Bell Ringer On a sheet of paper, write the following.

Your name Date All of your classes (1st period – 8th period) Teacher’s Names Current grade in that class (if you don’t know

your grade, write the grade you think you have)

If you have any grades below a C, also write what you can do to do better in that class in the second semester.

Good Morning

Friday, January 15 Bell Ringer Uniform & ID Check Debrief Bell Ringer Review Homework Turn in HW Chapter 1 Review Chapter 2 Review Chapter 3 Review Chapter 4 Review Break @ Bell

Debrief

The end of the semester is coming Monday-No School Tuesday-Chapter 2 and 3 Review Wednesday-Chapter 4 Review Thursday-Final Exam Other

Turn in Homework

Final Exam Review Chapter 1 Chapter 2 Chapter 3 Chapter 4

Test Review – Chapter 1 Adding numbers with the same sign Adding numbers with different signs Subtracting numbers Multiply/Dividing numbers with same sign Multiply/Divide numbers with different signs Order of Operations

Test Review – Chapter 1 Adding numbers with the

same sign Add the numbers

together Keep the sign

Questions to think about: Will the sum of two

positive numbers be positive or negative?

Will the sum of two negative numbers be positive or negative?

Examples1. 3 + 4 =2. -7 + -12 =3. 25 + 82 = 4. -12 + -17 = 5. 10 + 28 =

Test Review – Chapter 1 Adding numbers with

different signs Subtract the absolute

values of the numbers. Keep the sign of the

number with the greatest absolute value.

Question to think about: Why isn’t the sum of a

positive number and a negative number always negative?

Examples1. 4 + -2 = 2. -18 + 35 = 3. 18 + -18 = 4. -12 + 18 = 5. -10 + 13 =

Test Review – Chapter 1 Subtracting numbers

Change subtraction to adding the opposite.

Follow the rules for addition.

Questions to think about: Why can we write

subtraction as addition of the opposite?

What is the opposite of a number?

Examples1. 28 – 37 =2. -18 – 10 = 3. -45 - -17 =4. 12 - -12 =5. 10 – 8 =

Test Review – Chapter 1 Multiply/Dividing

numbers If the signs are the

same the answer is always positive.

If the signs are different the answer is always negative.

Questions to think about:

Examples1. -2 x 4 =2. -9 x -6 =3. 5 x -99 =4. 84 x 98 =5. -12 / -6 = 6. 55 / 11 =7. -27 / 9 =8. 64 / -16 =

Test Review – Chapter 1 Order of Operations

Parenthesis – Symbols of inclusion

Exponents Multiplication and Division

from left to right Addition and Subtraction

from left to right Questions to think about:

Why are mult. and div. in the same step?

Why are addition and subtraction in the same step?

Examples1. 3[8-3*2+4(5-2)]2. [7+3*2+8]/73. (20+22)/6+14. 5+3*4-8+2*75. 18/(9-15/5)6. 2*8-62

7. 2*27-13*28. 18/9-15/59. 2*(8-62)* means multiplication/ means division

Test Review – Chapter 2

Simplifying expressions Distribute Combine Like Terms

Solving linear equations Writing equations from word

problems (Guess Check Generalize) Solving word problems

Test Review – Chapter 2 Simplifying

expressions Distribute Combine Like Terms

Questions to think about: What are like terms? Why do we distribute

before combining like terms?

Examples1. 2(5x+4)2. (2x-4)33. -(14x-3)4. ¼ (12x-8)5. 6(5-3x)6. 7b-b-x+5-2x-7b7. 4a+3-2y-5a-7+4y8. 2x-5+3a-5x+10a9. -6m+3t+4-4m-2t10. 4-p-2x+3p-7x

Test Review – Chapter 2 Solving linear

equations Backtracking Number Tricks Flowcharts 5 Steps

Question to think about: What is your favorite

method for solving equations?

Why do you like it?

Examples1. 17 = -8 + x2. 5.2 + h = 0.33. -2 = d / 44. 6x = 155. 3x + 4 = 106. f/6 – 5 = -87. -4 = 8 - 3x 8. 3 - 4d = 6d – 17 9. 5e + 13 = 7e – 21 10. 3k + 5 = 2(k + 1)

Test Review – Chapter 2 Writing equations from

word problems Guess a correct answer Check to see if it works Make your third guess a

variable; generalize to make an equation

Questions to think about: Why should you make the

third guess a variable? Why is it so important

that you write all your steps and organize your work when you guess?

Examples It takes Trevon ten hours to

clean an attic. Cody can clean the same attic in seven hours. Find how long it would take them if they worked together.

A cattle train left Miami and traveled toward new York. 14 hours later a diesel train left traveling at 45m/h in an effort to catch up to the cattle train. After traveling for four hours the diesel train finally caught up. What was the cattle train’s average speed.

