Hayward Unified School District Algebra I Mathematics ... · Hayward Unified School District Algebra I Mathematics Curriculum Guide Unit Map Online Resources: GMR=General Math Resource

Hayward Unified School District

Algebra I Mathematics Curriculum Guide Unit Map

Online Resources: GMR=General Math Resource CP=Content Presentation Page 1 of 24 L=Lesson IM= Illustrative Math Task MCC@WCCUSD 08/25/16

Grade Level/Course Title: Algebra I Quarter 1 Academic Year: 2016-2017

Mathematics Focus for the Course: For the Model Algebra I course, instructional time should focus on four critical areas: (1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend.

Essential Question for this Unit: 1. How can students represent, analyze and interpret data using various representations?

Unit (Time) Standard Standard Description Content Resources

Unit 4A:

(Aug. – Sept.)

Statistical

Models

(11 days)

Ending Sept. 15

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. ★

Graphical representations of data

Create and use Two-Way Frequency Tables

Mean

Median

Mode

Outlier

Conceptual understanding of standard deviation

Note: For High School, block days are counted as

1.5 Days for the entire school year.

Suggested ending date for each unit is for high

school block scheduling.

Warm-Up Template (Word) (GMR) Multiple Methods Mat (GMR) Syntax - Expressions, Equations, and Inequalities (GMR) Adding Integers Worksheet (GMR) Adding/Subtracting Integers Worksheet (GMR) Order of Operations (L) Real Number Line Development & Venn Diagram (CP)

Module 8

8.1 Two-Way Frequency Tables

8.2 Relative Frequency and Probability

S-ID Support for a Longer School day? (IM) Module 9

9.1 Measure of Center and Spread

Standard Deviation and Variance (CP) 9.2 Data Distributions and Outliers

9.3 Histograms and Box Plots

S-ID 1, 2, 3 Speed Trap (IM)

S-ID Hair Cuts (IM)

S-ID Understanding Standard Deviation (IM)

Unit 4A Review and Assessment (2 days)

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). ★

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. ★

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/Domain/60/General%20Mathematics%20Resources/MCCwarmup2011templateV2.doc

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/Domain/60/General%20Mathematics%20Resources/MulipleMethodsMat.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/general%20mathematics%20resources/SyntaxV7.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/general%20mathematics%20resources/AddingIntegersWorksheetV4.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/general%20mathematics%20resources/AddingSubtractingIntegerWorksheet.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/Grade%207%20Lessons/OrderOfOperationsV5.pdf

http://www.wccusd.net/Page/3259

https://www.illustrativemathematics.org/content-standards/HSS/ID/B/5/tasks/2044

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/content%20presentations/StandardDeviationVarianceV4.mov

https://www.illustrativemathematics.org/content-standards/HSS/ID/A/1/tasks/1027








Essential Questions for this Unit: 1. How can students become facile with algebraic manipulation, including rearranging and collecting like terms, identifying zero pairs and equivalent forms of one? 2. How can students analyze, explain and justify the process of solving an equation or inequality? 3. How can students create and solve equations and inequalities?


Unit 1:

(Sept. – Oct.)

Quantities

And

Modeling

(14 days)

Ending Oct. 7

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. ★

Proper Syntax

Academic Vocabulary

Number Sets

Equivalent Form of zero

Equivalent Form of one

Tile Spacers

Number Lines

Quantity

Area Models

Area Models using Generic Rectangles

Simplifying

Expressions vs. Solving Equations

Graphical representations of data

Solving Equations using

multiple methods:

Bar Models

Decomposition

Inverse Operations

Algebra Tiles

Number Line

Justifications

Proper Syntax

Module 1

1.1 Solving Equations

Simplifying Expressions & Solving Equations With Two Column Proofs (CP)

Simplifying Expressions & Solving Equations With Two Column Proofs (L)

Algebra Tiles (CP)

1.2 Modeling Quantities

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. ★ (Lesson 1-3)

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-CED.1 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and

simple rational and exponential functions. CA ★



http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolveEquationsTwoColumnProofsV9.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolveEquationsTwoColumnProofsV9.pdf







Essential Questions for this Unit: 1. How can students become facile with algebraic manipulation, including rearranging and collecting like terms, identifying zero pairs and equivalent forms of one? 2. How can students analyze, explain and justify the process of solving an equation or inequality? 3. How can students create and solve equations and inequalities?


