algebra 1 - tn ready performance standards by unit algebra ......algebra 1 - tn ready performance...

Algebra 1 - TN Ready Performance Standards by Unit

Maury County Public Schools 5/8/18 Office of Instruction Pk-12

Algebra 1 – Curriculum Overview

The following Practice Standards and Literacy Skills will be used throughout the course:

Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency

1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies.

2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary.

3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas.

4. Model with mathematics. 4. Write mathematical arguments.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Ongoing Standards

• I can differentiate between linear, exponential, quadratic, absolute value, square root, and cube root functions by identifying key features in graphs and tables.

• I can move fluently between different representations of numbers, such as graphs, tables and equations.

• I can identify key features in graphs and tables if given the following types of functions: linear, quadratic, absolute value, exponential and piecewise.



Q1 - 1st Nine Weeks (44 days) Q2 - 2nd 9Weeks (39 days)

Unit 1 # Days=18

Unit 2 # Days=11

Unit 3 # Days=16

Unit 4 # Days=7

Unit 5 # Days= 14

Unit 6 # Days= 18

Quantities & Modeling Relations & Functions Linear Functions Piecewise & Step

Functions

Systems of Equations

& Inequalities

Geometric Sequences

& Exponential

Functions

A1.A.REI.A.1

A1.A.SSE.A.1a

A1.A.CED.A.1

A1.A.REI.B.2

A1.A.CED.A.4

A1.A.CED.A.3

A1.N.Q.A.1

A1.N.Q.A.2

A1.N.Q.A.3

(see footnote on unit 7)

(A.REI & A.CED are

25-33% of test)

A1.F.IF.B.3

A1.F.IF.A.1

A1.F.IF.A.2

A1.F.IF.B.4

A1.F.IF.B.5

A1.F.IF.C.6b

A1.F.BF.B.2

(25-33% of test from

F.IF & F.BF & F. LE)

A1.A.CED.A.2

A1.S.ID.C.5

A1.F.IF.B.4

A1.F.IF.B5

A1.F.BF.A.1

A1.F.LE.A.1

A1.F.LE.A.2

A1.F.LE.B.4

A1.F.IF.C.6a

A1.F.BF.B.2



(9-15% will be from

S.ID)

A1.F.IF.C.6

A1.A.CED.A.3

A1.A.REI.D.5

A1.A.REI.D.6

A1.A.REI.D.7

A1.F.IF.B.4

A1.A.REI.C.4

(A.REI & A.CED are

25-33% of test)

7.1, 7.3, 7.4, 7.5

8.EE.A.1 8.WCE.6 A1.A.SSE.B.3c

A1.F.IF.B.4

A1.F.LE.A.1

A1.F.LE.A.2

A1.F.LE.A.3



Gray = Major Content O: On-going standard On-going standards are continually instructed and assessed throughout the year.

E: Standard explicity instructed E standards are introduced and taught with explicit, direct instruction.



M: Standard instructed and assessed M indicates mastery, through re-teaching and assessments are expected through the end of the school

year.

Highlighted standards: Highlighted standards are identified as Power-Standards, based on TN Ready blueprints.

Q3 – 3rd Nine Weeks (44 DAYS) Q4 – 4th 9 Weeks (8 DAYS) **Remaining days to be used for EOC

Review!

After the EOC

Unit 7 # Days =22

Unit 8 # Days=20

Unit 9 # Days = 8

WE WILL HAVE BETWEEN 10 –15

DAYS TO COVER MATERIAL

Polynomial Operations & Factoring Quadratic Functions Statistical Models + Scatterplots &

Regression

A1.A.SSE.A.1

A1.A.APR.A.1

A1.A.SSE.A.2

(18-25% of test from A.SSE & A.APR

standard along with N.Q standard)

A1.A.SSE.B.3

A1.A.REI.B.3

A1.F.IF.B.4

A1.F.IF.C.6a

A1.F.IF.C.7

A1.F.IF.C.8

A1.F.BF.B.2

A1.A.APR.B.2

(25-33% of test from F.IF & F.BF &

F. LE)

A1.S.ID.A.1

A1.S.ID.A.2

A1.S.ID.A.3

A1.S.ID.B.4

A1.S.ID.C.6

A1.S.ID.C.7

(9-15% of test will be S.ID standard)

Radical Expressions and equations

Rational Expressions and equations

Gray = Major Content O: On-going standard On-going standards are continually instructed and assessed throughout the year.

E: Standard explicity instructed E standards are introduced and taught with explicit, direct instruction.



M: Standard instructed and assessed M indicates mastery, through re-teaching and assessments are expected through the end of the school

year.

Highlighted standards: Highlighted standards are identified as Power-Standards, based on TN Ready blueprints.

