Huntsville City Schools - Instructional Guide
2015 - 2016
Course: Algebra 1B Grade: 10
Math Practices
Online Resources
The Standards for Mathematical Practice describe varieties of expertise
that mathematics educators at all levels should seek to develop in their
students. These practices rest on important “processes and
proficiencies” with longstanding importance in mathematics education.
The first of these are the NCTM process standards of problem solving,
reasoning and proof, communication, representation, and connections.
The second are the strands of mathematical proficiency specified in the
National Research Council’s report Adding It Up: adaptive reasoning,
strategic competence, conceptual understanding (comprehension of
mathematical concepts, operations and relations), procedural fluency
(skill in carrying out procedures flexibly, accurately, efficiently and
appropriately), and productive disposition (habitual inclination to see
mathematics as sensible, useful, and worthwhile, coupled with a belief
in diligence and one’s own efficacy).
Dan Meyer’s Ted Talk about teaching math:
https://youtu.be/qocAoN4jNwc
Links to his 3-act activities, sorted by standard:
https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYd
EhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0
Granite City Math Vocabulary:
http://www.graniteschools.org/mathvocabulary/
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of
others.
4. Model with mathematics
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
For more:
Other online resources
1
Elaboration on each practice from the Common Core website:
www.corestandards.org/Math/Practice/
www.opencurriculum.org is a website that curates activities from all
over the web, sorted by standard.
Kid-friendly language:
www.buncombe.k12.nc.us/Page/37507
http://map.mathshell.org/lessons.php has great formative
assessments and group activities, searchable by standard.
Online tools
www.desmos.com is a free online calculator. Excellent for working
with linear equations, scatterplots, and best-fit lines.
https://teacher.desmos.com/ has some great activities for introducing
and working with functions.
www.geogebra.org is a free online geometry tool. It is great for
working with transformations.
FIRST NINE WEEKS
Unit 1 – Algebra IA Review
Standard
“I Can” Statements
(To be completed by School Teams)
Resources
Solving Equations
Solving Inequalities
Functions
Linear Functions
Systems of Equations
Pacing
Recommendation /
Date(s) Taught
5 days
5 days
2 days
5 days
5 days
Unit 2 – Exponents and Exponential Functions
Standard
“I Can” Statements
Resources
2
(To be completed by School Teams)
ALCOS #1 (N-RN1) Explain how
the definition of the meaning
of rational exponents follows
from extending the properties
of integer exponents to those
values, allowing for a notation
for radicals in terms of rational
exponents.
ALCOS #2 (N-RN2) Rewrite
expressions involving radicals
and rational exponents using
the properties of exponents.
ALCOS 33 (F-IF9) Compare
properties of two functions
each represented in a different
way (algebraically, graphically,
numerically in tables, or by
verbal descriptions).
Ch. 7.1, Ch. 7.2,
Ch. 7.3, Ch. 7.4
Pacing
Recommendation /
Date(s) Taught
Unit 7 Pacing:
28 days
Ch. 7.5
Ch. 7.6 and Ch.
7.7
F-IF7e Graph
Exponential….Function
Showing intercepts and end
behavior. 7.6
ALCOS 23 (A-REI11): Explain
why the x-coordinates of the
points where the graphs 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.
Include cases where f(x) and/or
g(x) are exponential or
logarithmic functions.
3
ALCOS 32b (F-IF8b) Use the
properties of exponents to
interpret expressions for
exponential functions.
ALCOS 34 (F-BF1) Write a
function that describes a
relationship between two
quantities.
ALCOS 7 [A-SSE1] Interpret
expressions that represent a
quantity in terms of its context.
ALCOS 7b [A-SSE1b] Interpret
complicated expressions by
viewing one or more of their
parts as a single entity.
Example: Interpret P(1+r)n as
the product of P and a factor
not depending on P
ALCOS 40 (F-LE5): Interpret the
parameters in a linear or
exponential function in terms
of a context.
