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Transcript
ALGEBRA 1
Scope and Sequence 2012-13
Unit 1: Expressions and Solving Equations
Day
Standard
1
A.SSE.1a
A.SSE.1b
A.SSE.2
●
●
●
●
●
●
Parts of an expression
Combining like terms
Associative Property
Commutative Property
Distributive Property
Review: Order of Operations
Algebraic Expressions
Terms
Coefficients
Factor
Variables
Simplify
Evaluate
Associative Property
Communicative Property
Distributive Property
2
A.REI.1
A.REI.3
●
●
●
●
●
Solving one-step equations
Solving two-step equations
Solving multistep equations
Solving verbal equations
Verifying Solutions
Algebraic Equation
Inverse Operations
3
A.REI.3
●
●
Graphing one variable inequalities
Solving one variable inequalities
Inequality
Greater Than
Less Than
Greater than or equal to
Less Than or not equal to
Equal to
Not Equal to
4
A.CED.4
●
Literal Equations
Formula
5
Topic
Materials
Vocabulary
REVIEW/TEST
Unit 1 Learning Targets: Expressions and Solving Equations
Key Idea
Equation and
Inequality Vocabulary
Solving Equations
Standard
Targets: I can…
A.SSE.1a
●
A.SSE.1b
●
I can identify the parts of an algebraic expression, including terms,
variables, coefficients, and factors.
I can interpret expressions in the context of a problem.
A.SSE.2
●
●
●
I can combine like terms.
I can apply the distributive property.
I can factor out a monomial.
A.REI.1
●
A.REI.3
●
●
●
I can apply order of operations and inverse operations to solve
equation.
I can solve a linear equation in one variable.
I can construct an argument to justify my solution process when solving
equations.
I can solve a linear inequality in one variable.
●
I can solve literal equations for a given variable.
A.CED.4
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 2: Linear Basics
Day Standard Topic
Materials Vocabulary
1
A.REI.10
●
●
Slope-Intercept Form
Verify a point is a solution to an equation
y=mx+b
Slope-Intercept Form
Slope
Y-intercept
2
F.IF.6
●
Calculating Slope
(Table, Graph, 2-points)
Applications of slope
Rate
Average Rate of
Change
Slope Formula
●
3
F.IF.7
A.CED.4
●
●
Graphing a linear equation
Changing equations from standard to slope-intercept
form
Standard Form
4
A.CED.2
F.LE.5
●
Writing an equation in slope-intercept form from a
graph or slope and a point
Include writing equations for verbal models
Starting Value
Rate
●
5
6
A.CED.2
F.LE.5
A.REI.12
F.LE.5
●
●
Writing an equation in slope-intercept form from two
points or a table
Include writing equations for verbal models
●
●
●
Graphing a two-variable inequalities
Writing a two-variable inequality
Include writing inequalities for verbal models
7
REVIEW
8
TEST
Unit 2 Learning Targets: Linear Basics
Key Idea
Standard
Pre-Req
●
I can graph a linear function.
F.IF.6
●
I can calculate and interpret the average rate of change (slope) of a linear
function given a graph or a table.
F.IF.7
●
I can graph linear functions and identify intercepts.
A.REI.10
●
●
I can explain that every point (x, y) on the graph represents values that make
the equation true.
I can verify that a point on a graph is a solution to an equation through
substitution.
A.REI.12
●
I can graph a linear inequality in two variables
A.CED.2
●
I can write a linear function given a written situation, equation, table or
graph.
F.LE.5
●
I can interpret the parameters (slope, y-intercept, etc.) given a linear
function in context.
A.CED.4
●
I can convert from standard to slope-intercept form.
Graphing
Writing Linear
Equations
Targets. I can…
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 3: Linear Functions
Day Standard Topic
Materials Vocabulary
1
F.IF.1
●
●
2
F.IF.1
●
●
3
F.IF.1
4
F.IF.2
●
Linear Sequences
Common
Difference
Arithmetic
Sequence
Explicit Formula
5
F.IF.3
●
Recursive Sequences (like the Fibonacci sequence)
Recursive
Formula
6
F.IF.2
N.Q.2
N.Q.3
●
●
Independent vs. Dependent Variables
Writing Linear Functions that model written scenarios
Independent
Dependent
7
N.Q.1
●
Graphing Linear Functions from a function or table
8
F.BF.4
●
Creating the Graph of the Inverse of a Linear Function
Inverse
9
F.BF.4
●
Writing the Inverse of Linear Function
Inverse
10
●
?
