teecs-mrsbhattad.weebly.comteecs-mrsbhattad.weebly.com/.../4/0/7/5/40756413/algebr… · web...

Thomas Edison EnergySmart Charter School 2016-17Curriculum for Algebra-1

Mrs.Bhattad

Big Idea: Expressions, Equations and Functions

Content: Mathematics Course: Algebra-1 Unit: 1 and 2

Essential questions Content Skills Key terms Assessment NJSLS Text

Why is it useful to repre-sent real life situations alge-braically?

Which of the terms inan algebraic equation stay the same and which term has the ability to change its value?

Why don't we combine vari-ables that are different?

How can I isolate a variable to one side of an equation so that I can find its value?

How can we use mathe-matical language to de-scribe nonlinear change?

How can patterns, relations, and functions be used as tools to best describe and help explain real-life situa-

Identify constant and variable terms in algebraic expres-sions and equations

Simplify algebraic expressions, discrim-inating between un-like variables.

Solve equations in oneVariable

Solve equations and inequalities in one variable

Create equations that describe num-bers or relationships

Identify solutions of inequalities in one variable. Write and

Identifying the constant

Identifying the variable

Simplifying algebraic expression

Solve an equation with variable on one or both sides

Solve an inequality with variable on one or both sides

Create equations

Graph inequalities

Write an equation for the word problem

Variable

Isolate

Expression

Equation

Function

Teacher created assessments

TeacherObservations

Rubrics

Benchmarks

Projects

Progress check 1

Progress check 2

Homework

Classroomobservations(whole group)

N.Q.A.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.A.2. Define appropriate quantities for the purpose of descriptive modeling.

N.Q.A.3. Choose a level of accuracy appropriate to limitations on mea-surement when reporting quantities.A.SSE.1 – Interpret expressions that represent a quantity in terms of its context.A.SSE.1a – Interpret parts of an ex-pression, such as terms, factors, and coefficients.

A.REI.1 - Explain each step in solving a simple equation as following from

Digits

tions?

How can we use algebraic representation to analyze patterns?

How are functions and their graphs related?

How can change be repre-sented mathematically?

graph inequalities in one variable

Solve inequalities that contain variable terms on both sides

Solve one-stepInequalities

Solve equations in one variable that contain variable terms on both sides

Write and solve problems involving proportions

Solve an equation intwo or more vari-ables for one of the variables

Solve an equation for the word problem

Individualobservations

the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable ar-gument to justify a solution method.

A.REI.3 - Solve linear equations and inequalities in one variable, including equations with coefficients repre-sented by letters.

A.CED.4 – Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.CED.1 – Create equations and in-equalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple ratio-nal and exponential functions.

A.CED.A.2. Create equations in two or more variables to represent relationships between quantities; Graph equations on coordinate axes with labels and scales.

A.REI.D.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).

Big Idea: Graphing and Writing Linear equations


Essential questions Content Skill Key terms Assessment NJSLS Text

How do we rewrite the equations in different forms?

How can change be best represented mathemati-cally?

How do I calculate the slope of a line?

How do I find a time depen-dent bar graph in the me-dia. How doI use the graph to calculate, label and compare the slopes between the inter-vals of time?

How can I use an equation written in slope intercept form to determine slope and y-intercept of a func-tion.

How does the graph change with changing values of m and b?

Understanding the difference between expression and equation

Equations with variables to represent quantitiesSolving equations

Converting numbers from one form to another like percents, decimals and fraction

Solving and graphing linear equations

Solving and graphing inequalities

Slope and y-intercept

Identify, write, andgraph direct variations

Differentiating be-tween an expression and an equation

Write an equation with a variable to represent quantities

Re write an equa-tion with different forms of numbers like percents, deci-mals and fractions

Solving and graph-ing linear equations

Solving and graph-ing inequalities

Calculating the slope of a line for a linear equation in the slope-intercept form

Finding the slope of a line looking at the graph

Expressions

Equations

Variable

Linear equations

Slopey-intercept

discount

tax

percents

decimals

fractions

solve

evaluate

graph

Teacher createdassessments

TeacherObservations

Rubrics

Benchmarks

Projects

Progress check 1

Progress check 2

Homework



F.LE.1 – Distinguish between situa-tions that can be modeled with linear functions and with exponential func-tions.

F.LE.1a - Prove that linear functions grow by equal differences over equal intervals, and that exponential func-tions grow by equal factors over equal intervals.

F.LE.1b – Recognize situations in which one quantity changes at a con-stant rate per unit interval relative to another.

