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Subject : Algebra I
UNIT ONE
TOPIC
Relationships Between Quantities and Reasoning with Equations (25 days)
ESSENTIAL QUESTIONS
What makes some units more appropriate than others for a given situation?
Why is important to be able to model real life situations using mathematics?
Why do we need to attend to precision when solving mathematical problems?
When is it appropriate to simplify expressions?
What valuable information can be found from the roots of an equation?
How can the manipulation of expressions and solving formulas be useful techniques to solve problems?
CONTENT
SKILLS:COMMON CORE STANDARDSReason quantitatively and use units to solve problems.
Ability to choose appropriate units of measure to represent context of the problem
Ability to convert units of measure using dimensional analysis
Ability to select and use units of measure to accurately model a given real world scenario
Knowledge of and ability to apply rules of significant digits
Ability to use precision of initial measurements to determine the level of precision with which answers can be reported N Q.1 Use units as a way to understand problems and to guide the solution of multi step problems;
choose and interpret units consistently in formulas; choose and interpret the scale and the origin
in graphs and data displays.
N Q.2 Define appropriate quantities for the purpose of descriptive modeling.
N Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities.
Interpret the structure of expressions
Ability to make connections between symbolic representations and proper mathematics vocabulary
Ability to identify parts of an expression such as terms, factors, coefficients, etc.
Ability to interpret and apply rules for order of operations
Use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely.
Simplify expressions including combining like terms, using the distributive property and other operations with polynomials.
A SSE.1 Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
For example, interpret P(1+r)n as the product of P and a factor not depending on P.
A SSE.2 Use the structure of an expression to identify ways to rewrite it. For 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).
Create equations that describe numbers or relationships
Ability to distinguish between linear and exponential relationships given multiple representations and then create the appropriate equation/inequality using given information
Ability to distinguish between linear and exponential relationships given multiple representations
Ability to determine unknown parameters needed to create an equation that accurately models a given situation
Ability to distinguish between a mathematical solution and a contextual solution. Is the solution feasible in real world terms?
Ability to recognize/create equivalent forms of literal equations
A CED.1 Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear, and simple rational and exponential functions.
A CED.2 Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
A CED.3 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. For
example, represent inequalities describing nutritional and cost constraints on combinations of
different foods.
A CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R
Standards of Mathematical Practices :
Model with mathematics. Use appropriate tools strategically. Attend to precision.
Look for and make use of structure. Look for and express regularity in repeated reasoning
ASSESSMENTS
Conferencing
Pre and Post Tests
Open-ended problems that involve a discovery approach to collaborative learning
Lead up problem solving tasks
Performance Based Assessment
Daily student work
Student/group presentationsMATERIALS & RESOURCES
Text book : Prentice Hall Mathematics Algebra I
Graphing calculators
Algebra Tiles and other manipulatives
Smart Board Demonstrations
Problem solving materials created by teachers
Reality In Mathematics Education Lesson Pack
HYPERLINK "http://nrich.maths.org/frontpage" http://nrich.maths.org/frontpage
HYPERLINK "http://www.Jmap.org"www.Jmap.org
Subject : Integrated Algebra
UNIT TWOTOPICReasoning With Equations and Inequalities (15 days)ESSENTIAL QUESTIONS
What makes something a mathematical term?
How do we translate written information into Mathematical terms?
What does it mean to balance an equation?
What does it mean to solve an equation?
What is the difference between an equation and an inequality?CONTENT
SKILLS:COMMON CORE STANDARDSUnderstand solving equations as a process of reasoning and explain the reasoning
Ability to identify the mathematical property (addition property of equality, distributive property, etc.) used at each step in the solution process as a means of justifying a step
A REI.1 Explain each step in solving a simple equation as following from 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.
Solve equations and inequalities in one variable
Ability to analyze the structure of an equation to determine the sequence of steps that need to be applied to arrive at a solution
Ability to accurately perform the steps needed to solve a linear equation/inequality
A REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.Mathematical Practices :
Model with mathematics. Use appropriate tools strategically. Reason abstractly and quantitatively
Make sense of problems and persevere in solving them.
