Here's the deal: I'm working on curriculum for my school and Algebra 2 is making my eyes cross. I think the major problem is the state of Virginia is in a transition year between "old" Standards of Learning (SOLs), and "new" ones. This year is supposed to be the year that we're still teaching and assessing the old SOLs, but we're supposed to teach the new ones, too. Those of you that teach Algebra 2 already know that there's an enormous amount of information to cover in a short period of time. To give you context, our school teaches it as a semester-long block course. There's only so much a brain can handle in one day, though!

Here's the first draft of my skills list and structure...I'm not sure what to do about the old vs. new SOLs (my skills list is based on the old SOLs because that is what will be assessed).

Note: Gray items are not included in old or new SOLs but might be necessary for student understanding

Blue items are being taken out of the SOLs starting next year

Red items are new to the SOLs starting this year

1 Solve multi-step equations and inequalities

2 Matrix +/-

3 Solve compound inequalities

4 Solve absolute value equations

5 Solve absolute value inequalities

6 Factor trinomial a = 1

7 Factor trinomial a > 1

8 Factor special cases (sum/diff of cubes, diff of squares, perfect square trinomials)

9 Factor out GCF first (factor completely)

10 Exponent rules

11 +/- polynomials

12 Multiply polynomials

13 Divide polynomials

14 Identify undefined values

15 Simplify rational expressions by factoring and canceling out common factors

16 Multiply and divide fractions

17 Multiply and divide rational expressions

18 Add and subtract fractions

19 Add and subtract rational expressions

20 Simplify complex fractions

21 Solve rational equations

22 Simplify numbers under radical

23 Simplify monomials under radical

24 Multiply and divide radicals

25 Add and subtract radicals

26 Nth roots to rational exponents and vice versa

27 Simplify expressions with nth roots and rational exponents

28 Solve radical equations

29 Simplify square roots with negative terms inside radical using i

30 Add and subtract complex numbers

31 Powers of i

32 Multiply complex numbers

33 Domain and range of relations (from ordered pairs, mapping, graph, table)

34 Identify relations that are functions and one-to-one

35 Given graph and a value k, find f(k)

36 Given graph, find zeros

37 Given graph and a value k, find where f(x)=k

38 Slope from graph, equation, points

39 Graph from equation

40 Equation from graph

41 x- and y- intercepts

42 Determine whether lines are parallel, perpendicular, or neither from equation or graph

43 Write equations for parallel and perpendicular lines given line and point off the line

44 Graph linear inequalities

45 Solve systems of equations by graphing

46 Multiply Matrices using a graphing calculator

47 Inverse matrix method of systems

48 Systems of equations word problems

49 Graph systems of linear inequalities

50 Linear programming max/min problems

51 Function math (addition, subtraction, multiplication, division)

52 Function composition, find a value i.e. f(g(3))

53 Function composition, find the function i.e. f(g(x))

54 Find an inverse function by switching variables

55 Graph from vertex form, identify max/min and zeros

56 Solve by factoring

57 Solve by Quadratic Formula (including complex solutions)

58 Determine roots using the discriminant

59 Write equation for quadratic given roots

60 Quadratic systems

61 Polynomials: relating x-intercept, zeroes and factors

62 End behavior for polynomials

63 Exponential growth or decay from function

64 Sketch base graph of exponential/log functions

65 Exponential to log and vice versa

66 Data analysis/curve of best fit for linear, quadratic, exponential and log

67 Graph absolute value functions

68 Horizontal and vertical translations of linear, quadratic, cubic, abs value, exponential and log

69 Reflections and stretching of linear, quadratic, cubic, abs value, exponential and log

70 Combinations of transformations on parent functions

71 Identify parent graphs of parent functions

72 Identify equations of parent functions

73 Identify a conic from graph

74 Identify a conic from equation

75 Write equation for direct, inverse and joint variation problems

76 Find the constant of variation

77 Write n terms of an arithmetic sequence

78 Find the sum of a finite arithmetic series

79 Write n terms of geometric sequence

80 Find sum of geometric series

81 Use formulas to find nth term

82 Identify sequence/series as arithmetic, geometric or neither

83 Determine probabilities associated with areas under the normal crve

84 Compute permutations and combinations

If you made it this far, here's my call for help: Anyone have advice/suggestions for how to make this work and/or a better way to organize the information into cohesive units that seem to occur in a somewhat logical order? There is and will continue to be an emphasis on function families and transformations (as there should be). I find it difficult to express on paper how each function category needs to be a resting place, but they are all connected in the ways that transformations apply. Any ideas?

...oh...and I'm going to be teaching one section of deaf students and one section of blind students...in case that makes a difference

**edit: I've added links to the old and new Virgina SOLs for Algebra 2 if anyone's interested**

Here's the first draft of my skills list and structure...I'm not sure what to do about the old vs. new SOLs (my skills list is based on the old SOLs because that is what will be assessed).

