Transcript 3 - WW-MFM1P

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.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Definition
Opposite Numbers – numbers
that are the same distance
from zero in the opposite
direction
-6 -5 -4 -3 -2 -1 0 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
30
20
10
0
-10
-30
20
-40
Negative Numbers Are Used to
Show Debt
Let’s say your parents bought a car but
had 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 = -3 COPY 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 = -3 COPY DOWN QUESTION
6–3=3
Subtract the numbers 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 = -3 COPY DOWN QUESTION
6–3=3
= -3
Subtract the numbers without
negative signs.
Keep the sign of the 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) = - 3 COPY 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) = - 3 COPY DOWN QUESTION
12 – 9 = 3
Subtract the numbers
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) = - 3 COPY DOWN QUESTION
12 – 9 = 3
= -3
Subtract the numbers
without negative signs.
Keep the sign of the 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
COPY 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
COPY DOWN QUESTION
7–5=2
Subtract the numbers
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
COPY DOWN QUESTION
7–5=2
Subtract the numbers
without negative signs.
Keep the sign of the larger
number.
=2
SUBTRACTING
INTEGERS
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 Integers
Rule: 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
ADD

SUBTRACT
1) (+6) + (-2)
1) (7) – (2)
2) (+7) + 3
2) (+8) – (-2)
3) (-5) + (+2)
3) (-9) – (+3)
4) (-6) – (-2)
ADD

SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2)
2) (+7) + 3
2) (+8) – (-2)
3) (-5) + (+2)
3) (-9) – (+3)
4) (-6) – (-2)
ADD

SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2)
2) (+7) + 3 = 10
2) (+8) – (-2)
3) (-5) + (+2)
3) (-9) – (+3)
4) (-6) – (-2)
TRY THESE
ADD

SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2)
2) (+7) + 3 = 10
2) (+8) – (-2)
3) (-5) + (+2) = -3
3) (-9) – (+3)
4) (-6) – (-2)
ADD
SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2) = 5
2) (+7) + 3 = 10
2) (+8) – (-2)
= (+8) + (+2)
= 10
3) (-5) + (+2) = -3
3) (-9) – (+3)
= (-9) + (-3)

4) (-6) – (-2)
ADD

SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2) = 5
2) (+7) + 3 = 10
2) (+8) – (-2)
= (+8) + (+2)
= 10
3) (-9) – (+3)
= (-9) + (-3)
= - 12
4) (-6) – (-2)
3) (-5) + (+2) = -3
ADD

SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2) = 5
2) (+7) + 3 = 10
2) (+8) – (-2)
= (+8) + (+2)
= 10
3) (-9) – (+3)
= (-9) + (-3)
= - 12
4) (-6) – (-2)
= (-6) + (2)
3) (-5) + (+2) = -3
ADD

SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2) = 5
2) (+7) + 3 = 10
2) (+8) – (-2)
= (+8) + (+2)
= 10
3) (-9) – (+3)
= (-9) + (-3)
= - 12
4) (-6) – (-2)
= (-6) + (2)
= -4
3) (-5) + (+2) = -3
MULTIPLYING
AND
DIVIDING
INTEGERS
ADD

SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2) = 5
2) (+7) + 3 = 10
2) (+8) – (-2)
3) (-5) + (+2) = -3
3) (-9) – (+3)
4) (-6) – (-2)
ADD
SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2) = 5
2) (+7) + 3 = 10
2) (+8) – (-2)
= (+8) + (+2)
3) (-5) + (+2) = -3
3) (-9) – (+3)

4) (-6) – (-2)
ADD
SUBTRACT
1) (+6) + (-2) = 4
1) (7) – (2) = 5
2) (+7) + 3 = 10
2) (+8) – (-2)
= (+8) + (+2)
= 10
3) (-5) + (+2) = -3
3) (-9) – (+3)

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 & 1.1.6
McGraw-Hill [Ch. 5.2]:
page(s) 182-183
questions 1, 3, 5, 6, 10