11
●
?
12
REVIEW
13
TEST
Function Notation
Evaluating Functions for inputs in from the domain
Domain and Range
Determine the domain and range from the
following...written scenario, set of ordered pairs, mapping
or graph
Note: Include non-linear examples
Function
Domain
Domain
Range
Function Table
●
●
Vertical Line Test
Determine if the following is a function...written scenario,
set of ordered pairs, mapping graph
Note: Include non-linear examples
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 3 Learning Targets: Linear Functions
Key Idea
Standard
Targets. I can…
Pre-Req.
●
●
I can evaluate variable expressions for given numerical values
I can identify independent and dependent variables.
F.IF.1
●
●
I can identify f(x) as ‘y’, the dependent variable.
I can determine domain and range from written scenarios, ordered pairs,
maps or plots.
I can determine if a written scenario, set of ordered pairs, mapping, or
graph is a function.
●
Functions
F.IF.2
●
●
Linear Patterns
Graphing Linear
Functions
I can use function notation to evaluate functions for inputs in a
domain.
I can connect variables in a function within a context. Example: h(t) would
connect height to time.
F.IF.3
●
I can recognize that some sequences are functions, which are sometimes
defined recursively.
N.Q.2
●
I can choose appropriate units for given problems.
N.Q.3
●
I can decide whether a problem calls for a rough estimate, approximation or
an exact answer.
N.Q.1
●
I can choose and interpret the scale and the origin in graphs and data
displays.
I can use units as a way to understand problems and guide solutions.
●
F.BF.1
●
I can write a linear function that describes a relationship between two
quantities.
F.BF.4
●
I can determine inverses of linear functions.
Inverses of Linear
Functions
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 4: Solving Systems of Equations
Day
Standard
Topic
Materials
1
A.REI.6
A.REI.11
●
●
●
Introduction to Systems
No Solution and Infinite Solutions on a Graph
Solve a System by Graphing
systems of equations
solution
ordered pair
no solution
infinite solution
parallel lines
2
A.REI.6
A.REI.5
●
Solve a System by Substitution
substitution
3
A.REI.6
A.REI.5
●
●
Solve a System by Substitution
No Solution and Infinite Solutions Algebraically
no solution
infinite solution
4
A.REI.6
A.REI.5
●
Solve a System by Elimination
elimination
5
A.REI.6
A.REI.5
●
●
Solve a System by Elimination
No Solution and Infinite Solutions Algebraically
no solution
infinite solution
6
A.REI.6
A.REI.5
●
●
Which one is the best method?
Solving Systems--Written Scenarios
7
A.REI.12
●
●
Solving Systems of Inequalities
Verify solutions with a test point
8
Review
9
Test
NCSD Algebra Scope and Sequence Working Document
Vocabulary
systems of inequalities
6/20/2012
Unit 4 Learning Targets: Solving Systems of Equations
Key Idea
Standard
A.REI.5
A.REI.6
Solving Systems
A.REI.11
Targets. I can…
●
●
●
●
●
I can solve a system of equations in two variables graphically.
I can solve a system of equations in two variables using substitution.
I can solve a system of equations in two variables by elimination.
I can determine if a system of equations in two variables has no solutions, one
solution, or infinitely many solutions.
I can use a graphing calculator to approximate the solution to a system of
equations in two variables.
A.REI.12
●
I can solve linear system of inequalities graphically.
A.CED.1
●
A.CED.3
●
I can write and solve the equation or inequality that best models a realworld problem.
I can write and solve a system of equations or inequalities that best models a
real-world problem
END SEMESTER 1: 1 or 2 days - Review for Final, Finals Week
NCSD Algebra Scope and Sequence Working Document
6/20/2012
BEGIN SEMESTER 2
Unit 5: Properties of Exponents
Day Standard
Topic
Materials
Vocabulary
1
Pre-Req.
●
●
Product Property
Power Property
exponent
(exponential form)
constant
2
Pre-Req.
●
●
Quotient Property
Quotient Power Property
quotient
canceling/cancellation
Pre-Req.
