## 8.09.2010

### ABG: Algebra 2 Skills Draft

This will be my first year teaching Algebra 2.

I'm using the McDougal Littell 2004 edition textbook.

I went through and pulled objectives straight from the text. A lot of them had a second objective thrown in that basically said: Use ____________ in real-life problems. I didn't number those because they seem redundant. It did make me think, should I be including real-life/word problems in the assessment for every standard? If so, I consider that a form of assessment instead of a separate standard.

I made a few notes on standards I didn't understand and thought should be separated.

I stopped at Chapter 11. The last three chapters of the book are:

Chapter 12- Probability and Statistics

Chapter 13- Trigonometric Ratios and Functions

Chapter 14- Trigonometric Graphs, Identities, and Equations

I would love to get to Chapter 12 but I doubt it. Also, this book throws in one probability and statistics lesson near the end of every chapter. I'm debating taking those out and adding them into this chapter that I may or may not get into.

Chapter 13 and 14 seem to me an introduction to Trig which I have decided is not necessary. But then I'm thinking, this is the last math class the majority of my students will take ever and especially before the ACT. So, are there things I should be teaching out of those last two chapters that will benefit my students' ACT scores?

Algebra 2 Obejctives

1 Use a number line to graph and order real numbers.
2 Identify properties of and use operations with real numbers.
3 Evaluate algebraic expression.
4 Simplify algebraic expressions by combining like terms.
5 Solve linear equations.
Use linear equations to solve real-life problems.
6 Rewrite equations with more than one variable.
7 Rewrite common formulas.
8 Use a general problem-solving plan to solve real life problems.
Use other problem-solving strategies to help solve real-life problems.
9 Solve simple inequalities.
10 Solve compound inequalities.
11 Solve absolute value equations and inequalities.
Use absolute value equations and inequalities to solve real-life problems.
12 Represents relations and functions.
13 Graph and evaluate linear functions.
14 Find slopes of lines and classify parallel and perpendicular lines. (Separate?)
15 Use slope to solve real-life problems.
16 Use the slope-intercept form of a linear equation to graph linear equations.
17 Use the standard form of a linear equation to graph linear equations.
18 Write linear equations.
19 Write direct variation equations.
20 Use a scatter plot to identify the correlation shown by a set of data.
21 Approximate the best-fitting line for a set of data.
22 Graph linear inequalities in two variables.
Use linear inequalities to solve real-life problems.
23 Represent piecewise functions. (What does represent mean?)
Use piecewise functions to model real-life quantities.
24 Represent absolute value functions. (What does represent mean?)
Use absolute value functions to model real-life situations.
25 Graph and solve systems of linear equations in two variables. (Separate?)
Use linear systems to solve real-life problems.
26 Use algebraic methods to solve linear systems.
Use linear systems to model real-life situations.
27 Graph a system of linear inequalities to find the solutions of the system.
Use systems of linear inequalities to solve real-life problems.
28 Solve linear programming problems.
Use linear programming to solve real-life problems.
29 Graph linear equations in three variables and evaluate linear functions of two variables. (Separate?)
30 Use functions of two variables to model real-life situations.
31 Solve systems of linear equations in three variables.
Use linear systems in three variables to model real-life situations.
32 Add and subtract matrices, multiply a matrix by a scalar, and solve matrix equations. (Definitely needs to be split in separate standards!)
Use matrices in real-life situations.
33 Multiply two matrices.
Use matrix multiplication in real-life situations.
34 Evaluate the determinants of 2 x 2 and 3 x 3 matrices.
35 Use Cramer’s rule to solve systems of linear equations.
36 Find and use inverse matrices.
Use inverse matrices in real-life situations.
37 Solve systems of linear equations using inverse matrices.
Use systems of linear equations to solve real-life problems.
EXTENSION Solve systems of linear equations using elementary row operations on augmented matrices.
38 Graph quadratic functions. (Shouldn’t this say more?)
Use quadratic functions to solve real-life problems.
40 Find zeros of quadratic functions.
41 Solve quadratic equations by finding square roots.
Use quadratic equations to solve real-life problems.
42 Solve quadratic equations with complex solutions and perform operations with complex numbers.
43 Apply complex numbers to fractal geometry. (Say what?)
44 Solve quadratic equations by completing the square.
45 Use completing the square to write quadratic functions in vertex form.
Use the quadratic formula in real-life situations.
47 Graph quadratic inequalities in two variables.
48 Solve quadratic inequalities in two variables.
49 Write quadratic functions given characteristics of their graphs.