Unit 1 Quantities & Modeling

#of Days = 18 Standards “I Can” Statements

Number and Quantity

A1.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.

I can give the solution of an equation using the correct units. I can convert unit rates of measurements in multistep arithmetic problems. For example, feet per second to miles per hour.

A1.N.Q.A.2 ★Identify, Interpret, and justify appropriate quantities for the purpose of descriptive modeling.

I can define appropriate quantities. I can use the scale to read the data correctly.

A1.N.Q.A.3 ★Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

I can determine the accuracy of values based on their limitations in the context of the situation.

Algebra

A1.A.REI.A.1 Explain each step in solving an 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.

I can solve a simple equation and justify each step using properties.

A1.A.SSE.A.1 ★ Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients.

I can define and recognize parts of an expression, such as terms, factors, and coefficients for expressions that represent a contextual quantity. I can interpret parts of an expression, such as terms, factors, and coefficients in terms of the context for expressions that represent a contextual quantity.

A1.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.

I can solve multi-step equations and equations with variables on both sides. I can recognize and explain when 1 solution, no solution, or infinite solutions are the result of solving an equation. I can create linear equations and inequalities in one variable and use them in a contextual situation to solve problems.



A1.A.REI.B.2 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

I can solve linear equations in one variable, including those with coefficients represented by letters. I can solve and graph multi-step & compound linear inequalities in one variable, including those with coefficients represented by letters. I can solve inequalities in one variable and use them in a contextual situation to solve problems.

A1.A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

I can describe the calculations needed to model a function between two quantities. I can write equations to solve contextual problems that involve distance/time/rate, mixture, consecutive integers, and cost. I can solve multi-variable formulas or literal equations for a specific variable

A1.A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Clarification: For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

I can take a real- world problem and use equations and inequalities to write constraints. I can interpret solutions as viable or nonviable options in a modeling context.

Functions

Statistics and Probability



Unit 1 Quantities & Modeling

#of Days = 18

Sections/Topics Essential Vocabulary Activities/Resources/Materials

• Pre-assessment

• Translate Between Words and

Algebra & Classifying Numbers.

• Simplifying Expressions

(Distributive Prop. & Combine

Like Terms)

• Solve one-step equations & one-

step inequalities (graph solutions)

by addition or subtraction.

• Solve one-step equations & one-

step inequalities (graph solutions)

by multiplication or division

• Solve Equations in one variable that

contain more than one operation

(variables on same side).

• Solve Inequalities in one variable

that contain more than one

operations (variables on same side)

and graph the solutions.

• Solve equations that contain

variable terms on both sides.

• Solve inequalities that contain

variable terms on both sides and

graph the solutions.

• Solve for a given variable (ie. Solve

for y = mx + b)

• Solve absolute value equations.

• Absolute Value

• Additive Inverse

• Algebraic

Expression

• Base

• Coefficient

• Compound

Inequality

• Constant

• Cube Root

• Equation

• Evaluate

• Exponent

• Formula

• Inequality

• Integers

• Intersection

• Irrational Number

• Like Terms

• Literal Equation

• Multiplicative

Inverse

• Natural Numbers

• Perfect Square

• Power

• Rational Number

• Real Number

• Reciprocal

• Solution of Equation

• Solution of

Inequality

• Square Root

• Term

• Union

Resources Found On High School and 8th Grade Sharepoint

• What’s My Number

• Video Game

• New York Location

• Ladder Length

• Building Equations with M&M’s

• Just Jogging

• Resistance

• Literal Equations Applications

Short Tasks (Found on www.mathshell.org)

• A19: Leaky Faucet

• A24: Yogurt

• Creating Equations (Parts 1, 2)

• Reasoning With Equations and Inequalities (Part 6)

Illustrative Math:

• Fishing Adventures 3

• Bernardo and Silvia Play a Game

• Reasoning With Linear Inequalities

CCAs

• Rational and Irrational Numbers 1

• Sorting Equations and Identities

• Interpreting Algebraic Expressions

• Solving Linear Equations in One Variable

Extra Resources

• https://www.tenmarks.com/

• https://www.powerschool.com/

• http://www.jmap.org/JMAP_RESOURCES_BY_TOPIC.htm#A2T

• https://emathinstruction.com/

• https://www.illustrativemathematics.org/ • https://www.opened.com/

http://www.mathshell.org/

http://map.mathshell.org/tasks.php?unit=HA19&collection=9


http://map.mathshell.org/tasks.php?collection=9&unit=HN04#task292

http://map.mathshell.org/tasks.php?collection=9&unit=HN05#task293

https://www.illustrativemathematics.org/content-standards/HSA/CED/A/3/tasks/644


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

http://map.mathshell.org/lessons.php?unit=9105&collection=8




https://www.tenmarks.com/

https://www.powerschool.com/

http://www.jmap.org/JMAP_RESOURCES_BY_TOPIC.htm#A2T

https://emathinstruction.com/

https://www.illustrativemathematics.org/

https://www.opened.com/



• Solve compound inequalities with

one variable.