ALCOS 35 (F-BF2) Write
arithmetic and geometric
sequences both recursively and
with an explicit formula, use
them to model situations, and
translate between the two
forms.
Ch. 7.8
ALCOS 38 (F-LE2): Construct
linear and exponential
functions, including arithmetic
4
and geometric sequences,
given a graph, a description of
a relationship, or two inputoutput pairs.
ALCOS 34 (F-BF1): Write a
function that describes a
relationship between two
quantities.
ALCOS 34a (F-BF1a): Determine
and explicit expression, a
recursive process, or steps for
calculation from a context.
ALCOS 27 (F-IF3): Recognize
that sequences are functions,
sometimes defined recursively,
whose domain is a subset of
the integers.
Quality Core Standards:
C.1.b. Translate real-world
problems into expressions
using variables to represent
values
F.1.a. Use properties of
exponents (including zero and
negative exponents) to
evaluate and simplify
expressions
Helpful Resources
for Ch. 7:
1. LTF: ALCOS
#12, #13, and
#4:
Exponential
Function
5
Exploration (2
days); ALCOS
#12:
Exponential
Growth (2
days)
FIRST BENCHMARK ASSESSMENT
6
Huntsville City Schools - Instructional Guide
2015 - 2016
Course: Algebra 1B Grade: 10
SECOND NINE WEEKS
Unit 8 – Polynomials and Factoring
Standard
ALCOS 10 (A-APR1) Understand
that polynomials form a system
analogous to the integers;
namely, they are closed under
the operations of addition,
subtraction, and multiplication;
add, subtract and multiply
polynomials.
ALCOS 7 a. (A-SSE1a) Interpret
parts of an expression such as
terms, factors, and coefficients.
“I Can” Statements *
Resources
Ch. 8.1, Ch. 8.2,
Ch. 8.3, Ch. 8.4
Ch. 8.5, Ch. 8.6,
Ch. 8.7, Ch. 8.8
Pacing
Recommendation /
Date(s) Taught
Ch. 8.1 (1 Day)
Ch. 8.2(1 Day)
Ch. 8.3(2 Day
w/graphing calculator
practice)
Ch. 8.4(1 Day)
Unit 8 Pacing:
30 days
ALCOS 8 (A-SSE2): Use the
structure of an expression to
identify ways to rewrite it.
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).
Quality Core Standards:
C.1.a Solve single-step and
multistep equations and
inequalities in one variable
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C.1.b Solve equations that
contain absolute value
C.1.c Solve formulas for a
specified variable
C.1.d Write and graph linear
equations and inequalities
from real-world situations
(e.g., a constant-rate
distance/time
problem)
C.1.e Write linear equations in
standard form and slopeintercept form when given two
points, a point and the slope,
or the graph of the equation
C.1.f Identify, formulate, and
obtain solutions to problems
involving direct and inverse
variation
E.1.a Factor perfect square
trinomials and the difference
of two squares
E.1.b Factor trinomials in the
forms ax2 + bx + c
F.1.a Use properties of
exponents (including zero and
negative exponents) to
evaluate and simplify
expressions
LTF: none
SECOND BENCHMARK ASSESSMENT
8
Huntsville City Schools - Instructional Guide
2015 - 2016
Course: Algebra 1B Grade: 10
THIRD NINE WEEKS
Unit 9 – Quadratic Functions and Equations
Standard
ALCOS 13 (A-CED2): Create
equations in two or more
variables to represent
relationships between
quantities: graph equations on
coordinate axes with labels and
scales.
“I Can” Statements *
Resources
Ch. 9.1 and Ch.
9.2
Pacing
Recommendation /
Date(s) Taught
Unit 9 Pacing:
30 days
ALCOS 31a (F-IF7a) Graph
linear and quadratic functions,
and show intercepts, maxima,
and minima.
ALCOS 30(F-IF6): Calculate and
interpret the average rate of
change of a function over a
specified interval. Estimate the
rate of change from a graph.
ALCOS 31 (F-IF7): Graph
functions expressed
symbolically and show key
features of the graph, by hand
9
in simple cases and using
technology for more
complicated cases.
