HS_Algebra_1A_1B by xiaoyounan

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Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)

Lesson Plan
Instr     COS                                                                                                                                          Date
Course of Study Objective                            Suggested Lesson Resources/Activities   (description,
Seq       #                                                                                                                                        Implemented
number, etc.)

Explain how the definition of the meaning of rational              A1133
exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals
3         1
in terms of rational exponents. [N-RN1]
Example: We define 51/3 to be the cube root of 5 because we
want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
Rewrite expressions involving radicals and rational exponents      A1133
3         2
using the properties of exponents. [N-RN2]
Explain why the sum or product of two rational numbers is          A1121, A1125, A1131
rational; that the sum of a rational number and an irrational
1         3     number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational. [N-
RN3]
Use units as a way to understand problems and to guide the         (graphs) A1316, A1615, A1617; (area/surface
solution of multistep problems; choose and interpret units         area) GE711, GE721, GE723, GE725, GE727,
1,2,
4     consistently in formulas; choose and interpret the scale and       GE1011, GE1013, GE1015, GE1017, GE1031,
3,4
the origin in graphs and data displays. [N-Q1]                     ge1428 (WS); (volume) GE1021, GE1023, GE1025,
GE1027, GE1033
Define appropriate quantities for the purpose of descriptive
1,2,4      5
modeling. [N-Q2]
Choose a level of accuracy appropriate to limitations on
1         6
measurement when reporting quantities. [N-Q3]
Interpret expressions that represent a quantity in terms of its
1         7
context.* [A-SSE1]
a. Interpret parts of an expression such as terms, factors, and A1211, A1231, a11612 (WS)
coefficients. [A-SSE1a]
1        7a
Example: Interpret P(1+r)n as the product of P and a factor not
depending on P.
b. Interpret complicated expressions by viewing one or more of A11431, a11612 (WS)
their parts as a single entity. [A-SSE1b]
1        7b
Example: Interpret P(1+r)n as the product of P and a factor not
depending on P.
2010 Alabama Course of Study Mathematics                                                                                                              1
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
Use the structure of an expression to identify ways to rewrite Same as A-SSE1a and A-SSE1b
it. [A-SSE2]
4         8
Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 - y2)(x2 + y2).
Choose and produce an equivalent form of an expression to
4         9     reveal and explain properties of the quantity represented by
the expression.* [A-SSE3]
a. Factor a quadratic expression to reveal the zeros of the         A11011, A11021, A11031, a11628
function it defines. [A-SSE3a]
4        9a     Example: The expression 1.15t can be rewritten as
(1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.
b. Complete the square in a quadratic expression to reveal the A11151, A11153
4        9b     maximum or minimum value of the function it defines. [A-
SSE3b]
c. Determine a quadratic equation when given its graph or
4        9c
roots.
d. Use the properties of exponents to transform expressions         A1911, A1913, A1915, a2270
4        9d
for exponential functions. [A-SSE3c]
Understand that polynomials form a system analogous to the A1921, A1923, A1931, a2180, a2190, a11627
integers; namely, they are closed under the operations of           (WS)
4        10
multiply polynomials. [A-APR1]
Create equations and inequalities in one variable, and use          (solving equations) A1311, A1313, A1321, A1331;
them to solve problems. Include equations arising from linear (writing equations) A1341, a11614 (WS);
and quadratic functions, and simple rational and exponential (ratios/proportions) A1411, a11615 (WS);
1,2       11
functions. [A-CED1]                                                 (inequalities) A1511, A1521, A1523, A1531,
A1541, A1551, a11618 (WS); (exponential)
A11211, A11213
Create equations in two or more variables to represent              (arithmetic) A1661; (graphing) A1751, A1761;
relationships between quantities; graph equations on                (functions) A1851, A11111, A11321, A11421,
1,2       12     coordinate axes with labels and scales. [A-CED2]                    a2060, a2170, a2320, a2360, a2370, a2380,
a11632 (WS), a2810 (WS), a2850 (WS), a2870
(WS), a2890 (WS)
Represent constraints by equations or inequalities, and by          (solving systems of equations) A1341, A1811,
1,2,3     13
systems of equations and/or inequalities and interpret              A1821, A1831, A1841, a11614 (WS), a11624
2010 Alabama Course of Study Mathematics                                                                                          2
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
solutions as viable or non-viable options in a modeling            (WS); (solving systems of inequalities) A1843,
context. [A-CED3]                                                  a11625 (WS); A11411, a2310, a2490, a2500,
Example: Represent inequalities describing nutritional and cost a2900 (WS)
constraints on combinations of different foods.