• Solve absolute value inequalities

and graph the solutions.

• 1 quiz (Placement within the unit is

your choice)

• Unit Review

• Unit Test

• Variable

• Whole Number

• https://www.khanacademy.org/

• https://www.ixl.com/

• http://www.shodor.org/interactivate/

• Kuta Software (Drill and Practice)

• Questar Classroom Assessment Builder

https://www.khanacademy.org/

https://www.ixl.com/

http://www.shodor.org/interactivate/



Unit 2 Relations & Functions

# of Days = 11 Standards “I Can” Statements

Number and Quantity

Algebra

Functions

A1.F.IF.B.3 ★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. Clarification: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

I can determine from context if a graph should be discrete or continuous. I can, given a linear function, identify key features in graphs and tables including: intercepts, intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries; end behavior. I can interpret and explain features of the graph of the function in terms of the context of the problem. I can sketch a graph if given the key features of a function

A1.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).

I can (given the function f(x)) identify x as an element of the domain, the input, and f(x) is an element in the range, the output. I can know that the graph of the function, f, is the graph of the equation y=f(x). I can write an expression in function notation. I can represent a relation in different formats (graph, table, list, and mapping). I can determine whether or not a relation is a function and use the f(x) notation.

A1.F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

I can use function notation to express a contextual problem. I can evaluate functions for inputs in their domain. I can interpret statements that use function notation in terms of the context in which they are used.



A1.F.IF.B.4 ★Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Clarification: For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

I can (given the graph) choose the practical domain of the function as it relates to the numerical relationship it describes. I can describe a situation that matches a graph based on its shape. I can explain when a relation is determined to be a function, use f(x) notation. I can state the appropriate domain of a function that represents a problem situation, defend my choice, and explain why other numbers might be excluded from the domain.

A1.F.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

I can identify key features of an absolute value function, by looking at the graph, a table of values, or the equation. I can graph absolute value functions. I can identify the parent function of an absolute value graph as f(x)=|x|. I can identify transformations of an absolute value function from the parent function by looking at the graph or the equation.

A1.F.BF.B.2 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Clarification: i) Identifying the effect on the graph of replacing f(x) by f(x) + k, k f(x), and f(x+k) for specific values of k (both positive and negative) is limited to linear, quadratic, and absolute value functions. ii) f(kx) will not be included in Algebra 1. It is addressed in Algebra 2. iii) Experimenting with cases and illustrating an explanation of the effects on the graph using technology is limited to linear functions, quadratic functions, absolute value, and exponential functions with domains in the integers. iv) Tasks do not involve recognizing even and odd functions

I can transform absolute value functions. I can use technology to experiment with the graphs of various functions when transforming the equations using different values of k. I can form conjectures based on my experiments with substituting different values into the general (parent) functions.




Unit 2 Relations & Functions

# of Days = 11


• Pre-assessment

• Introduction to Functions: Review

plotting points, coordinate planes,

generating ordered pairs given a

function.

• Match simple graphs with

situations.

• Identify functions, find the domain

and range of relations and

functions

• Identify independent and

dependent variables, write

equations based on real world

scenarios, evaluate a function for a

given input value.

• Graphing Functions

• Unit Review

• Unit Test

• Axis/Axes

• Continuous Graph

• Coordinate Plane

• Correlation

• Dependent Variable

• Discrete Graph

• Domain

• Function

• Function Notation

• Function Rule

• Independent

• Input

• Variable

• Negative Correlation

• No Correlation

• Ordered Pair

• Origin

• Output

• Positive Correlation

• Quadrant

• Range

• Relation

• Scatter Plot

• Sequence

• Term

• Trend Line

• x-axis

• x-coordinate

• y-axis

• y-coordinate


• From Wonderland to Function Land


• N06: Interpreting Functions

CCAs

• Interpreting Distance-Time Graphs

Illustrative Math

• Interpreting the Graph (4-3)

• Influenza Epidemic

Extra Resources












http://map.mathshell.org/tasks.php?unit=HN06&collection=9


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













Unit 3 Linear Functions


Number and Quantity

Algebra

A1.A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales.

I can create equations in two or more variables to represent relationships between quantities. I can graph equations in two variables on a coordinate plane and label the axes and scales. I can decide which functions are relatively easy to sketch accurately by hand and which should be graphed using technology.

Functions

A1.F.BF.A.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.

I can determine if a sequence is arithmetic or not. I can use tables, graphs and expressions to model situations. I can write an algebraic expression or equation to generalize the pattern in a table. I can find the common difference in an arithmetic sequence. I can write an arithmetic sequence using both an explicit and recursive rule. I can identify patterns and write an explicit expression using context.

