Huntsville City Schools
Pacing Guide 2016-2017
Course: Algebra 1 Grade 8th-10th
Note: Please see documents on A+ College Ready website for more details.
Eighth Grade Standards are required for eighth grade Algebra I classes only (in italics).
Below is the 8 Mathematical Practices
Huntsville City Schools
Pacing Guide
Course Algebra 1 Grade 8th-10th
First Nine Weeks
Standard / Resources / Approximate Pacing Number of DaysUNIT 1: Foundations for Algebra
Vocabulary
additive inversealgebraic expressioncoefficientequivalent expressions
evaluateintegerslike termsorder of operations
real numbersimplifytermvariable
ALCOS 7.a (6.a). (A-SSE1a) Interpret parts of an expression such as terms, factors, and coefficients. / Ch.1.1,1.2 / Unit 1 Pacing:
9 Days (including 1st week of school obligations)
ALCOS 3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. [N-RN3] / Ch. 1.6
ALCOS 7a(A-SSE1a) Interpret parts of an expression such as terms, factors, and coefficients. / Ch.1.7
ALCOS 22 (A-REI10) Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). / Ch.1.9
Quality Core Standards:
A.1.a Set up and solve problems following the correct order of operations (including proportions, percent, and absolutevalue) with rational numbers (integers, fractions, decimals)
C.1.a Evaluate and simplify expressions requiring addition, subtraction, multiplication, and division with and without
grouping symbols
C.1.bTranslate real-world problems into expressions using variables to represent values
LTF Lessons:
none
SMALLabs:
Constant Velocity
Review:
Ch. 1.3, 1.4, 1.5, 1.6 support N-RN3
Notes:
Pg. 22 #71 is the only explicit mention for cube roots A-REI1
Ch. 1.8 will be covered in Ch. 2.1
Unit 2: Solving Equations
Vocabulary
conversion factorcross productsequivalent equationsformula
inverse operationliteral equationpercent changeproportion
rateratioscaleunit analysis
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. / Ch. 2.1, Ch. 2.3, Ch. 2.4, Ch. 2.8 / Unit 2 Pacing:
15 days
ALCOS 17 (A-REI3) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. / Ch. 2.2, Ch. 2.7
**Note: Integrate geometry questions from Ch. 2.2
ALCOS 15 (A-CED4) Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Example: Rearrange Ohm’s law V = IR to highlight resistance R.
ALCOS 16 (A-REI1): Explain each step in solving a simple equation as following 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. 2.5
ALCOS 4 (N-Q1): Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. / Ch. 2.6
ALCOS 6 (N-Q3): Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. / Ch. 2.9, Ch. 2.10
Quality Core Standards:
C.1.b. Translate real-world problems into expressions using variables to represent values
D.1.d. Write and graph linear equations and inequalities from real-world situations (e.g., a constant-rate distance/time problem)
D.1.e. Write linear equations in standard form and slope-intercept form when given two points, a point and the slope, or the graph of the equation
D.1.f. Identify, formulate, and obtain solutions to problems involving direct and inverse variation
D.1.c Solve formulas for a specified variable
D.2.c. Evaluate functions at given values
LTF Lessons:
ALCOS #4, #13
Connecting a Verbal Description to a Table or Graph (1.5 days)
Walk the Line (2 days) also partially covers 8-F5
ALCOS #15, #16, #17
Literal Equations – Reviewing and Foreshadowing (1 day)
ALCOS #12, #15 Linear Functions (1 day)
Dan Meyer:
Circle-Square
World Record Airbag
Falling Glowsticks
Falling Rocks
SMALLabs:
Constant Velocity
Chemical Titration
Unit 3: Solving Inequalities
Vocabulary
complement of a setcompound inequalitydisjoint setsempty set
equivalent inequalitiesintersectioninterval notationroster form
set-builder notationsolution of an inequalityunionuniversal set
ALCOS 17 (A-REI3) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. / Ch.3.1, Ch. 3.2, Ch. 3.3, Ch. 3.4, Ch. 3.6 / Unit 3 Pacing:
9 days
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 / Ch. 3.7
Quality Core Standards:
C.1.b Translate real-world problems into expressions using variables to represent values
D.1.a Solve single-step and multistep equations and inequalities in one variable