Rearrange formulas to highlight a quantity of interest, using      A2040
the same reasoning as in solving equations. [A-CED4]
1        14
Example: Rearrange Ohm’s law V = IR to highlight resistance
R.
Explain each step in solving a simple equation as following
from the equality of numbers asserted at the previous step,
1        15     starting from the assumption that the original equation has a
solution. Construct a viable argument to justify a solution
method. [A-REI1]
Solve linear equations and inequalities in one variable,           (solving equations) A1311, A1313, A1321, A1331;
including equations with coefficients represented by letters.      (solving inequalities) A1511, A1521, A1523,
1,2      16
[A-REI3]                                                           A1531, A1541, A1551, a11618 (WS); (literal
equations) a2040
4        17     Solve quadratic equations in one variable. [A-REI4]
a. Use the method of completing the square to transform any        A11151, A11153, A11161, A11163, a11630 (WS)
quadratic equation in x into an equation of the form (x - p)2 = q
4        17a
that has the same solutions. Derive the quadratic formula from
this form. [A-REI4a]
b. Solve quadratic equations by inspection (e.g., for x2 = 49),    A11021, A11031, A11111, A11121, A11131,
taking square roots, completing the square and the quadratic       A11141, A11151, A11153, A11161, A11163,
formula, and factoring as appropriate to the initial form of the a11628 (WS), a11629 (WS), a11630 (WS)
4        17b
equation. Recognize when the quadratic formula gives
complex solutions, and write them as a ± bi for real numbers a
and b. [A-REI4b]
Prove that, given a system of two equations in two variables, A1831, a11624 (WS)
replacing one equation by the sum of that equation and a
3        18
multiple of the other produces a system with the same
solutions. [A-REI5]
Solve systems of linear equations exactly and approximately        A1811, A1821, A1831, A2480, A11624 (WS)
3,4      19     (e.g., with graphs), focusing on pairs of linear equations in
two variables. [A-REI6]
4        20     Solve a simple system consisting of a linear equation and a        A2030, A2480, A2490
2010 Alabama Course of Study Mathematics                                                                                         3
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
quadratic equation in two variables algebraically and
graphically. [A-REI7] Example: Find the points of intersection
between the line y = –3x and the circle x2 + y2 = 3.
Understand that the graph of an equation in two variables is          A1751, A1761, A1851, A11111, A11321, A11421,
the set of all its solutions plotted in the coordinate plane,         A2060, A2170, A2320, A2360, A2370, A2380,
1        21
often forming a curve (which could be a line). [A-REI10]              A11632 (WS), A2810 (WS), A2820 (WS), A2870
(WS), A2880 (WS), A2890 (WS)
Explain why the x-coordinates of the points where the graphs A1821, A1831, A2480, A2490, A11624 (WS)
of the equations y = f(x) and y = g(x) intersect are the
solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions,
1,4       22
make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic
functions.* [A-REI11]
Graph the solutions to a linear inequality in two variables as a A2500, A2510, A2900 (WS)
half-plane (excluding the boundary in the case of a strict
3,4       23     inequality), and graph the solution set to a system of linear
inequalities in two variables as the intersection of the
corresponding half-planes. [A-REI12]
Understand that a function from one set (called the domain)           A1631, A2010, A2020
to another set (called the range) assigns to each element of
the domain exactly one element of the range. If f is a function
1        24
and x is an element of its domain, then f(x) denotes the
output of f corresponding to the input x. The graph of f is the
graph of the equation y = f(x). [F-IF1]
Use function notation, evaluate functions for inputs in their         A2010
1,2       25     domains, and interpret statements that use function notation
in terms of a context. [F-IF2]
Recognize that sequences are functions, sometimes defined             A1661, A11231, A2590, A2600
recursively, whose domain is a subset of the integers. [F-IF3]
2,3       26
Example: The Fibonacci sequence is defined recursively by
f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥1.
