3)( 3)

We did the work inside the parenthesis. Now do we multiply the threes or divide the 45 by 3?

= 15(3)= 45.

Do not be tempted to multiply to get 9. That would mean that you did not return to the left to begin step 3.

Example 3 :
3 - ( 5 + 8*2÷4 - 1)

The (5+8*2÷4-1) is done first becauseof the parenthesis, but the Steps 2 through 4 must be followed

as you work inside the parenthesis. Step 2 (exponents, not needed). Step 3 says do multiply or divide ( start on the left).

So do 8*2 then divide by the 4. Then step 4 says do add or subtract( start on the left).

5+4 - 1=8. We have finished inside the parenthesis. 3-(5+8*2÷4 -1)= 3-(5+4 -1) =

I hope you are writing these on your paper as I have them typed. 3 - (8) = -5

Example 4:
5 + (- 6^2) NOTE: the ^2 means exponent of 2. We use that on computers sometimes.

5 - 36 = -31 Do you know why this has - 36 and not +36? We discussed that above.

Sometimes we use the "/" to mean "divide by".

Example 5 :
60/3 + 2(-2) ^2 = What is the first thing to do?

There is NO Step 1. We begin with Step 2, SEARCH for the exponents.

Then we go to Step 3, NO SEARCHING just start on the left.

We have one division and then one multiply for Step 3. And, we have one addition to do for Step 4.

60/3 + 2(-2)^2= The ^2 means exponent of 2. We use that on computers sometimes.

60/3 + 2(4) =

20 + 8 = 28

Example 6:
35 - (- 4 -2)^2 - 8^2 = Step 1: Search for the grouping symbols and

work INSIDE the ( ).

35 - (- 4 -2)^2 - 8^2=

35 - (- 6)^2 - 8^2= Search for the exponents for Step 2 and evaluate those.

35 - (+36) - 64 = Now what? Step 3. START on the LEFT.

Begin on the left and do what? The subtract or the multiply or the add?

Well , of course we multiply before we subtract. I hope you know -(+36) is same as -36.

35 - 36 - 64 =

-1 - 64.

The final answer is -65. Did you get that?

You really should copy some of the examples above into your notebook and use them to help you.

Order of Operations Game. Try to get a score of 3000.

Tutoring by email or ?

2011-01-12T18:52:00.003-06:00

Math in a Box www.mathinabox.com

email Susan O. Johnsey
sjohnsey at bellsouth dot net

Online Math assistance:

some free and some for a small fee.

I give free advice (I will gladly help you with 2 or 3 problems for free) and I tutor online for a reasonable rate. You may pay me by using the Google Shopping cart below. $13 for 30 minutes of work or $25 for one hour.

Online Math Courses

You may find the prices and registration information for my online math classes (Algebra 1 and 2, Geometry)here: Online Math Courses by Susan O. Johnsey

Prices range from $85 to $165

Please email me first or send the problems and discuss what you need. I answer email at least 350 days of the year, several times a day.

sjohnsey at bellsouth dot net

SUSAN O. JOHNSEY

Multiplying and Dividing Numbers

2011-01-12T15:55:00.004-06:00

Post 2 Multiplying and Dividing Numbers and special note on ZERO.

- 4 times 5 = -20 50 divided by -10 = - 5

(- 8) 9 =-72

If multiplying or dividing by one positive number and one negative then the answer is negative.

- 4(- 8) = +32 or 32 (-7)(- 6) = +42 or 42

-18 divided by - 3 = 6

If multiplying or dividing by a negative number and another negative then the answer is positive.

+4(+ 8) =+32

You know a positive number multiplied or divided by another positive number yields a positive answer.

HOW to write a Multiply in Algebra!

In algebra we do NOT use the x or the dot for multiply.

We write the numbers next to each other; some times we use parentheses.
3(6) or (3)(6) means multiply 3 and 6.

You must use only two of the numbers at a time to determine their sign.

Try these examples:
     A.   -6(-7)(-4) = +42(-4) = - 168.     The -6 times the -7 gives + 42. Then multiply by the -4.
         B.     (-4)6(-2) = -24(-2) = +48 or 48. The -4 times the 6 gives -24. Then multiply by the -2.
The rules for deciding the sign of the answer for multiplying and dividing are the same.
The / symbol means divide by or is the fraction bar.
  It is also the divide key on the calculator.

FRACTIONS:

which ones are less than 1 whole? 5/8 or 8/5. And 9/11 or 11/9?