F.IF.6 - Calculate and interpret the av-erage rate of change of a function (presented symbolically or as a table) over a specified interval.Estimate the rate of change from a graph.

A.CED.2 – Create equations in two or more variables to represent relation-ships between quantities; graph equations on coordinate axes with la-bels and scales.

Digits

What happens to the graph if a function if I change the values of m and b?

How can you determine if an answer is viable based on the context of the prob-lem?

Write equations for lines in slope inter-cept form from sev-eral different pieces of given information

Use an equation written in slope in-tercept form to de-termine slope and y-intercept of a func-tion.

Describe the effects of changing the val-ues of m and b in a function on a graph

Determine the via-bility of solutions to a linear equation or inequality in a real world context

Understanding slope as a rate of change

Understanding the effects of changing the slope and y-in-tercept on the graph

Determining the reasonableness of the solution in real world context

inequalities

greater than

greater than or equal to

less than

less than or equal to

F.BF.1 - Write a function that de-scribes a relationship between two quantities.

F.BF.1a - Determine an explicit ex-pression, a recursive process, or steps for calculation from a context.

F.LE.2 - Construct linear and expo-nential functions, including arith-metic and geometric sequences, given a graph, a description of a rela-tionship, or two input-output pairs (include reading these from a table).

S.ID.7 - Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

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 val-ues 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 rec-ognizing even and odd functions from their graphs and algebraic ex-pressions for them.

F.IF.B.5. Relate the domain of a func-tion to its graph and, where applica-ble, to the quantitative relationship it describes

F.IF.C.9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Big Idea: Systems of Equations and inequalities



How can changebe best represented mathe-matically?

How can we use mathe-matical language to de-scribe change?

Which method to use to solve a system of equations?

How can I determinea special system by looking at a graph or an equation?

Graphs and equa-tions are alternative ways for depicting and analyzing pat-terns of change.

Solve systems of equations by graph-ing

Solve systems of equations by substi-tution

Represent and solve equations and in-equalities graphically

Graphing systems of equations

Analyzing the system

Solving the system of equations by graphing

Solving the system of equations by substituting

Solving the system of equations by elimination

System of equations

Solution

Slope

Y-intercept


TeacherObservations

Rubrics

Benchmarks

Projects

Progress check 1

Progress check 2

A.REI.5 - Prove that, given a system of two equations in two variables, re-placing 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.

A.REI.11 - Explain why the x-coordi-nates 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

Digits

How do you determine if a point is part of the solution to a system of linear in-equalities?

Solve systems of equations by elimi-nation

Solve special systems

Determine if a point is part of the solu-tion to a system of linear inequalities

Determine the via-bility of solutions to a system of linear equations or in-equalities in a real world context.

Identifying the special systems of equations

Solving the special systems of equations

Homework



approximately, e.g., using technology to graph the functions, make tables of values, or find successive approxi-mations. Include cases where f(x) and/or g(x) are linear, polynomial, ra-tional, 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

A.CED.3 – Represent constraints by equations or inequalities, and by sys-tems of equations and/or inequali-ties, and viable or non-viable options in a modeling context. For example, represent inequalities describing nu-tritional and cost constraints on com-binations of different foods.

A.REI.D.11. Explain why the x-coordi-nates 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 approxi-mations. Include cases where f(x) and/or g(x) are linear, polynomial, ra-tional, absolute value, exponential, and logarithmic functions.

Big Idea: Exponents and exponential functions

Content: Mathematics Course: Algebra-1 Unit: 7


How do we extend the properties of exponents to rational exponents?

How do I create a table of values for an exponential function with an integer base whose domain is con-secutive integers whose lowest and highest values have equal absolute values?

How do we evaluate ex-pressions containing zero and integer exponents

How do I use multiplication properties of exponents to evaluate and simplify ex-pressions?

How do I use division prop-erties of exponents to eval-uate and simplify expres-

Extending the con-cept of exponents to rational exponents

Evaluating expres-sions containing fractional exponents

Evaluating expres-sions containing zero and integer expo-nents

Solve problems in-volving exponential growth and decay, including compound interest

Understanding rational exponents

Evaluating rational exponents

Evaluating zero and integer exponents

Solving problems involving exponential growth and decay

Solving problems involving compound interest

Using the rules of exponents to multiply/divide

Simplifying expressions with

Exponents

Rational numbers

Base

Power

Exponential growth

Exponential decay

Half-life

Compound interest


TeacherObservations

Rubrics

Benchmarks

Projects

Progress check 1

Progress check 2

Homework


N.RN1 - Explain how the definition of the meaning of rational exponents follows from extending the proper-ties of integer exponents to those values, allowing for a notation for radicals in terms of rational expo-nents.