50 Use technology to find quadratic models for data.
51 Use properties of exponents to evaluate and simplify expressions involving powers.
Use exponents and scientific notation to solve real-life problems.
52 Evaluate a polynomial function.
53 Graph a polynomial function.
54 Add, subtract, and multiply polynomials. (Separate?)
Use polynomial operations in real-life problems.
55 Factor polynomial expressions.
56 Use factoring to solve polynomial equations.
57 Divide polynomial and relate the result to the remainder theorem and the factor theorem. (This confuses me.)
Use polynomial division in real-life problems.
58 Find the rational zeros of a polynomial function.
Use polynomial equations to solve real-life problems.
59 Use the fundamental theorem of algebra to determine the number of zeros of a polynomial function.
60 Use technology to approximate the real zeros of a polynomial function.
61 Analyze the graph of a polynomial function. (…And that means what exactly?)
62 Use the graph of a polynomial function to answer questions about real-life situations.
63 Use finite differences to determine the degree of a polynomial function that will fit a set of data.
64 Use technology to find polynomial models for real-life data.
65 Evaluate the nth roots of real numbers using both radical notation and rational exponent notation.
Use nth roots to solve real-life problems.
66 Use properties of rational exponents to evaluate and simplify expressions.
Use properties of rational exponents to solve real-life problems.
67 Perform operations with functions including power functions. (Separate?)
Use power functions and function operations to solve real-life problems.
68 Find inverses of linear functions.
69 Find inverses of nonlinear functions.
70 Graph square root and cube root functions. (Should these be separated? And how will students know if they have successfully graphed them?)
71 Use square root and cube rot functions to find real-life quantities.
72 Solve equations that contain radicals or rational exponents. (Separate?)
Use radical equations to solve real-life problems.
73 Use measures of central tendency and measures of dispersion to describe data sets.
74 Use box-and-whisker plots and histograms to represent data graphically.
75 Graph exponential growth functions.
Use exponential growth functions to model real-life situations.
76 Graph exponential decay functions.
Use exponential decay functions to model real-life situations.
77 Use the number e as the base of exponential functions.
Use the natural base e in real-life situations.
78 Evaluate logarithmic functions.
79 Graph logarithmic functions.
80 Use properties of logarithms.
Use properties of logarithms to solve real-life problems.
81 Solve exponential equations.
82 Solve logarithmic equations.
83 Model data with exponential functions.
84 Model data with power functions.
85 Evaluate and graph logistic growth functions. (Separate?)
Use logistic growth functions to model real-life quantities.
86 Write and use inverse variation models.
87 Write and use joint variation models. (Idk what joint variation is?)
88 Graph simple rational functions.
Use the graph of a rational function to solve real-life problems.
89 Graph general rational functions.
Use the graph of a rational function to solve real-life problems.
90 Multiply and divide rational expressions. (Separate?)
Use rational expressions to model real-life quantities.
91 Add and subtract rational expressions.
92 Simplify complex fractions.
93 Solve rational equations.
Use rational equations to solve real-life problems.
94 Find the distance between two points and find the midpoint of the line segment joining two points. (Separate?)
Use the distance and midpoint formulas in real-life situations.
95 Graph and write equations of parabolas. (Separate?)
Use parabolas to solve real-life problems.
96 Graph and write equations of circles. (Separate?)
Use circles to solve real-life problems.
97 Graph and write equations of ellipses. (Separate?)
Use ellipses in real-life situations.
98 Graph and write equations of hyperbolas. (Separate?)
Use hyperbolas to solve real-life problems.
99 Write and graph an equation of a parabola with its vertex at (h, k) and an equation of a circle, ellipse, or hyperbola with its center at (h,k). (Separate many times?)
100 Classify a conic using its equation.
101 Solve systems of quadratic equations.
Use quadratic systems to solve real-life problems.
EXTENSION: Find the eccentricity of a conic section.
102 Use and write sequences.
103 Use summation notation to write series and find sums of series. (Separate?)
104 Write rules for arithmetic sequences and find suns of arithmetic series.
Use arithmetic sequences and series in real-life problems.
105 Write rules for geometric sequences and find sums of geometric series. (Separate?)
Use geometric sequences and series to model real–life quantities.
106 Find sums of infinite geometric series.
Use infinite geometric series as models of real-life situations.
107 Evaluate and write recursive rules for sequences.
Use recursive rules to solve real-life problems.
EXTENSION: Use mathematical induction to prove statements about all positive integers.

