LESSON 1.1 INTEGERS

MFM1P

Homework Check

McGraw-Hill [Ch. 5.1]: pages 175-178 Q# 5a, 6, 8, 10, 11, 12, 13, 14, 16

Definition

Positive number – a number greater than zero.

0 1 2 3 4 5 6

Definition

Negative number – a number less than zero.

0 1 2 3 4 5 6-1-2-3-4-5-6

Definition

Opposite Numbers – numbers that are the same distance from zero in the opposite direction

0 1 2 3 4 5 6-1-2-3-4-5-6

Definition

Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero.

7 opposite -7

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level

0102030

-10-20-30-40-50

Negative Numbers Are Used toShow Debt

Let’s say your parents bought a car buthad to get a loan from the bank for $5,000.When counting all their money they add in -$5.000 to show they still owe the bank.

Remember….

Red Algebra Tiles indicates (-)

“Zero Pairs” are two matching tiles, one red, and one another color, that cancel each other out and equal 0

For example:

ADDING INTEGERS

Addition of Integers Addition can be viewed as “combining”.

Combining involves the forming and removing of all zero pairs.

For each of the given examples, use algebra tiles to model the addition.

To demonstrate understanding, you may be asked to use Algebra Tiles to solve a problem in front of teacher OR draw pictorial diagrams which show the

modeling.

Addition of Integers (+3) + (+1) =

(-2) + (-1) =

Addition of Integers

(+3) + (-1) =

(+4) + (-4) =

ADDING INTEGERS

Positive + Positive = Positive( +3) + (+2) = +5

When a number is positive, you do not have to use the (+) sign.

(+3) + (+2) = 5

ADDING TWO NEGATIVE NUMBERS

Negative + Negative = Negative(- 6) + (- 3) = - 9

When a number is NEGATIVE, you do have to use the (-) sign.

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 1:

(- 6) + 3 = -(- 6) + 3 = -33

COPY DOWN QUESTIONCOPY DOWN QUESTION

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 1:

(- 6) + 3 = -(- 6) + 3 = -33

COPY DOWN QUESTIONCOPY DOWN QUESTION

6 – 3 = 36 – 3 = 3 Subtract the numbers Subtract the numbers without negative signs.without negative signs.

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 1:

(- 6) + 3 = -(- 6) + 3 = -33

COPY DOWN QUESTIONCOPY DOWN QUESTION

6 – 3 = 36 – 3 = 3 Subtract the numbers Subtract the numbers without negative signs.without negative signs.

= = -3-3 Keep the sign of the Keep the sign of the larger number.larger number.

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 2:

9 + (-12) = - 9 + (-12) = - 33

COPY DOWN QUESTIONCOPY DOWN QUESTION

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 2:

9 + (-12) = - 9 + (-12) = - 33

COPY DOWN QUESTIONCOPY DOWN QUESTION

12 – 9 = 312 – 9 = 3 Subtract the numbers Subtract the numbers without negative signs.without negative signs.

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 2:

9 + (-12) = - 9 + (-12) = - 33

COPY DOWN QUESTIONCOPY DOWN QUESTION

12 – 9 = 312 – 9 = 3 Subtract the numbers Subtract the numbers without negative signs.without negative signs.

= -3= -3 Keep the sign of the Keep the sign of the larger number.larger number.

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 3:

(- 5) + 7 = 2(- 5) + 7 = 2 COPY DOWN QUESTIONCOPY DOWN QUESTION

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 3:

(- 5) + 7 = 2(- 5) + 7 = 2 COPY DOWN QUESTIONCOPY DOWN QUESTION

7 – 5 = 27 – 5 = 2 Subtract the numbers Subtract the numbers without negative signs.without negative signs.

ADDING POSITIVE AND NEGATIVE INTEGERS Sum of a negative and a positive number - Keep the sign of the larger

number and subtract

EXAMPLE 3:

(- 5) + 7 = 2(- 5) + 7 = 2 COPY DOWN QUESTIONCOPY DOWN QUESTION

7 – 5 = 27 – 5 = 2 Subtract the numbers Subtract the numbers without negative signs.without negative signs.

= 2= 2 Keep the sign of the Keep the sign of the larger number.larger number.

SUBTRACTINGINTEGERS

Subtraction of Integers Subtraction can be interpreted as “take-away.”

Subtraction can also be thought of as “adding the opposite.”

For each of the given examples, use algebra tiles to model the subtraction.

To demonstrate understanding, you may be asked to use Algebra Tiles to solve a problem in front of teacher OR draw pictorial diagrams which show the

modeling.

