Exploring IntegersChapter 2

Chapter 2 – Exploring IntegersChapter Schedule 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

M-MONDAY

T-TUESDAY

B-BLOCK

F- FRIDAY

2.1 Integers and Absolute Value

Objective: Graph integer on a number line and find absolute value

Warm-up: Answers:1) 202) 253) 234) 285) 246) 287) 38) 9

More PEMDAS

Answers:9) 110)111)812)113)814)4

NOTES:

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 HOMEWORKP69 (18 - 48 EVEN)

Math LabSection 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 Pairs2-2 The Coordinate System

Objectives: To locate and graph points on number line and in all quadrants of the coordinate plane

1-7 Ordered Pairs2-2 The Coordinate System

Objectives: To locate and graph points on number line and in all quadrants of the coordinate plane

Team A – NEGATIVES! Team B – POSTIVIES!

Rules:• Play 1 coin per

turn• Must alternate

(+) and (-) each turn

• First team past their 5 wins!

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 Graphx 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 OrderingObjective: 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

Chapter 1 Test Average

91%A-

87%B

92%A-

Quiz Average80%

B-90%A-

85%B

Binder Check Average 35/50 30/50 27/30

(NO MATH Lab WS)

Overall Class Average

(as of 9/21)

70%C-

73%C

71%C-

2.3 Comparing and OrderingNOTES: Graphing Inequalities on a Number

Line1. X < 0

2. X < 0

3. Y >15

4. Y > 15

2.3 Comparing and OrderingNOTES: Graphing Inequalities with ABSOLUTE

VALUES

J ) I s 4 < | - 4 | ? A n s w e r : _ _ _ _ _ _ _

O ) I s - 4 < | - 4 | ? A n s w e r : _ _ _ _ _ _ _

E ) I s | 4 | < | - 4 | ? A n s w e r : _ _ _ _ _ _ _

Y ) I s 4 < | 4 | ?

A n s w e r : _ _ _ _ _ _ _

K ) I s - 4 < | 4 | ? A n s w e r : _ _ _ _ _ _ _

R ) I s 4 < | 4 | ? A n s w e r : _ _ _ _ _ _ _

2.3 Comparing and OrderingP79 - 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 ? – 4Write 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) 6 < 114) -42 > -

46

2.4 Adding IntegersNOTES:

Remember! If the signs are different, subtract their

ABSOLUTE VALUES!

Adding Integers Game

2.4 Adding IntegersP86-87 (10 – 44 EVEN)

MATH LAB – 2.5 Subtracting IntegersSection A – Individual WS

◦ Inequalities and Their Graphs◦Solving One-Step Inequalities

by Adding/Subtracting

Section B – Teacher◦2.5 Subtracting Integers

Lesson

Section C – Group◦Math Games

MATH LAB – 2.5 Subtracting IntegersObjective: To subtract integers

Warm-up:1. Draw this “Magic Triangle” on

your paper

2. Then look up “inverse”. How would it be useful when

solving equations?

2.5 Subtracting Integers

9 – (- 3) =9 + (+3) = 12

-7 – (-5) = -7 + (+5) = -2

21 – (-19) = 21 + (+19) = 40

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

-25 - (+25) =-25 + (-25) = -50 -10 + (+15) = 5

-10 - (-15) =

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 IntegersP 91-92 (6 – 45 x3)

2.6 Problem Solving: Look for a PatternObjective: To solve problem by

looking for a patternWarm-up:Solve each equation1. N = 9 – ( - 1)2. X = - 3 – (21)3. T = - 8 – (-3)

Simplify each equation4. 8m – ( - 6m)5. - 15c – 17c

Answers:1) 102) - 243) - 54) 14m5) - 32c

2.6 Problem Solving: Look for a PatternP 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 integers2. 5, 10, 20, 40, _____, _____3. -2, 6, -18, 54, _____, _____4. N, O, R, S, V, _____, _____5. J, F, M, A, M, J, J, A, _____, _____

Answers:1) 2,4962) 80, 1603) - 162,

4864) W, Z5) S (Sept.),

O (Oct.)

2.7 Multiplying Integers

NOTES: Multiplying IntegersRule 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.

VIDEO???

2.7 Multiplying IntegersNOTES: Multiplying IntegersIntegers Product Rule Used(+7) (+3) = +21

Rule 2(+7) (-3) = -21

Rule 1(-7) (+3) = -21

Rule 1(-7) (-3) = +21

Rule 2

2.7 Multiplying IntegersNOTES: Multiplying Two IntegersIntegers Product Rule Used(+8) (+4) = +32Rule 2(+11) (-2) = -22Rule 1(-14) (+3) = -42Rule 1(-9) (-5) = +45Rule 2

2.7 Multiplying Integers

NOTES: Multiplying Three IntegersIntegers 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 IntegersP 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 IntegersObjective: To divide integers

Warm-up:

Solve each equation1. (- 5)(-3)(4) = a2. (20)(- 6)(2) = bFind the product3. (-8x) (-9)4. (3xy)(-3)(7)5. -9(-m)(-n)

Answers:1) 602) -2403) 72x4) -63xy5) -9mn

2.8 Dividing IntegersNOTES: Dividing IntegersWhen we divide integers, the same rules for multiplying apply.

Example:(+6) ÷ (+2) = +3 (+6) ÷ (–2) = –3 (–6) ÷ (+2) = –3 (–6) ÷ (–2) = +3

VIDEO???Calculate the following:

A) (–8) ÷ (–2) =B) (12) ÷ (–4) =

Solutions:A) (–8) ÷ (–2) =

4B) (12) ÷ (–4) = –

3

2.8 Dividing IntegersP 106 -107 (6 - 45 x3)

Chapter 2 Test:Preparation Week

Monday – NO SCHOOLTuesday – Review Math

Lab PacketsBlock- Math Lab – Quiz

Reviews/Study GuidesFriday – Chapter 2 Test

(Substitute)

REMINDER:NEXT WEEK IS MID-TERMS!!

Chapter 2 Test:Math Lab Worksheets

Graphing Inequalities:◦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".

x > 2

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 PreparationExamples:

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