N.RN2 – Rewrite expressions involv-ing radicals and rational exponents using the properties of exponents

F.IF.A.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.A.2. Use function notation,

Digits

sions?

How do I evaluate exponen-tial functions?

Evaluate and graph expo-nential functions

How do we solve problems involving exponential growth and decay, including compound interest

exponents

Evaluate and graph the exponential functions

Modelling or graphing exponential functions


evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more com-plicated cases.

F.LE.5 - Interpret the parameters in a linear or exponential function in terms of a context.

F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.LE.1 – Distinguish between situa-tions that can be modeled with linear functions and with exponential func-tions.

F.IF.A.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers

F.IF.B.5. Relate the domain of a func-

tion to its graph and, where applica-ble, to the quantitative relationship it describes


F.IF.6 - Calculate and interpret the av-erage rate of change of a function (presented symbolically or as a table) over a specified interval.Estimate the rate of change from a graph.

F.LE.A.3. Observe using graphs and tables that a quantity increasing ex-ponentially eventually exceeds a quantity increasing linearly, quadrati-cally, or (more generally) as a polyno-mial function.

Big Idea: Radicals



How can we use proper-ties of rational and irra-tional numbers

Evaluate expressions con-taining zero and integer ex-ponents

Performing opera-tions on numerical or algebraic expres-

Rational numbers


N.RN.3 - Explain why the sum or product of two

Digits

How do we multiply, di-vide, and manipulate numerical or algebraic expressions with square roots.

How do we add, sub-tract, and manipulate numerical or algebraic expressions with square roots

Multiply, divide, and manip-ulate numerical or algebraic expressions with square roots.

sions with square roots.

Evaluating expres-sions with zero and integer exponents

Sol

Irrational numbers

Square roots

Radicals

Exponents

Base

Power

TeacherObservations

Rubrics

Benchmarks

Projects

Progress check 1

Progress check 2

Homework



rational numbers is rational; that the sum of a ra-tional number and an irrational number is irra-tional; and that the product of a nonzero rational number and an irrational num-ber is irrational.

Big Idea: Polynomials and factoring



How do we classify polynomials?

How do I find a degree and leading coefficient

Finding the degree and lead-ing coefficient of a polyno-mial?

Classifying polynomials

Finding the highest degree of the poly-nomial

Multiply, divide,

Polynomial

Binomial

Trinomial


TeacherObservations

A.SSE.1 – Inter-pret expressions that represent a quantity interms of its

Digits

of a polynomial?

How do I determine ifa polynomial is a mono-mial, a binomial, or a polynomial?

What terms can I com-bine when adding or subtracting polynomi-als?

What terms can I com-bine when multiplying polynomials?

Are there any special cir-cumstances that need to be known when multi-plying binomials?

How do we choose an appropriate method for factoring polynomials?

What are the different methods for factoring polynomials and when should I use them?

Find special products ofBinomials

Factor polynomials using the Greatest Common Factor

Factor perfect square trino-mials and the difference of two squares

Choose an appropriate method for factoring polyno-mials

and manipulate nu-merical or algebraic expressions with square roots.

Factoring the poly-nomials using the GCF

Factor special prod-uct binomials

Factor perfect square trinomials

Deciding the appro-priate method to factor polynomials

Degree Rubrics

Benchmarks

Projects

Progress check 1

Progress check 2

Homework



context.

A.APR.1 – Under-stand that poly-nomials form a system analo-gous to the inte-gers, namely, they are closed under the opera-tions of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

A.SSE.2 - Use the structure of an expression to identify ways to rewrite it.

A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and ex-plain properties of the quantity represented by the expression.

A.SSE.3a - Factor a quadratic ex-pression to re-veal the zeros of the function it defines.

A.APR.B.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.

Big Idea: Quadratic equations



How do I identify a qua-dratic function?

How do I determine if a quadratic function has a minimum and maxi-

Identify quadratic functions and determine whether they have a minimum and maxi-mum.

Find the zeros of a quadratic function from its graph

Finding the discriminant

Determining if the function has a maximum or the minimum

Quadratic

Roots

Maxima

Minima


TeacherObservations

Rubrics

F.IF.4 - For a function that models a rela-tionship between two quantities, interpret key fea-tures of graphs

Digits

mum?

How do I use the graph of a quadratic function to identify the zeroes?