Unit 1:

(Sept. – Oct.)

Quantities

And

Modeling

(14 days)

Ending Oct. 7

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. ★

Solving Equations using

multiple methods:

Bar Models

Decomposition

Inverse Operations

Algebra Tiles

Number Line

Justifications

Proper Syntax

Inequalities:

Sense of an inequality

Multiple-Representations: verbal, symbolic, graph

Build on multiple-methods for equation solving

Proper Syntax

Set Notation

Module 2

2.1 Modeling with Expressions

Distributive Property (CP)

2.2 Creating and Solving Equations

Solving Equations with Variables on Both Sides (CP)

Solving Equations with Variables on Both Sides (L)

Distance = Rate X Time: Focus on Student Talk (L)

Motion Problems (L)

2.3 Solving for a Variable

Solving and Using Literal Equations (L)

2.4 Creating and Solving Inequalities

Solving Inequalities (L)

2.5 Creating and Solving Compound Inequalities

N-Q Felicia’s Drive (IM)

N-Q Fuel Efficiency (IM)

N-Q Harvesting the Fields (IM)

N-Q Traffic Jam (IM)

A-REI Reasoning with Linear Inequalities (IM)

Unit 1 Review and Assessment (2 days)

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. ★

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.

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



http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolvingEquationsVariablesBothSidesV4.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/GraphsBarModelforDrtIntroV3.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/AlgMotionProblemsV3.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolvingAndUsingLiteralEquationsV4.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolvingInequalitiesV6.pdf

https://www.illustrativemathematics.org/content-standards/HSN/Q/A/1/tasks/80



https://www.illustrativemathematics.org/content-standards/HSN/Q/A/tasks/84

https://www.illustrativemathematics.org/content-standards/HSA/REI/B/3/tasks/807






Essential Questions for this Unit: 1. How can students build on their prior knowledge when learning to define, evaluate, and compare functions, and use them to model relationships between

quantities? 2. How can students learn function notation and develop the concepts of domain and range? 3. How can students focus on functions, including sequences; interpret function graphically, numerically, symbolically and verbally; translate between

representations; and understand the limitations of various representations? 4. How can students interpret arithmetic sequences as linear functions?


Unit 2:

(October)

Understanding

Functions

(13 days)

Ending Oct. 28

A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate plane axes with

labels and scales. ★

Label axes on coordinate plane

Accuracy and scale when graphing

Academic vocabulary

Function values

Function notation

Proper syntax

Discrete functions

Continuous functions

Module 3

3.1 Graphing Relationships

3.2 Understanding Relations and Functions

3.3 Modeling with Functions

3.4 Graphing Functions

Family of Functions Graphing Worksheet (GMR)

F-IF Interpreting the Graph (IM)

F-IF Oakland Coliseum (IM)

F-IF The Restaurant (IM)

F-IF Warming and Cooling (IM)

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 ≥ 1.

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/Domain/60/General%20Mathematics%20Resources/FamilyFunctionsGraphWorksheet.pdf

https://www.illustrativemathematics.org/content-standards/HSF/IF/A/tasks/636

https://www.illustrativemathematics.org/content-standards/HSF/IF/B/5/tasks/631








Essential Questions for this Unit: 1. How can students build on their prior knowledge when learning to define, evaluate, and compare functions, and use them to model relationships between

quantities? 2. How can students learn function notation and develop the concepts of domain and range? 3. How can students focus on functions, including sequences; interpret function graphically, numerically, symbolically and verbally; translate between

representations; and understand the limitations of various representations? 4. How can students interpret arithmetic sequences as linear functions?


