## 7.15.2010

### SBG: Algebra 1 Skills Draft

These came straight from the lesson objectives in my textbook. I literally went through and typed them out with no thoughts of my own whatsoever. I stopped at factoring because that's where I ended last year and because I don't know what should come next.

I want to take this list and rip it apart in whatever way necessary.

What skills can be combined? I know adding real numbers and subtracting seem like they could be combined, but I like being super specific. I want remediation to be simple.

What skills aren't appropriate for this course? Are some too easy, too hard? Do any skills need to be completely removed?

Does the order and progression make sense? I think the standards within each chapter make sense but does the order of the chapters? Is there anything that needs to be moved or rearranged?

Where do I go from here? Are there any skills that are obviously lacking? Did I miss anything important? What comes next? I need your direction. You are my vertical team, my curriculum person, my pacing guide.

What about the wording? Is it too specific, or not enough? Should it be written in student-friendly language or ACT jargon (ACT is my state test)?

Anything else you can think of to say is helpful.

Algebra 1:

Translating problems into solvable equations AKA Math is a beast. Make it your pet.

Ruff Draft:

Chapter 1 – Foundations for Algebra
1. Translate between words and algebra.
2. Evaluate algebraic expressions.
4. Subtract real numbers.
5. Multiply real numbers.
6. Divide real numbers.
7. Evaluate expressions containing exponents.
8. Evaluate expressions containing square roots.
9. Classify numbers within the real number system.
10. Use the order of operations to simplify expressions.
11. Use the Commutative, Associative, and Distributive Properties to simplify expressions.
12. Combine like terms.
13. Graph ordered pairs in the coordinate plane.
14. Graph functions from ordered pairs.

Chapter 2- Equations

15. Solve one-step equations in one variable by using addition or subtraction.
16. Solve one-step equations in one variable by using multiplication or division.
17. Solve one-step equations in one variable that contain more than one operation.
18. Solve equations in one variable that contain variable terms on both sides.
19. Solve a formula for a given variable.
20. Solve an equation in two or more variables for one of the variables.
21. Write and use ratios, rates, and unit rates.
22. Write and solve proportions
23. Use proportions to solve problems involving geometric figures.
24. Use proportions and similar figures to measure objects indirectly.
25. Solve problems involving percents.
26. Use common applications of percents.
27. Estimate with percents.
28. Find percent increase and decrease.
EXTENSION: Solve equations in one variable that contain absolute-value expressions

Chapter 3- Inequalities
29. Identify solutions of inequalities in one variable.
30. Write and graph inequalities in one variable.
31. Solve one-step inequalities by using addition.
32. Solve one-step inequalities by using subtraction.
33. Solve one-step inequalities by using multiplication.
34. Solve one-step inequalities by using division.
35. Solve inequalities that contain more than one operation.
36. Solve inequalities that contain variable terms on both sides.
37. Solve compound inequalities in one variable.
38. Graph solution sets of compound inequalities in one variable.
39. Solve inequalities in one variable involving absolute-value expressions.

Chapter 4- Functions

40. Match simple graphs with situations.
41. Graph a relationship.
42. Identify functions.
43. Find the domain and range of relations and functions.
44. Identify independent and dependent variables.
45. Write an equation in function notation and evaluate a function for given input values.
46. Graph functions given a limited domain.
47. Graph functions given a domain of all real numbers.
48. Create and interpret scatter plots.
49. Use trend lines to make predictions.
50. Recognize and extend an arithmetic sequence.
51. Find a given term of an arithmetic sequence.

Chapter 5- Linear Functions

52. Identify linear functions and linear equations.
53. Graph linear functions that represent real-world situations and give their domain and range.
54. Find x and y intercepts and interpret their meanings in real-world situations..
55. Use x and y intercepts to graph lines.
56. Find rates of change and slopes.
57. Relate a constant rate of change to the slope of a line.
58. Find slope by using the slope formula.
59. Identify, write, and graph direct variation.
60. Write a linear equation in slope-intercept form.
61. Graph a line using slope-intercept form.
62. Graph a lie ad write a linear equation using point-slope form.
63. Write a linear equation given two points.
64. Identify and graph parallel and perpendicular lines.
65. Write equations to describe lines parallel or perpendicular to a given line.
66. Describe how changing slope and y intercept affect the graph of a linear function.
EXTENSION: Graph absolute-value functions.
EXTENSION: Identify characteristics of absolute-value functions and their graphs.

Chapter 6- Systems of Equations and Inequalities

67. Identify solutions of systems of linear equations in two variables.
68. Solve systems of linear equations in two variables by graphing.
69. Solve systems of linear equations in two variables by substitution.
70. Solve systems of linear equations in two variables by elimination.
71. Compare and choose an appropriate method for solving systems of linear equations.
72. Solve special systems of linear equations in two variables.
73. Classify systems of linear equations and determine the number of solutions.
74. Graph and solve linear inequalities in two variables
75. Graph and solve systems of linear inequalities in two variables.