ASSESSMENTS
Conferencing
Pre and Post Tests
Open-ended problems that involve a discovery approach to collaborative learning
Lead up problem solving tasks
Performance Based Assessment
Daily student work
Student/group presentationsMATERIALS & RESOURCES
Text book : Prentice Hall Mathematics Algebra I
Graphing calculators
Algebra Tiles and other manipulatives
Smart Board Demonstrations
Problem solving materials created by teachers
Reality In Mathematics Education Lesson Pack
HYPERLINK "http://nrich.maths.org/frontpage" http://nrich.maths.org/frontpage
HYPERLINK "http://www.Jmap.org"www.Jmap.org
Subject : Integrated Algebra
UNIT THREETOPICLinear and Exponential Relationships (20 days)ESSENTIAL QUESTIONS
How many different ways can I solve systems of equations?
When I solve a system of equations what is it that I am actually finding?
How does the graph of an inequality differ for the graph an equation?
How can technology help me with solutions to system of equations problems?CONTENT
SKILLS:COMMON CORE STANDARDSSolve systems of equations
Ability to use various methods for solving systems of equations algebraically
Ability to identify the mathematical property (addition property of equality, distributive property, etc.) used at each step in the solution process as a means of justifying a step
Ability to extend experiences with solving simultaneous linear equations from 8EE.8 b&c to include more complex situations
Ability to solve systems using the most efficient method
A REI.5 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.
A REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs
of linear equations in two variables.
Represent and solve equations and inequalities graphically
Ability to construct an argument as to how the points that make up a curve connect to an algebraic representation of the function that is being represented by the graph
Ability to show the equality of two functions using multiple representations
Ability to explain why a particular shaded region represents the solution of a given linear inequality or system of linear inequalities
Ability to convey the mathematics behind the dotted versus solid boundary lines used when graphing the solutions to linear inequalities
A REI.10 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).
A REI.11 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.
A REI.12 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 linear
inequalities in two variables as the intersection of the corresponding half planes.
Mathematical Practices :
Model with mathematics. Use appropriate tools strategically. Reason abstractly and quantitatively
Make sense of problems and persevere in solving them. Use appropriate tools strategically.
ASSESSMENTS
Conferencing
Pre and Post Tests
Open-ended problems that involve a discovery approach to collaborative learning
Lead up problem solving tasks
Performance Based Assessment
Daily student work
Student/group presentationsMATERIALS & RESOURCES
Text book : Prentice Hall Mathematics Algebra I
Graphing calculators
Algebra Tiles and other manipulatives
Smart Board Demonstrations
Problem solving materials created by teachers
Reality In Mathematics Education Lesson Pack
HYPERLINK "http://nrich.maths.org/frontpage" http://nrich.maths.org/frontpage
HYPERLINK "http://www.Jmap.org"www.Jmap.org
Subject : Integrated Algebra
UNIT FOURTOPICGraphing and Knowing Different Types of Functions (25 days)ESSENTIAL QUESTIONS
What is a function?
Why is the domain and the range of a function important information to know?
What makes a pattern a sequence?
Why is it important to know about rates of change?
What does it mean graphically for a rate of change to be constant?
Why is it important to be able to use functions to model real life situations?CONTENT
SKILLS:COMMON CORE STANDARDSUnderstand the concept of a function and use function notation
Ability to determine if a relation is a function
Ability to identify the domain and range of a function from multiple representations
Ability to use of function notation
Knowledge of and ability to apply the vertical line test
Ability to make connections between context and algebraic representations which use function notation
Understand the nature and formulae for different types of sequences.F IF.1 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).
F IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements
that use function notation in terms of a context.
F IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a
subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) =
1, f(n+1) = f(n) + f(n 1) for n e" 1.Interpret functions that arise in applications in terms of the context
Ability to translate from algebraic representations to graphic or numeric representations and identify key features using the various representations
Ability to relate the concept of domain to each function studied
Ability to describe the restrictions on the domain of all functions based on real world context
Knowledge that the rate of change of a function can be positive, negative or zero
Ability to identify the rate of change from multiple representations F IF.4 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; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
F IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes. For example, if the function h(n) gives the number of person hours it
takes to assemble n engines in a factory, then the positive integers would be an appropriate
domain for the function.
F IF.6 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.Analyze functions using different representations
Understand the nature of the constants and what they mean to the graph. Be able to find axis of symmetry and maximum and minimum points.
Ability to recognize common attributes of a function from various representations
F IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
a. Graph linear functions and show slopes and intercepts.
F IF.9 Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one
quadratic function and an algebraic expression for another, say which has the larger maximum.Build a function that models a relationship between two quantities
Understand how to write and function from relationships between quantities.
Ability to add, subtract, multiply and divide functions
F BF.1 Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a
context.
Build new functions from existing functions
Understand how constants in a functions impact on the physical graph. Understand the nature of the shifts and how these relationships between different types of functions.F BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k 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. 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.
Construct and compare linear, quadratic, and exponential models and solve problems
Ability to recognize a linear relationship
Ability to recognize an exponential relationship
Ability to produce an algebraic model
Which types of functions increase more quickly and what is the rationale behind this.F LE.1 Distinguish between situations that can be modeled with linear functions and with exponential
functions.
a. Prove that linear functions grow by equal differences over equal intervals, and that b. Recognize situations in which one quantity changes at a constant rate per unit interval
relative to another.
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit
interval relative to another.
F LE.2 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).
F LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly or (more generally) as a polynomial function.
Interpret expressions for functions in terms of the situation they model
Ability to interpret the slope and y-intercept of a linear model in terms of context
Ability to identify the initial amount present in an exponential model
F LE.5 Interpret the parameters in a linear or exponential function in terms of a contextMathematical Practices :
Model with mathematics. Use appropriate tools strategically. Reason abstractly and quantitatively
Make sense of problems and persevere in solving them. Use appropriate tools strategically.
ASSESSMENTS
Conferencing
Pre and Post Tests
Open-ended problems that involve a discovery approach to collaborative learning
Lead up problem solving tasks
Performance Based Assessment
Daily student work
Student/group presentationsMATERIALS & RESOURCES
Text book : Prentice Hall Mathematics Algebra I
Graphing calculators
Algebra Tiles and other manipulatives
Smart Board Demonstrations
Problem solving materials created by teachers
Reality In Mathematics Education Lesson Pack
HYPERLINK "http://nrich.maths.org/frontpage" http://nrich.maths.org/frontpage
HYPERLINK "http://www.Jmap.org"www.Jmap.org
Subject : Integrated Algebra
UNIT FIVETOPICDescriptive Statistics (20 days)ESSENTIAL QUESTIONS
Why does anyone collect data?
Why is it important to be able to display data in a number of different ways?
What information can I get about a set of data from the different measures of central tendency?
How can we use data to make predictions about real life situations?
CONTENT
SKILLS:COMMON CORE STANDARDSSummarize, represent, and interpret data on a single count or measurement variable
Ability to determine the best data representation to use for a given situation
Knowledge of key features of each plot
Ability to correctly display given data in an appropriate plot
Ability to analyze data given in different formats
Ability to interpret measures of center and spread (variability) as they relate to several data sets
Ability to identify shapes of distributions (skewed left or right, bell, uniform, symmetric)
Ability to recognize appropriateness of mean/standard deviation for symmetric data; 5 number summary for skewed data
Ability to recognize gaps, clusters, and trends in the data set
Ability to recognize extreme data points(outliers) and their impact on center
Ability to effectively communicate what the data reveals
Knowledge that when comparing distributions there must be common scales and units S ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
S ID.2 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.
S ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
Summarize, represent, and interpret data on two categorical and quantitative variables
Knowledge of the characteristics of categorical data
Ability to read and use a two-way frequency table
Ability to use and to compute joint, marginal, and conditional relative frequencies
Ability to read a segmented bar graph
Ability to recognize types of relationships that lend themselves to linear and exponential models
Ability to create and use regression models to represent a contextual situation
Ability to create a graphic display of residuals
Ability to recognize patterns in residual plots
Ability to calculate error margins (residuals) with a calculator
Ability to recognize a linear relationship displayed in a scatter plot
Ability to determine an equation for the line of best fit for a set of data points S ID.5 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.
S ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables
are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the
data. Use given functions or choose a function suggested by the context. Emphasize linear,
quadratic, and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.
Interpret linear models
Look at lines of best fit and linear models and determine and use the slope and intercept to gain information about the data.
Knowledge of the range of the values ()and the interpretation of those values for correlation coefficients "1 d" r d" 1
Ability to compute and analyze the correlation coefficient for the purpose of communicating the goodness of fit of a linear model for a given data set
Ability to provide examples of two variables that have a strong correlation but one does not cause the other
S ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the
context of the data.
S ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
S ID.9 Distinguish between correlation and causation.Mathematical Practices :
Model with mathematics. Attend to precision. Look for and make use of structure.
Reason abstractly and quantitatively Make sense of problems and persevere in solving them.
ASSESSMENTS
Conferencing
Pre and Post Tests
Open-ended problems that involve a discovery approach to collaborative learning
Lead up problem solving tasks
Performance Based Assessment
Daily student work
Student/group presentationsMATERIALS & RESOURCES
Text book : Prentice Hall Mathematics Algebra I
Graphing calculators
Algebra Tiles and other manipulatives
Smart Board Demonstrations
Problem solving materials created by teachers
Reality In Mathematics Education Lesson Pack
HYPERLINK "http://nrich.maths.org/frontpage" http://nrich.maths.org/frontpage
HYPERLINK "http://www.Jmap.org"www.Jmap.org
Subject : Integrated Algebra
UNIT SIXTOPIC
Expressions and Equations Quadratics (25 days)ESSENTIAL QUESTIONS
Why do we have irrational numbers?
Can a number be both rational and irrational?
Why is it useful to be able to factor a polynomial?
What does it mean if a number set is closed under a given operation?CONTENT
SKILLS:COMMON CORE STANDARDSUse properties of rational and irrational numbers.
Ability to perform operations on both rational and irrational numbers
N RN.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.Interpret the structure of expressions
Ability to extend knowledge of A.SSE.1b from Unit 1 of this course to include quadratic and exponential expressions
Ability to use properties of mathematics to alter the structure of an expression
Ability to select and then use an appropriate factoring technique
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$7$8$H$Ifgd $Ifgd\ $Ifgd-ZU SSE.1 Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
A SSE.2 Use the structure of an expression to identify ways to rewrite it. For 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).
Write expressions in equivalent forms to solve problems
Ability to connect the factors, zeros and x-intercepts of a graph
Ability to use the Zero-Product Property to solve quadratic equations
Ability to recognize that quadratics that are perfect squares produce graphs which are tangent to the x-axis at the vertex
Ability to connect experience with properties of exponents from Unit 2 of this course to more complex expressions
A SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions. For
example the expression 1.15t can be rewritten as (1.15 1/12)12t H" 1.01212t to reveal the
approximate equivalent monthly interest rate if the annual rate is 15%.18
Perform arithmetic operations on polynomials
Ability to show that when polynomials are added, subtracted or multiplied that the result is another polynomial
A APR.1 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.
Understand the relationship between zeros and factors of polynomials
Know graphically what information you have when you look at factors and then set each factor equal to zero to find solutions.A APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.Mathematical Practices :
Model with mathematics. Attend to precision. Look for and make use of structure.
Reason abstractly and quantitatively Make sense of problems and persevere in solving them.