●
●
Zero Property
Negative Exponent Property
zero exponent
negative exponent
4
Pre-Req.
●
●
Scientific Notation
Multiplying and Dividing number in Scientific Notation
scientific notation
5
N.RN.2
●
Rewrite between radical form and rational exponents
radical
radical sign
rational exponents
3
Example:
6
REVIEW
7
TEST
Note: 2012-13 it may not be possible to teach applying the exponent properties to rational exponents, but the
expectation for the next year (2013-14) is to do so (N.RN.1).
Unit 5 Learning Targets: Properties of Exponents
Key Idea
Standard
Targets
Pre-Req.
●
●
●
●
●
●
●
Apply the Product Rule.
Apply the Quotient Rule.
Apply the Power Rule.
Apply the Power of a Product Rule.
Apply the Power of a Quotient Rule.
Use negative exponents.
Apply the zero property.
N.RN.1
●
Apply rules to rational exponents.
N.RN.2
●
●
Rewrite between radical and rational exponents.
Evaluate radical and rational expressions with and without
a calculator.
Rules of Exponents with Integers
Extend Rules to Rational Exponents
Convert between radical and rational
exponents
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 6: Exponential Functions
Day Standard Topic
Materials Vocabulary
1
F.IF.4
●
Graphing Exponential Functions with a Table
○ Increasing/Decreasing Graphs
Function Table
2
F.IF.4
F.BF.3
●
Intercepts
Asymptote
Domain
Translate
●
Identifying Key Features of the graph for an Exponential
Functions
○ Intercepts
○ Increasing/Decreasing
○ Asymptotes (restrictions on the domain)
○ Domain
Translate Exponential Graphs, vertically only
Initial Value
Growth Rate/
Constant
Multiplier
Time
Exponential
Growth
Exponential
Decay
3
F.IF.8
●
●
Form of an Exponential Function f(x) =
Exponential Patterns
4
F.IF.8
F.LE.5
●
Exponential Growth/Decay
5
F.LE.5
●
Identify the parts of a Growth/Decay function
○ Percent Growth/Decay
○ Initial Value
6
F.BF.1
F.LE.2
●
Write an exponential function from a table or graph
7
F.LE.1
●
Which is a better fit? Linear vs. Exponential Functions
(looking at written scenarios)
8
F.LE.1
●
Comparing the graphs and tables of Linear and
Exponential Functions
9
REVIEW
10
TEST
Percent Change
Linear
Note: For the 2013-14 school year, students will need to write arithmetic and geometric sequences, and use
them to build models. (F.BF.2)
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 6 Learning Targets: Exponential Functions
Key Idea
Standard
Targets
Pre-Req.
●
Graph a function using a t-table.
F.IF.4
●
●
Graph an exponential function with a table.
Interpret key features of graphs and tables, and sketch graphs
using key features.
◦
Intercepts
◦
Increasing/decreasing
◦
Asymptotes (restrictions on domain)
F.IF.5
●
Relate the domain of a function to its graph.
F.BF.3
●
Vertically translate exponential functions.
F.IF.8
●
●
●
Write functions in equivalent forms to reveal/explain properties.
Use properties of exponents to identify exponential growth/decay.
Use properties of exponents to identify percent increase/decrease.
F.BF.1
F.LE.2
F.LE.5
●
I can construct an exponential function from a graph or table, or
description of a relationship (situation).
I can interpret the parameters (initial value, growth
rate/constant multiplier, etc.) given an exponential function in
context.
F.LE.1
●
Distinguish between situations modeled by linear and
exponential functions.
F.BF.2
●
Write arithmetic and geometric sequences, and use them to build
models.
