1. Bell Ringer  On a sheet of paper, write the following. Your name Date All of your classes (1 st period – 8 th 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.

2. Good Morning

3. 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

4. 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

5. Turn in Homework

6. Final Exam Review  Chapter 1  Chapter 2  Chapter 3  Chapter 4

7. 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

8. 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? Examples 1.3 + 4 = 2.-7 + -12 = 3.25 + 82 = 4.-12 + -17 = 5.10 + 28 =

9. 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? Examples 1.4 + -2 = 2.-18 + 35 = 3.18 + -18 = 4.-12 + 18 = 5.-10 + 13 =

10. 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? Examples 1.28 – 37 = 2.-18 – 10 = 3.-45 - -17 = 4.12 - -12 = 5.10 – 8 =

11. 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: Examples 1.-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 =

12. 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? Examples 1.3[8-3*2+4(5-2)] 2.[7+3*2+8]/7 3.(20+22)/6+1 4.5+3*4-8+2*7 5.18/(9-15/5) 6.2*8-6 2 7.2*27-13*2 8.18/9-15/5 9.2*(8-6 2 ) * means multiplication / means division

13. Test Review – Chapter 2  Simplifying expressions Distribute Combine Like Terms  Solving linear equations  Writing equations from word problems (Guess Check Generalize)  Solving word problems

14. 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? Examples 1.2(5x+4) 2.(2x-4)3 3.-(14x-3) 4.¼ (12x-8) 5.6(5-3x) 6.7b-b-x+5-2x-7b 7.4a+3-2y-5a-7+4y 8.2x-5+3a-5x+10a 9.-6m+3t+4-4m-2t 10.4-p-2x+3p-7x

15. 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? Examples 1.17 = -8 + x 2.5.2 + h = 0.3 3.-2 = d / 4 4.6x = 15 5.3x + 4 = 10 6.f/6 – 5 = -8 7.-4 = 8 - 3x 8.3 - 4d = 6d – 17 9.5e + 13 = 7e – 21 10.3k + 5 = 2(k + 1)

16. 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.

17. 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.

18. Test Review – Chapter 3  Absolute value equations  Using equations as point testers  Graphing equations using (x,y) table  Solving for a variable

19. 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? Examples 1.|6m| = 42 2.|k – 10| = 3 3.|7 + p| = 7 4.|n| + 1 = 2 5.|-3p| = 15 6.|h| = 5 7.|6x + 2| + 3 = 4 8.|8y – 2| + 12 = 8

20. 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?  Example Find 5 points on each graph and 5 points not on each graph. 1.4x + 2y = 20 2.7 + 3x = y 3.10y + x = 30 4.2x + 3y = 8 5.x + y = 4

21. 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? Examples 1.y = -5x – 1 2.y = -7x + 3 3.y = 5 4.x = -3 5.y – 2x = -5 6.y – 1 = -6x 7.y = -5/2 x + 5

22. 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? Examples 1.5x + 3 = y; solve for x 2.2x + 3y = 8; solve for y 3.x = 3(y + 2); solve for y 4.2x + 8y = 0; solve for x

23. 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.

24. Test Review – Chapter 4  Find slope between two points m(A,B) = rise run Rise = y 2 – y 1 run x 2 – x 1  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?  Examples 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)

25. 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  Examples Which 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)

26. 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?

27. 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:

28. 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:  Examples Find 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)

29. 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.

31. Homework