Grade 8 enVisionmath2.0 HMH Algebra 1 2017-2018 SY · PDF fileA1.1.2.1.2 2-4 Equations with No Solutions or Infinitely Many Solutions ... Creating and Solving Compound Inequalities

THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 1

Grade 8 enVisionmath2.0 + HMH Algebra 1 2017-2018 SY

Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4

Dat

es September 5 - October 31

BM Window Nov 1-17 November 2 - January 26 BM Window Jan 29-Feb 13

January 30 - May 8 BM Window May 9-25

May 10 - June 12

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Total Days: 39 Including 1 Half Day

Total Days: 50 Days Including 4 Half Days

Total Days Before PSSA: 50 Including 9 Half Days Total Days in Cycle: 60 Including 13 Half Days

Total Days: 22 Including 1 Half Day

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enVisionmath2.0 2-1 – 2-4: Analyze and Solve Linear Equations 3-1, 3-2, 3-5, 3-6: Use Functions to Model Relationships

Algebra 1 (HMH) 1.1: Solving Equations (properties only) 2.3 - 2.5: Algebraic Models 13.3, 13.4: Absolute Value Equations and Inequalities 3.2, 3.3: Functions and Models

enVisionmath2.0 2-5 – 2-9: Analyze and Solve Linear Equations (cont’d) 3-3, 3-4: Use Functions to Model Relationships 5-1 – 5-4: Analyze and Solve Systems of Linear Equations 4-1 – 4-5: Investigate Bivariate Data

Algebra 1 (HMH) 6.2, 6.3: Forms of Linear Equations 7.3: Linear Inequalities in Two Variables 9.1-9.4: One-Variable Data Distributions 12.2: Graphing Systems of Linear Inequalities

enVisionmath2.0 6-1 – 6-6*: Congruence and Similarity 1-1 – 1-9: Real Numbers 7-1 – 7-4: Understand and Apply the Pythagorean Theorem

Algebra 1 (HMH) 14.2: Simplifying Radicals** 17.1-17.3: Adding and Subtracting Polynomials 18.1-18.3: Multiplying Polynomials 21.1: Solving Equations by Factoring x2 + bx + c***

*Note: Lessons 6-8 to 6-10 do not contain eligible content and so can be covered in Cycle 4 **Note: Integer exponents & index 2 radicals only ***Note: Factoring only; no solving

enVisionmath2.0 1-10: Operations in Scientific Notation 6-7 – 6-10: Congruence and Similarity (cont’d) 8 – Solve Problems Involving Surface Area and Volume

Note: A cycle is defined as the time allotted to teach the content that is on each benchmark, and assumes the benchmark is taken on the first day of the window. This means that though it is fine to give the test later in the window, you should be moving on to new content as of the above listed dates, or you will fall behind.


Table of Contents

Benchmark Cycle 1 Standards (8th Grade) ......................................................................................................................................................................... 3

Benchmark Cycle 1 Standards (Algebra 1) .......................................................................................................................................................................... 4

Benchmark Cycle 1 Scope and Sequence ........................................................................................................................................................................... 5

Benchmark Cycle 2 Standards (8th Grade) .......................................................................................................................................................................... 7

Benchmark Cycle 2 Standards (Algebra 1) ........................................................................................................................................................................ 11

Benchmark Cycle 2 Scope and Sequence ......................................................................................................................................................................... 14

Benchmark Cycle 3 Standards (8th Grade) ........................................................................................................................................................................ 18

Benchmark Cycle 3 Standards (Algebra 1) ........................................................................................................................................................................ 21

Benchmark Cycle 3 Scope and Sequence ......................................................................................................................................................................... 23

Cycle 4 Standards (8th Grade) ........................................................................................................................................................................................... 27

Cycle 4 Scope and Sequence ............................................................................................................................................................................................. 28

8th Grade Standards and Eligible Content by Quarter ...................................................................................................................................................... 29

Algebra Eligible Content by Quarter ................................................................................................................................................................................. 33

Document Information Page ............................................................................................................................................................................................ 36


Benchmark Cycle 1 Standards (8th Grade)

PA Core Standard PA Eligible Content Common Core Standard

2.2.8.B.3 Analyze and solve linear equations and pairs of simultaneous linear equations

M08.B-E.3.1.1 Write and identify linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

8.EE.7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

M08.B-E.3.1.2 Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.7. Solve linear equations in one variable. b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

2.2.8.C.1 Define, evaluate, and compare functions.

