Algebra 1 - Beverly High School
LEGENDS
Next time: Fill in blanks for unit 9-13. THEN, focus on stage 3 and list activities that we do.
Unit 1: Algebra Foundations
Stage 1-Desired Results | ||
ESTABLISHED GOALS N-RN.B: Use properties of rational and irrational numbers N-Q.A: Reason quantitatively and use units to solve problems | ||
Transfer | ||
Students will be able to independently use their learning to… Classify Real numbers Apply properties of Real numbers Evaluate numerical expressions using order of operations Simplify algebraic expressions by combining like terms and using the distributive property | ||
Meaning | ||
UNDERSTANDINGS Numerical expressions can be evaluated to one number Algebraic expressions can be simplified Unlike terms can not be combined | ||
ESSENTIAL QUESTIONS How do you simplify an expression? How do we classify real numbers? How do we apply the properties of real numbers | ||
Acquisition | ||
Students will know… Expressions Whole numbers, integers, rational numbers, irrational numbers | ||
Students will be skilled at… Evaluating numerical expressions Simplifying algebraic expressions Classifying real numbers Identifying properties of real numbers | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Evaluate numerical expressions Simplify algebraic expressions Classify real numbers Apply properties of real numbers | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Examine classifying Real numbers -Explore how to apply properties of Real numbers -Examine how to evaluate numerical expressions using order of operations -Explore how to simplify algebraic expressions by combining like terms and using the distributive property | ||
Unit 2: Solving Equations
Stage 1-Desired Results | ||
Math State Standards: A-REI.B: Solve equations and inequalities in one variable A-REI.A: Understand solving equations as a process of reasoning and explain the reason A-CED.A: Create equations that describe numbers or relationships A-SSE.B: Write expressions in equivalent forms to solve problems | ||
Transfer | ||
Students will be able to independently use their learning to… Solve one variable equations. Solve absolute value equations. Solve literal equations for a specified variable. | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… Every equation has one solution, no solution, or infinitely many solutions. Every absolute value equation has one solution, two solutions, or no solution. Using properties of equality, any formula can be rewritten in terms of a particular variable. | ||
ESSENTIAL QUESTIONS How can we use properties of equality to find the solution to the equation? | ||
Acquisition | ||
Students will know… how to solve a variable with one variable. how to solve a literal for a specified equation. | ||
Students will be skilled at… using properties of equality. understanding the solution to equations. | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Solve one variable equation Solve literal equations for a specified equation Solve absolute value equation | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will… -Explore how to solve single variable 1 and 2 step equations (CP) -Examine how to solve multi-step single variable equations -Explore how to solve absolute value equations -Examine how to solve literal equations for a specified variable | ||
Unit 3: Solving Inequalities
Stage 1-Desired Results | ||
ESTABLISHED GOALS A-REI.B: Solve equations and inequalities in one variable A-CED.A: Create equations and inequalities that describe numbers or relationships | ||
Transfer | ||
Students will be able to independently use their learning to… Solve multi-step inequalities with one variable and graph their solutions on a number line. Solve compound inequalities and graph their solutions on a number line. Solve absolute value inequalities and graph their solutions on a number line. Model real-world situations with inequalities. | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… An inequality has many solutions, whereas an equation typically has one solution. The solutions to an inequality can be represented a graph on a number line. When you multiply or divide an inequality by a negative number, the inequality symbol reverses directions. An absolute value inequality can be re-written as a compound inequality. | ||
ESSENTIAL QUESTIONS What are the steps to solving an inequality? Why do we reverse the inequality symbol when we multiply or divide by a negative? How can we model real-world situations using inequalities? | ||
Acquisition | ||
Students will know… How to solve an inequality How to graph the solutions to an inequality on a number line | ||
Students will be skilled at… Solving inequalities Graphing inequalities | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Solving multi-step, compound, and absolute value inequalities. | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will… -Explore solving multi-step inequalities -Explore solving compound inequalities -Examine solving absolute value inequalities | ||
Unit 4: Linear Functions
Stage 1-Desired Results | ||
ESTABLISHED GOALS F.IF.B: Interpret linear, quadratic, and exponential functions with integer exponents that arise in applications in terms of the context F-LE.A: Construct and compare linear, quadratic, and exponential models and solve problems A-REI.D: Represent and solve equations and inequalities graphically A-CED.A: Create equations that describe numbers or relationships | ||
Transfer | ||
Students will be able to independently use their learning to… -calculate slope of a line from a graph or from an equation -write an equation in slope intercept form -write an equation in standard form -calculate the x and y intercept of a line
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Meaning | ||