A1.F.LE.A.1 ★Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Recognize 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.

I can describe whether a given situation in question has a linear pattern of change or a nonlinear pattern of change. I can show that linear functions change at the same rate over time. I can describe situations where one quantity changes at a constant rate per unit interval as compared to another.



c. Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another.

A1.F.LE.A.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.)

I can write an arithmetic sequence, given either the first few terms of a sequence, a graph of the sequence, two terms in the sequence, or a table of values of the sequence. I can graph an arithmetic sequence and identify it as a discrete, linear function

A1.F.LE.B.4 ★Interpret the parameters in a linear or exponential function in terms of a context. Clarification: For example, the total cost of a plumber who charges 50 dollars for a house call and 85 dollars per hour would be expressed as the function y= 85x +50. If the rate were raised to 90 dollars per hour, how would the function change?

I can explain the meaning of the coefficients, factors, exponents, and/or intercepts in a linear function based on the context of a situation.

A1.F.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

I can determine the parent function for the line f(x) = x. I can identify and compare the different forms of linear functions. (point-slope, standard, slope-intercept) I can identify the intercepts of a function. I can compare the key features of two linear functions represented in different ways. I can describe a line as a translation of the parent function y = x.

A1.F.BF.B.2 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Clarification: i) Identifying the effect on the graph of replacing f(x) by f(x) + k, k f(x), and f(x+k) for specific values of k (both positive and negative) is limited to linear, quadratic, and absolute value functions. ii) f(kx) will not be included in Algebra 1. It is addressed in Algebra 2. iii) Experimenting with cases and illustrating an explanation of the effects on the graph using technology is limited to linear functions, quadratic functions, absolute value, and exponential functions with domains in the integers. iv) Tasks do not involve recognizing even and odd functions.

I can transform linear functions. I can find the value of k, given the graphs of a parent function, f(x), and the transformed function: f(x) + k, k f(x), or f(x + k). I can use technology to experiment with the graphs of various functions when transforming the equations using different values of k and form conjectures based on those experiments. I can identify the effect on the graph given a single transformation on a function (symbolic or graphic).



A1.F.IF.B.5 ★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.

I can explain the connection between average rate of change and the slope formula. I can estimate the average rate of change over a specified interval of a function presented either algebraically, in a table, or from the function’s graph. I can interpret the meaning of the average rate of change (using units) as it relates to a real-world problem. I can compare the rates of change of two or more functions when represented with function notation, with a graph, or with a table.


I can (given a linear graph) choose the practical domain of the function as it relates to the numerical relationship it describes. I can state the appropriate domain of a linear function that represents a problem situation, defend my choice, and explain why other numbers might be excluded from the domain.


A1.S.ID.C.5 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

I can explain the meaning of the slope in terms of the units stated in the data. I can explain the meaning of the y-intercept in terms of the units stated in the data. I can show that a linear function has a constant rate of change. I can describe and explain the difference between having no slope and having zero slope. I can predict and articulate what happens when the slope changes and/or y-intercept changes.



Unit 3 Linear Functions

# of Days = 16


• Pre-assessment

• Recognize and extend an arithmetic

sequence

• Identify linear functions. Graph

linear functions that represent real

world situations and give their

domain and range.

• Find x and y intercepts and

interpret their meaning in real-

world situations. Use x and y

intercepts to graph lines.

• Find slope using the slope formula.

• Find rates of change. Explain the

meaning of a rate of change in

context to a real-world problem.

• Write a linear equation in slope

intercept form.

• Transforming Linear Functions.

• Parallel and Perpendicular lines.

(Write an equation of a the line that

passes through a point and is

parallel or perpendicular to a given

line)

• Arithmetic Sequence

• Common Difference

• Constant of

Variation

• Direct Variation

• Domain

• Linear Equation

• Linear Function

• Midpoint

• Parallel Lines

• Parent Function

• Perpendicular Lines

• Range

• Rate of Change

• Reflection

• Rise

• Rotation

• Run

• Slope

• Slope-Intercept

Form

• Transformation

• Translation

• X-intercept

• Y-intercept


• Parallel Lines with Cabri Jr.