How do we graph a qua-dratic function in the form:y = ax^2 + bx + c

How do we find the ver-tex of a quadratic func-tion by completing the square

How we solve quadratics by graphing?

How do I use the qua-dratic formula to solve quadratic equations?

How do I use factoring to solve quadratic equa-tions?

How do I use square roots to solve quadratic equations?

How can I solve systems involving linear and qua-

Graph a quadratic function in the form:y = ax^2 + bx + c

Find the vertex of a qua-dratic function by complet-ing the square

Solve equations by using the quadratic formula and deter-mine the number of solu-tions by using the discrimi-nant

Solve quadratics by graphing

Solve quadratic equations by factoring

Solve quadratics by using square roots

Solve systems involving lin-ear and quadratic equations, both algebraically and graph-ically.

Identifying the maximum or the minimum

Finding the vertex of a quadratic function

Solving the quadratics by graphing

Solving by factoring

Solving by using square roots

Solving systems involving quadratic equationsUsing the formula to find the roots of a quadratic equations

Vertex

Solution

Benchmarks

Projects

Progress check 1

Progress check 2

Homework



and tables in terms of the quantities, and sketch graphs showing key fea-tures given a ver-bal description of the relationship. Key features in-clude: intercepts; intervals where the function is in-creasing, de-creasing, posi-tive, or negative; relative maxi-mums and mini-mums; symme-tries; end behav-ior; and periodic-ity.

F.IF.7 - Graph functions ex-pressed symboli-cally and show key features of the graph, by hand in simple cases and using technology for more compli-cated cases.

dratic equations?F.IF.7a - Graph linear and qua-dratic functions and show inter-cepts, maxima, and minima.

A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and ex-plain properties of the quantity represented by the expression.

A.SSE.3b - Com-plete the square in a quadratic ex-pression to re-veal the maxi-mum or mini-mum value of the function it de-fines.

A.REI.4 – Solve quadratic equa-tions in one vari-able.

A.REI.4b – Solve quadratic equa-tions by taking square roots, completing the square, the qua-dratic formula and factoring, as appropriate to the initial form of the equation.Recognize when the quadratic for-mula gives com-plex solutions and write them as a ± bi for real numbers a and b

F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and ex-plain different properties of the function.

F.IF.8a - Use the process of factor-ing and complet-ing the square in

a quadratic func-tion to show ze-ros, extreme val-ues, and symme-try of the graph, and interpret these in terms of a context.

A.REI.7 - Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebra-ically and graphi-cally. For exam-ple, find the points of inter-section between the line y = –3x and the circle x^2 + y^2 = 3.

F.IF.B.5. Relate the domain of a function to its graph and, where applicable, to the quantitative rela-tionship it de-scribes


F.IF.6 - Calculate and interpret the average rate of change of a func-tion (presented symbolically or as a table) over a specified interval.Estimate the rate of change from a graph.

Big Idea: Statistics and probability



How can we collect, organize, interpret and

Interpreting categorical and quantitative data

Displaying data by graphing

Graphs Teacher createdassesments

S.ID.2. – Use sta-tistics to the

Digits

display of data that can be used to answer questions?

How can representation of data influence decision?

How do we create a list of values that satisfies given measures of central tendency?

How do we create a scatter plot?

How do we create two-way tables?

How do we interpret two-way tables?

Summarizing, representing data on a single count or measurement variable

Scatter plots

Two-way tables

Measure of center

Measures of variability

Making a scatter plot

Creating a scatter plot

Interpreting graphs

Two-way tables

Scatter plots

Trend

Mean

Median

Mode

Range

Inter quartile range

Standard deviation

Outliers

TeacherObservations

Rubrics

Benchmarks

Projects

Progress check 1

Progress check 2

Homework



shape of the data distribution to compare center(median, mean) and spread (inter quartile range, standard devia-tion) of two or more different data sets.

S.ID.3 – Interpret differences in shape, center and spread in the context of the data sets, ac-counting for pos-sible effects of extreme data points(outliers)

S.ID.5- Summa-rize categorical data for two cat-egories in two-way frequency tables. Interpret relative frequen-cies in the con-text of the data (including joint,

marginal and conditional rela-tive frequencies). Recognize possi-ble associations and trends in data.

S.ID.6 – Repre-sent data on two quantitative vari-ables on a scatter plot and describe how the variable are related.

F.IF.B.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.B.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

teecs-mrsbhattad.weebly.comteecs-mrsbhattad.weebly.com/.../4/0/7/5/40756413/algebr… · web...

Documents