Transcript Exploring Integers - Bishop Alemany High School

Exploring Integers
Chapter 2
Chapter 2 – Exploring Integers
Chapter Schedule
MMONDAY
TTUESDAY
BBLOCK
FFRIDAY

T - 2-1 Integers and Absolute Values

B - Math Lab – 1-7 & 2-2 The Coordinate System
FRIDAY - QUIZ 2A

M - 2-3 Comparing and Ordering

T - 2-4 Adding Integers

B - Math Lab - 2-5 Subtracting Integers
FRIDAY - Quiz 2B

M - 2-6 Problem Solving: Look for a Pattern

T - 2-7 Multiplying Integers

B - Math Lab - 2-8 Dividing Integers
FRIDAY - Quiz 2C

M - No School – Columbus Day

T- Chapter 2 Quiz Reviews

B - Chapter 2 Review Math Lab
FRIDAY - Chapter 2 Test

M- Chapter 1 Review

T- Chapter 2 Review

Mid-Term Review

THURSDAY/FRIDAY – MID-TERMS!!!!! –
Report Cards – END OF 1st Quarter
2.1 Integers and Absolute Value

Objective: Graph integer on a number line and find
absolute value

Warm-up:
Answers:
1)
2)
3)
4)
5)
6)
7)
8)
20
25
23
28
24
28
3
9
More  PEMDAS
NOTES:
Answers:
9) 1
10) 1
11) 8
12) 1
13) 8
14) 4
2.1 Integers and Absolute Value

What is an “Integer”?
2.1 Integers and Absolute Value
Can you graph numbers on a number line?
Graph these on a number line:
A=-2
B=3
C=4
Which one has the largest ABSOLUTE VALUE?
B = 4  Because it is the farthest from ZERO
2.1 Integers and Absolute Value


The absolute value of an integer is the numerical value without
regard to whether the sign is negative or positive.
On a number line it is the distance between the number and zero.
◦ The absolute value of -15 is 15.
◦ The absolute value of +15 is ALSO 15

The symbol for absolute value is to enclose the number between
vertical bars such as |-20| = 20 and read "The absolute value of -20
equals 20“.
2.1 HOMEWORK

P69 (18 - 48 EVEN)
Math Lab

Section A – Individual
◦ WS- One-Step Equations With Integers
◦ WS - One-Step Equations with Decimals

Section B - Teacher
◦ 1-7 Ordered Pairs
 P59 (50-55 ALL)
◦ 2-2 The Coordinate System
 P74-75 (6-39 x3)

Section C - Group
◦ Equation Scrabble
FOR POINTS – Winners get EC!!!
1-7 Ordered Pairs
2-2 The Coordinate System

Objectives: To locate and graph points on number line
and in all quadrants of the coordinate plane
1-7 Ordered Pairs
2-2 The Coordinate System

Objectives: To locate and graph points on number
line and in all quadrants of the coordinate plane
•
•
•
Team A – NEGATIVES!
Rules:
Play 1 coin per turn
Must alternate (+)
and (-) each turn
First team past their
5 wins!
Team B – POSTIVIES!
2.2 The Coordinate System
NOTES:
 We will start off with
the Rectangular
Coordinate system.

This is just the
standard axis system
that we use when
sketching our graphs.
Sketch the Graph
x
y
-2
5
-1
0
0
-3
1
-4
2
-3
3
0
4
5
Math Lab - HOMEWORK

1-7 Ordered Pairs
◦ P59 (50-55 ALL)

2.2 The Coordinate System
◦ P74-75 (14 - 38 EVEN)
2.3 Comparing and Ordering

Objective: To compare and order integers
 Warm-up: (USE Graph Paper!)
Graph the following coordinates X and Y Axes:
1.
E (1, -3)
2.
M (-4, 2)
3.
I (0, -2)
4.
L (2, 0)
5.
Y (-3, -4)
Graph the following inequalities individually:
6.
J > -2
7.
O<6
8.
E<4
9.
Y < -3
Answers:
On Graph
Quiz 2A – Results!
Period 1
Period 2
Period 3
91%
A80%
B-
87%
B
90%
A-
92%
A85%
B
Binder Check
Average
35/50
30/50
27/30
Overall Class
Average
(as of 9/21)
70%
C-
73%
C
Chapter 1 Test
Average
Quiz Average
(NO MATH Lab WS)
71%
C-
2.3 Comparing and Ordering
NOTES:
Graphing Inequalities on a Number Line