M08.B-F.1.1.1 Determine whether a relation is a function.

8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

2.2.8.C.2 Use concepts of functions to model relationships between quantities.

M08.B-F.2.1.2 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch or determine a graph that exhibits the qualitative features of a function that has been described verbally.

8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.


Benchmark Cycle 1 Standards (Algebra 1)

PA Eligible Content PA Core High School Standards

A1.1.2.1.1 Write, solve, and/or apply a linear equation (including problem situations).

CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: Linear equations only

CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation. Note: Linear equations only.

CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems.

A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).

CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.


Benchmark Cycle 1 Scope and Sequence

Unit 1: Solving Equations and Inequalities

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Topic- Lesson

Lesson Title Lesson Objective(s) Eligible Content

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2-1 Combine Like Terms to Solve Equations

- Combine like terms - Solve equations with like terms on one side of the equation - Make sense of scenarios and represent them with equations

M08.B-E.3.1.2 A1.1.2.1.1

2-2 Solve Equations with Variables on Both Sides

- Solve equations with like terms on both sides of the equation - Make sense of scenarios and represent them with equations

M08.B-E.3.1.2 A1.1.2.1.1 A1.1.2.1.3

2-3 Solve Multistep Equations - Plan multiple solution pathways and choose one to find the solution to multistep equations

M08.B-E.3.1.2 A1.1.2.1.2

2-4 Equations with No Solutions or Infinitely Many Solutions

- Determine the number of solutions to an equation M08.B-E.3.1.1

1.1 (HMH)

Solving Equations (Properties Only)

- Understand and apply the properties of equality A1.1.2.1.2

2.3 (HMH)

Solving for a Variable - Use the properties of equality to undo operations to isolate a variable - Rewrite and use common formulas

A1.1.2.1.1

13.3 (HMH)

Solving Absolute Value Equations - Solve absolute value equations A1.1.3.1.1

2.4 (HMH)

Creating and Solving Inequalities

- Use a verbal or tabular model to write an inequality - Solve inequalities - Check solutions for reasonableness

A1.1.3.1.2 A1.1.3.1.3

2.5 (HMH)

Creating and Solving Compound Inequalities

- Write compound inequalities - Solve and graph compound inequalities

A1.1.3.1.1 A1.1.3.1.2 A1.1.3.1.3

13.4 (HMH)

Solving Absolute Value Inequalities

- Solve absolute value inequalities algebraically or graphically - Use absolute value inequalities to solve real-life problems

A1.1.3.1.1 A1.1.3.1.2 A1.1.3.1.3


Unit 3: Introduction to Functions

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3-1 Understand Relations and Functions

- Identify whether a relation is a function - Interpret a Function

M08.B-F.1.1.1 A1.2.1.1.1 A1.2.1.1.2

3-2 Connect Representations of Functions

- Identify functions by their equations, tables, and graphs - Represent linear and nonlinear functions with graphs

M08.B-F.1.1.1 A1.2.1.1.3

3-5 Intervals of Increase and Decrease - Describe the behavior of a function in different intervals M08.B-F.2.1.2

3-6 Sketch Functions from Verbal Descriptions

- Draw a sketch of a graph for a function that has been described verbally - Analyze and interpret the sketch of a graph of a function

M08.B-F.2.1.2

3.3 (HMH)

Modeling with Functions - Use function notation - Represent dependent and independent variables with function notation

A1.2.1.2.2

Benchmark 1 Window: 11/1 – 11/17




2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations.