• Algebra Walk

• Fun with Wikki Stix

• How Deep

• Battery Power (CBL)

• Distance Match and Walking Rates

• Walk for Charity

• Ball Drop

• Bungee Jumping

• Linear Motion


• N06: Interpreting Functions

Illustrative Math:

• Transforming the Graph of a Function

• The Restaurant

• Mathmefish Population

CCAs


• Matching Situations, Graphs and Linear Equations

• Comparing Lines and Linear Equations

Extra Resources










https://www.illustrativemathematics.org/content-standards/HSF/BF/B/3/tasks/742

https://www.illustrativemathematics.org/content-standards/HSF/IF/B/5/tasks/2161

https://www.illustrativemathematics.org/content-standards/HSF/IF/B/6/tasks/686














• 1 quiz (Placement within the unit is

your choice)

• Unit Review

• Unit Test







Unit 4 Piecewise & Step Functions


Number and Quantity

Algebra

Functions

A1.F.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

I can graph square root, cube root, and piecewise functions including step and absolute value. I can evaluate a piecewise function for specific inputs from looking at the graph or by using the equation. I can graph piecewise functions given the equation.




Unit 4 Piecewise Functions

# of Days = 7 Sections/Topics Essential Vocabulary Activities/Resources/Materials

• Pre-assessment

• Identifying Piecewise functions,

evaluating piecewise functions,

interpreting domain and range.

• Graphing piecewise functions and

relating to real-world scenarios.

• Unit Review

• Unit Test

• Piecewise Function

• Parent Function

• Domain

• Range


•


•

CCAs

•

Extra Resources

• https://www.tenmarks.com/ • https://www.powerschool.com/





















Unit 5 Systems of Equations & Inequalities

# of Days = 14

Standards “I Can” Statements

Number and Quantity

Algebra

A1.A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Clarification: For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

I can write and use a system of equations and/or inequalities to solve a real world problem. I can represent constraints by equations or inequalities and by systems of equations and/or inequalities. I can interpret solutions as viable or nonviable options in a modeling context. I can solve systems of equations and inequalities with and without technology.

A1.A.REI.D.5 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).

I can explain that all solutions to an equation in two variables are contained on the graph of that equation.

A1.A.REI.D.6 ★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 approximate solutions using technology. Clarification: Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential functions. For example, f(x) = 3x + 5 and g(x) = x^2 + 1. Exponential functions are limited to domains in the integers.

I can explain why the intersection of y=f(x) and y=g(x) for any linear function. (I can find the solutions by using technology to graph the equations and determine their point of intersection, using tables of values, or using successive approximations that become closer and closer to the actual value.)

A1.A.REI.D.7 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.

I can graph linear inequalities on the coordinate plane and describe the meaning of the solution set. I can graph the solutions to a linear inequality in two variables as a half-plane, excluding the boundary for non-inclusive inequalities I can graph the solution set to a system of linear inequalities in two variables as the intersection of their corresponding half-planes.

A1.A.REI.C.4 Write and solve a system of linear equations in context. I can graph a system of equations and determine its solution. I can use technology to solve a linear system graphically. I can solve a system of equations algebraically, by using substitution and elimination.



I can solve a system of linear equations in two variables graphically. I can determine if a linear system has no solution, 1 solution of infinite solutions. I can choose the best method for solving a linear system, and I can justify my method.


I can state the appropriate domain of a function that represents a problem situation, defend my choice, and explain why other numbers might be excluded from the domain.

Functions




Unit 5 Systems of Equations & Inequalities

# of Days =14 Sections/Topics Essential Vocabulary Activities/Resources/Materials

• Pre-assessment

• Solve Systems of Equations by

graphing

• Solve systems of equations by

elimination

• Solving systems of equations real-

world scenarios

• Graph linear inequalities in two

variables. Determine whether an

ordered pair is a solution to a

linear inequality.

• Graph systems of linear

inequalities in two variables.

Determine whether and ordered

pair is a solution to the system.

• 1 Quiz (Placement within unit is

your choice).

• Unit Review

• Unit Test

• Consistent System

• Dependent System

• Elimination

• Inconsistent System

• Independent System

• Linear Inequality

• Solution of a Linear

Inequality

• Solution of a System

of a Linear Equations

• Solution of a System

of Linear Inequalities

• Substitution

• System of Linear

Equations

• System of Linear

Inequalities


• Escape from the Tomb

• Round Robin

• Measuring with Unknown values

• Sorting Pennies


• N05: Reasoning with Equations and Inequalities

• Printing Tickets

Illustrative Math:

• Growing Coffee

CCAs

• Solving Linear Equations in Two Variables

• Representing Inequalities Graphically

Extra Resources

• https://www.tenmarks.com/ • https://www.powerschool.com/


























Unit 6 Geometric Sequences & Exponential Functions

# of Days = 18


Number and Quantity

Algebra

8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

For example, 3 2 x 3 −5 = 3 −3 = 1

33=

1

27.

I can apply properties of integer exponents to generate equivalent numerical expressions.

8.WCE.6 Apply properties of exponents to include variable expressions. For example, (2m3) (3m4 ).

I can multiply and divide variable expressions with exponents to generate equivalent expressions.