For a function that models a relationship between two                 A1751, A1761
1,2,4     27     quantities, interpret key features of graphs and tables in            A11111, A11321
terms of the quantities, and sketch graphs showing key                A11421, tr080, tr090, tr100, tr130, tr140
2010 Alabama Course of Study Mathematics                                                                                         4
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
features given a verbal description of the relationship. Key
features include intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and
periodicity.* [F-IF4]
Relate the domain of a function to its graph and, where            A2020
applicable, to the quantitative relationship it describes.* [F-    A2080
IF5]                                                               A2090
1,2,4   28
Example: If the function h(n) gives the number of person-hours A2320
it takes to assemble n engines in a factory, then the positive     A2360
integers would be an appropriate domain for the function.
Calculate and interpret the average rate of change of a            A1711
function (presented symbolically or as a table) over a
1,2     29
specified interval. Estimate the rate of change from a graph.*
[F-IF6]
Graph functions expressed symbolically and show key
1,2
30     features of the graph, by hand in simple cases and using
3,4
technology for more complicated cases.* [F-IF7]
1,2            a. Graph linear and quadratic functions, and show intercepts,      A1641, A1751,A1761
30a
3,4            maxima, and minima. [F-IF7a]                                       A11111
b. Graph square root, cube root, and piecewise-defined             A11321
1,2
30b    functions, including step functions and absolute value
3,4
functions. [F-IF7b]
c. Graph exponential and logarithmic functions, showing            a2370, a2380, tr080, tr090, tr100, tr130, tr140
1,2
30c    intercepts and end behavior, and trigonometric functions,
3,4
showing period, midline, and amplitude. [F-IF7e]
Write a function defined by an expression in different but
1,2
31     equivalent forms to reveal and explain different properties of
3,4
the function. [F-IF8]
a. Use the process of factoring and completing the square in a     Aa11011, A11021, A11031, A11151, A11153
1,2            quadratic function to show zeros, extreme values, and
31a
3,4            symmetry of the graph, and interpret these in terms of a
context. [F-IF8a]
b. Use the properties of exponents to interpret expressions for A1911, A1913, A1915, A11211, A11213
1,2
31b    exponential functions. [F-IF8b]
3,4
Example: Identify percent rate of change in functions such as y
2010 Alabama Course of Study Mathematics                                                                                         5
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
= (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and
classify them as representing exponential growth and decay.
Compare properties of two functions each represented in a             A1761, A11111, A11321, A11421, tr080, tr090,
different way (algebraically, graphically, numerically in tables, tr100, tr130, tr140
or by verbal descriptions). [F-IF9]
2,3,4     32
Example: Given a graph of one quadratic function and an
algebraic expression for another, say which has the larger
maximum.
1,2              Write a function that describes a relationship between two
33
3,4              quantities.* [F-BF1]
1,2              a. Determine an explicit expression, a recursive process, or          A1651, A1771, a2070
33a
3,4              steps for calculation from a context. [F-BF1a]
b. Combine standard function types using arithmetic                   A1921, A1923, A1931, A11462, A1661
operations. [F-BF1b]
1,2
33b    Example: Build a function that models the temperature of a
3,4
cooling body by adding a constant function to a decaying
exponential, and relate these functions to the model.