Graphing Exponential
Functions
Writing Exponential Functions
Distinguish Between Linear
and Exponential Functions
Sequences
●
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 7: Quadratic Functions
Day
Standard
Topic
1
A.APR.1
●
●
Classifying Polynomial/Descending Order
Adding/Subtracting Polynomials
monomial
binomial
trinomial
polynomial
2
A.APR.1
A.REI.4
●
●
Multiplying Monomials
Factoring the GCF
GCF
3
A.APR.1
A.REI.4
●
Multiplying Binomials and Special Cases (FOIL)
FOIL
4
A.REI.4
●
Factoring (coefficient is 1)
factoring
5
A.REI.4
●
Factoring (coefficient is greater than 1)
6
F.IF.4
●
Properties of a Quadratic Graph
○ Min/Max
○ Axis of Symmetry
○ Intercepts/Roots
Graphing a Quadratic Function with a table
●
Materials
○
Vocabulary
minimum
maximum
axis of symmetry
intercepts/roots/zeros
vertex
Vertex Formula
7
A.SSE.3
●
●
Review Graphing a Quadratic Function
Solving Quadratics with Square Roots
Radical
Radical Sign
8
A.REI.4
●
Solving Quadratics by Factoring
Zero Product Property
9
A.SSE.3
●
●
Completing the Square
Vertex Form and converting to/from General Form
Completing the Square
Vertex Form
10
A.SSE.3
●
Solving Quadratics with the Quadratic Formula
Quadratic Formula
●
Application of Quadratics
○ Falling Objects
○ Projectile Motion
●
Inverse of Simple Quadratic Functions
11
12
F.BF.4
Inverse
Example:
13
REVIEW
14
TEST
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 7 Learning Targets: Quadratic Functions
Key Idea
Standard
Targets. I can…
A.APR.1
●
●
I can add and subtract polynomials.
I can multiply polynomials.
Pre-req
●
I can construct a graph of a quadratic function using a table.
N.RN.3
●
●
I can identify a number as rational or irrational.
I can show the sum of rational numbers is rational, and product of a nonzero rational and an irrational is irrational.
A.SSE.3
●
●
●
●
I can take square roots of a quadratic. (
)
I can identify the roots of a quadratic given a graph.
I can use the quadratic formula to reveal the zeros.
I can complete the square in a quadratic expression to reveal the
vertex.
I can factor a quadratic expression to reveal the zeros.
I can graph a linear, exponential, and quadratic function using technology.
I can find the roots of a quadratic using technology.
Operations on
Polynomials
Solving Quadratic
Equations
A.REI.4
F.IF.8
●
●
●
F.IF.4
●
●
Graph a quadratic function with a table.
Interpret key features of graphs and tables, and sketch graphs using
key features.
◦
Intercepts
◦
Symmetry
◦
Vertex, Maximum, Minimum
F.IF.5
●
Relate the domain of a function to its graph.
F.IF.6
●
Calculate and interpret average rate of change.
F.BF.3
●
Vertically and horizontally translate quadratic functions.
F.IF.8
●
Write functions in equivalent forms to reveal/explain properties (convert
between general and vertex form).
F.BF.1
●
●
Write a function that describes a relationship between two quantities.
I can interpret the parameters (Vertex, Maximum, Minimum) of a
quadratic function in context.
●
I can determine the inverse of a simple quadratic function.
Graphing Quadratic
Functions
Writing Quadratic
Functions
F.LE.5
Inverses of Functions
F.BF.4
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 8: Statistics
Day Standard Topic
1
●
Review Data Displays: Dot Plots, Histograms, Box Plots,
Stem and Leaf
Dot Plot
Histogram
Bin Width
Box Plot
First/Third
Quartile
range
Stem and Leaf
Plot
S.ID.1
S.ID.2
●
●
●
Collecting and Organizing Data
Review Calculating Measures of Central Tendency
Compare measures of central tendency and interquartile
range between two or more plots
Mean
Median
Mode
Outlier
Interquartile
Range
S.ID.2
●
Compare the standard deviation between two or more
plots
Describe the shape and distribution of the data
Standard
Deviation
Line of Best Fit
Correlations
Pre-Req.
S.ID.1
2
Materials Vocabulary
3
●
4
S.ID.6
S.ID.7
●
●
Fitting a linear function to a scatter plot.
Interpret the slope and intercept of a linear model in
context
5
S.ID.6
●
Fitting functions to non-linear data using technology.
6
REVIEW
7
TEST
Note: 2013-14 technology needs to be used to introduce fitting data to linear, exponential, and quadratic
models.
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 8 Learning Targets: Statistics
Key Idea
Standard
Targets
Pre-Req.
●
●
●
●
Display data as dot plots, histograms, and box plots
Determine mean, median and interquartile range.
Use data from a random sample to draw inferences about a
population and inferences about two populations compared.