ALCOS 33 (F-IF9) Compare
properties of two functions
each represented in a different
way (algebraically, graphically,
numerically in tables, or by
verbal descriptions).
ALCOS 34 (F-BF1) Write a
function that describes a
relationship between two
quantities.
ALCOS 36 (F-BF3): Identify the
effect on the graph of
transformations. Experiment
with cases and illustrate the
effects on the graph using
technology.
ALCOS 39 (F-LE3) Observe,
using graphs and tables, that a
quantity increasing
exponentially eventually
exceeds a quantity increasing
linearly, quadratically, or (more
generally) as a polynomial
function.
ALCOS 18b (A-RE14b) Solve
quadratic equations by
inspection (e.g. for x2 = 49),
taking square roots,
completing the square and the
quadratic formula, and
factoring as appropriate to the
Ch. 9.3 and Ch.
9.4
10
initial form of the equation.
Recognize when the quadratic
formula gives complex
solutions, and write them as a
+ bi for real numbers a and b.
ALCOS 9 (A-SSE3): Choose and
produce an equivalent form of
an expression to reveal and
explain properties of the
quantity represented by the
expression.
ALCOS 9a(A-SSE3a): Factor a
quadratic expression to reveal
the zeros of the function it
defines.
ALCOS 9b(A-SSE3b): Factor a
quadratic expression to reveal
the zeros of the function it
defines.
ALCOS 9c(AL standard):
Determine a quadratic
equation when given its graph
or roots
ALCOS 9d(A-SSE3c): Use the
properties of exponents to
transform expressions for
exponential functions.
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%.
11
ALCOS 16 (A-REI1): Explain
each step in solving a simple
equation as following form the
equality of numbers asserted
at the previous step, starting
from the assumption that the
original equation has a
solution. Construct a viable
argument to justify a solution
method.
CH. 9.5
ALCOS 18 (A-REI4): Solve
quadratic equations in one
variable.
ALCOS 32 (F-IF8): Write a
function defined by an
expression in different but
equivalent forms to reveal and
explain different properties of
the function.
ALCOS 32a (F-IF8a): Use the
process of factoring and
completing the square in a
quadratic function to show
zeros, extreme values, and
symmetry of the graph, and
interpret these in terms of a
context.
ALCOS 31a (F-IF8a) Use the
process of factoring and
completing the square in a
quadratic function to show
zeros, extreme values, and
symmetry of the graph, and
12
interpret these in terms of a
context.
ALCOS 18a (A-RE14a) Use a
method of completing the
square to transform any
quadratic equation in x into an
equation of the form (x – p)2 =
q that has the same solutions.
Derive the quadratic formula
from this form.
ALCOS 34b (F-BF1b): Combine
standard function types using
arithmetic operations.
Ch. 9.6
Ch. 9.7
ALCOS 37a (F-LE1a) Prove that
linear functions grow by equal
differences over equal
intervals, and that exponential
functions grow by equal factors
over equal intervals.
ALCOS 37 [F-LE1]
Distinguish between situations
that can be modeled with linear
functions and with exponential
functions.
ALCOS 37c [F-LE1c] Recognize
situations in which a quantity
grows or decays by a constant
percent rate per unit interval
relative to another.
ALCOS 45a (S-ID6a) Fit a
function to the data; use
functions fitted to data to solve
problems in the context of the
data. Use given function or
13
choose a function suggested by
the context. Emphasize linear,
quadratic, and exponential
models.
ALCOS 45b (S-ID6b) Informally
assess the fit of a function by
plotting and analyzing
residuals.
ALCOS 21 (A-REI7) Solve a
simple system of linear
equation and quadratic
equations in two variables
algebraically and graphically.
Ch. 9.8
ALCOS 14 (A-CED3): Represent
constraints by equations or
inequalities, and by systems of
equations and/or inequalities
and interpret solutions as
viable or non-viable options in
a modeling context.
Example: represent
inequalities describing
nutritional and cost constraints
on combinations of different
foods.