Write arithmetic and geometric sequences both recursively             A1661, A11231, a2590, aqa2600
2,3       34     and with an explicit formula, use them to model situations,
and translate between the two forms.* [F-BF2]
Identify the effect on the graph of replacing f(x) by f(x) + k, k     a2100, a2110, tr110, tr120
f(x), f(kx), and f(x + k) for specific values of k (both positive
and negative); find the value of k given the graphs.
2,3,4     35     Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing
even and odd functions from their graphs and algebraic
expressions for them. [F-BF3]
1        36     Find inverse functions. [F-BF4]
a. Solve an equation of the form f(x) = c for a simple function f     a2130
that has an inverse, and write an expression for the inverse. [F-
1        36a
BF4a]
Example: f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
Distinguish between situations that can be modeled with
3,4       37
linear functions and with exponential functions. [F-LE1]
a. Prove that linear functions grow by equal differences over         A1711, A1715, A11211, A11213
3,4       37a
equal intervals, and that exponential functions grow by equal
2010 Alabama Course of Study Mathematics                                                                                         6
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
factors over equal intervals. [F-LE1a]
b. Recognize situations in which one quantity changes at a           A1711, A1715, A1716
3,4       37b
constant rate per unit interval relative to another. [F-LE1b]
c. Recognize situations in which a quantity grows or decays by       A11211, A11213
3,4       37c    a constant percent rate per unit interval relative to another. [F-
LE1c]
Construct linear and exponential functions, including                A1341, A1661, A1771, A11231
arithmetic and geometric sequences, given a graph, a
1,2,3     38
description of a relationship, or two input-output pairs
(include reading these from a table). [F-LE2]
Observe, using graphs and tables, that a quantity increasing         A1761, A11111, A11211, A11213
exponentially eventually exceeds a quantity increasing
4        39
linearly, quadratically, or (more generally) as a polynomial
function. [F-LE3]
Interpret the parameters in a linear or exponential function in A1761, A11211, A11213, A11221
2,3       40
terms of a context. [F-LE5]
Represent data with plots on the real number line (dot plots, A1613, A1615
4        41
histograms, and box plots). [S-ID1]
Use statistics appropriate to the shape of the data                  a2420, a2430
distribution to compare center (median, mean) and spread
4        42
(interquartile range, standard deviation) of two or more
different data sets. [S-ID2]
Interpret differences in shape, center, and spread in the            a2420, a2430
4        43     context of the data sets, accounting for possible effects of
extreme data points (outliers). [S-ID3]
Summarize categorical data for two categories in two-way
frequency tables. Interpret relative frequencies in the context
4        44     of the data (including joint, marginal, and conditional relative
frequencies). Recognize possible associations and trends in
the data. [S-ID5]
Represent data on two quantitative variables on a scatter
2        45
plot, and describe how the variables are related. [S-ID6]
a. Fit a function to the data; use functions fitted to data to       A1791, a2440, a2450
solve problems in the context of the data. Use given functions
2        45a
or choose a function suggested by the context. Emphasize
linear, quadratic, and exponential models. [S-ID6a]
2010 Alabama Course of Study Mathematics                                                                            7
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
b. Informally assess the fit of a function by plotting and             a2440, a2450
2        45b
analyzing residuals. [S-ID6b]
c. Fit a linear function for a scatter plot that suggests a linear     A1791
2        45c
association. [S-ID6c]
Interpret the slope (rate of change) and the intercept                 A1791
1,2      46     (constant term) of a linear model in the context of the data.
[S-ID7]
Compute (using technology) and interpret the correlation
2        47
coefficient of a linear fit. [S-ID8]
2        48     Distinguish between correlation and causation. [S-ID9]
Describe events as subsets of a sample space (the set of
outcomes), using characteristics (or categories) of the
4        49
outcomes, or as unions, intersections, or complements of
other events (―or,‖ ―and,‖ ―not‖). [S-CP1]
Understand that two events A and B are independent if the
probability of A and B occurring together is the product of
4        50
their probabilities, and use this characterization to determine
if they are independent. [S-CP2]

2010 Alabama Course of Study Mathematics                                                                              8

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