Chapter 7- Exponents and Polynomials
76. Evaluate expressions containing zero and integer exponents.
77. Simplify expressions containing zero and integer exponents.
78. Evaluate and multiply by powers of 10.
79. Convert between standard notation and scientific notation.
80. Use multiplication properties of exponents to evaluate and simplify expressions.
81. Use division properties of exponents to evaluate and simplify expressions.
82. Classify polynomials and write polynomials in standard form.
83. Evaluate polynomial expressions.
85. Multiply polynomials.
86. Find special products of binomials.

Chapter 8- Factoring Polynomials

87. Write the prime factorization of numbers.
88. Find the GCF of monomials.
89. Factor polynomials by using the greatest common factor.
90. Factor quadratic trinomials of the form x2 + bx + c
91. Factor quadratic trinomials of the form ax2 + bx + c
92. Factor perfect square trinomials.
93. Factor the difference of two squares.
94. Choose an appropriate method for factoring a polynomial.
95. Combine methods for factoring a polynomial.

1. Last year, I started out by writing very specific objectives in student-friendly language. I had 15 objectives for Algebra 1 during first quarter (and 32 for Geometry). It was a nightmare. How do you grade a quiz that addresses a dozen objectives? How do you handle the test at the end of the term? I was drowning in paperwork and I couldn't see the forest for the trees.

For second quarter, I cut the number of objectives down to 8. This was much more manageable for me and for the students. To do this, I had to write broader objectives, but this turned out to be a good thing.

To do this, I had to identify the big ideas for the quarter and the threads that tied it all together. The objectives were broader, but that meant we addressed each of them more often, at different levels, and coming from different directions. It made it easier for me to assess an objective many times over the quarter, allowing students to show real learning and growth.

For example, what if you took most of the stuff out of Chapter 1 that deals with evaluating real number expressions (objectives 3-8 and 10) and put it in one big objective called Evaluating Real Number Expressions.

The first time you get to it, maybe you're just doing the four basic operations and making sure the students know that multiply/divide come before add/subtract in the order of operations. Exponents get added to the mix later. Once they have that down, here come parentheses.

I mean, this is something we do every day in Algebra, but the students don't have to be experts from day one. Each week or so, you add a new wrinkle, slowly turning up the difficulty until they've become really proficient at it by the end of the quarter.

In the end, they get one score for Evaluating Expressions in the gradebook, but it is based on multiple pieces of data collected over a period of several months and is probably more valid than a grade from a traditional grading system.

But more importantly, students can track their own progress over time. I have them record their scores and hang on to their quizzes and every so often, we look back and they realize that what was challenging a month ago is second nature today. Once I can get them to see that they really are learning algebra, their level of buy-in goes through the roof and makes my job a piece of cake.

2. I agree with baho. It was a little easier for my kids because they were taking two years to complete Algebra 1, but I had to combine alot of objectives to make it realistic. Once I got it to 36 for the year, I felt comfortable knowing that 1 per week would get the job done.

The district has a pacing guide that is almost 1 chapter section per day, so it was no big deal to have two or three sections per concept per week. Plus, once you compare the objectives to your course of study you can eliminate some of the junk in your book that you don't really need.

3. OK, so first of all...breathe! It is not going to go perfectly! In fact, you will leave this year feeling as frustrated at your own lack of success as last year. You will do that every single year, because your expectations for yourself will constantly be raising. That's a good thing! And then from time to time, you'll reflect back and think..."Wow, I'm really getting better." But you will never satisfy your own goals for yourself. And amen to that! If you ever "reach it"...time to retire. ;)

That being said, I know since I am the same place you are with all of this, that the last thing you want is a pep talk. You want specifics. And I do not envy you trying to do this stuff without state mandated specific objectives to tell you where to focus. The textbook can be so ridiculously comprehensive. But I think the tactic you are trying right now is the best approach you can given your context. It does, however, leave you with a crazy list of stuff to try to cover and I think you are going to want to whittle that down by figuring out which things can be combined and which can just be relegated to Algebra 2. I know, I just reformulated your question rather than answering it. Irritating, aren't I? :) I don't feel like I can help with the second part (what can be relegated to Alg2) because my assumptions about that are going to be entirely based on my state objectives and may not fit in your context at all. But I will throw a few suggestions at you about the whittling stuff:
* I see the vast majority of Chapter One as middle school math standards. I'm not saying you shouldn't cover them, or even hold them accountable by assessing, but I think that might be an area where you can be a bit more vague. Perhaps:
- Translate between...
- Evaluate expressions (which necessitates O of O)
- Compute with real numbers
- Combine like terms

But that suggestion is just my own philosophical leaning because I wouldn't spend an inordinate amount of time on that chapter. Others might feel that it is so foundational that it is worth a great deal of time.

My other whittling suggestion involves the inequality chapter. I think that students who can solve an equation can solve an inequality with the added challenge of the sign reversal aspect. That is essentially the only new skill involved in the inequality itself so I would probably disaggregate the broad objective of inequalities as:
- can determine when the sign should be reversed in inequalities
- can graph the solutions of inequalities
- can solve compound inequalities
- can graph the results of compound inequalities
etc, etc. all for one variable of course

Those are just initial thoughts. And I know I ramble. Part of my charm. :)

I'm just really, really glad that as I wade into these terrifying waters of sbg, there are others that I know are treading water nearby. We will conquer this beast!!!!