SUBTRACTING INTEGERS

Negative - Positive = Negative

(same as adding two negative numbers)

(- 8) - 3 = -8 + (-3) = -11

Another way of saying this:

ADD THE OPPOSITE

(- 8) - 3 = -8 + (-3) = -11

SUBTRACTING INTEGERS

Positive - Negative = Positive + Positive = Positive

4 - (-3) = 4 + 3 = 7

Once again you are adding the opposite

4 - (-3) = 4 + 3 = 7

SUBTRACTING INTEGERS

Negative - Negative = Negative + Positive =

Keep the sign of the larger number and subtract

(-7) - (-5) = ( -7) + 5 = -2

(-5) - ( -7) = (-5) + 7 = 2

Subtracting IntegersRule: Add the opposite.

(+3) – (-5)

(-4) – (+1)

When doing subtraction problems, CHANGE the subtraction sign to an addition sign. Then “flip” the sign of the number after the new addition sign.

For example: (+3) – (-5) becomes (+3) + (+5) (-4) – (+1) becomes (-4) + (-1)

Subtracting Integers

(+3) – (-3)

TRY THESE

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2)1) (+6) + (-2) 1) (7) – (2)1) (7) – (2)

2) (+7) + 32) (+7) + 3 2) (+8) – (-2)2) (+8) – (-2)

3) (-5) + (+2)3) (-5) + (+2) 3) (-9) – (+3)3) (-9) – (+3)

4) (-6) – (-2)4) (-6) – (-2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2)1) (7) – (2)

2) (+7) + 32) (+7) + 3 2) (+8) – (-2)2) (+8) – (-2)

3) (-5) + (+2)3) (-5) + (+2) 3) (-9) – (+3)3) (-9) – (+3)

4) (-6) – (-2)4) (-6) – (-2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2)1) (7) – (2)

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

3) (-5) + (+2)3) (-5) + (+2) 3) (-9) – (+3)3) (-9) – (+3)

4) (-6) – (-2)4) (-6) – (-2)

TRY THESE

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2)1) (7) – (2)

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

4) (-6) – (-2)4) (-6) – (-2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2) 1) (7) – (2) = 5= 5

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

= (+8) + (+2)= (+8) + (+2)

= 10= 10

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

= (-9) + (-3)= (-9) + (-3)

4) (-6) – (-2)4) (-6) – (-2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2) 1) (7) – (2) = 5= 5

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

= (+8) + (+2)= (+8) + (+2)

= 10= 10

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

= (-9) + (-3)= (-9) + (-3)

= - 12= - 12

4) (-6) – (-2)4) (-6) – (-2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2) 1) (7) – (2) = 5= 5

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

= (+8) + (+2)= (+8) + (+2)

= 10= 10

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

= (-9) + (-3)= (-9) + (-3)

= - 12= - 12

4) (-6) – (-2)4) (-6) – (-2)

= (-6) + (2)= (-6) + (2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2) 1) (7) – (2) = 5= 5

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

= (+8) + (+2)= (+8) + (+2)

= 10= 10

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

= (-9) + (-3)= (-9) + (-3)

= - 12= - 12

4) (-6) – (-2)4) (-6) – (-2)

= (-6) + (2)= (-6) + (2)

= -4= -4

MULTIPLYING AND

DIVIDING INTEGERS

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2) 1) (7) – (2) = 5= 5

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

4) (-6) – (-2)4) (-6) – (-2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2) 1) (7) – (2) = 5= 5

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

= (+8) + (+2)= (+8) + (+2)

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

4) (-6) – (-2)4) (-6) – (-2)

ADDADD SUBTRACTSUBTRACT

1) (+6) + (-2) 1) (+6) + (-2) = 4= 4 1) (7) – (2) 1) (7) – (2) = 5= 5

2) (+7) + 3 2) (+7) + 3 = 10= 10 2) (+8) – (-2)2) (+8) – (-2)

= (+8) + (+2)= (+8) + (+2)

= 10= 10

3) (-5) + (+2) 3) (-5) + (+2) = -3= -3 3) (-9) – (+3)3) (-9) – (+3)

4) (-6) – (-2)4) (-6) – (-2)

MEMORY TRICK!

SUCCESS CRITERIA I understand the difference between rational and irrational

numbers

I understand the meaning of the term “operations”

I understand the meaning of other words related to addition, subtraction, multiplication, division and equal.

I am able to add and subtract positive and negative integers using algebra tiles

I am able to add and subtract positive and negative integers using the rules provided.

I can multiply and divide positive and negative integers using the help of a memory trick (the love/hate analogy).

Homework for Wednesday

Exercise 1.1.5 & 1.1.6McGraw-Hill [Ch. 5.2]:

page(s) 182-183 questions 1, 3, 5, 6, 10