ASSESSMENTS
Conferencing
Pre and Post Tests
Open-ended problems that involve a discovery approach to collaborative learning
Lead up problem solving tasks
Performance Based Assessment
Daily student work
Student/group presentationsMATERIALS & RESOURCES
Text book : Prentice Hall Mathematics Algebra I
Graphing calculators
Algebra Tiles and other manipulatives
Smart Board Demonstrations
Problem solving materials created by teachers
Reality In Mathematics Education Lesson Pack
HYPERLINK "http://nrich.maths.org/frontpage" http://nrich.maths.org/frontpage
HYPERLINK "http://www.Jmap.org"www.Jmap.org
Subject : Integrated Algebra
UNIT SEVENTOPIC
Quadratic Functions (25 days)ESSENTIAL QUESTIONS
What is the difference between a linear functions and quadratic function?
How is the rate of change for a quadratic different than that of a linear function?
How is it useful to model with quadratics when we are looking for maximums or minimums? CONTENTSKILLS:COMMON CORE STANDARDSInterpret functions that arise in applications in terms of the context
Determine when a quadratic has a maximum or a minimum and how to find the coordinates of this point.
Ability to connect experiences with linear and exponential functions from Unit 2 of this course to quadratic models
Ability to connect appropriate function to context
Determine the axis of symmetry for a quadratic function.
Ability to connect experiences with linear and exponential functions from Unit 2 of this course to quadratic models
Ability to describe the restrictions on the domain of a function based on real world context
Ability to recognize and use alternate vocabulary for domain and range such as input/output or independent/dependent
Knowledge that the rate of change of a function can be positive, negative or zero
Ability to identify the rate of change from multiple representations F IF.422 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; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
F IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes. For example, if the function h(n) gives the number of person hours it
takes to assemble n engines in a factory, then the positive integers would be an appropriate
domain for the function.
F IF.623 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.
Analyze functions using different representations
Ability to connect experience with graphing linear functions from Unit 2 of this course to include quadratic functions
Ability to make a quick sketch of each parent function over the set of real numbers
Ability to make connections between a function s domain and range and the appearance of the graph of the function
Knowledge of how parameters introduced into a function alter the shape of the graph of the parent function
Ability to make connections between different algebraic representations, a graph and a contextual model
Ability to connect experience with properties of exponents from Unit 2 Linear and Exponential Relationships of this course to more complex expressions
Ability to connect experience with comparing linear and exponential functions from Unit 2 of this course to include quadratic functions
" Ability to recognize common attributes of a function from multiple representations
F IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise defined functions, including step functions and
absolute value functions.
F IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain
different properties of the function.
a. 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.
F IF.924 Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one
quadratic function and an algebraic expression for another, say which has the larger maximum.
Build a function that models a relationship between two quantities
Ability to connect experience with linear and exponential functions from Unit 2 of this course to quadratic functions
Ability to write the algebraic representation of a quadratic function from a contextual situation
Ability to connect experience with linear and exponential functions from Unit 2 of this course to quadratic functions
Ability to add, subtract, multiply and divide functions
F BF.125 Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Build new functions from existing functions
Ability to make generalizations about the changes that will result in the graph of any function as a result of making a particular change to the algebraic representation of the function
F BF.326 Identify the effect on the graph of replacing f(x) by f(x) + k, k 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. 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.
Construct and compare linear, quadratic, and exponential models and solve problems
Examine and compare the rates of change and how they impact on the relationship between the variables for different types of functions.F LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as a polynomial function.Mathematical Practices :
Model with mathematics. Attend to precision. Look for and make use of structure.
Reason abstractly and quantitatively Make sense of problems and persevere in solving them.
ASSESSMENTS
Conferencing
Pre and Post Tests
Open-ended problems that involve a discovery approach to collaborative learning
Lead up problem solving tasks
Performance Based Assessment
Daily student work
Student/group presentationsMATERIALS & RESOURCES
Text book : Prentice Hall Mathematics Algebra I
Graphing calculators
Algebra Tiles and other manipulatives
Smart Board Demonstrations
Problem solving materials created by teachers
Reality In Mathematics Education Lesson Pack
HYPERLINK "http://nrich.maths.org/frontpage" http://nrich.maths.org/frontpage
HYPERLINK "http://www.Jmap.org"www.Jmap.org
High School Algebra I Curriculum Map
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