Moving+Straight+Ahead

Moving Straight Ahead
Map - 2.3 - Walking for Charity Notes: EQ: What is the relationship between a situation, a graph, a table, and an equation? Problem: 2.3 A 1. This is a Table of the pledge plans from all three people A 2. need to insert graph A 3. Leanne's pledge plan is the equation y = 1x Gilberto's pledge plan is the equation y = 2x Alana's pledge plan is the equation y = 5 + 0.5x B. The effect of increasing the amount pledged per mile, on a table you would see a bigger rate of chage in numbers, on a graph you would see a stepper incline of the line, in an equation you would see bigger X coefficient. C. I used a table to figure this out, 8 miles using leanne's plan, you would earn $8 8 miles using Gilberto's plan, you would earn $16 8 miles using Alana's plan, you would earn $ 9 D. I used a table to figure this out, For a sponsor to owe a student $ 10: Leanne's plan - 10 miles Gilberto's plan - 5 miles Alana's plan - 10 miles E. On a table Alana's plan starts off at $5 so at 0 miles she would have $5 On a graph Alana's plan would start at $5 on the y axis On an equation the equation would look like this Y = **__//5//__** + 0.5x
 * Distance (Miles) || Leanne's Pledge plan || Gilberto's Pledge plan || Alana's pledge plan ||
 * 0 || $ 0 || $ 0 || $ 5 ||
 * 1 || $ 1 || $ 2 || $ 5.5 ||
 * 2 || $ 2 || $ 4 || $ 6 ||
 * 3 || $ 3 || $ 6 || $ 6.5 ||
 * 4 || $ 4 || $ 8 || $ 7 ||
 * 5 || $ 5 || $ 10 || $ 7.5 ||
 * 6 || $ 6 || $ 12 || $ 8 ||
 * 7 || $ 7 || $ 14 || $ 8.5 ||
 * 8 || $ 8 || $ 16 || $ 9 ||
 * 9 || $ 9 || $ 18 || $ 9.5 ||
 * 10 || $ 10 || $ 20 || $ 10 ||

JD - 3.4 - Planning a Skating Party Notes - EQ - How can technology help investigate linear patterns around us?

//(y=mx+b)//

Problem 3.4 -

Suppose your class is planning a skating party to celebrate the end of the school year. Your committee is in charge of finding a place to rent in-line skates for a reasonable price. You get quotes from two companies: Wheelie's Skates and Stuff charges $100 plus $3 per person.** Which company should you choose if you wan tto keep the cost to a minimum? Explain how you made your choice.
 * Roll-Away Skates charges $5 per person.

A: Since our class only has ten people in it the Roll-Away Skates company is a better choice because their plan is better for a smaller amount of people. you could also make a table and compare on that.


 * x || Y1 || Y2 ||
 * 0 || 0 || 100 ||
 * 1 || 5 || 103 ||
 * 2 || 10 || 106 ||
 * 3 || 15 || 109 ||
 * 4 || 20 || 112 ||
 * 5 || 25 || 115 ||
 * 6 || 30 || 118 ||
 * 7 || 35 || 121 ||
 * 8 || 40 || 124 ||
 * 9 || 45 || 127 ||
 * 10 || 50 || 130 ||

Follow Up -

1 a. For each company, write an equation for the relationship between the number of people and the cost. RAS - //y=5x// WSS - //y=3x+100// b. In the same window, graph the equations for both companies

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[[image:http://math7e-2008.wikispaces.com/i/mime/32/image/tiff.png width="32" height="32" link="http://math7e-2008.wikispaces.com/space/showimage/5.1+graph.tiff"]][| 5.1 graph.tiff][[image:http://math7e-2008.wikispaces.com/i/mime/32/image/tiff.png width="32" height="32" link="http://math7e-2008.wikispaces.com/space/showimage/Graph+2+5.1.tiff"]][| Graph 2 5.1.tiff][[image:http://math7e-2008.wikispaces.com/i/mime/32/image/tiff.png width="32" height="32" link="http://math7e-2008.wikispaces.com/space/showimage/5.1+graph.tiff"]][| 5.1 graph.tiff]
 * 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) Feb/12/2008 Notes EQ:** How Do I Find Difference between integers A1.
 * Problem 3.1 Subtracting on a Chip Board

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

Notes (include the Essential Question)(Heading 3)
Essential Question: What is my location? In the apparent context, I think this refers to what might be your location on a graph, and the significance of that particular point. The point may be described by the following details: the quadrant in which it is situated, and its coordinate details.

5.1: Extending the Coordinate Grid (Problem 5.1)
A. Describe how Melina located each of the four points on the coordinate grid. On a normal coordiante grid, we plot the points using the information derived from the coordinate pair. We then use the x and y axis to locate those particualar points. Melina also probably used this method, drawing vertical or horizontal lines originating from the relevant points on the x and y axis, and marking the point where the two lines intersected.

B. What polygon could you make by connecting the four points? Justify your answer. If we connect the points on Melina's graph, we obtain a quadrilatereal know as a parallelogram. In other words, a four sided shape, in which, all the line segments opposite each other are parallel.However, the parallelogram will be slightly tilted, as all he points are located on separate grid lines. C. On a coordinate grid, plot four points that are the vertices of a square, such that both coordinates of each point are negative integers. Graph shown below.

D. On a coordinate grid, plot four points that are vertices of a square, such that both coordinatesof each point are negative integers. Graph shown below. E. On a coordinate grid, plot four points that are vertices of a square, such that one point has two negative-integer coordinates, one point has two positive-integer coordinates, and each of the other has one positive-integer coordinate and one negative integer coordinate. Graph shown below. F. Two vertices of a square are (3, 1) and (-1, 1). Find the coordinates for every pair of points that could be the other two vertices. Using a graph, I found that the coordiantes that would complete the square would be (-1,-3) and (3,-3); or (3,5) and (-1,5). (Graph shown below.)

Problem 5.1 Follow Up 1. For each pairs of points, describe two minimal paths from the first point to the second point. (a) (-4,-2) to (5,3): Nine steps to the right, five steps upwards; five steps upwards, nine steps to the right (b) (-4,3) to (5,2): Nine steps to the right, one step down; one step down, nine steps to the right (c) (2,-4) to (-1,-2): Two steps upwards, three steps to the left; three steps to the left, two steps upwards

2. (a) Locate two points on the coordinate grids such that there is a gap of twelve steps between them. The minimal path from (-4,-2) to (4,2) requires only twelve steps. (b)In my view, everyone probably would'nt choose the same points, as there are endless possiblities and the chances of everyone choosing the same points is very low.

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)