M08.B-E.2.1.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

M08.B-E.2.1.2 Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.

8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. M08.B-E.2.1.3 Derive the equation y = mx for a line

through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

2.2.8.B.3 Analyze and solve linear equations and pairs of simultaneous linear equations.

M08.B-E.3.1.3 Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

8.EE.8. Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

M08.B-E.3.1.4 Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

8.EE.8. Analyze and solve pairs of simultaneous linear equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.



2.2.8.C.1 Define, evaluate, and compare functions.

M08.B-F.2.1.1 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.

8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

M08.B-F.1.1.2 Compare properties of two functions each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions). Example: Given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

8.F.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

M08.B-F.1.1.3 Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear.

8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

2.2.8.C.2 Use concepts of functions to model relationships between quantities.


8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.




8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

2.4.8.B.1 Analyze and/or interpret bivariate data displayed in multiple representations.

M08.D-S.1.1.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative correlation, linear association, and nonlinear association.

8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

M08.D-S.1.1.2 For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line.

8.SP.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

M08.D-S.1.1.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Example: In a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

8.SP.3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.



2.4.8.B.2 Understand that patterns of association can be seen in bivariate data utilizing frequencies.

M08.D-S.1.2.1 Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible associations between the two variables. Example: Given data on whether students have a curfew on school nights and whether they have assigned chores at home, is there evidence that those who have a curfew also tend to have chores?

8.SP.4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?




A1.2.2.1.1 Identify, describe, and/or use constant rates of change.

CC.2.2.HS.C.1Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections

between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two

quantities.

CC.2.2.HS.C.5Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable.

A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.

A1.2.2.1.3 Write or identify a linear equation when given

• the graph of the line,

• two points on the line, or

• the slope and a point on the line. Note: Linear equation may be in point-slope, standard,

and/or slope-intercept form.

A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.

A1.2.1.2.1 Create, interpret, and/or use the equation, graph, or table of a linear function.

CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays.

CC.2.1.HS.F.4Use units as a way to understand problems and to guide the solution of multi-step problems.

CC.2.2.HS.C.2Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two

quantities.

CC.2.2.HS.C.4Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.

A1.2.1.2.2 Translate from one representation of a linear function to another (i.e., graph, table, and equation).



A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations.

CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement

when reporting quantities.

CC.2.2.8.B.3Analyze and solve linear equations and pairs of simultaneous linear equations. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or

relationships.

CC.2.2.HS.D.9Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations.

A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities.

C.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

CC.2.2.HS.D.7Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities.

A1.2.3.2.1 Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation.

CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or

measurement variable.

CC.2.4.HS.B.3Analyze linear models to make interpretations based on the data. CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. A1.2.3.2.2 Analyze data, make predictions, and/or

answer questions based on displayed data (box-and- whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations).

A1.2.3.2.3 Make predictions using the equations or graphs of best-fit lines of scatter plots.



A1.2.3.3.1 Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent.

CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability

models.

CC.2.4.HS.B.4Recognize and evaluate random processes underlying statistical experiments. CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.



Unit 4: Linear Functions

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2-5 Compare Proportional Relationships

- Analyze equations, linear graphs, and tables to find unit rates and compare proportional relationships

M08.B-E.2.1.1 A1.2.2.1.1

2-6 Connect Proportional Relationships and Slope

- Find the slope of a line using different strategies - Interpret a slope in context and relate it to steepness on a graph

M08.B-E.2.1.2 M08.B-E.2.1.3

A1.2.2.1.1

2-7 Analyze Linear Equations y=mx

- Understand how the constant of proportionality and the slope relate in a linear equation - Write a linear equation in the form y = mx when the slope is given - Graph a linear equation in the form y = mx