D.1.b Solve equations that contain absolute variable
D.2.a Graph linear inequalities in one variable on the real number line to solve problems
LTF Lessons:
None
Dan Meyer:
Circle-Square
World Record Airbag
Falling Glowsticks
Falling Rocks
SMALLabs:
Constant Velocity
Unit 4: An Introduction to Functions
Preparation:
Ch. 4.1 preparation for F-IF4
Vocabulary
continuous graphdependent variablediscrete graphdomain
functionnotationindependent variablelinear function
nonlinear functionrangerelationsequence
ALCOS 22 (A-REI10) Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). / Ch. 4.2, Ch. 4.3
(On schoolnet- Standard AREI.22) / Unit 4 Pacing:
2 days
8.12 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2]
8.13 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [8-F3] / Ch. 4.2, Ch. 4.3
ALCOS 25 (F-IF1) Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function 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). / Ch. 4.2, Ch. 4.3
(On schoolnet-Standard F-IF.25)
LTF Lessons:
Introduction to Function Notation
Connecting a Verbal Description to Table and Graph Using Tables and Graphs to Determine the Better Deal
Connecting Table Graph and Function Notation Discrete and Continuous Data
Dan Meyer:
Taco Cart
SMALLabs:
Chemistry Titration
Gear Ratio Game
Constant Acceleration
**Please Note Benchmark 1 only consist of material in Unit 1-3 (Ch. 1-3)
*Only the power standards will be tested on the benchmark.
First Nine Weeks Power Standards – ALCOS 7a (A-SSE1a), ALCOS 12 (A-CED1), ALCOS 15 (A-CED4) ALCOS 16 (A-REI1), ALCOS 17 (A-REI3)
Second Nine Weeks
Standard / Resources / Approximate Pacing Number of DaysALCOS 29 (F-IF5) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. / Ch. 4.4
(In schoolnet listed as FIF.29) / Unit 4 Pacing:
9 days
ALCOS 5 (N-Q2): Define appropriate quantities for the purpose of descriptive modeling. / Ch. 4.5
(In schoolnet listed as NQ.5)
ALCOS 25 (F-IF1) Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function 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).
8.11 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) [8-F1] / Ch. 4.6
(In schoolnet listed as FIF.25)
ALCOS 27 (F-IF3) Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
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. 4.7
(In schoolnet as FIF.27)
(In schoolnet FBF.35)
ALCOS 26 (F-IF2) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. / Ch. 4.7
(In schoolnet as FIF.26)
Quality Core Standards:
C.1.b. Translate real-world problems into expressions using variables to represent values
D.2.b. Give the domain and range of relations and functions
D.2.d Identify graphs of relations and functions and analyze them to determine whether a relation is a function (e.g., vertical line test)
D.2.h. Graph a linear equation using a table of values, x- and y-intercepts, slope-intercept form, and technology
D.2.i. Translate between different representations of relations and functions: graphs, equations, sets of ordered pairs, verbal descriptions, and tables
LTF Lessons:
Introduction to Function Notation
Connecting a Verbal Description to Table and Graph Using Tables and Graphs to Determine the Better Deal
Connecting Table Graph and Function Notation Discrete and Continuous Data
Arithmetic Sequences (MG)
Dan Meyer:
Taco Cart
SMALLabs:
Chemistry Titration
Gear Ratio Game
Constant Acceleration
Unit 5: Linear Functions
Helpful Notes/Resources for Ch. 5:
1.Ch. 5.6 is covered in Geometry
2. Step Functions and Piece Wise functions should be covered after 5.8
Vocabulary
direct variationlinear equationparallel linesperpendicular lines
point-slope formrate of changeslopeslope-intercept form
standard formtrend lineX-intercepty-intercept
ALCOS 37b (F-LE1b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
ALCOS 30 (F-IF6) Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. / CH. 5.1
(In schoolnet as FLE.37.b)
(In schoolnet as FIF.30) / Unit 5 Pacing:
15 days
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. / CH. 5.2
(In schoolnet as ACED.13)
ALCOS 36 (F-BF3) Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. 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.