Unit 2:

(October)

Understanding

Functions

(13 days)

Ending Oct. 28

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. ★

Domain of a linear function vs. domain of an arithmetic sequence

Graph of a linear function vs. graph of an arithmetic sequence

Explicit formula vs. recursive formula

Write formulas in function notation

Module 4

4.1 Identifying and Graphing Sequences

4.2 Constructing Arithmetic Sequences

Arithmetic Sequences (L)

4.3 Modeling with Arithmetic Sequences


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

context. ★

F-BF.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between

the two forms. ★

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). ★

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/Arithmetic%20Sequences201314.pdf






Essential Questions for this Unit: 1. How can students build upon their prior experiences when graphing, evaluating and writing linear functions? 2. How can students use the key features of linear functions to graph, write and compare linear functions? 3. How can students create linear functions or inequalities to model relationships between quantities?


Unit 3:

(Nov. – Dec.)

Linear

Functions,

Equations,

and

Inequalities

(16 days)

Ending Dec. 2

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. ★

Identify key features of the graph of a function


Proper Syntax

Advantages of the various forms of a linear function when graphing

Concept of Rate of Change

Interpret rate of change algebraically, from a table, from a graph

Module 5

5.1 Understanding Linear Functions

Family of Linear Functions (CP)

Evaluating Linear Functions (L)

5.2 Using Intercepts

5.3 Interpreting Rate of Change and Slope

Average Rate of Change (CP) Discovering Slope (L) Average Rate of Change (L) Key Features of Graphs (L)

F-IF Cell Phones (IM) F-IF Mathemafish Population (IM) F-IF Point on a Graph (IM)

F-IF The Customers (IM) F-IF Using Function Notation (IM) F-IF Yam in the Oven (IM)

Benchmark #1 (Units 1, 2 and Modules 5, 8, 9)

Benchmark #1 Testing Window: Nov. 7 – 18

N-Q.2

Define appropriate quantities for the purpose of descriptive

modeling. ★

A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on

coordinate plane 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-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. ★

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/content%20presentations/FamilyOfLinearFunctions.mov

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/EvaluatingLinearFunctions.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/content%20presentations/AverageRateOfChangeV1.mov

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/DiscoveringSlopeV1.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/AverageRateOfChange10062013v3.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/KeyFeaturesOfGraphsv1.pdf

https://www.illustrativemathematics.org/content-standards/HSF/IF/A/2/tasks/634













Unit 3:

(Nov. – Dec.)

Linear

Functions,

Equations,

and

Inequalities

(16 days)

Ending Dec. 2

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.

Find the y-intercept graphically and algebraically


Domain

Range

Proper Syntax Advantages of the various

forms of a linear function when graphing

Module 6

6.1 Slope-Intercept Form

Slope-Intercept Sort (L)

6.2 Point-Slope Form

Point-Slope Application Problems (L)

6.3 Standard Form

Three Forms of an Equation of a Line (L)

6.5 Comparing Properties of Linear

Functions

Family of Functions Graphing Worksheet

(GMR)

Shifting Linear Equations in Function Notation

(L)

F-LE Do two points always determine a Linear Function? (IM)

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.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. ★

F-IF.7a Graph linear and quadratic functions and show intercepts,

maxima, and minima. ★

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.

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SlopeInterceptSortV3.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/Alg1PointSlopeFLE2v2.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/ThreeFormsOfEquationLineV4.pdf


http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/ShiftingLinearEquationsInFunctionNotationV3.pdf










Unit 3:

(Nov. – Dec.)

Linear

Functions,

Equations,

and

Inequalities

(16 days)

Ending Dec. 2

F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) +

k, kf(x), f(kx), and f(x + k) for specific values of k (both

positive and negative); find the value of k given the

graphs. Experiment with cases and illustrate an

explanation of the effects on the graph using technology.