And 14/7 or 7/14?

DO YOU KNOW?

5/8 means 5 divided by 8.

This should give you a decimal number that is less than 1 whole if you complete the division.

Do NOT confuse it with 8 divided by 5 or also called 8-fifths.

This is more than 1 whole. It is 1 and 3/5.

Be sure you know which "way" to divide.

Do the division for the 5/8 and send me your answer in an email
Click: Susan O. Johnsey .

WHAT ABOUT ZERO in division? Zero is well understood with adding, subtracting and multiplying. But it is a bit peculiar, some would say, when it comes to division.

Look carefully:

      0/4 = 0              4/4= 1           4/(-4)= -1                0/-4 = 0

   -4 / 4 = -1     -4/(-4) = 1       4/0 is undefined.

    Division by zero    and Division into zero are quite different.

A common fraction that most students know is 4/5,
that is, 4-fifths. 4/5 means 4 divided by 5 .

Will the division give you a number larger than 1 or smaller than 1??

Can you read these fractions? Watch out!!

6/5 is read "6-fifths" 5/5 is read "5-fifths" and equals 1 whole 5/4 is read "5-fourths".

OK? Keep going please:

             5/3 is read_______    5/2 is read_________    5/1 is read__________
             5/3 is read 5-thirds 5/2 is read 5-halves 5/1 is read 5 wholes
   5/0 is read_______   oops what did you say here? 5- zeroths!!!
                      what is that?    there is no such fraction!          And what about the 5/0?
                       5/0 is undefined (have you ever heard of 5-zeroths?   I hope not! )

5/0 means 5 divided by 0.

There is not a simple number answer that can be given.

This is studied in Calculus so I will tell you for now to just know division BY zero is undefined. Do not confuse it with division into zero. 0/4 = 0

All division BY zero is undefined:

6 /0 or 6 divided by 0, and even, 0/0 are undefined.

0 divided by 3 (zero-thirds) is 0,

but 3 divided by 0 (that is 3-zeroths) is undefined.

2010-10-29T11:17:00.003-05:00

Adding and subtracting integers (or any real number) can be a very daunting task for those beginning algebra or prealgebra. Most students will understand the rules for adding signed numbers, but once introduced to subtraction that are quite confused. The multiplication and division rules for signed numbers are usually quite easy for the students to master. The addition and subtraction rules are quite confusing for many and thus can prevent a student from be successfull in their first semester of Algebra.

So what do we do??? I was teaching students with learning disabilities and decided that I had to create a way to present addition and subtraction in a simpler manner and definitely not with the normal "math" rules presented in textbooks. Our budget was also low so I could not use manuipulatives; I also did not want to have to keep up with them.

Unteaching a topic can be tough because there are usually rules that the student has misunderstood or only "half-way" remember. Thus I do have to ask students that already have been taught the school rules, but are not succesful at using them to please try to forget those and just think about what I am presenting. After we complete a few problems they will see how it all works together.

Here is my way of teaching addition and subtraction of signed numbers. Please note that I will teach these all at once and will not really focus on whether we are subtracting or adding!! And yes, teachers the kids get it.

TWO RULES:
1. All numbers have a sign.
IT is always on the left side of the number.

-2 + 4 There is a negative 2 and a positive 4.
3 - 5 There is a positive 3 and a negative 5.
- 5 - 8 There is a negative 5 and a negative 8.

Do you see the sign is on the left always.
If no sign is written then it is positive. That is why the 3 is positive.

2. What if there are 2 signs on the left?

+-7 or +(-7) or -(+7) are all = -7.
We can ignore "extra" positives sometimes, but never negatives!!

- (-6) or - - 6 are the same number. They both mean Positive 6.

“Double negatives”, that is a negative sign followed immediately
by another negative sign yields one positive.

[Note: I did not say one negative number followed by another negative number,
such as -7-8. That is not what I am explaining here. The 7 is negative and the 8 is negative.]

7- (-6) becomes 7 +6 The “double negatives” disappear and become one positive. Why is this true? A little logic will explain that. Positive and negatives are opposites of each other. Right? yes. 3 and -3 are opposites. The opposite of a -6 is a +6. Another way to think of negatives is to think the word opposite. -2 can be called negative 2, minus 2, or opposite of 2.

Thus the OPPOSITE of -6 is a positive 6 can be written as a math expression:
-( -6) = +6.

