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.
Translating problems into solvable equations AKA Math is a beast. Make it your pet.
Chapter 1 – Foundations for Algebra
1. Translate between words and algebra.
2. Evaluate algebraic expressions.
3. Add real numbers.
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.
84. Add and subtract polynomials
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.