Construct and interpret plots for bivariate measurement data, describe
patterns such as clustering, outliers, linear/non-linear and
positive/negative correlation.
Recognize linear trends in data, putting slope and intercept in context.
S.ID.1
●
●
●
Represent data with plots on the real number line.
Dot Plots, histograms, box plots
Stem and Leaf, Box and Whisker plots
S.ID.2
●
Use statistics appropriate to the shape of the data distribution to
compare center and spread.
Calculate and compare mean and median.
Calculate and compare interquartile range, and standard
deviation.
●
Represent and interpret data
using a single variable.
Represent and interpret
using two quantitative
variables.
●
●
S.ID.3
●
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for outliers.
S.ID.5
●
●
●
Summarize data for two categories in two-way frequency tables.
Include joint, marginal, and conditional relative frequencies.
Recognize possible associations and trends in the data.
S.ID.6
●
Represent data on two quantitative variables on a scatter plot,
and describe how the variables are related.
Fit a function to data quadratic, linear and exponential models.
Informally assess the fit of the function by plotting and analyzing
residuals.
Fit a linear function to a scatter plot that suggests a linear
association.
●
●
●
Analyzing Linear Data Fitting
S.ID.7
●
Interpret the slope and intercept of a linear model in context.
S.ID.8
●
Compute (using technology) and interpret the correlation coefficient of
a linear fit.
S.ID.9
●
Distinguish between correlation and causation.
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 9: Comparing Functions
Day Standard Topic
Materials Vocabulary
1
F.LE.1
F.LE.3
●
Compare key characteristics of linear, exponential, and
quadratic functions
○ Functions
○ Graphs
2
F.LE.1
F.LE.3
●
Compare key characteristics of linear, exponential, and
quadratic functions
○ Tables
3
F.LE.1
●
Translating the Graphs of linear, exponential and quadratic
functions
4
A.REI.7
F.LE.3
●
Solve systems of linear, quadratic, and exponential
equations graphically
NCSD Algebra Scope and Sequence Working Document
6/20/2012
Unit 9 Learning Targets: Comparing Functions
Key Idea
Standard
Targets. I can…
●
F.LE.1
Comparing Linear,
Exponential, and
Quadratic Functions
●
●
●
●
●
F.LE.3
●
●
●
A.REI.7
Analyzing Graphs
Graphing Key
Features of
Functions
Writing Functions
I can define a linear function as y = mx + b, an exponential function as y =
abx, and a quadratic function as y = ax2+bx+c.
I can identify a graph as being linear, exponential, or quadratic.
I can define a linear function as having a constant rate of change.
I can define an exponential function as having a common ratio over
equal intervals.
I can use graphs or tables to compare the rates of changes of linear,
quadratic, and exponential functions.
I can use graphs or tables to compare the output values of linear, exponential,
or quadratic functions.
I can use technology to find the point at which the graphs of two functions
intersect.
I can solve a system algebraically and graphically consisting of a linear
and quadratic equation.
I can explain why exponential functions eventually have greater output values
than linear or quadratic functions.
F.IF.4
●
●
I can identify maxima/minima in quadratic and absolute value functions.
I can identify the intercepts of linear, exponential, quadratic and
absolute value.
F.IF.5
●
F.IF.9
●
I can identify the domain for linear, exponential, quadratic, absolute value,
step and piecewise functions from a graph.
I can compare properties of functions represented in different ways (one as a
graph, the other as a table or description).
F.IF.6
●
I can calculate the average rate of change over a specified interval.*
F.BF.3
●
I can explain why f(x) + k translates the original graph of f(x) up k units
and why f(x) – k translates the original graph of f(x) down k units.
I can explain why f(x+k) translates the original graph of f(x) left k units
and why f(x-k) translates the original graph of f(x) right k units.
●
F.IF.7
F.BF.1
●
I can graph linear, exponential, quadratic, absolute value, step and
piecewise functions and show their intercepts, maxima/minima, “holes”,
and other key features.
●
I can write a linear, exponential, quadratic, absolute value, step and piecewise
function from a table, or a graph.
I can write a linear, exponential, quadratic, absolute value, step and piecewise
function for a written scenario.
●
NCSD Algebra Scope and Sequence Working Document
6/20/2012