ALCOS 31a (F-IF7a) Graph linear and quadratic functions, and show intercepts, maxima, and minima. / Ch. 5.3
(In schoolnet as FBF.36)
(In schoolnet as FIF.31a)
ALCOS 38 (F-LE2) Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). / Ch. 5.4
(In schoolnet as FLE. 38)
ALCOS 34a (F-BF1) Write a function that describes a relationship between two quantities / Ch. 5.5
**Note: Concept Byte- Inverse of a Linear Function (Immediately following Ch. 5.5)
(In schoolnet as FBF.34)
ALCOS 45c (S-ID6c) Fit a linear function for a scatter plot that suggests a linear association.
ALCOS 45 (S-ID-6) Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
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 choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
ALCOS 46(S-ID7) Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
ALCOS 40 (F-LE5) Interpret the parameters in a linear orexponential function in terms of a context. / Ch. 5.7
**Note: Concept Byte- Using Residuals (Immediately following Ch. 5.7)
(In schoolnet as SID.45c)
(In schoolnet as SID.45)
(In schoolnet as SID.46)
(In schoolnet as FLE.40)
ALCOS 45b (S-ID6b) Informally assess the fit of a function by plotting and analyzing residuals.
ALCOS 31b (F-IF7b) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. / Ch. 5.8
**Please note there are two days for this standard so that you can cover on Piecewise and step functions.
(In schoolnet as SID.45)
(In schoolnet as FIF. 31.b)
Quality Core Standards:
C.1.b Translate real-world problems into expressions using variables to represent values
D.1.d Write and graph linear equations and inequalities from real-world situations (e.g., a constant-rate distance/time problem)
D.1.e Write linear equations in standard form and slope-intercept form when given two points, a point and the slope, or the graph of the equation
D.1.f Identify, formulate, and obtain solutions to problems involving direct and inverse variation
D.2.c Evaluate functions at given values
LTF Lessons:
Walk the Line (MG)
Average Rate of Change (MG)
Calculating Average Rate of Change
Slope Investigation
Analysis of Functions
Translations of Linear Functions
Write the equation of the Line Review
Piecewise functions
Dan Meyer:
Taco Cart
Penny Circle
Unit 6: Systems of Equations and Inequalities
Vocabulary
consistentdependentelimination methodinconsistent
independentlinear inequalitysubstitution method
8.10 Analyze and solve pairs of simultaneous linear equations. [8-EE8]
a.Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs because points of intersection satisfy both equations simultaneously. [8-EE8a]
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. [8-EE8b]
c.Solve real-world and mathematical problems leading to two linear equations in two variables. [8-EE8c]
ALCOS 20 (A-REI6) Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables.
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, e.g., using technology to graph the functions, 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. / Ch. 6.1-6.3
(In Schoolnet as AREI.20)
(In schoolnet as AREI.23) / Half of Unit 6 Pacing:
6.1-6.3, review, and Mid Ch. Test to be completed by December 10th. This leaves 2 days for review before exams and benchmark 2.
**Please note the remainder of the days are for the following: Cumulative review , Benchmark 2, and Exams
ALCOS 19 (A-REI5) Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. / (In schoolnet as AREI.19)
Quality Core Standards:
C.1.b Translate real-world problems into expressions using variables to represent values
D.1.d Write and graph linear equations and inequalities from real-world situations (e.g., a constant-rate distance/time problem)
D.1.e Write linear equations in standard form and slope-intercept form when given two points, a point and the slope, or the graph of the equation
D.1.f Identify, formulate, and obtain solutions to problems involving direct and inverse variation
D.1.g Solve systems of two equations using various methods, including elimination, substitution, and graphing with and without technology
D.2.c Evaluate functions at given values
LTF Lessons:
Literal equations- Reviewing and Foreshadowing
Linear Functions (MG)
Painting the House
Solving systems of Linear Equations
Dan Meyer:
Circle-Square
SMALLabs:
Constant Velocity
Second Benchmark and Final Exams
**Please note Benchmark 2 is comprehensive and will cover the entire first semester unit 1 to unit 6.3.
*Only the power standards will be tested on the benchmark.