A1.A.SSE.B.3c Use the properties of exponents to rewrite exponential expressions. Clarification: For example, the growth of bacteria can be modeled by either f(t) = 3(t+2) or g(t) = 9(3t) because the expression 3(t+2) can be rewritten as (3t)(32) = 9(3t).

I can define an exponential function as f(x)=abx. I can rewrite exponential functions using the properties of exponents. I can use properties of exponents, including rational exponents (such as power of a power, product of powers, power of a product, and rational exponents, etc…) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay (including negative and zero exponents). I can write exponential functions to represent growth and decay.

Functions

A1.F.LE.A.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).

I can identify a sequence as being geometric. I can identify the common ratio of a geometric sequence. I can write the explicit and recursive rule for a geometric sequence, given either the sequence, a graph of the sequence, a table of values, or two consecutive terms in the sequence.



I can differentiate between an arithmetic and geometric sequence, based on if the sequence has a common difference or common ratio between successive terms. I can create linear and exponential functions, from a simple context, given the following situations: arithmetic and geometric sequences, a graph, a description of a relationship, and two points which can be read from a table.


I can (given an exponential graph) choose the practical domain of the function as it relates to the numerical relationship it describes. I can describe a situation that matches a graph based on its shape. I can state the appropriate domain of a function that represents a problem situation, defend my choice, and explain why other numbers might be excluded from the domain.

A1.F.LE.A.1 ★Distinguish between situations that can be modeled with linear functions and with exponential functions. a) Recognize 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 factor per unit interval relative to another.

I can describe whether a given situation in question has a linear pattern of change or an exponential pattern of change. I can show that linear functions change at the same rate over time and that exponential functions change by equal factors over time. I can describe situations where one quantity changes at a constant rate per unit interval as compared to another. I can describe situations where a quantity grows or decays at a constant percent rate per unit interval as compared to another. I can determine if a table of values is linear, exponential, or quadratic. I can write an equation in the appropriate form given a table of values or a graph of the equation.

A1.F.LE.A.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.

I can make the connection using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any other polynomial function.




Unit 6 Geometric Sequences and Exponential Functions

# of Days = 18


• Pre-assessment

• Evaluate and Simplify expressions

containing zero and integer

exponents

• Multiplication Properties of

Exponents

• Division Properties of Exponents

• Rational Exponents & Square Roots

• Recognize and extend Geometric

Sequences. Find the nth term of a

geometric sequence.

• Evaluate exponential functions.

Identify and graph exponential

functions.

• Exponential Growth (including

Compound Interest) and Decay

(Including Half-Life)


your choice)

• Unit Review

• Unit Test

• Common Ratio

• Compound Interest

• Cubic

• Exponential Decay

• Exponential Growth

• Extraneous Solution

• Geometric Sequence

• Half-Life

• Index

• Square-Root


• Overrun by Skeeters

• Get a Half Life

• Falling Balconies

• Tower of Hanoi

• Paper Folding

• Applications Involving Interest

• Skeeters


• A20: Multiplying Cells

• N08: Linear and Exponential Models

• Table Tiling

• Sorting Functions

Illustrative Math:

• Exponential Parameters

CCAs

• Modeling Population Growth: Having Kittens

• Estimating Length Using Scientific Notation

Extra Resources














http://map.mathshell.org/tasks.php?unit=HE11&collection=9


https://www.illustrativemathematics.org/content-standards/HSF/BF/A/tasks/2116














Unit 7 Polynomials & Factoring

# of Days = 22


Number and Quantity

Algebra

A1.A.SSE.A.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.

I can decompose polynomial expressions and make sense of multiple factors and terms by explaining the meaning of the individual parts focusing on quadratic and exponential expressions.

A1.A.APR.A.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

I can add, subtract, and multiply polynomials. I can classify a polynomial based on its number of terms, as well as identify the degree, the leading coefficient, and the constant term.

A1.A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

I can rewrite algebraic expressions in different equivalent forms such as combining like terms, using the distributive property, and factoring. I can factor using greatest common factors and grouping. I can factor a trinomial with a leading coefficient of 1. I can factor a trinomial with a leading coefficient other than 1. I can factor using the difference of two squares. I can factor perfect square trinomials. I can choose the appropriate methods for factoring a polynomial.

Functions




Unit 7 Polynomials & Factoring

# of Days = 22


• Pre-assessment

• Classify polynomials. Arrange

polynomials into descending order.