UNDERSTANDINGS Students will understand that… The goal is for all students in the class to reach a level of comfort finding the slope of a line. The students need to be able to recognize what a linear equations looks like and be able graph it. Students should also be able to write an equation in standard or y-intercept form and be able to go from one form to another. | ||
ESSENTIAL QUESTIONS How can you use the understanding of linear equations to apply to real life situations? Where do we find slope in real life? | ||
Acquisition | ||
Students will know… -how to calculate slope of a line from a graph or from an equation -how to write an equation in slope intercept form -how to write an equation in standard form -how to calculate the x and y intercept of a line | ||
Students will be skilled at… -understanding slope of a line. -understanding different equations of a line. -understanding different ways to calculate the x and y intercepts. | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Solving equations in slope intercept form including finding slope, converting to standard form, and calculating intercepts | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will… -Explore how to find the slope -Examine how to find the slope intercept form -Examine how to find Standard Form -Explore how to find the x and y intercepts | ||
Unit 5 Scatterplots
Stage 1-Desired Results | ||
ESTABLISHED GOALS S.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables S.ID.C: Interpret linear models | ||
Transfer | ||
Students will be able to independently use their learning to… Create scatterplots by Hand Create scatterplots by Calculator Interpret correlation coefficients/ Correlation and Causation | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… A scatterplot can be used to predict future events The slope of a line represents the change in y for each 1 unit increase in x The correlation coefficient describes the direction and strength of the linear relationship between two variables. | ||
ESSENTIAL QUESTIONS How do we make a scatter plot? How do we use a scatter plot to predict future events? What is a correlation coefficient? | ||
Acquisition | ||
Students will know… how to graph and interpret scatter plots how to use correlation coefficients | ||
Students will be skilled at… Using Scatter plots to predict future events | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Construct and interpret scatterplots | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Students will: -Construct and interpret scatterplots to show the relationship between two variables -Use linear models to predict future events | ||
Unit 6 Functions
Stage 1-Desired Results | ||
ESTABLISHED GOALS F-IF.A: Understand the concept of a function and use function notation F-IF.C: Analyze functions using different representations F-BF.A: Build a function that describes a relationship between quantities F-BF.B: Build new functions from existing functions F-LE.B: Interpret expressions for functions in terms of the situation they model | ||
Transfer | ||
Students will be able to independently use their learning to… Express a relation as a table, graph, and mapping diagram Determine whether a relation is a function Identify the domain and range of a relation Use function notation Identify features of graph Graph functions by making a table of values | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… In a function, each x value corresponds to exactly one y value Function rules can be written using function notation | ||
ESSENTIAL QUESTIONS What makes a relation a function? What is the domain and range of a relation? What are the important features of graphs? | ||
Acquisition | ||
Students will know… Express a relation as a table, graph, and mapping diagram Determine whether a relation is a function Identify the domain and range of a relation Use function notation Identify features of graph Graph functions by making a table of values | ||
Students will be skilled at… Graphing functions Identify domain and range Using function notation | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Different ways to represent functions and relations. Identifying domain and range of a function. Using and understanding function notation. Identifying features of graphs. | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Express a relation as a table, graph, and mapping diagram -Determine whether a relation is a function -Identify the domain and range of a relation -Use function notation -Identify features of graph -Graph functions by making a table of values | ||
Unit 7 Linear Systems of Equations
Stage 1-Desired Results | ||
ESTABLISHED GOALS A-REI.C: Solve systems of equations | ||
Transfer | ||
Students will be able to independently use their learning to… Solve a system of 2 simultaneous linear equations by:
Solve word problems involving systems of 2 simultaneous linear equations Graph linear inequalities Graph systems of linear inequalities (with or without constraints) | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… The solution to a system of equations is the intersection point on a graph A system of two parallel lines has no solution The solution of a linear inequality is a region on the graph bounded by a solid or dotted line | ||
ESSENTIAL QUESTIONS How can you solve a system of equations using multiple methods? How can you model real world situations using systems of equations? | ||
Acquisition | ||
Students will know… How to select a method to solve a system of equations. what the solution to a system of equations mean. how to solve real world problems using a system of equations. | ||
