January 20 th - Your next hand-in day is Friday, January 24 th - Look at the following equations,...

January 20th - Your next hand-in day is Friday, January 24th -

Look at the following equations, and try to figure out what x equals:

2x = 42x = 83x = 9

- Algebra, Variables, Graphing -

http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=zbIU9dKA7fjnPM&tbnid=yKw7uQtnZiqfWM:&ved=0CAgQjRw&url=http://www.math.com/school/subject2/lessons/S2U4L3GL.html&ei=hIfcUvN_zYKiBPr2gaAN&psig=AFQjCNHkZ_TFJcLaX7lJyKhPOVlLjWe_IQ&ust=1390270724056121

This unit will help you develop an understanding of Algebraic

Equations. This will help you prepare and practice

for equations with variables.

We will learn how to work with:- Algebraic Rules

- Variables- Graphing

What Are They!?

- A type of equation with variables

(ex) y = 2x + 1

- When we solve it, we can graph it to form a straight line!

Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

y = 2x + 1

- When x gets bigger, y gets bigger twice as fast- That’s why it is 2x

- When x = 0, y = 1- That’s why it is +1




2x = 4 + 22x = 8 + 43x = 9 + 9

y = 2x + 1

- What if x= (-1)

- What if x= (0)

- What if x= (1)Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

STOP!

Before we can start, we need to

learn/remember how to work with variables in equations


January 22nd - Your next hand-in day is Friday, January 24th -


2x + x = 4 + 2x7 + 2x = 8x + 4

3x = 9-3

January 23rd - Your next hand-in day is Friday, January 24th -


2x +3 + 3x = x + 11

x + x = 10 + 2

3x + x = 15 + 5

Algebra Tiles

- Linear equations can be modeled using algebra tiles

- Rods (tall, skinny)- Represent variables

- Cubes (short, square)- Represent constants

(numbers we know)

x

-x

1

-1

Algebra Tiles

- Linear equations can be modeled using algebra tiles

- Light Colours (green, yellow)- Represent positive integers

- Dark Colours (red, black)- Represent negative integers

x

-x

1

-1

Algebra Tiles

Model example-2x + 5

-x -x

Algebra Tiles

Who can show how to model:

m + 6

Algebra Tiles


– 2m + 7

Algebra Tiles

Please show:

3m – 2

-6m + 4

4m – 3

Algebra Tiles


– 2m + 7

Word Problems

Dez is participating in a alpaca-racing contest.

She gets 3 points for every race she wins.

Because of a technical penalty, Dez lost 5 points.

Dez is currently sitting at 19 points, how many races did she win?

Word Problems

- Do we know how many races Dez has won?

- Lets find a variable to represent this

- She gets 3 points for every race she wins.- Lets factor in her 5 point penalty.- Dez’s alpaca racing can be represented

by the equation 3x – 5 = 19


Model the following using algebra tiles:

3x + 5

6x – 12

2x + 5 = 3x -2

Textbook Practice

Questions:5 (just solve for the variable)6 (just solve for the variable)

78

10

January 28th - Your next hand-in day is Monday, Feb 3rd -

Model the following using algebra tiles and then solve for the variable x:

7x + 2

-4x – 4

4x + 10 = 2x -2

Station 1Computer

- Algebra Tiles Interactive -

Equation Practice Centers!!

In groups of 2-3 please:

Station 2Big Table Group- Conference -

Station 4Back Table Group

- Textbook Practice Qs -

Station 5Couches

- Hands-On Equations -

Station 3Middle Table Group

- Word Problem Posters -

January 30th - Your next hand-in day is Monday, Feb 3rd -


12x + 2 = 26

-5x – 2 = 13

6x + 2 = 4x -2

Station 1Computer







Station 5Couches




February 3rd - Hand-In Day!! -

Create an original word problem that requires an equation with a variable in

order to solve it.

Please fully solve the problem you create.

Station 1Computer







Station 5Couches




Textbook Practice

Page 331, Questions 5-15:

When could we correct this together?

February 4th - Your next hand-in day is Monday, February 10th -


2x + x – x + 1 = x + 9

4 + 3x – 2x + x = x + 5


Jesse brings 4 cakes for dessert. Erica brings 2 individual servings of dessert.

Altogether, there will be 34 eating dessert & Mr. Morin makes sure each

person only gets 1 serving.

Create & solve an equation, to represent the number of pieces the cake must be

cut into.



4x - 2x + 4 = x + 10

x + 3x - x = 30

8 + 2x + 3 - x = 2x+ 1

Create an entry in your Interactive Notebook summarizing our

introduction to Equations with Variables.

Your entry needs to include:- Algebra Tiles (rods, cubes, positives,

negatives, ex)- Word Problem (original, modeled, solved)

February 10th - Hand-In Day!! February 4th to Today -

Alison thought of her favourite number.She subtracted 2.

Then Alison multiplied the difference by 5.

The product was 60.What is Alison’s favourite number?

The Distributive Property

Landen is buying cookies that cost $2 each. He needs 19 cookies for everyone in his

class but would also like some extras to give to his best

friend. He has $56, how many cookies could he buy?


- Do we know how many extra cookies he can buy?