Proper Syntax


Represent Cost and Rate problems using a linear function

Compare linear rate functions to determine which real-world scenario has the better rate

Use a graph tool to find points of intersection


Accuracy in graphing linear inequalities


Advantages of the various forms of a linear function when graphing

Interpret rate of change algebraically, from a table, from a graph

Module 7 7.1 Modeling Linear Relationships

7.2 Using Functions to Solve One-Variable

Equations

7.3 Linear Inequalities in Two-Variables

Graphing Linear Inequalities Sort (L)

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 exponential functions

grow by equal factors over equal intervals. ★

b. Recognize situations in which one quantity changes at

a constant 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.5 Interpret the parameters in a linear or exponential

function in terms of a context. ★

[Linear and exponential of form f(x)=bx+k.]

S-ID.7 Interpret the slope (rate of change) and the intercept

(constant term) of a linear model in the context of the

data. ★

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/GraphingLinearInequalitiesV2.pdf






Essential Questions for this Unit: 1. How can students build upon prior experiences with data, and explore a more formal means of assessing how a model fits data? 2. How can students use graphical representations and knowledge of context to make judgements about the appropriateness of linear models?


Unit 4B:

(Nov. – Dec.)

Statistical

Models

(4 days)

Ending Dec. 12

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. ★

c. Fit a linear function for a scatter plot that

suggests a linear association. ★

Scatter Plot

Correlation

Correlation Coefficient

Best Fitting Line

Use a graphing calculator to find the “1-Variable Statistics” for a data set

Module 10

10.1 Scatter Plots and Trend Lines

Correlation and Line of Best Fit (L)

Units 3 & 4B Review and Assessment (2 days)

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. ★

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/CorrelationLineBestFit.pdf






Essential Questions for this Unit: 1. How can students build on their previous learning to solve linear equations in one variable and apply graphical and algebraic methods to analyze and solve

systems of linear equations in two variables? 2. How can students analyze and explain the process of solving an equation and justify the process used in solving a system of equations? 3. How can students explore systems of equations and inequalities, and find and interpret their solutions?


Unit 5A:

(Dec. – Jan.)

Linear

Systems

And

Piecewise-

Defined

Functions

(11 days)

Ending Jan. 13

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. ★

Connection between the solution to a system and the graph of the system

Accuracy and mastery when graphing

Infinitely Many Solutions vs. No Solution vs. One Solution

Solve systems using multiple methods

Build flexibility in solving systems

Estimating solutions to a system using a graphing calculator

Apply systems to real world context

Proper Syntax

Module 11

11.1 Solving Linear Systems by Graphing

Graphing Systems (L)

11.2 Solving Linear Systems by Substitution

Solving a System by Substitution (L)

11.3 Solving Linear Systems by Adding

11.4 Solving Linear Systems by Multiplying

First

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.

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.

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/GraphingSystemsV4.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SystemBySubstitutionV4.pdf






Essential Questions for this Unit: 1. How can students build on their previous learning to solve linear equations in one variable and apply graphical and algebraic methods to analyze and solve

systems of linear equations in two variables? 2. How can students analyze and explain the process of solving an equation and justify the process used in solving a system of equations? 3. How can students explore systems of equations and inequalities, and find and interpret their solutions?


Unit 5A:

(Dec. – Jan.)

Linear

Systems

And

Piecewise-

Defined

Functions

(11 days)

Ending Jan. 13

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.

Apply systems to real world context

Solution to a linear inequality is a shaded region that contains infinite solutions in that region

Module 12

12.1 Creating Systems of Linear Equations

12.2 Graphing Systems of Linear Inequalities

Solving Systems of Inequalities (L)

12.3 Modeling with Linear Systems

Unit 5A Review and Assessment (2 days)

End of Semester 1

F-LE.5

Interpret the parameters in a linear or exponential



F-IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value

functions. ★

F-LE.5




http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolvingSystemsOflinequalitiesV5.pdf






Essential Questions for this Unit: 1. How can students expand their experience with functions to include more specialized functions- absolute value, step and those that are piecewise-defined? 2. How can students explore piecewise-defined and absolute value functions; interpret functions graphically, numerically, symbolically, and verbally; translate

between representations; and understand the limitations of various representations? 3. How can students solve absolute value equations and inequalities graphically and algebraically, analyze and interpret solution?