Students will be skilled at… solving systems of equations using three different methods solving real world problems using a systems of equations | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Different ways of solving systems of equations including substitution, elimination, and graphing. Graphing Systems and Inequalities
| PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will… -Explore systems of equations -Examine solving systems by graphing -Examine solving systems by elimination -Examine solving systems by substitution -Explore word problems -Examine inequalities | ||
Unit 8 Properties of Exponents
Stage 1-Desired Results | ||
ESTABLISHED GOALS N-RN.A: Extend the properties of exponents to rational exponents A.F-LE: Construct and compare linear, quadratic, and exponential models and solve problems F-IF.B: Interpret linear, quadratic and exponential functions with integer exponents that arise in applications in terms of the context F-IF.C: Analyze functions using different representations | ||
Transfer | ||
Students will be able to independently use their learning to… Rewrite radical expressions using rational exponents Rewrite expressions with exponents using radicals Estimate the values of radicals using perfect squares and perfect cubes as a reference Calculate % tax and discount Simplify and evaluate exponential expressions Solve word problems involving exponential relationships Calculate simple interest Identify growth rates | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… radicals can be rewritten using rational exponents. exponential equations can be written from a table and graph. real world scenarios can be modeled as exponential equations. | ||
ESSENTIAL QUESTIONS How can you write a radical with an exponent? And vice versa? What is the final price of an item? How do you simplify exponential expressions? How do you solve real world problems modeled exponentially? What is the simple interest given the principle, rate, and time? | ||
Acquisition | ||
Students will know… how to translate back and forth between exponential notation and radicals. how to calculate the final price of an item. how to simplify expressions with exponents. how to solve real world problems that are modeled exponentially. how to calculate simple interest given the principle, rate, and time. | ||
Students will be skilled at… simplifying expressions with exponents. exponential functions. | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Solving radical expressions using exponents, radical expressions, estimating square roots, calculating taxes, solving exponential expressions, and growth rates | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Explore properties of exponents -Simplify perfect squares -Simplify perfect cubes -Examine approximate perfect squares and cubes -Explore how to convert between rational exponents and radicals -Examine percent tax/discount -Examine exponential word problems -Explore compound interest -Identify growth rates | ||
Unit 9 Sequences
Stage 1-Desired Results | ||
ESTABLISHED GOALS F-IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers F-BF.A: Build a function that models a relationship between two quantities 1.a: determine an explicit expression, a recursive process, or steps for calculation from a context 2: write arithmetic and geometric sequences both recursively and with an explicit formula them to model situations, and translate between the two forms | ||
Transfer | ||
Students will be able to independently use their learning to… Write the explicit formula for an arithmetic sequence Write the explicit formula for a geometric sequence Find missing term(s) in arithmetic and geometric sequences | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… Students will understand that the terms of an arithmetic sequence are separated by a common difference Students will understand that the terms of a geometric sequence are separated by a common ratio | ||
ESSENTIAL QUESTIONS How do you use a formula to find a given term of a sequence? | ||
Acquisition | ||
Students will know… how to write the explicit formula for an arithmetic sequence how to write the explicit formula for a geometric sequence how to find missing terms in a sequence how to find the common difference and common ratio from a given sequence | ||
Students will be skilled at… using explicit formulas of sequences to find the nth term | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | ||
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Explore sequences -Examine arithmetic sequences - explicit -Examine geometric sequences - recursive -Examine arithmetic sequences - recursive -Explore geometric sequences - explicit | ||
Unit 10 Polynomials
Stage 1-Desired Results | ||
ESTABLISHED GOALS A-APR.A: perform arithmetic operations on polynomials | ||
Transfer | ||
Students will be able to independently use their learning to… Add and subtract polynomials Multiply two binomials Multiply a binomial and a trinomial Factor an expression by finding the greatest common factor Factor a quadratic trinomial Factor a difference of squares | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… A quadratic trinomial that is factorable can be broken down into the product of two binomials | ||
ESSENTIAL QUESTIONS How do you add and subtract polynomials? How do you multiply polynomials? How do you factor a quadratic trinomial? | ||
Acquisition | ||
Students will know… How to add and subtract polynomials. How to multiply polynomials. How to factor a quadratic trinomial. | ||
Students will be skilled at… Adding and subtract polynomials multiply polynomials factor polynomials | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Add, subtract, and multiply polynomials. Factor polynomials by GCF, factor quadratic trinomials. | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Examine adding polynomials -Explore subtracting polynomials -Examine multiplying polynomials -Explore factoring of polynomials -Examine greatest common factor | ||