1. X < 0
2. X < 0
3. Y >15
4. Y > 15
2.3 Comparing and Ordering
NOTES:
Graphing Inequalities with ABSOLUTE
VALUES

J) Is 4 < |-4| ?
Answer : _______
Y) Is 4 < |4| ?
Answer : _______
O) Is -4 < |-4| ?
Answer : _______
K) Is -4 < |4| ?
Answer : _______
E) Is |4| < |-4| ?
Answer : _______
R) Is 4 < |4| ?
Answer : _______
2.3 Comparing and Ordering

P79 - 80 (15-42 x3 & 44)
2.4 Adding Integers

Objective: To add integers
Warm-up:
Replace the ? with a < , < , >, > , or = :
1. - 9 ? 8
2. 0 ? – 4
Write an inequality using the numbers in
each sentence. Use “relation symbols”.
3. A turkey sandwich cost $6 and a turkey
dinner costs $11.
4. The low temperature was - 42°F and the
temperature now is - 46°F.

Answers:
1)
2)
3)
4)
<
>
6 < 11
-42 > - 46
2.4 Adding Integers

NOTES:
Remember!
If the signs are different, subtract their ABSOLUTE
VALUES!
Adding Integers Game
2.4 Adding Integers

P86-87 (10 – 44 EVEN)
MATH LAB –
2.5 Subtracting Integers
 Section A – Individual WS
◦ Inequalities and Their Graphs
◦ Solving One-Step Inequalities by
Adding/Subtracting
 Section B – Teacher
◦ 2.5 Subtracting Integers Lesson
 Section C –
◦ Math Games
Group
MATH LAB –
2.5 Subtracting Integers

Objective: To subtract integers
 Warm-up:
1. Draw this “Magic Triangle”
paper
on your
Then look up “inverse”.
How would it be useful when solving
equations?
2.
2.5 Subtracting Integers
-10 - (-15) =
-10 + (+15) = 5
-25 - (+25) =
-25 + (-25) = -50
9 – (- 3) =
9 + (+3) = 12
-7 – (-5) =
-7 + (+5) = -2
3 - (+5) =
3 + (-5) = -2
21 – (-19) =
21 + (+19) = 40
2.5 Subtracting Integers
Magic Triangle
• A magic triangle is an arrangement of six positive or negative integers such
that the sum (+) of each side is the same.
•Solve the set of equations listed below.
•Then put the solutions to the equations into an empty magic triangle
similar to the one pictured.
1.
x = 4 + 5 - (-6) - 4 + 9
2.
a = 20 + (-10) - 2 + 4 + (-2)
3.
60 - (-2) - 22 + (-20) - 2 = n
4.
z = 5 + (-6) - 3
5.
-6 + 5 + 7 - 3 + 5 = h
6.
-6 + 7 - (-2) - 5 = y
26
2.5 Subtracting Integers

P 91-92 (6 – 45 x3)
2.6 Problem Solving: Look for a Pattern
Objective: To solve problem by looking
for a pattern
 Warm-up:
Solve each equation
1. N = 9 – ( - 1)
2. X = - 3 – (21)
3. T = - 8 – (-3)

Simplify each equation
4. 8m – ( - 6m)
5. - 15c – 17c
Answers:
1)
2)
3)
4)
5)
10
- 24
-5
14m
- 32c
2.6 Problem Solving: Look for a
Pattern

P 96-97 (9 - 21 x3)
2.7 Multiplying Integers

Objective: To multiply integers

Warm-up:
1.
◦
◦
◦
◦
Use the pattern below to find the
product of 48 x 52
8 x 12 = 96
18 x 22 = 396
28 x 32 = 896
38 x 42 = 1596
Find the next two integers
1. 5, 10, 20, 40, _____, _____
2. -2, 6, -18, 54, _____, _____
3. N, O, R, S,V, _____, _____
4. J, F, M, A, M, J, J, A, _____, _____
Answers:
1)
2)
3)
4)
5)
2,496
80, 160
- 162, 486
W, Z
S (Sept.), O
(Oct.)
2.7 Multiplying Integers
NOTES: Multiplying Integers
Rule 1:
The product of a positive integer and a
negative integer is a negative integer.
Rule 2:
The product of two negative integers or
two positive integers is a positive integer.
2.7 Multiplying Integers
NOTES: Multiplying Integers
Integers
Product
 (+7) (+3) =
+21
Rule Used
Rule 2