Unit 5B:

(Jan. – Feb.)

Linear

Systems

And

Piecewise-

Defined

Functions

(9 days)

Ending Feb. 10

A-CED.1 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and

exponential functions. CA ★

Family of Functions and graphing transformations

Mathematical understanding of absolute value

Solve absolute value equations and inequalities both algebraically and graphically

Module 13

13.1 Understanding Piecewise-Defined

Functions

Graphing Piecewise Functions (L)

13.2 Absolute Value Functions and

Transformations

Family of Absolute Value Functions (CP)

13.3 Solving Absolute Value Equations

Absolute Value Equations & Inequalities (CP) 13.4 Solving Absolute Value Inequalities

F-IF Pizza Place Promotion (IM)

F-IF The Parking Lot (IM)

Unit 5B Review and Assessment (2 days)

A-REI.3.1 Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. CA

F-BF.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these

functions to the model. ★

F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) +




explanation of the effects on the graph using

technology.

F-LE.5




http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/GraphingPiecewiseFunctionsV1.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/content%20presentations/FamilyOfAbsoluteValueFunctions.mov

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/content%20presentations/AbsoluteValueEquationInequalities.mov

https://www.illustrativemathematics.org/content-standards/HSF/IF/B/tasks/578







Essential Questions for this Unit: 1. How can students extend the laws of exponents to strengthen their ability to see structure in and create quadratic expressions? 2. How can students use various methods to add, subtract and multiply polynomials?


Unit 7:

(February)

Polynomial

Operations

(9 days)

Ending Feb. 28

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. ★

Combine like terms

Algebra tiles

Area models

Area models using generic rectangle

Note: Unit 6 is after Unit 7

Module 17

17.1 Understanding Polynomial Expressions

17.2 Adding Polynomial Expressions

Algebra Tiles (CP)

17.3 Subtracting Polynomial Expressions

Module 18

18.1 Multiplying Polynomial Expressions by

Monomials

18.2 Multiplying Polynomial Expressions

Connecting Binomial Multiplication and Factoring Trinomials Using Algebra Tiles (L)

18.3 Special Products of Binomials


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

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.




http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/MultiplyingBinomialsFactoringTrinomialsV3.pdf







Essential Questions for this Unit: 1. How can students focus on quadratic functions; interpret given graphically, numerically, symbolically, and verbally; translate between representations; and

understand the limitations of various representations? 2. How can students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions, and in particular, identify the real

solutions of the quadratic equation as the zeros of the related quadratic function?


Unit 8:

(March)

Quadratic

Functions

(10 days)

Ending Mar. 16



Function Notation

Comparison of Linear vs. Exponential vs. Quadratic


Interpret Average Rate of Change

Proper Syntax

Graphing in vertex form and using symmetry

Build flexibility in graphing

Module 19

Exploring Quadratic Graphs (L)

19.1 Understanding Quadratic Functions

19.2 Transforming Quadratic Functions

Family of Quadratic Functions (CP)

Graphing Family of Functions (L)

Family of Functions Graphing Worksheet (GMR)

19.3 Interpreting Vertex Form and Standard

Form

Families of Functions Sort (L)

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. ★

b. Complete the square in a quadratic expression to reveal the maximum or minimum value 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 (1.151/12) 12t ≈ 1.01212t to reveal the approximate

equivalent monthly interest rate if the annual rate is 15%. ★

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.

A-REI.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)

2 = q that has the same solutions.

Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x

2 = 49), taking square roots, completing

the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation.