Unit 11 - Quadratics
Stage 1-Desired Results | ||
ESTABLISHED GOALS F-IF.C: Analyze functions using different representations F-IF.B: interpret linear, quadratic, and exponential functions with integer exponents that arise in applications in terms of the context F-LE.A: Construct and compare linear, quadratic, and exponential models to solve problems A-SSE.A: interpret the structure of linear, quadratic, and exponential expressions with integer exponents | ||
Transfer | ||
Students will be able to independently use their learning to… Graph system of equations (one linear and one quadratic) Solve a quadratic equation by inspection (graphing) Solve a quadratic equation by factoring Solve a quadratic equation by completing the square Rewrite a Standard Form Quadratic Equation in Vertex-form Solve a quadratic equation by using the quadratic formula | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… A system of a linear equation and quadratic can have no solution, one solution, or two solutions. A solution to a quadratic is the x intercepts. There are many ways to solve a quadratics--all techniques are doing the same thing. | ||
ESSENTIAL QUESTIONS What is the solution to the system with a linear function and a quadratic? What is the solution to a quadratic? | ||
Acquisition | ||
Students will know… How to solve a system of equations with a linear function and quadratic function. How to solve a quadratic equation. | ||
Students will be skilled at… Solving a system of equations with a line and quadratic. The many ways to solve a quadratic. | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Solve a system of equations with a line and quadratic. Solve a quadratic. | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Examine graphing systems with linear and quadratics -Explore solving quadratics by graphing, -factoring, -completing the square and -using the quadratic formula | ||
Unit 12 - Transformation of Functions
Stage 1-Desired Results | ||
F-IF.C: Analyze functions using different representations F-BF.B: Build new functions from existing functions F-LE.A: Construct and compare linear, quadratic, and exponential models to solve problems F-LE.B: Interpret expressions for functions in terms of the situation they model | ||
Transfer | ||
Students will be able to independently use their learning to… Transform functions by shifting Transform functions by scalar multiplication Transform functions over axes | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… functions can be transformed by adding or subtracting numbers to the parent function functions can be transformed multiplying a number by the parent function expressions for functions can be interpreted by the situation they model quadratics, exponential and linear models can be used to solve problems | ||
ESSENTIAL QUESTIONS What are the different types of transformations that can be performed on a function? | ||
Acquisition | ||
Students will know… How to perform transformations on functions when the instructions are given in function notation. | ||
Students will be skilled at… Understanding transformations in function notation. Performing transformations on functions. | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Transformations on functions-vertical, horizontal translations, stretches and reflections, and finding the value of k. | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Explore transformations of functions through scalar multiplication -Analyze functions using different representations -Build new functions from existing functions -Construct and compare linear, quadratic, and exponential models to solve problems -Interpret expressions for functions in terms of the situation they model
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UNIT 13
Stage 1-Desired Results | ||
-A1.S-1D S-CP-4 - A. Summarize, represent, and interpret data on a single count or measurement variable. Use calculators, spreadsheets, and other technology as appropriate. Summarize, represent, and interpret data on a single count or measurement variable. Use calculators, spreadsheets, and other technology as appropriate. -B. Summarize, represent, and interpret data on two categorical and quantitative variables.
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Transfer | ||
Students will be able to independently use their learning to… create dot plots, histograms, and box plots calculate median, mean, IQR, and Standard Deviation describe shape, center, and outliers create 2-way frequency tables (joint, marginal, and conditional) | ||
Meaning | ||
UNDERSTANDINGS Students will understand that… data can be used to to interpret data on a sin | ||
ESSENTIAL QUESTIONS How can you use data displays to interpret categorical and quantitative variables? | ||
Acquisition | ||
Students will know… how to find measures of central tendency such as mean, median, IQR, etc. how to interpret and analyze different data representations | ||
Students will be skilled at… finding measures of central tendency interpreting and analyzing different data displays | ||
Stage 2 - Evidence | ||
Evaluative Criteria | Assessment Evidence | |
Mean, median, mode, IQR, dot plots, histograms, box plots, describe shape, outliers, standard deviation. | PERFORMANCE TASK(S): Teacher worksheets Formative assessments Unit Test | |
Stage 3 – Learning Plan | ||
Summary of Key Learning Events and Instruction Students will... -Explore dot plots, histograms and box-plots -Examine median, mean, 1QR, standard deviation -Explore shape, center and outliers -Examine 2-way frequency tables - joint, marginal and conditional | ||