Integers: Addition and Subtraction

INTEGERS:ADDITION & SUBTRACTIONPresented by: CARLO JUSTINO J. LUNA

Conrado P. Macapinlac, Sr. High SchoolSST-1 / Math Leader

EXPLORE!JOSE’s SAVINGS

Jose saves Php 8 from his day’s allowance. However, he has to pay Php 5 to the class treasurer. After paying the class treasurer, how much is left of his savings for the day?

COLORED COUNTERS can be used to model this problem. The idea of using colored counters or rods to represent signed numbers goes a long way back.

HISTORICAL TRIVIAIn 200 BC, Chinese accountants used black (negative) rods for debts and red (positive)

rods for credits. However, it was Girolamo Cardano (1501-1576) who introduced negative numbers and their properties formally.Nowadays, if there are more credits, the account is positive or “in the black.” If there are more debits than credits, the account is in debt or is “in the red.”

Operations with integers can be modeled using two-colored counters.

Positive+1

Negative-1

ZERO PAIRSThey have a value of zero.

Now, we’re ready to solve the problem above using counters. Let us represent – 5 + ( 8 ) using red and yellow counters.

When using two-colored counters to model addition, build each addend then find the value of the collection.

(– 5) + ( 8 ) = 3

Jose has Php 3 left. zero pairs

Modeling addition of integers using counters:

Here is another example:

(Notice that there are no zero pairs.)

Build the following addition problems:1. 5 + (–3)2. –5 + (9)3. –4 + (–2)4. 1 + (8)5. –9 + (6)

While using counters helps us visualize addition of integers, these are inconvenience to use with large numbers. And so, we have a rule on adding integers with the same sign and adding integers with unlike signs.

Adding Integers with the Same Sign To add integers with the same sign, add

their absolute values and common their common sign.

Adding Integers with Different Signs To add integers with different signs, get

the difference between their absolute values and use the sign of the integer with the greater absolute value in the answer.

Try this!1. 12 + (15)2. –3 + (7)3. –9 + (-4)4. 4 + (–12)5. –2 + (–3) + (–4)6. 5 + (–7) + (–2)

EXPLORE!Distance Between

A submarine cruises at a depth of 40 meters. Directly above it, an airplane flies at an altitude of 192 meters. How far apart are they?

To find the distance between the submarine and the airplane, we represent a depth of 40m as –40 and a height of 192m as +192. To obtain the difference between the two, we write 192 – (–40).

Based on the illustration, it is clear that the distance from the plane to the submarine is 232 meters, that is 192 + 40 = 232. Thus, we say that these two expressions are equal. 192 – (–40) = 192 + 40 232 = 232

Subtracting –40 has the same effect as adding +40. We state this finding as a rule on subtracting signed numbers.Subtracting Signed NumbersTo subtract a signed number, add its additive inverse.

For any real numbers x and y:

Examples: Subtract.

1. 2.

EVALUATIONACTIVITY: FACEing MATH by Kristin DeWitMaterials: crayons

copy of the blank facecopy of the 27 questions

The learners will answer 27 questions. They will do this by creating wonderful faces while answering the questions. In this activity, the learners who do not typically enjoy lecture/discussion days will find themselves motivated to complete the lesson in order to draw and color the desired face. Although all the student’s drawings should have the same facial features, each face will look unique because of the distracters in the choices of answers. FACEing MATH has never been this fun!