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/ExploringQuadraticGraphsV3.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/content%20presentations/FamilyOfQuadraticFunctions.mov

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/GraphingFamilyFunctionsV4.pdf


http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/FamiliesOfFunctionsSortV2.pdf










Unit 8:

(March)

Quadratic

Functions

(10 days)

Ending Mar. 16


functions. ★

Graphing using intercepts and symmetry

Comparison of Linear vs. Exponential



Build flexibility in solving quadratic equations

Recognize forms of quadratic equations

Solve quadratic equations using multiple methods

Derive the Quadratic Formula

Module 20

20.1 Connecting Intercepts and Zeros

Quadratics – Matching Game (L)

20.2 Connecting Intercepts and Linear Factors

20.3 Applying the Zero Product Property to

Solve Equations

A-SSE Graphs of Quadratic Functions (IM)

F-IF Which Function? (IM)


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;


F-IF.7a Graph linear and quadratic functions and show

intercepts, maxima, and minima. ★

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/MatchgameQuadractics.pdf

https://www.illustrativemathematics.org/content-standards/HSF/IF/C/7/tasks/388

https://www.illustrativemathematics.org/content-standards/HSF/IF/C/8/tasks/640










Unit 8:

(March)

Quadratic

Functions

(10 days)

Ending Mar. 16

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, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t , y = (0.97)t , y = (1.01)12t, and y = (1.2)t/10, and classify them as representing exponential growth or decay.

Graphing using intercepts and symmetry

Comparison of Linear vs. Exponential







Continue Module 19 and Module 20 Unit 8 Review and Assessment (2 days)

Benchmark #2 (Modules 6, 7, 10, and Units 5 and 8)

Benchmark #2 Testing Window: Mar. 20 – 30

Note: Begin Unit 9 prior to giving Benchmark #2

F-BF.1 Write a function that describes a relationship between

two quantities. ★

F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

F-LE.6 Apply quadratic functions to physical problems, such as

the motion of an object under the force of gravity. CA ★




Grade Level/Course Title: Algebra I Quarter 3-4 Academic Year: 2016-2017


Essential Questions for this Unit: 1. How can students create and solve equations, and systems of equations involving quadratic expressions? 2. How can students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions, and select

from these functions to model phenomena?


Unit 9:

(Mar. – Apr.)

Quadratic

Equations and

Modeling

(18 days)

Ending April 21


Multiple methods for factoring:

Area Models

Generic rectangles

Guess and check

Grouping


Module 21

21.1 Solving Equations by factoring cbxx 2

21.2 Solving Equations by factoring cbxax 2

21.3 Using Special Factors to Solve Equations

Connecting Binomial Multiplication and Factoring Trinomials Using Algebra Tiles (L)

Factoring Quadratics – Class Notes (GMR)

Factoring: GCF, Multiple Methods for Factoring Trinomials, Difference of Squares (CP)

A-SSE.3a Factor a quadratic expression to reveal the zeros

of the function it defines. ★

A-SEE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the

function it defines. ★

A-CED.2 Create equations in two or more variables to

represent relationships between quantities; graph

equations on coordinate plane axes with labels

and scales. ★

A-REI.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)

2 = q that has the

same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x

2 = 49), taking square roots,

completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation.

A-REI.7 Solve a simple system consisting of a linear

equation and a quadratic equation in two

variables algebraically and graphically.



http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/general%20mathematics%20resources/FactoringQuadraticsClassNotesV7.pdf












Unit 9:

(Mar. – Apr.)

Quadratic

Equations and

Modeling

(18 days)

Ending April 21

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;






Interpret average rate of change

Apply knowledge of quadratic functions to physical problems

Possible outcomes for Linear-Quadratic Systems: One Solution, Two Solutions, No Solution

Graphing Calculator investigations

Module 22

22.1 Solving Equations by Taking Square Roots

22.2 Solving Equations by Completing the Square

Quadratics: Completing the Square, Factoring, Quadratic Formulas, and Standard Form (CP)

22.3 Using the Quadratic Formula to Solve Equations

Derivation of Quadratic Formula (L)

22.4 Choose a Method for Solving Quadratic Equations

22.5 Solving Nonlinear Systems

Linear-Quadratic Systems (L)

Average Rate of Change (L)

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 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.