(+7) (-3) =
-21
Rule 1

(-7) (+3) =
-21
Rule 1

(-7) (-3) =
+21
Rule 2
2.7 Multiplying Integers
NOTES: Multiplying Two Integers
Integers
Product
Rule Used
 (+8) (+4) =
+32
Rule 2
 (+11) (-2) =
-22
Rule 1
 (-14) (+3) =
-42
Rule 1
 (-9) (-5) =
+45
Rule 2
2.7 Multiplying Integers
NOTES: Multiplying Three Integers
Integers Product of First Two Integers and the Third Product
(+5) (+3) (+2) =
(+15) (+2) =
+30
(+8) (+2) (-5) =
(+16) (-5)
=
-80
(-6) (+3) (+4) =
(-18) (+4)
=
-72
(-9) (-3) (+2) =
(+27) (+2) =
+54
(-4) (-3) (-5) =
(+12) (-5)
=
-60
2.7 Multiplying Integers

P 102-103 (6 – 36 x3)
MATH LAB –
2.8 Dividing Integers
 Section A – Individual
◦ Solving One-Step Inequalities
by Multiplying/Dividing
 Section B - Teacher
◦ 2.8 Dividing Integers
◦ Math Games
 Section C – Group
◦ Climb the Cliff boardgame
MATH LAB –
2.8 Dividing Integers

Objective: To divide integers

Warm-up:
Solve each equation
1. (- 5)(-3)(4) = a
2. (20)(- 6)(2) = b
Find the product
3. (-8x) (-9)
4. (3xy)(-3)(7)
5. -9(-m)(-n)
Answers:
1)
2)
3)
4)
5)
60
-240
72x
-63xy
-9mn
2.8 Dividing Integers
NOTES: Dividing Integers
When we divide integers, the same
rules for multiplying apply.

Example:
(+6) ÷ (+2) = +3
(+6) ÷ (–2) = –3
(–6) ÷ (+2) = –3
(–6) ÷ (–2) = +3
Calculate the following:
A) (–8) ÷ (–2) =
B) (12) ÷ (–4) =
Solutions:
A) (–8) ÷ (–2) = 4
B) (12) ÷ (–4) = –3
2.8 Dividing Integers

P 106 -107 (6 - 45 x3)
Chapter 2 Test:
Preparation Week
Monday – NO SCHOOL
 Tuesday – Review Math Lab
Packets
 Block- Math Lab – Quiz
Reviews/Study Guides
 Friday – Chapter 2 Test
(Substitute)

REMINDER:
NEXT WEEK IS MID-TERMS!!
Chapter 2 Test:
Math Lab Worksheets

Graphing Inequalities:
x>2
◦ Draw your number line
--------I--------------I-----------------I--------
1
2
3
◦ Mark this point with the appropriate notation
(an open dot indicating that the point x=2 was
NOT included in the solution)
◦ Then shade everything to the right, because
"greater than" means "everything off to the
right".
MATH LAB –
Chapter 2 Test Preparation
 Section A – Individual
◦ Chapter 2 Study Guide and
Assessment
 P110 – 112 (8-68 EVEN)
 Section B - Teacher
◦ Quiz Reviews (2A, 2B & 2C)
 Section C – Group
◦ Sequence Game (Pairs)
Chapter 2 Test Preparation
A Game of Sequence:
Recognizing number patterns is an
important ability.
By becoming familiar with them, you can
save time in the future.
Here’s a game that teaches you some of the
most common sequences in mathematics.
Chapter 2 Test Preparation
Examples:
1.
2, 4, 6, 8, 10 … “Multiples of 2”
2.
1, 4, 9, 16, 25 … “The squares”
3.
5, -10, 15, -20, 25 … “Multiples of 5, with alternating signs.”
4.
4, 12, 36, 108, 324… “Multiply each term by 3”
5.
1, 1, 2, 3, 5 … “Add the previous two terms” (Fibonacci)
6.
1, 2, 4, 8, 16 … “Powers of 2”
7.
5, -10, 15, -20, 25 … “Multiples of 5, with alternating signs.”
8.
3x + 1, 6x + 2, 12x + 4, 24x + 8, 48x + 16 … “Double the previous term.”
9.
1, 2, 2, 4, 8 … “Multiply the previous two terms.”
WIN PLANNER POINTS!!

If you can find 20 patterns, you will receive a “Planner Sticker”.

For ever 10 more patterns, you will receive another sticker. (Max 50 patterns)
NOTE: For a pattern to count, you must gave FIVE pieces of the pattern AND write the
pattern