• Add and Subtract Polynomials

• Multiplying Polynomials (mono x

mono, mono x bi, FOIL, bi x tri) (2

days)

• GCF and Factoring by GCF and

Factoring by Grouping (3 days)

• Factoring ax2 + bx + c (3 days)

• Factoring Special Products

• Choosing a Factoring Method


your choice)

• Unit Review

• Unit Test

• Binomial

• Cubic

• Degree of a

Monomial

• Degree of a

Polynomial

• Difference of two

squares

• Greatest Common

Factor

• Leading Coefficient

• Monomial

• Perfect-Square

Trinomial

• Polynomial

• Prime Factorization

• Quadratic

• Standard Form of a

Polynomial

• Trinomial


• Representing anf Manipulating Polynomials (Tiles and

Technology)

• Southern Yards and Gardens

• Tiling Pools Learning Task

• I’ve Got Your Number

• Zoom Algebra

• Building Rectangles With a Fixed Area


• Seeing Structure in Expressions Part 3

• A02: Patchwork

• N04: Creating Equations

CCAs


• Generating Polynomials From Patterns

Extra Resources




























Unit 8 Quadratic Functions

# of Days = 20


Number and Quantity

Algebra

A1.A.APR.B.2 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.

I can find the zeros of a polynomial when the polynomial is factored. I can use the zeros of a function to sketch the graph of the function

A1.A.REI.B.3 Solve quadratic equations and inequalities in one variable. a. Use the method of completing the square to rewrite 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 x2 = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions.

I can transform a quadratic equation written in standard form to an equation in vertex form (x – p)2 = q by completing the square (only with a leading coefficient of 1.) I can derive the quadratic formula by completing the square on the standard form of a quadratic equation. I can recognize that a quadratic will have non-real solutions when there is a negative under the radical. I can solve quadratic equations by taking square roots. I can understand why taking the square root of both sides of an equation yields two solutions. I can solve quadratic equations by completing the square. I can solve quadratic equations by factoring. I can use the quadratic formula to solve any quadratic equation, recognizing the formula produces all complex solutions. I can compute the discriminants and interpret the results as having no real solutions, 1 real solution, or 2 real solutions.

A1.A.SSE.B.3★ Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

I can complete the square to rewrite a quadratic expression (ax2+bx+c) with the form a(x-h)2 +k.



I can recognize the connection among factors, solutions (roots), zeros of related functions, and x-intercepts in quadratic functions. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression in the form AX2 + Bx + C where A = 1 to reveal the maximum or minimum value of the function it defines.

I can predict whether a quadratic will have a minimum or a maximum based on the value of a.

Functions

A1.F.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

I can graph quadratic functions and show intercepts, maxima, and minima. I can identify the axis of symmetry, vertex, and intercepts of a quadratic from the graph of the quadratic. I can algebraically find the axis of symmetry, vertex, and intercepts of a quadratic when given the equation in standard form. I can identify the parent function of a quadratic as f(x)=x2 I can identify the transformations of a quadratic function when compared to the parent function.

A1.F.IF.C.7 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a) Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

I can use the process of factoring and completing the square in a quadratic function to determine the vertex, axis of symmetry, direction of opening, and zeros/roots from the graph of a quadratic function. I can graph a quadratic function from standard and vertex form. I can describe all of the properties of a quadratic function.

A1.F.BF.B.2 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Clarification: i) Identifying the effect on the graph of replacing f(x) by f(x) + k, k f(x), and f(x+k) for specific values of k (both positive and negative) is limited to linear, quadratic, and absolute value functions. ii) f(kx) will not be included in Algebra 1. It is addressed in Algebra 2. iii) Experimenting with cases and

I can transform a variety of functions including linear, quadratic, and absolute value. I can use technology to experiment with the graphs of various functions when transforming the equations using different values of k. I can form conjectures based on my experiments with substituting different values into the general (parent) functions.



illustrating an explanation of the effects on the graph using technology is limited to linear functions, quadratic functions, absolute value, and exponential functions with domains in the integers. iv) Tasks do not involve recognizing even and odd functions.

A1.F.IF.C.8 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

I can use a variety of function representations (algebraically, graphically, numerically in tables, or by verbal descriptions) to compare and contrast properties of two functions.

A1.F.IF.B.4 ★Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Clarification: For example, if the function h(n) gives the number of person hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

I can (given the graph) choose the practical domain of the function as it relates to the numerical relationship it describes. I can describe a situation that matches a graph based on its shape. I can explain when a relation is determined to be a function, use f(x) notation. I can state the appropriate domain of a function that represents a problem situation, defend my choice, and explain why other numbers might be excluded from the domain.




Unit 8 Quadratic Functions

# of Days = 20


• Pre-assessment

• Identify Quadratic Functions and

determine characteristics of

quadratic functions. (3 days)

• Graphing Quadratic Functions

• Transform quadratic functions.

• Solve quadratic functions by

graphing.


factoring.

• Solve quadratic functions using

square roots.


completing the square (2 days)

• Solve quadratic functions using the

Quadratic Formula. (2 days).