F-IF.8a

Use the process of factoring and completing the square in a quadratic function to show, extreme values, and symmetry of the graph, and interpret these in terms of a context.



http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/DerivationQuadraticForumalWorksheetsV2.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/LinearQuadraticSystemsV3.pdf










Unit 9:

(Mar. – Apr.)

Quadratic

Equations and

Modeling

(18 days)

Ending April 21

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 exponential functions grow by equal factors

over equal intervals. ★

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. ★

Key features of graphs

Comparisons between graphs

Recognizing Linear Models vs. Exponential Models vs. Quadratics Models


Module 23

23.2 Comparing Linear, Exponential, and Quadratic

Models

Average Rate of Change (L)

Comparing Linear and Quadratic Functions (L)

A-CED Throwing a Baseball (IM)

F-IF Throwing Baseballs (IM)


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. ★

F-LE.6 Apply quadratic functions to physical problems, such as the motion of an object under the force

of gravity. CA ★


http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/CompareLinearAndQuadraticFunctionsV1.pdf

https://www.illustrativemathematics.org/content-standards/HSA/CED/A/2/tasks/437







Essential Questions for this Unit: 1. How can students build upon their prior learning to extend the laws of exponents to rational exponents involving roots and apply this new understanding of

number; and strengthen their ability to see structure in and create exponential expressions? 2. How can students focus on exponential functions, including sequences; interpret functions graphically, numerically, symbolically, and verbally; translate between

representations; and understand the limitations of various representations? 3. How can students build on and extend their understanding of integer exponents to consider exponential functions, and compare and contrast linear and

exponential functions, distinguishing between additive and multiplicative change? 4. How cans students master solving linear equations and apply related techniques and laws of exponents to the creation and solution of exponential equations?


Unit 6:

(Apr. – May)

Exponential

Relationships

(18 days)

Ending May 19

N-RN.1 Explain how the definition of the meaning of rational

exponents follows from extending the properties of

integer exponents to those values, allowing for a

notation for radicals in terms of rational exponents.

For example, we define 51/3

to be the cube root of 5 because

we want (51/3

)3 = 5

(1/3)3 to hold, so (5

1/3)3 must equal 5.

Equivalent forms of one

Decomposition to simplify

Prime factors to simplify

Proper Syntax

Module 14

14.1 Understanding Rational Exponents and Radicals

14.2 Simplifying Expressions with Rational Exponents

Simplifying Radicals (L)

Properties of Exponents (CP)

Fractional Exponents (L)

Roots and Fractional Exponents (L) N-RN Evaluating Exponential Expressions (IM) N-RN Operations with Rational and Irrational Numbers (IM)

N-RN.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

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.

A-SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12) 12t ≈ 1.01212t to reveal the approximate equivalent

monthly interest rate if the annual rate is 15%. ★



http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SimplifyingRadicalsDay1V2.pdf


http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/FractionalExponents.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/RootsFractionalExponenetsV2.pdf

https://www.illustrativemathematics.org/content-standards/HSN/RN/A/1/tasks/1866

https://www.illustrativemathematics.org/content-standards/HSN/RN/B/3/tasks/690











Unit 6:

(Apr. – May)

Exponential

Relationships

(18 days)

Ending May 19


functions. ★

Domain of an exponential function vs. the domain of a geometric sequence

Graph of an exponential function vs. graph an of a geometric sequence

Explicit formula vs. recursive formula

Basic Understanding of the graph of a simple exponential function

Introduction to the concept of an asymptote

Accuracy when graphing

Key features of the graph



Module 15

15.1 Understanding Geometric Sequences

15.2 Constructing Geometric Sequences

Geometric Sequences (L)