So we know -5 - (-3) becomes -5 +3 .
1. Every number has a sign and it is always on its left side.
2. We know by logic that "double negatives" yield a positive.

How do we add or subtract signed numbers?
Create or draw 2 boxes. One is for the negatives and one for positives.

TWO BOXES:

Now that we know about the signs, let’s use the positive and negative boxes to explain adding and subtracting of integers. Most books teach this in 2 lessons, first adding and then subtracting. I do not. When we are “adding integers” there are times when we actually subtract the numbers!! And when “subtracting integers” there are times when we add the numbers.!! Confused? Yes ? no? Please read on. First, lose your “mind set” about this topic from any prior knowledge you may have. This is simple.
Warning: DO NOT write the signs inside the box.

-5 + 3 or 3 - 5 both mean

a 5 is placed in the negative box and 3 is placed in the positive box.

Remember, the sign of the number is on its left. If a number has no sign on its left then it is positive.

In both expressions above the 5 is negative and the 3 is positive. Now we ask these 2 questions.

TWO QUESTIONS:

1. which box has more in it? DO NOT write the signs inside the box.
2. how much more does it have?

For -5 +3 or 3 - 5 the negative box has more and it has 2 more than the positive box.

Our answer is thus negative 2. Thus -5 +3 = -2.
We have more negatives. The negative box has 2 more than the positive box.
-5 +3 or 3 - 5 are equal to -2.

-2 - 4 means you have 2 in the negative box and then 4 more are placed into the negative box.

Which box has more? The negative box.
How much more? Since the positive box has none and the negative box has 6 then obviously the negative box has 6 more. The answer is -6. that is, -2 - 4 = - 6

- 4 +4 means 4 is placed in the negative box and 4 is placed in the positive box.
If the amounts in the 2 boxes are equal then your answer is 0, ZERO
Also -3+3 =0 can be written +3 - 3=0 or 3 - 3 =0.
Remember the sign of a number is on its left.

-12 + 4 means you have 12 in the negative box and 4 in the positive box .

Which box has more? The negative box has 8 more. The answer is - 8. That’s -12+ 4 = - 8.

This is the same problem as +4 - 12. Be sure you see that. Just look at the signs.

What about when there are double signs?

-2 - +3 or
-2 - (+3) or
-2 + (- 3)
Recall I suggest ignoring the extra positives. I said extra positives. We can never ignore negatives. All three of these become - 2 - 3. Cover the extra positive with your pencil.
The above problems are the same as -2 - 3. We have 2 in the negative box and another 3 is placed into the negative box . The answer is - 5.

What about double negative signs?
- -4 is an example . Think of this as the opposite of negative 4. The opposite of negative is, of course, positive. - - 4 is simply +4. or -(-4) = +4 or 4

- -4 +6 becomes +4+6. This is also printed as - (-4) +6 and it becomes 4+6.
Both are in the positive box so our answer is +10 or just 10.

-7- (-8) becomes -7 +8 . LOOK at that. The double negative was on the 8. The sign of a number is always on its left. -7 +8 = +1. There is one more in the positive box than in the negative.

WARNING: DO NOT USE the boxes until you have changed your "double signs".

-7- (-8) = -7 +8 = 1

I know these are not the usual math rules. But if you are struggling then forget what you know and try these. They work. Using the other stuff you sort of know can really get in the way. Now go back and do this, please:

Write all of the above examples with their boxes on a card for reference.

-8+8 = 0
The boxes have the same amount so neither one has more. Answer is 0.

There are rules also for multiplying and dividing, but they are easy. A positive number times a negative number is always a negative number. A negative number times another negative number always equals a positive number. These 2 rules apply to division also, BUT not adding and subtracting!!! ( Use your box for adding and subtracting.)

Compute and email you answers. It is a free service or check below.

1. -6+9

2. -6 -9
3. -6 -(-6)
4. 6- 9
5. 6 -(-9)

6. 8 - (-5)
7. 8 - (5)
8. -8 +8
9. -5 -8
10. -5 -(-8)

Susan Johnsey http://www.mathinabox.com/

11. -7 -9
12. -8 +10
13. 14-(-8)
14. 8+(-9)
15. 8-(-9)

16. -9 +7
17. -8 -10
18. 8 - 10
19. -8 +(-9)
20. 9-(-6)

21. 7 - 9
22. -10 +8
23. -10 -8
24. -9-8
25. -6+9