February 24, 2014

Manipulating Integers (MDAS)

Objective: To elaborate to the kids the basic processes (addition, subtraction, multiplication, and division) used in manipulating

integers, positive and negative integers in particular.

I. Lesson Proper

A. Recall. Starting with positive integers, review the four basic processes (addition and subtraction first)

1. 2+2=4

2. 17-5=12

3. 3*5=15

4. 10/2=5

*These are just some examples. You can provide more.

**Also, please note the notations for multiplication and subtraction that the kids are used to (i.e. or * for

mult., / or for div.)

B. Introduce the number line and absolute value. Discuss the number line and the directions of positive and negative.

Use a graphical representation for easy reference. Explain that integers are also known as whole numbers.

This is where you introduce the concept of absolute value as the distance or units from a reference point, the

origin. The notation is |a| for any real number a.

We can use the number line as a model to help us visualize adding and subtracting of signed integers. Just think of

addition and subtraction as directions on the number line. There are also several rules and properties that define

how to perform these basic operations:

1. To add integers having the same sign, keep the same sign and add the absolute value of each number.

2. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract

the smallest absolute value from the largest.

C. Provide examples.

1. Here's how to add two positive integers:

4 + 7 = ?

If you start at positive four on the number line and move seven units to the right, you end up at positive eleven.

Also, these integers have the same sign, so you can just keep the sign and add their absolute values, to get the same

answer, positive eleven.

Here's how to add two negative integers:

-4 + (-8) = ?

2. If you start at negative four on the number line and move eight units to the left, you end up at negative twelve.

Also, these integers have the same sign, so you can just keep the negative sign and add their absolute values, to get

the same answer, negative twelve.

Here's how to add a positive integer to a negative integer:

-3 + 6 = ?

3. If you start at negative three on the real number line and move six units to the right, you end up at positive three.

Also, these integers have different signs, so keep the sign from the integer having the greatest absolute value and

subtract the smallest absolute value from the largest.

Subtract three from six and keep the positive sign, again giving positive three.

Here's how to add a negative integer to a positive integer:

5 + (-8) = ?

4. If you start at positive five on the real number line and move eight units to the left, you end up at negative three.

Also, these integers have different signs, so keep the sign from the integer having the greatest absolute value and

subtract the smallest absolute value from the largest, or subtract five from eight and keep the negative sign, again

giving negative three.

5. To subtract a number, add its opposite:

5 - 8 = ?

Because they give the same result, you can see that subtracting eight from five is equivalent to adding negative eight

to positive five. The answer is - 3.

6. To subtract a number, add its opposite:

-3 - (-6) = ?

Because they give the same result, you can see that subtracting negative six from negative three is equivalent to

adding positive six to negative three. The answer is 3.

D. Once they understand addition and subtraction of integers, move on to multiplication and division. Study some

examples listed below and ask them if they spot any patterns.

E. You multiply or divide integers just as you do whole numbers, except you must keep track of the signs. To multiply

or divide signed integers, always multiply or divide the absolute values and use these rules to determine the sign of the

answer.

1. When you multiply two integers with the same signs, the result is always positive. Just multiply the absolute values

and make the answer positive.

Positive x positive = positive

Negative x negative = positive

2. When you multiply two integers with different signs, the result is always negative. Just multiply the absolute values

and make the answer negative.

Positive x negative = negative

Negative x positive = negative

3. When you divide two integers with the same sign, the result is always positive. Just divide the absolute values and

make the answer positive.

Positive positive = positive

Negative negative = positive

4. When you divide two integers with different signs, the result is always negative. Just divide the absolute values

and make the answer negative.

Positive negative = negative

Negative positive = negative

F. Provide some examples.

Apply the knowledge they learned about absolute values.

II. Ask if they have questions or need further clarifications.

*Make sure that you discuss adding, subtracting, multiplying, and dividing zero by this time.

III. Quiz Bee

*Since the lesson proper is extremely long, only six questions will be answered during the quiz. You may add more if the time

allows, or not include some if there is no more time.

1. 7 + 6 = ?

2. 13 + (6) + (12) = ?

3. 70 + 60 (28) = ?

4. 16 4 = ?

5. 22 (11 1) = ?

6. (9 12) 3 =?

Answers:

1. -1

2. -5

3. 18

4. -4

5. 2

6. -36

Reference:

https://www.google.com.ph/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CC8QFjAA&url=http%3A%2F%2Fwww.

math.com%2Fschool%2Fsubject1%2Flessons%2FS1U1L11DP.html&ei=hbsIU8q9Fo69iAfC84CgBA&usg=AFQjCNFk-

jmAeeTw9E0ZKHyBr0mYdRBZmQ&bvm=bv.61725948,d.aGc