**If time add NON-linear systems of

equations.


your choice)

• Unit Review

• Axis of Symmetry

• Completing the

Square

• Discriminant

• Maximum

• Minimum

• Parabola

• Quadratic Equation

• Quadratic Function

• Quadratic Formula

• Solution of a

Quadratic Function

• Transformation

• Vertex

• Zero of a Function


• Traffic Jam

• Quadratic Function Characteristics

• Ball Toss

• Discriminant Card Match

• Function Card Match

• Quadratic Function Family

• Wylie Coyote


• Creating Equations #4

• Patchwork

• Skeleton Tower

• Functions

• Sorting Functions

• Seeing Structure in Expressions Part 4

• Building Functions • Sidewalk Stones

Illustrative Math:

• Seeing Dots

CCAs

• Representing Quadratic Functions Graphically

• Solving Quadratic Equations

Extra Resources




























• Unit Test









Unit 9

Statistical Models + Scatterplots & Regression


Number and Quantity

Algebra

Functions


A1.S.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

histograms, and box plots). I can construct dot plots, histograms, and box plots for data on a real number line. I can make predictions based on graphs and data sets. I can construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-andwhiskers, stem-and-leaf, and frequency tables).

A1.S.ID.A.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.

I can describe a situation using center and spread. I can use the correct measure of center and spread to describe a distribution that is symmetric or skewed. I can identify outliers (extreme data points) and their effects on data sets. I can compare two or more different data sets using the center and spread of each.

A1.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

I can interpret differences in data sets in context. I can interpret differences due to possible effects of outliers. I can identify a set of data as being skewed left, skewed right, or having a normal distribution. I can find and interpret the population standard deviation of a set of data.



I can use the bell curve to analyze data distributions.

A1.S.ID.B.4 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. b. Fit a linear function for a scatter plot that suggests a linear association.

I can determine when linear, quadratic, and exponential models should be used to represent a data set. I can determine whether linear and exponential models are increasing or decreasing. I can determine the relationship shown in a scatterplot. I can sketch the function of best fit on the scatter plot. I can use technology to find the function of best fit for a scatter plot. I can find the equation for the line of best fit and use it to make predictions. I can sketch a line of best fit on a scatter plot that appears linear.

A1.S.ID.C.6 Use technology to compute and interpret the correlation coefficient of a linear fit.

I can use a calculator or computer to find the correlation coefficient for a linear association. I can interpret the meaning of the correlation coefficient in the context of the data.

A1.S.ID.C.7 Distinguish between correlation and causation. I can distinguish between correlation and causation.



Unit 10

Statistical Models + Scatterplots & Regression

# of Days = 8 Sections/Topics Essential Vocabulary Activities/Resources/Materials

• Pre-assessment

• Interpret Scatterplots & Use them

to Make Predictions

• Correlation Coefficient and

Regression Lines

• Organizing and Displaying Data

(Choosing an appropriate graph for

a given situation). Reading a

graph.

• Data Distribution (Mean, Median,

Modem Range)

• Box and Whisker Plots (Creating

and Reading)

• Histograms (Creating and

Reading)

• Unit Review

• Unit Test

• Bar Graph

• Box-and-Whisker

Plot

• Circle Graph

• First Quartile

• Frequency

• Frequency Table

• Histogram

• Interquartile Range

• Line Graph

• Mean

• Median

• Mode

• Outlier

• Stem-and-Leaf Plot

• Third Quartile


•


• N11: Interpreting Categorical and Quantitative Data

• A09: Sugar Prices

Illustrative Math:

• Haircut Costs

• Speed Trap

• Identifying Outliers

• Restaurant Bills and Party Size (4-5)

CCAs

• Devising a Measure for Correlation

• Representing Data With Box Plots

• Representing Data Using Frequency Graphs

Extra Resources
















https://www.illustrativemathematics.org/content-standards/HSS/ID/A/3/tasks/1888

https://www.illustrativemathematics.org/content-standards/HSS/ID/B/6/tasks/2046















After the EOC

# of Days =Between 10-15 Standards “I Can” Statements

Number and Quantity

Algebra

Functions


After the EOC

# of Days = Between 10-15


Rational Expressions:

• Simplifying Expressions and

Excluded Values

• Multiply Rational Expressions

• Divide Rational Expressions

• Add and Subtract Rational

Expressions with LIKE

denominators.

• Add and Subtract Rational

Expressions with UNLIKE

denominators.

Radical Expressions:

• Simplify Radicals

• Add and Subtract Radicals

• Multiply and Divide Radicals

• Solve equations with Radicals.

• Asymptote

• Discontinuous

Function

• Excluded Value

• Like Radicals

• Inverse Function

• Radical Equation

• Radical Expression

• Radicand

• Rational Equation

• Rational Expression

• Rational Function


•


•

CCAs

•

Extra Resources





















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