1. Keep the stats and probability. It will do your students more good than most of the rest of Algebra 2.

2. Here are my comments on your list. I have taught Algebra 2 for 14 years and my comments are based on my experiences in three different districts, so I hope they are helpful to you.

As far as the "in real life" problems - I would use them in the assessing. Don't make them separate standards. There is one exception, and I'll mention it later.

Personally, I would groud the probability/stats stuff in each chapter together as one unit.

I will say this a few times for individual standards, but I feel this is REALLY important, so I am going to say this now. You MUST talk to whomever teaches Pre-Calculus in your building and find out what he or she thinks is important for you to cover. This is the "vertical" team we've talked about before. You are part of that - but "vertical team" goes both ways and Pre-Calculus is your next course. Here's why I think it's important - in my district, the teacher who teaches Pre-Calc does not cover Sequences and Series at all. Doesn't do Binomial Theorem. Both of these concepts are important to Calculus. So, I make sure I cover it in my Algebra 2 course. He covers Conics and Trigonometry, so I skip those concepts in favor of Sequences and Series and Probability (and Statistics if I have time). Without having had the conversation with the Pre-Calculus teacher, I wouldn't know that. If I followed the sequence of the book, I would cover Conics and Probability and our students would never see Sequences and Series.

One final comment and then I'll get to the individual standards you listed. You don't have to follow the book's order. I have been guilty of that for many years. The book's order is someone's opinion of what they think is the right sequence of the material. It is not the only way. Feel free to regroup and tweak the order so it makes sense to you. In fact, I'd encourage it - there is ALWAYS something that is in a weird place to you that you want to move and it's real easy to be afraid of changing things around. Don't be afraid. Do what makes sense to you.

Individual standards in next comment.

3. Okay, I'll get off my soap box - here are my comments on the individual standards:
14 - I would separate

23 and 24 - To figure out what the author meant by "represent," look at the problems in the textbook. That should clue you in.

25 - I don't think you have to separate these. You need to look at it and decide whether it's important to separate them to you. If you were to separate them, I would have graph systems and solve systems by graphing.

29 - I don't do this. Not sure whether you need to. Check w/ your Pre-Calc teacher (see above comments).

31 - Again, not sure if you need this. Check w/ Pre-Calc teacher.

32 - Definitely split.

33 - This is the ONE exception on the real-life situations. I would include a separate standard on using matrices in real-life situations because with matrix multiplication in particular, it is kind of different.

I would skip the extension for using elementary row ops. Most students won't ever see this again and solving by using inverse matrices should be plenty.

38 - In my opinion, doesn't have to say more unless you want to assess something more with it. Up to you.

43 - I'd skip

47 and 48 - I'd skip but check with your Pre-Calc teacher.

50 - Probably would skip it also.

54 - I would separate it as addition/subtraction and multiplication.

55 - I'd separate into smaller parts. Possibly: x^2 + bx + c, ax^2 + bx + c, polynomials with degree higher than 2

57 - I'm sure there is a better way to word this but it escapes me at the moment.

61 - again, check the problems to clarify this.

63 and 64 - I'd probably skip this. Check with your Pre-Calc teacher.

67 - Separate. Check with Pre-Calc on Power Functions.

70 - Separate (although it's up to you).

72 - Separate (although it's up to you).

75/76 - I would combine these as graph exponential functions. Too specific here.

83 thru 85 - I'd probably skip - check with Pre-Calc teacher.

87 - joint variation has multiple direct variation variables (y = kxz for example)

90 - NO on separating. Division is the inverse of multiplication.

