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Strategies

Strategies for Pre-Algebra students

SEEING PATTERNS IN INTEGERS

by Rmark Moore

....This is for Pre-Algebra students or the curious who wonder about numbers....
Place the following on the board:
or print this and try to solve the problems and look for patterns.
1. 3 + 3 = __ means three plus three equals __?
2. 3 + 2 = __ means three plus two equals __?
3. 3 + 1 = __ means three plus one equals __?
4. 3 + 0 = __ means three plus zero equals __?
5. 3 + -1 = __ means three plus negative one equals __?
6. 3 + -2 = __ means three plus negative two equals __?
7. 3 + -3 = __ means three plus negative three equals __?
8. 3 + -4 = __ means three plus negative four equals __?
9. 3 + -5 = __ means three plus negative five equals __?
10. 3 + -6 = __ means three plus negative six equals __?
Take a look. See a pattern ?
Now reverse the numbers.
1. -3 + 3 = __ means negative three plus three equals __?
2. -3 + 2 = __ means negative three plus two equals __?
3. -3 + 1 = __ means negative three plus one equals __?
4. -3 + 0 = __ means negative three plus zero equals __?
5. -3 + -1 = __ means negative three plus negative one equals __?
6. -3 + -2 = __ means negative three plus negative two equals __?
7. -3 + -3 = __ means negative three plus negative three equals __?
8. -3 + -4 = __ means negative three plus negative four equals __?
9. -3 + -5 = __ means negative three plus negative five equals __?
10. -3 + -6 = __ means negative three plus negative six equals __?
Take a look. See the same pattern ?
O.K. now do you have the idea? Look the examples above and see if you can answer the following questions.
A positive number plus a positive number equals ________?
A positive number plus a negative number equals ________?
A negative number plus a positive number equals ________?
A negative number plus a negative number equals ________?
You are opening a new window for you to explore.
Ok now what about subtraction?
1. 3 - 3 = __ means three minus three equals __?
2. 3 - 2 = __ means three minus two equals __?
3. 3 - 1 = __ means three minus one equals __?
4. 3 - 0 = __ means three minus zero equals __?
5. 3 - ( -1) = __ means three minus negative one equals __?
6. 3 - ( -2) = __ means three minus negative two equals __?
7. 3 - ( -3) = __ means three minus negative three equals __?
8. 3 - ( -4) = __ means three minus negative four equals __?
9. 3 - ( -5) = __ means three minus negative five equals __?
10. 3 - ( -6) = __ means three minus negative six equals __?
Take a look. See a pattern ?
Now reverse the numbers.
1. -3 - 3 = __ means negative three minus three equals __?
2. -3 - 2 = __ means negative three minus two equals __?
3. -3 - 1 = __ means negative three minus one equals __?
4. -3 - 0 = __ means negative three minus zero equals __?
5. -3 - ( -1) = __ means negative three minus negative one equals __?
6. -3 - ( -2) = __ means negative three minus negative two equals __?
7. -3 - ( -3) = __ means negative three minus negative three equals __?
8. -3 - ( -4) = __ means negative three minus negative four equals __?
9. -3 - ( -5) = __ means negative three minus negative five equals __?
10. -3 - ( -6) = __ means negative three minus negative six equals __?
Take another look. See a familiar pattern ?
O.K. now do you still have the idea? Look the examples above and see if you can answer the following questions.
A positive number minus a positive number equals ________?
A positive number minus a negative number equals ________?
A negative number minus a positive number equals ________?
A negative number minus a negative number equals ________?
Take a few minutes to relax, you earned it.
Ok now what about multiplication?
1. 3 X 3 = __ means three times three equals __?
2. 3 X 2 = __ means three times two equals __?
3. 3 X 1 = __ means three times one equals __?
4. 3 X 0 = __ means three times zero equals __?
5. 3 X -1 = __ means three times negative one equals __?
6. 3 X -2 = __ means three times negative two equals __?
7. 3 X -3 = __ means three times negative three equals __?
8. 3 X -4 = __ means three times negative four equals __?