15.3 Constructing Exponential Functions

15.4 Graphing Exponential Functions

Graphing Exponential Functions (L)

15.5 Transforming Exponential Functions

(optional)


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 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.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric

functions, showing period, midline, and amplitude. ★

(Exponential only in Alg. 1)

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/GeometricSequencesV4.pdf

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/GraphingExponentialFunctionsV1.pdf











Unit 6:

(Apr. – May)

Exponential

Relationships

(18 days)

Ending May 19

F-IF.8b

Use the properties of exponents to interpret expressions

for exponential functions.

For example, identify percent rate of change in functions such as

y = (1.02)t, y = (0.97)

t, y = (1.01)

12t, and y = (1.2)

t/10, and classify

them as representing exponential growth or decay.

Solve simple exponential equations by graphing or finding a common base

Property of Equality for Exponential Equations

Proper Syntax


Comparison of Exponential growth vs. decay

Comparison Linear vs. Exponential

Graphing Calculator investigation

Module 16 16.1 Using Graphs and Properties to Solve

Equations with Exponents

Solving Exponential Equations (L)

16.2 Modeling Exponential Growth and Decay

16.4 Comparing Linear and Exponential Models Average Rate of Change (L) F-BF Lake Algae (IM)

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.

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. ★

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and

relate these functions to the model. ★

F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to

model situations, and translate between the two forms. ★

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolveExponentialEquationsv1.pdf


https://www.illustrativemathematics.org/content-standards/HSF/BF/A/1/tasks/533











Unit 6:

(Apr. – May)

Exponential

Relationships

(18 days)

Ending May 19

F-BF.3

Identify the effect on the graph of replacing f(x) by f(x) +




explanation of the effects on the graph using technology.

Basic Understanding of the graph of a simple exponential function

Introduction to the concept of an asymptote

Accuracy when graphing

Key features of the graph



Comparison of Exponential growth vs. decay

Comparison Linear vs. Exponential


Continue Module 14, Module 15 and Module 16 Unit 6 Review and Assessment (2 days) Note: A week window is given for CAASPP State Testing before Unit 10

F-LE.1b Recognize situations in which one quantity changes at a

constant rate per unit interval relative to another. ★

F-LE.1c 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, quadratically, or (more generally) as a

polynomial function. ★






Essential Questions for this Unit: 1. How can students expand their experience with functions to include inverse functions, square root and cube root functions? 2. How can students focus on inverse functions; interpret inverse functions graphically, numerically, symbolically, and verbally; translate between representations;

and understand the limitations of various representations? 3. How can students restrict the domain of a function so that its inverse is also a function?


Unit 10:

(May – June)

Inverse

Relationships

(3 days)

Ending June 1

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. ★

Basic understanding of an inverse function

Relationship between a linear function and its inverse function

Inverse function notation

Basic understanding of graphing Square Root and Cube Root Functions


Key features of graphs

Comparisons between graphs

Interpret average rate of change when comparing functions


Module 24

24.2 Understand Inverse Functions

Inverse Functions (L)

F-BF Invertible or Not? (IM) F-BF US Households (IM) Review and Assessment (1 day)

End of Semester 2

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 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-BF.4a Solve an equation of the form f(x) = c for a

simple function f that has an inverse and write

an expression for the inverse. For example,

f(x) =2x3 or f(x) = (x + 1)/(x − 1) for x ≠ 1.

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/InverseFunctions201314v1.pdf

https://www.illustrativemathematics.org/content-standards/HSF/BF/B/4/tasks/1374

https://www.illustrativemathematics.org/content-standards/HSF/BF/B/4/tasks/234

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Hayward Unified School District Algebra I Mathematics ... · Hayward Unified School District Algebra I Mathematics Curriculum Guide Unit Map Online Resources: GMR=General Math Resource