Test Review – Chapter 2 Solving word

problems Solve the equation

that you created when you Guess-Checked-Generalized.

Question to think about: Why should you

check your answer again?

What should you check for?

Examples A passenger plane made a

trip to Las Vegas and back. On the trip there it flew 432mph and on the return trip it went 480 mph. How long did the trip there take if the return trip took nine hours?

An aircraft carrier made a trip to Guam and back. The trip there took three hours and the trip back took four hours. It averaged 12m/h on the return trip. Find the average speed of the trip there.

Test Review – Chapter 3

Absolute value equations Using equations as point testers Graphing equations using (x,y) table Solving for a variable

Test Review – Chapter 3 Absolute value

equations Create two equations Solve both equations

Questions to think about: What does absolute

value represent? Why do we create

two equations? Why can absolute

value not = 0?

Examples1. |6m| = 422. |k – 10| = 33. |7 + p| = 74. |n| + 1 = 25. |-3p| = 156. |h| = 57. |6x + 2| + 3 = 48. |8y – 2| + 12 = 8

Test Review – Chapter 3 Using equations as point

testers Substitute the x value

and y value into the equation

Simplify to see if it comes out true

Questions to think about: What does it mean for a

point to make an equation true?

What does it mean if a point does not make an equation true?

ExampleFind 5 points on each graph

and 5 points not on each graph.

1. 4x + 2y = 202. 7 + 3x = y3. 10y + x = 304. 2x + 3y = 85. x + y = 4

Test Review – Chapter 3 Graphing equations

using (x,y) table Make a table for your

points Choose values for x Solve for y Write your points into

the table Plot your points Connect the points

Questions to think about: Why do we make a

table? How do we know what

values to choose for x?

Examples1. y = -5x – 1 2. y = -7x + 33. y = 54. x = -35. y – 2x = -56. y – 1 = -6x7. y = -5/2 x + 5

Test Review – Chapter 3 Solving for a variable

Identify the variable that you are solving for.

Move everything else to the other side of the equation

Questions to think about: Why is it helpful to solve

for a variable? When is the answer

going to be just a number and when will the answer be an expression?

Examples1. 5x + 3 = y; solve for x2. 2x + 3y = 8; solve for y3. x = 3(y + 2); solve for y4. 2x + 8y = 0; solve for x

Test Review – Chapter 4

Find slope between two points Determine if points are collinear Find a collinear point Use slope to determine if line goes up

to the right, down to the right, horizontal or vertical.

Test Review – Chapter 4 Find slope between two

points m(A,B) = rise run Rise = y2 – y1

run x2 – x1

Questions to think about: What happens to the

slope when you change the order of the points?

When is it easier to find the slope using rise/run and when is it easier to use the slope formula?

Examples1. (19,-16) and (-7,-15)2. (1,-19) and (-2,-7)3. (12,-18) and (-15,-18)4. (-4,7) and (-6,-4)5. (20,8) and (9,16)6. (17,-13) and (17,8)7. (3,0) and (-11,-15)8. (19,3) and (20,3)9. (-2,6) and (-2,15)10. (6,-12) and (15,-3)

Test Review – Chapter 4 Use slope to

determine how a line looks. Positive slope—line

goes up to the right Negative slope—

line goes down Slope = 0 line is

horizontal Slope is undefined

line is vertical

ExamplesWhich directions do these

lines go in?1. (19,-16) and (-7,-15)2. (1,-19) and (-2,-7)3. (12,-18) and (-15,-18)4. (-4,7) and (-6,-4)5. (20,8) and (9,16)6. (17,-13) and (17,8)7. (3,0) and (-11,-15)8. (19,3) and (20,3)9. (-2,6) and (-2,15)10. (6,-12) and (15,-3)

Test Review – Chapter 4

Use slope to determine how a line looks.

Questions to think about: When is the slope of a line undefined? When is the slope of a line = 0? What is another way of determining what

the line looks like without using slope?

Test Review – Chapter 4 Determine if points

are collinear In order for points

A,B, and C to be collinear: m(A,B)=m(B,C)

Questions to think about:

Test Review – Chapter 4 Find a collinear

point Graph the two

points and find another point on the line

Use the slope to create a point tester

Questions to think about:

ExamplesFind a point C, collinear with

these points.1. (19,-16) and (-7,-15)2. (1,-19) and (-2,-7)3. (12,-18) and (-15,-18)4. (-4,7) and (-6,-4)5. (20,8) and (9,16)6. (17,-13) and (17,8)7. (3,0) and (-11,-15)8. (19,3) and (20,3)9. (-2,6) and (-2,15)10. (6,-12) and (15,-3)

Test Review – Chapter 4

Find slope between two points Determine if points are collinear Find a collinear point Use slope to determine if line goes up

to the right, down to the right, horizontal or vertical.

Homework