9. 3 X -5 = __ means three times negative five equals __?
10. 3 X -6 = __ means three times negative six equals __?
Take another look. See a familiar pattern ?
Now reverse the numbers.
1. -3 X 3 = __ means negative three times three equals __?
2. -3 X 2 = __ means negative three times two equals __?
3. -3 X 1 = __ means negative three times one equals __?
4. -3 X 0 = __ means negative three times zero equal __?
5. -3 X -1 = __ means negative three times negative one equals __?
6. -3 X -2 = __ means negative three times negative two equals __?
7. -3 X -3 = __ means negative three times negative three equals __?
8. -3 X -4 = __ means negative three times negative four equals __?
9. -3 X -5 = __ means negative three times negative five equals __?
10. -3 X -6 = __ means negative three times negative six equals __?
Take a look. See the same pattern ?
O.K. now does the pattern still work or is it different? Look the examples above and see if you can answer the following questions.
A positive number times a positive number equals ________?
A positive number times a negative number equals ________?
A negative number times a positive number equals ________?
A negative number times a negative number equals ________?
Is this easy or what? It is so easy anyone can do it.
Ok now what about division?
1. 9 / 3 = __ means nine divided by three equals __?
2. 6 / 2 = __ means six divided by two equals __?
3. 3 / 1 = __ means three divided by one equals __?
4. 3 / 0 = __ Division by zero not allowed.
5. 3 / -1 = __ means three divided by negative one equals __?
6. 6 / -2 = __ means six divided by negative two equals __?
7. 9 / -3 = __ means nine divided by negative three equals __?
8. 12 / -4 = __ means 12 divided by negative four equals __?
9. 15 / -5 = __ means 15 divided by negative five equals __?
10. 18 / -6 = __ means 18 divided by negative six equals __?
Take another look. See a familiar pattern ?
Now reverse the numbers.
1. -9 / 3 = __ means negative nine divided by three equals __?
2. -6 / 2 = __ means negative six divided by two equals __?
3. -3 / 1 = __ means negative three divided by one equals __?
4. -3 / 0 = __ Division by zero not allowed.
5. -3 / -1 = __ means negative three divided by negative one equals __?
6. -6 / -2 = __ means negative six divided by negative two equals __?
7. -9 / -3 = __ means negative 9 divided by negative three equals __?
8. -12 / -4 = __ means negative 12 divided by negative four equals __?
9. -15 / -5 = __ means negative 15 divided by negative five equals __?
10. -18 / -6 = __ means negative 18 divided by negative six equals __?
Take a look. See the same pattern ?
O.K. now does the pattern still work or is it different? Look the examples above and see if you can answer the following questions.
A positive number divided by a positive number equals ________?
A positive number divided by a negative number equals ________?
A negative number divided by a positive number equals ________?
A negative number divided by a negative number equals ________?
This is the hard part. Select your own problems. Do your ideas about solving the problems still work? That is the real test. If your answer is yes or maybe, you may be on the way, if not, go back to the top of the page, save it to a disk and do it again on another day.
In exploring ideas, anything a learner can do for themselves, let them.
It's exciting, it's fun, it is called INQUIRY and it is what learning is all about.

If you have comments about strategies or an idea that you want to share, write us at Rose's Corner at our email address below.

For more on operations with positive and negative numbers you want to get our Basic Space Age Math II, which does focus on the concepts and operations with integers.

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Write: RMark Moore c/o Schoolbus Software
105 North Douty Street
Hanford, CA USA 93230
559-582-7229
or you may email Mr. Moore at
schoolbus@schoolbussoftware.com
rmarkmoore@comcast.net

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Strategies

Strategies for Pre-Algebra students

SEEING PATTERNS IN INTEGERS

by Rmark Moore

Phone: 559-582-7229 for Technical Assistance.