First Nine Weeks Power Standards – ALCOS 7a (A-SSE1a), ALCOS 12 (A-CED1), ALCOS 15 (A-CED4) ALCOS 16 (A-REI1), ALCOS 17 (A-REI3)
Second Nine Weeks Power Standards – ALCOS 13 (A-CED2), ALCOS 20 (A-REI6), ALCOS 25 (F-IF1), ALCOS 26 (F-IF-2), ALCOS 30 (F-IF6), ALCOS 31 (F-IF7a)
Third Nine Weeks
Standard / Resources / Approximate Pacing Number of DaysALCOS 20 (A-REI6) Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables. / CH. 6.4 / Unit 6 Pacing (second half):
8 days
ALCOS 24 (A-REI12) Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of inequalities in two variables as the intersection of the corresponding half-planes. / Ch. 6.5 and Ch. 6.6
**Note: Immediately following Ch. 6.6 Concept Byte using Graphing Calculators
Quality Core Standards:
C.1.b Translate real-world problems into expressions using variables to represent values
D.1.d Write and graph linear equations and inequalities from real-world situations (e.g., a constant-rate distance/time problem)
D.1.e Write linear equations in standard form and slope-intercept form when given two points, a point and the slope, or the graph of the equation
D.1.g Solve systems of two equations using various methods, including elimination, substitution, and graphing with and without technology
D.2.c Evaluate functions at given values
Graph linear inequalities with two variables on the standard (x,y) coordinate plane
D.2.e Graph linear inequalities with two variables on the standard (x,y) coordinate plane
D.2.f. Use the terminology associated with the Cartesian plane in describing points and lines
D.2.g. Recognize the concept of slope as a rate of change and determine the slope when given the equation of a line in
standard form or slope-intercept form, the graph of a line, two points, or a verbal description
D.2.h. Graph a linear equation using a table of values, x- and y-intercepts, slope-intercept form, and technology
D.2.i. Translate between different representations of relations and functions: graphs, equations, sets of ordered pairs, verbal descriptions, and tables
LTF Lessons:
Maximizing Profit
Dan Meyer:
Circle-Square
SMALLabs:
Constant Velocity
Unit 7: Exponents and Exponential Functions
Vocabulary
compound interestdecay factorexponential decayexponential function
exponential growthgrowth factorscientific notation
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. / Ch. 7.1, Ch. 7.2, Ch. 7.3, Ch. 7.4 / Unit 7 Pacing:
14 days
ALCOS 2 (N-RN2) Rewrite expressions involving radicals and rational exponents using the properties of exponents. / Ch. 7.5
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 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 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 / Ch. 7.6 and CH. 7.7
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
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
LTF Lessons:
Exponential Function Exploration
Exponential Growth (Found under Mathematical Foundations)
How do you start and how do you change? (Non LTF Lesson available on apluscollegeready.com)
Writing Equations Using Sequences
Limits- A Physical Approach (MG)
Dan Meyer:
Super Stairs
Taco Cart
Unit 8: Polynomials and Factoring
Vocabulary
binomialdifference of two squaresfactoring by groupingmonomial
perfect-square trinomialpolynomialtrinomial
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. / Ch. 8.1, Ch. 8.2, Ch. 8.3, Ch. 8.4 / Ch. 8.1 (1 Day)
Ch. 8.2(1 Day)
Ch. 8.3(2 Day w/graphing calculator practice)
Ch. 8.4(1 Day)
ALCOS 7a (A-SSE1a) Interpret parts of an expression such as terms, factors, and coefficients.
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). / Ch. 8.5, Ch. 8.6, Ch. 8.7, Ch. 8.8 / All of Unit 8 Pacing:
12 days
Quality Core Standards:
C.1.a Solve single-step and multistep equations and inequalities in one variable
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 slope-intercept 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 Lessons:
None
Dan Meyer:
None
SMALLabs:
None
**Power Standards are in Bold: