Accentuate+the+Negative

Accentuate the Negative
hw_journal_record_accentuate_the_negative.doc

MeP - 1.1 Extending the Number Line Initials (normal)

1.1: Playing Math Mania
Super Brains: -300 Rocket Scientist: + **150** Know-It-Alls: -**500**
 * A**. Rocket Scientist have the highest score and the know it all have the lowest points.Because once you go to negative numbers, as the number gates bigger the value is less.

Know it alls: -500 Rocket scientists: 150
 * B.** They are 650 points away.

Super Brains could have got there by: Know -it -alls could have got there by:
 * C.** Rocket Scientists could have got there by:
 * 150
 * 200-50
 * 250-100
 * 0-250-50
 * 0-250-250

Super brains: -300+200= -100 - 150= -250+ 50=-200+ 50= **-150** Rocket Scientist: 150-50=100- 200= -100 + 100= 0 - 150= -**150** Know-It-Alls: -500 -100= -600+200= -400+150= -250- 50 = **-300** Rocket Scientist: -150 Know-It-Alls: -300 Super Brains and Rocket scientists are 150 points ahead.
 * D.** Super Brains: -150
 * E** Know it alls are in last place because they have the highest negative number

Problem Follow Up:
 * A** They could have tied if the Smarties got two 50 point questions correct while the Brain Surgeons got two 50 point questions wrong

They also could have done it this way, the smarties got one 150 point question wrong, then the brain surgeons got two 50 questions wrong and finally the Smarties got a 150 question correct.

Homework : ACE1: pg 12-16; 1-7,9-14,26,(27**)**
Assigned: (normal)
 * Collected: (normal)

JD - 1.2 Winning the Game Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

RI - 2.1 Adding on a Number Line Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

IK - 2.2 Inventing a New Model Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

MaP - 3.1 Subtracting on a Chip Board Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

JN - 3.2 Subtracting on a Number Line Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

LD - 3.3 Exploring Patterns Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

AD - 3.4 “Undoing” with Add. And Subt.**

**EQ: How do I find the difference between integers?**
To find the difference between integers, we need to first convert a subtraction sentence into an addition sentence. x - x becomes x + (-x); and x -(-x) becomes x+x. We can then solve the question following the procedures we studied in investigation two. In this problem, we learn that we can 'undo' addition sentences usingsubtraction sentences and vice versa. In other words, we can use opposite operations to verify our answers.**
 * To find the difference between integers, we can use previously studied methods like using a number line or chip board. Instead of adding numbers or chips, we take away the required number or amount of chips.

**Problem 3.4: "Undoing" with Addition and Subtraction**
Using a chip board, I found that -17+13 equals -4 A2. To 'undo' or verify my addition sentence, I can use the following subtraction sentence: -4 -13 = (-4) + (-13) = -17
 * A1. Complete the addition sentence -17+ 13 = ?

B1. Complete the addition sentence -4 + (-18) = ? I found out that -4 + (-18) = -22 B2. To undo or verify this addition sentence, I can use the following subtraction sentence: -22 - (-18) = -22 + 18 = -4

C1. x + (-18) = 6 Therefore 6 - (-18) = x 6 - (-18) = 6 + 18 = 24 Therefore x = 24, and 24 + (-18) = 6

C2. x + (-13) = -41 Therefore -41 - (-13) = x -41 - (-13) = -41 + 13 = -28 Therefore x = -28, and -28 + (-13) = -41

C3. x + 6.1 = -3.2 Therefore x = -3.2 - 6.1 = -3.2 + -6.1 = -9.3 Therefore -9.3 + 6.1 = -3.2

C4. x + -1/3 = 1/3 Therefore x = 1/3 - -1/3 = 1/3 + 1/3 = 2/3 Therefore 2/3 + -1/3 = 1/3

D1. x - (-6) = -6 Therefore x = -6 + -6 = -12 Therefore -12 - (-6) = -6

D2. x - (-2) = 3 Therefore x = 3 + -2 = 1 Therefore 1 - (-2) = 3

D3. x - 5.3 = -7.1 Therefore x = -7.1 + 5.3 = -1.8 Therefore -1.8 - 5.3 = -7.1

D4. x - -1/4 = -3/4 Therefore -3/4 + -(1/4) = -4/4 Therefore -4/4 - (-1/4) = -3/4

__Problem 3.4 Follow Up__

1. In the introduction to this problem, we wrote the number sentence 11 = 14 - 3 from the sentence 11 + 3 = 14. We could also write 3 + 11 = 14. Another subtraction sentence to go with this addition sentence would be 14 - 11 = 3.

2(a). 3.8 + -2.6 = 1.2 2(b). A subtraction sentence that would be related to the addition sentence above would be 1.2 - (-2.6) = 3.8

3(a). -11 - 6 = (-11) + (-6) = -17 3(b). A subtraction sentence that would be related to the addition sentence above would be -17 + 6 = -11

4. When we add positive or negative integers, we may get a positive or negative sum. The same goes for subtraction. If we subtract a negative from a positive, we get a positive difference. However, if we subtract a positive from a negative, we will always obtain a negative difference.**

**Homework**
Assigned: ACE 3- 21-24, 33 (39*); Mathemtical Reflections, pg 52
 * Collected: None

BL - 4.1 Rising and Falling Temperatures**

**Notes**

 * EQ- How do I multiply and divide integers?**

**4.1 Rising and Falling Temperatures**

 * A1.**
 * Number of Hours || 1 || 2 || 3 || 4 || 5 ||
 * Total Temperature Change || 3 || 6 || 9 || 12 || 15 ||


 * A2. Multiplication Sentences: 5x3; 10x3

B1.**
 * Number of Hours || 1 || 2 || 3 || 4 || 5 ||
 * Total Temperature Change || -3 || -6 || -9 || -12 || -15 ||


 * B2. Multiplication Sentences: 5x(-3); 10x(-3)

C1a. 2+2+2=6 C1b. -3+(-3)=(-6) C1c. -2+(-2)+(-2)+(-2)=(-8) C2a. 2x3=6 C2b. -3x2=(-6) C2c. -2x4=(-8)

D. 4x(-10): In one hour, the temperature decreases by 10 degrees. In 4 hours, the temperature was -40 the original.

E1. 5x(-4)=(-20) E2. 20x(-4)=(-80) E3. -4x20=(-80) E4. -5x4=(-20)

Follow Up 1. 10x2=20+(-4)=16 2. 10x(-1.5)=(-15)+25=10 3. No, if you multiply a positive by a negative (vice versa) it will always be negative.**

**Ace4: 1-3, page 60**
Assigned:**
 * Collected:

PR - 4.2 Studying Multiplication Patterns

**Notes**
In this investigation - positive symbol is used to represent a rise in temperature, and a negative symbol to represent a drop in temperature. Essential Question -

Equation Pattern:
 * 5 x 5 = 25
 * 5 x 4 = 20
 * 5 x 3 = 15
 * 5 x 2 = 10
 * 5 x 1 = 5
 * 5 x 0 = 0

A. As the integers multiplied by 5 gets smaller, the products decrease by 5.

B.
 * 5 x (-1) = (-5) since (-1) is 1 space below 0, so it decreases by 5.
 * 5 x (-2) = (-10)
 * 5 x (-3) = (-15)
 * 5 x (-4) = (-20)
 * 5 x (-5) = (-25)

C.
 * 5 x (-4) = (-20)
 * 4 x (-4) = (-16)
 * 3 x (-4) = (-12)
 * 2 x (-4) = (-8)
 * 1 x (-4) = (-4)
 * 0 x (-4) = 0

D. As the integers multiplied by (-4) get larger, the products get larger -> closer to positive by 4.

E.
 * (-1) x (-4) = 4 since (-1) is 1 space below 0, so it increases by 4.
 * (-2) x (-4) = 8
 * (-3) x (-4) = 12
 * (-4) x (-4) = 16
 * (-5) x (-4) = 20

F.
 * 1) (-3) x 7 = 21
 * 2) 5 x (-8) = (-40)
 * 3) (-11) x 12 = (-132)
 * 4) (-3.6) x 2.7 = (-9.72)

Follow-up

1. a. b. When you multiply integers, the order of the numbers do not matter (commutative).
 * (-6) x 7 = (-42)
 * 7 x (-6) = (-42)

2. a. b. When you add integers, the order of the numbers do not matter (commutative).
 * (-6) + 7 = 1
 * 7 + (-6) = 1

3. a. b. When you subtract integers, the order of the numbers matter because it's not commutative since you are taking away.
 * (-6) - 7 = (-13)
 * 7 - (-6) = 13

4. When you add to negative integers, you get a negative result, when you multiply two negative integers, you get a positive result, for example (-6) x (-6) is 36.

Homework

 * Collected:**
 * Assigned:** ACE 4: 4-8, 17-21 odds, 26, 32

JD - 4.3 Playing the Integer Product Game Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

4.4 Dividing Integers
E.Q. - How do we multiply integers?

Problem 4.4 A. 1.-5 x 6 = -30 2.-5 = -30 / 6 6 = -30 / -5 B. 1 -8 x -4 = 32 2.-8 = 32 / -4 -4 = 32 / -8 C. 1.-11 x 12 = -132 2.-8 x 7 = -56 3.-33 x -4 = -132 4. 5.2 x -1.7 = -8.84 D. 1. 24 x -3 = -8 2. 91 / -13 = -7 3. -187 / 11 = -17 4. -19.95 / -2.1 = 9.5

Follow-Up 1. a.-121 / 11 = -11 b. 121 / -11 = -11 c. -96 / -4 = -24 d. 96 / 4 = 24 2. a.18 / 3 = 6 b. It is the same problem accept with different integers.

Homework
Assigned-ACE 4 9-16, 22-25, 27**

AD - 5.1 Extending the Coordinate Grid Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

MeP - 5.2 Breaking Even Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

LD - 5.3 Using a Calculator to Exp. Lines Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

MaP - 5.4 Exploring Window Settings Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)

IK - 5.5 Revisiting Jean’s Problem Initials (normal) Date-Day(heading 2) Notes (include the Essential Question)(Heading 3) Problem Number and Title (Heading 3) Homework (Heading 3) Collected: (normal) Assigned: (normal)