94 - Separate

95-99 I would separate.

99 This is a duplicate I believe.

101 - I'd definitely skip this and the extension, but ask your Pre-Calc teacher.

103 - separate

105 - separate

skip the end extension
--Lisa

4. Lisa,

First of all thank you for actually reading them all!

I will talk to the Pre-Calc teacher to sort things out. In other conversations, I have been frustrated because the vertical team is basically me alone but you are right, I have to have conversations and open communication to make sure my students are getting the best we can offer.

5. I hope that you were able to follow all that I gave you - if not, let me know and I'll try to clarify it further for you. I have found over the years that when teaching Alg 2, you have to know where they are headed. As you see, there is SO much material and it is important to understand what they really need out of it. Each district is different b/c each teacher has their own "pet" topics. You have to know what they need.

I am 1 of 3 in my school that teaches math - I understand the frustration of feeling like you are the vertical team. Fortunately, our admininstration has listened to us when we have expressed our concerns and has arranged our courses such that students don't have to have the same teacher 2 years in a row (although in some cases that is unavoidable). That may be a conversation you want to have with your admin if you feel that's important.

I'd love to see your revision of this list once you have a chance to talk to your Pre-Calc teacher and cull some of it out and tweak it.
--Lisa

6. I second what Lisa said about talking to the PreCal teacher. Here are my thoughts (having taught Alg II and Precal tons before). Keep in mind though, NC is a strict curriculum. So, it may differ a bit.

14 - Separating will depend on how good (or bad) your students are.

23 - We don't do piecewise in our A2 curriculum.

25 - I would just teach graphing, substitution and elimination as you normally would. No real need to separate.

29 - I would separate. Although, we don't graph 3D in our A2 curriculum.

32 - I think you can leave add, subtract, scalar mult in one standard and then solving them into another. (+, - and scal. mult are pretty easy)

35 - I only do Cramer's with Honors.

37 Extension - I only do actual row operations with Honors. And, do it on the calculator (rref) with Regular.

43 - I don't do complex numbers with fractals.

45 - In regular, I only complete the square when it's x^2. With honors, I'll add in ax^2. To write in vertex form, I teach them to use x = -b/2a to get the x, plug in to get y.

54 - I would leave add/sub together, then have a multiply standard.

57 - Pretty big in A2, I think. They can use division to find factors and factor it.

61 - I would assume they mean discuss increasing, decreasing, finding relative and absolute maximums and minimums, zeroes, etc.

67 - We don't do power functions in A2 in NC.

70 - Can leave together. And, can use calculator to check it (kind of). Lots of websites out there will graph full function.

73 & 74 - We do not teach statistics in our A2 curriculum.

85 - Separate if you want. Depends on your kids.

87 - Joint variation combines direct and indirect (inverse) variations. Make sure you cover direct before going into it all.

90 - Don't really need to separate. Because dividing is copy dot flop and becomes multiplication. Basically the same thing.

94 - Should be review, so may not need to separate.

95, 96, 97, 98 - Yes, separate.

99 - could be intertwined with the above separate standards.

101 Extension - I don't do eccentricity.

102 and on - We don't do sequences, series, sums, etc in our A2 curriculum.

Hope that helps a bit. Ask away!

7. Just leaving a quick comment on #38--graphing quadratics.

I teach this in two different ways, so I would separate it into two skills personally.

#1. I call this A+ graphing. Make a t-table and plot the points. Needs to have a minimum number of points and needs to clearly show the whole parabola.
#2. Sketching the parabola using intercepts. Can add the vertex as well, but technically not necessary. I have found that having the line of symmetry drawn in helps students though.

You certainly don't need anymore standards though. :)

8. I am currently reading an ACT 2010 book. It states there are 4 trig questions on the test, so I would cover trig in algebra 2. In my district, there are some seniors who take algebra 2. They need that intro to trig before taking the ACT.

9. Something tells me you have too many standards. It feels to me that you are listing skills instead of standards. I would work on combining some of them together and I would definitely include the real world application problems since students tend to be able to do "naked" math but they forget everything when you put it in a problem situation. Do you feel like you're going to be able to get through all of those standards in the school year?