- Lets use a variable of “E” for extra- (E + 19)

- Each cookie costs $2- 2(E + 19)

- He can spend up to $56- 2(E+19) = 56


-The distributive property states that a product can be written as a sum or as a difference of two products

(ex) 2(28) = 56 2(9 + 19) = 56 2(9) + 2(19) = 56 18 + 38 = 56


- While we use the distributive property with equations, it can be really helpful for mental math too!

(ex) 4 x 53 4(50) + 4(3) 200 + 12 212

February 11th - Your next hand-in day will be Tuesday, February 18th

-

Solve each equation using the distributive property. Show ALL of your

steps please.

3(x + 5) = 36

4(p – 6) = 36

The Distributive Property- Practice Questions –

-3(x + 5) = 36

4(p – 6) = 36

14 = 3(x + 4)


-


steps please.

7(x + 1) = 63

11(p – 7) = -22


Complete the following questions in your textbook as practice, we will correct them together when done:

Pg 347 Qs: 4, 5, 6, 7, 9, 10, 14, 17


-


steps and verify please.

2(2x + 1) = 18

2(x + 4) + x = x + 12

February 18th - Hand-In Day!! A Mental Math from Feb 11th to Today -


steps and verify please.

2(x + 3) = 9 + x

2(2x + 1) = 3x + 8

2(2x + 3) = x + 9

February 19th - Your next hand-in day is Monday, March 3rd -

Create a word problem that requires you to use the distributive method in

order to arrive at the answer.

Please fully solve your question and verify your work.


Copy & complete the table of values, given the equation: y = 2x-5

x y

-3

-2

-1

0

1

2

3

What Are They!?

- A type of equation with variables

(ex) y = 2x + 1

- When we solve it, we can graph it to form a straight line!


What Are They!?

- An equation/function is linear if the rate of change is constant between any two variables

- The variables are points on the Cartesian Plane


What Do They Look Like?


x y

0 0

1 3

2 5

3 7



x y

0 2

3 4

6 6

9 8


LINEAR!Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

x y

1 2

2 3

3 4

4 5



x y

1 2

2 4

3 6

4 8



x y

1 -1

2 -3

3 -5

4 -7


NON-LINEAR!Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

x y

1 6

2 9

3 13

4 16


NON-LINEAR!Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

x y

1 7

2 9

3 -7

4 -9


Using the following table of values, plot the coordinates

on a Cartesian Plane.Is it a linear equation?

Is so, is it positive or negative?

x y

1 3

2 5

3 7

4 9

A New Formula!

- The most common way to simplify linear equations is written as:

y=mx+b


A New Formula!

The equation of a linear relation is:y = -3x + 5

- Create a table of values- Plot the values on the table- Graph the line*In our formula, y = mx + b, what does each variable mean?


A New Formula!

Y = y-axis (how far up)X = x-axis (how far along)M = slope (how steep)B = where it crosses the y-axis Linear Equations. (2013). Uploaded by Math Is Fun. Available online at:

http://www.mathsisfun.com/algebra/linear-equations.html

A New Formula!

M = slope (how steep)

- Determined by rise run(ex) m =


Slope Music Video!

http://www.youtube.com/watch?v=qnMaWTmdbKk

Let’s Practice!

http://www.mathopolis.com/questions/q.php?id=358&site=1&ref=/

equation_of_line.html&qs=358_359_517_518_1156_1157_3204_3205_3206_3207



on a Cartesian Plane.Create an equation to

represent the line.Hint* y=mx+b

x y

1 2

2 4

3 6

4 8



on a Cartesian Plane.Create an equation to

represent the line.Hint* y=mx+b

x y

1 2

2 3

3 4

4 5

March 3rd - Hand-In Day!! Pick a Mental Math from Feb 19th to Mar

3rd -

Draw a negative line on a Cartesian Plane.

Create an appropriate Table of Values that fits your line (3 points)

Create an equation torepresent the line.Hint* y=mx+b

March 4th - Your next hand-in day will be Monday, March 10th -

Draw a positive line on a Cartesian Plane.

Create an appropriate Table of Values that fits your line (3 points)

Create an equation torepresent the line.Hint* y=mx+b


Sam works as an adventure blogger. She is paid $5 per post plus $10 per hour for each hour that she works. She is only paid for whole hours (no half hours).

An equation that relates her earnings to the number of hours she works is e=10n+5, where e represents her earnings and n is the hours worked.

Create a table of values & graph Sam’s earnings.

Today’s Jobs

1) Finish textbook questions from the center activity

- Page 363- Questions 6(abc), 9, 11

2) Begin summative project for this unit- See handout- If you feel like you need more practice first,

practice 155-157 in workbook (I can help if needed)


On a Cartesian Plane create TWO lines- One positive line- One negative line

They can have different slopes (m-value) but must have the same b-value.

March 10th - Hand-In Day moved to Wednesday, exit-slip today -

Complete a table of values for the equation, y=-2x +5

Plot the line, is it positive or negative.

Could you have plotted the line without creating a table of values?

Explain.

March 12th - Hand-In Day!! -

Please state the new formula we have been using in the last half of this unit.

In your own words, explain what each variable represents in this equation.

Draw a graph to accompany your explanation.

January 20 th - Your next hand-in day is Friday, January 24 th - Look at the following equations,...

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