Note: Gray items are not included in old or new SOLs but might be necessary for student understanding

Blue items are being taken out of the SOLs starting next year

Red items are new to the SOLs starting this year

**Unit 1 Algebra 1 Review/Solving Equations**1 Solve multi-step equations and inequalities

2 Matrix +/-

3 Solve compound inequalities

4 Solve absolute value equations

5 Solve absolute value inequalities

**Unit 2 Polynomial Review/Add Depth**6 Factor trinomial a = 1

7 Factor trinomial a > 1

8 Factor special cases (sum/diff of cubes, diff of squares, perfect square trinomials)

9 Factor out GCF first (factor completely)

10 Exponent rules

11 +/- polynomials

12 Multiply polynomials

13 Divide polynomials

**Unit 3 Rational Expressions**14 Identify undefined values

15 Simplify rational expressions by factoring and canceling out common factors

16 Multiply and divide fractions

17 Multiply and divide rational expressions

18 Add and subtract fractions

19 Add and subtract rational expressions

20 Simplify complex fractions

21 Solve rational equations

**Unit 4 Radicals, Radical Equations and Complex Numbers**22 Simplify numbers under radical

23 Simplify monomials under radical

24 Multiply and divide radicals

25 Add and subtract radicals

26 Nth roots to rational exponents and vice versa

27 Simplify expressions with nth roots and rational exponents

28 Solve radical equations

29 Simplify square roots with negative terms inside radical using i

30 Add and subtract complex numbers

31 Powers of i

32 Multiply complex numbers

**Unit 5 Functions (intro)**33 Domain and range of relations (from ordered pairs, mapping, graph, table)

34 Identify relations that are functions and one-to-one

35 Given graph and a value k, find f(k)

36 Given graph, find zeros

37 Given graph and a value k, find where f(x)=k

**Unit 6 Linear Functions**38 Slope from graph, equation, points

39 Graph from equation

40 Equation from graph

41 x- and y- intercepts

42 Determine whether lines are parallel, perpendicular, or neither from equation or graph

43 Write equations for parallel and perpendicular lines given line and point off the line

44 Graph linear inequalities

**Unit 7 Systems**45 Solve systems of equations by graphing

46 Multiply Matrices using a graphing calculator

47 Inverse matrix method of systems

48 Systems of equations word problems

49 Graph systems of linear inequalities

50 Linear programming max/min problems

**Unit 8 Functions (reprise)**51 Function math (addition, subtraction, multiplication, division)

52 Function composition, find a value i.e. f(g(3))

53 Function composition, find the function i.e. f(g(x))

54 Find an inverse function by switching variables

**Unit 9 Quadratics**55 Graph from vertex form, identify max/min and zeros

56 Solve by factoring

57 Solve by Quadratic Formula (including complex solutions)

58 Determine roots using the discriminant

59 Write equation for quadratic given roots

60 Quadratic systems

61 Polynomials: relating x-intercept, zeroes and factors

62 End behavior for polynomials

**Unit 10 Exponential/Logarithmic functions**63 Exponential growth or decay from function

64 Sketch base graph of exponential/log functions

65 Exponential to log and vice versa

66 Data analysis/curve of best fit for linear, quadratic, exponential and log

**Unit 11 Transformations and Parent Functions**67 Graph absolute value functions

68 Horizontal and vertical translations of linear, quadratic, cubic, abs value, exponential and log

69 Reflections and stretching of linear, quadratic, cubic, abs value, exponential and log

70 Combinations of transformations on parent functions

71 Identify parent graphs of parent functions

72 Identify equations of parent functions

**Unit 12 Conics**73 Identify a conic from graph

74 Identify a conic from equation

**Unit 13 Variations**75 Write equation for direct, inverse and joint variation problems

76 Find the constant of variation

**Unit 14 Sequences/Series**77 Write n terms of an arithmetic sequence

78 Find the sum of a finite arithmetic series

79 Write n terms of geometric sequence

80 Find sum of geometric series

81 Use formulas to find nth term

82 Identify sequence/series as arithmetic, geometric or neither

**Unit 15 Statistics**83 Determine probabilities associated with areas under the normal crve

84 Compute permutations and combinations

If you made it this far, here's my call for help: Anyone have advice/suggestions for how to make this work and/or a better way to organize the information into cohesive units that seem to occur in a somewhat logical order? There is and will continue to be an emphasis on function families and transformations (as there should be). I find it difficult to express on paper how each function category needs to be a resting place, but they are all connected in the ways that transformations apply. Any ideas?

...oh...and I'm going to be teaching one section of deaf students and one section of blind students...in case that makes a difference

**edit: I've added links to the old and new Virgina SOLs for Algebra 2 if anyone's interested**

Every state and school is different, so of course I can only speak from my experience ... AND I haven't taught Alg2 in years, but I did teach precal and calculus for a long time. One suggestion is for you to ask the precalculus teacher which of your topics she/he would deem most important to stress and why. Another suggestion is to actually show the students this nice outline you made and keep referring back to it to see how much they've learned and how things are grouped. Another suggestion, if you have to cut things is to do without or minimize time spent on #s: 2,3,13, ... and anything the precalculus teacher says they teach.

ReplyDeleteGood luck,

Ms. Cookie

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