Quality Core Standards:
E.1.c. Solve quadratic
equations using multiple
methods, including graphing,
factoring, and the square root
principle
E.2.a Identify graphs of
quadratic functions
E.2.b Relate factors, solutions
(roots), zeros of related
functions, and x-intercepts in
14
equations that arise from
quadratic functions
Helpful Resources
for Ch. 9:
1. LTF: ALCOS
#31a and #36
(linear only):
Translations of
Linear
Functions (2.5
days);
ALCOS#34,
#40, and #6:
Study of
Population
Growth (2 or 3
days; ALCOS
#15: Literal
Equations –
Geometric
FormulasProblem 2 ab
(15 min);
ALCOS#9c,
#13, #28, and
#36:
Investigation –
Graphing
Quadratic
Functions;
ALCOS#29 and
31a: Graphing
Quadratic
15
Functions –
Example 1 (2
days);
ALCOS#7a,
#7b, #9a, and
#18b: Another
Way to Look at
Factoring (2
days);
ALCOS#12,
#29, #32a, and
#33: Graphing
Quadratic
Functions –
Example 2 and
Problems #1
and #2 (3
days); ALCOS#
31a, #28, and
#30:
Adaptation of
AP Calculus
1997 AB-2 (2
days);
ALCOS#28,
#31b, #13, and
#29:
Adaptation of
Algebra I 2007
EOC Free
Response (2
days)
16
Unit 10 – Radical Expressions and Equations
Standard
ALCOS 31b (F-IF7b) Graph
square root, cube root, and
piecewise-defined functions,
including step functions and
absolute value functions.
“I Can” Statements *
Resources
Ch. 10.1, 10.2,
and 10.5
Pacing
Recommendation /
Date(s) Taught
Unit 10 Pacing:
12 days
**Please note 1.
10.1 is not
required for high
school.
2. Graphing
Calculators are a
great resource for
section 10.5
Quality Core Standards:
F.1.a Use properties of
exponents (including zero and
negative exponents) to
evaluate and simplify
expressions
F.1.d Find rational number
square roots (without
calculators) and approximate
irrational square roots (with
and without calculators)
F.1.e Evaluate and simplify
radical expressions
F.1.f Multiply radical
expressions
F.1.g Simplify an algebraic
quotient by rationalizing an
irrational monomial
denominator
17
Helpful
Notes/Resources
for Ch. 10:
8th Grade ALCOS #23:
Pythagorean Theorem
Applications Problems
1 – 4(1 day)
THIRD BENCHMARK ASSESSMENT
18
Huntsville City Schools - Instructional Guide
2015 - 2016
Course: Algebra 1B Grade: 10
FOURTH NINE WEEKS
Unit 11 – Radical Expressions and Functions
Standard
ALCOS 11 (A-APR7) Understand
that rational expressions form
a system analogous to the
rational numbers, closed under
addition, subtraction,
multiplication, and division by
a nonzero rational expression;
add, subtract, multiply, and
divide rational expressions.
ALCOS 12 (A-CED1) Create
equations and inequalities in
one variable, and use them to
solve problems. Include
equations rising from linear
and quadratic functions, and
simple rational and exponential
functions.
ALCOS 29 (F-IF5) Relate the
domain of a function to its
graph and, where applicable,
to the quantitative relationship
it describes.
“I Can” Statements *
Resources
Ch. 11.1, 11.2,
11.3 and Ch. 11.4
**Please Note:
11.1 is not a standard
but prepares for 11.2.
Pacing
Recommendation /
Date(s) Taught
Unit 11 Pacing:
25 days
Ch. 11.5
Ch. 11.6
19
ALCOS 28 (F-IF4) For a function
that models a relationship
between two quantities,
interpret key features of
graphs and tables in terms of
the quantities, and sketch
graphs showing key features
given a verbal description of
the relationship. Key features
include intercepts; relative
maximums and minimums;
symmetries; end behavior; and
periodicity.
Quality Core Standards:
F.1.a Use properties of
exponents (including zero and
negative exponents) to
evaluate and simplify
expressions
F.1.b Evaluate and simplify
rational expressions
F.1.c Add, subtract, multiply,
and divide rational expressions
F.1.d Find rational number
square roots (without
calculators) and approximate
irrational square roots (with
and without calculators)
F.1.e Evaluate and simplify
radical expressions
F.1.f Multiply radical
expressions
Ch. 11.7
Helpful Resources
for Ch. 11:
LTF: ALCOS #28:
Analysis of Functions
(2 days); ALCOS#13
and #28: Quadratic
20
Optimization (2 days);
ALCOS #14, #22, #28,
#28, #31b, and #36:
Characteristics of
Functions (3 days);
ALCOS#35:
Transformations of
Functions Explorations
(2 days); ALCOS#31b
and #36: Even/Odd
Functions (2days)
Unit 12 – Data Analysis and Probability
Standard
ALCOS 41 (S-ID1) Represent
data with plots on the real
number line (dot plots,
histograms, and box plots).
ALCOS 45 (S-ID6): Represent
data on two quantitative
variables on a scatter plot, and
describe how the variables are
related.
ALCOS 42 (S-ID2) Use statistics
appropriate to the shape of the
data distribution to compare
center (median, mean) and
spread (interquartile range,
standard deviation) of two or
more different data sets.
“I Can” Statements *
Resources
Ch. 12.2
Pacing
Recommendation /
Date(s) Taught
Unit 12 Pacing:
13 days
Ch. 12.3 and Ch.
12.4
Ch. 12.5
ALCOS 43 (S-ID3) Interpret
differences in shape, center,
and spread in the context of
21
the data sets, accounting for
possible effects of extreme
data points (outliers).
ALCOS 44 (S-ID5) Summarize
categorical data for two
categories in two-way
frequency tables. Interpret
relative frequencies in the
context of the data (including
joint, marginal, and conditional
relative frequencies).
Recognize possible associations
and trends in the data.
ALCOS 47 (S-CP2) Understand
that two events A and B are
independent if the probability
of A and B occurring together is
the product of their
probabilities, and use this
characterization to determine
if they are independent.
Quality Core Standards:
G.1.a Identify the effect on
mean, median, mode, and
range when a set of data is
changed
G.1.b Interpret data from line,
bar, and circle graphs,
histograms, scatterplots, boxand-whisker plots, stem-andleaf plots,
and frequency tables to draw
inferences and make
predictions
G.1.c Identify arithmetic
sequences and patterns in a set
of data
Ch. 12.8
1 Day
22
G.1.d Identify patterns of
growth (e.g., patterns of
exponential growth) in a set of
data
G.1.e Find the probability of a
simple event
G.1.f Distinguish between
independent and dependent
events
G.1.g Identify an approximate
line of best fit to model data
and make predictions
G.1.h Identify the most
efficient way to display data
Helpful Resources
for Ch. 12:
8th Grade ALCOS #26,
#27, #28: Fitting a
Line to Data (2 days);
ALCOS#41: Use Dot
Plots to Determine
Mean, Median, Mode
and Range (1 day);
ALCOS#41: Bar Graphs
and Histograms (.5
day); ALCOS#43:
Measures of Central
Tendencies (1 day);
ALCOS#41: Box and
Whisker Plots (.5 day);
ALCOS#4 and #42:
Linear Functions,
Transformations, and
Graphical Displays Part
1 only (.5 day);
ALCOS#44 and #47:
The Jury (2 days)
23
QUALITY CORE TEST AND FINAL EXAM
Overall Algebra 1 Helpful Resources:
1. Cumulative Reviews at end of sections.
Helpful in teacher book for list of
standards next to questions.
2. Interactmath.com,
commoncorepal.com, and
poweralgbra.com are good resources for
practice and review.
3. Concept Bytes are located at the end of
each chapter for in-depth practice
problems.
**Please Note: For each chapter, the
“Total Days” includes one day for review
and one day for testing of the chapter.
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