M08.B-E.2.1.2 M08.B-E.2.1.3

A1.2.2.1.2

2-8 Understand the y-intercept of a Line

- Interpret and extend the table or graph of a linear relationship to find its y-intercept - Analyze graphs in context to determine and explain the meaning of the y-intercept

M08.B-E.2.1.2 M08.B-E.2.1.3

A1.1.2.1.3

2-9 Analyze Linear Equations y = mx + b

- Graph a line from an equation in the form y = mx + b - Write an equation that represents the given graph of a line

M08.B-E.2.1.2 M08.B-E.2.1.3

A1.2.2.1.4

3-3 Compare Linear and Nonlinear Functions

- Use different representations to compare linear and nonlinear functions

M08.B-F.1.1.2 M08.B-F.1.1.3

3-4 Construct Functions to Model Linear Relationships

- Write an equation in the form y = mx + b to describe a linear function

M08.B-F.1.1.2 M08.B-F.2.1.1

A1.2.2.1.2

6.2 (HMH)

Writing Equations in Point-Slope Form

- Write equations in point-slope form - Use linear equations to solve real-life problems

A1.2.1.2.1 A1.2.1.2.2

6.3 (HMH)

Writing Equations in Standard Form

- Write equations in standard form - Use linear equations to solve real-life problems

A1.2.1.2.1


Unit 5: Systems

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5-1 Estimate Solutions by Inspection

- Examine the graphs of a linear system of equations to determine the number of solutions to the system - Compare the equations in a linear system to determine the number of solutions

M08.B-E.3.1.4 M08.B-E.3.1.5

A1.1.2.2.1 A1.1.2.2.2

5-2 Solve Systems by Graphing - Create and examine graphs of linear systems of equations to determine the solution

M08.B-E.3.1.3 M08.B-E.3.1.5

A1.1.2.2.1 A1.1.2.2.2

5-3 Solve Systems by Substitution

- Understand how substitution can be used to solve a linear system of equations - Apply this understanding to interpret the results with one solution, no solution or infinitely many solutions

M08.B-E.3.1.4 M08.B-E.3.1.5

A1.1.2.2.1 A1.1.2.2.2

5-4 Solve Systems by Elimination

- Understand how the process of elimination can be used to solve a system of linear equations with no solution, one solution, or infinitely many solutions - Apply this understanding to solve mathematical and real-world problems

M08.B-E.3.1.4 M08.B-E.3.1.5

A1.1.2.2.1 A1.1.2.2.2

7.3 (HMH)

Linear Inequalities in Two Variables - Write linear inequalities in two variables - Graph linear inequalities in two variables

A1.1.3.2.1 A1.1.3.2.2

12.2 (HMH)

Graphing Systems of Linear Inequalities

- Check solutions of systems of linear inequalities - Graph systems of linear inequalities - Write systems of linear inequalities

A1.1.3.2.1 A1.1.3.2.2


Unit 6: Probability, Data Analysis and Displays

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Construct and Interpret Scatter Plots

- Construct a scatter plot to model paired data - Utilize a scatter plot to identify and interpret the relationship between paired data

M08.D-S.1.1.1

4-2 Analyze Linear Associations - Recognize whether the paired data have a linear association, a nonlinear association, or no association

M08.D-S.1.1.2

M08.B-F.1.1.3 M08.B-F.2.1.1

A1.2.1.1.1

4-3 Use Linear Models to Make Predictions

- Use the slope and y-intercept of a trend line to make a prediction - Make a prediction when no equation is given by drawing trend lines and writing the equation of the linear model

M08.D-S.1.1.3

M08.B-F.1.1.3 A1.2.2.2.1 A1.2.3.2.3

4-4 Interpret Two-Way Frequency Tables

- Organize paired categorical data into a two-way frequency table - Compare and make conjectures about data displayed in a two-way frequency table

M08.D-S.1.2.1

4-5 Interpret Two-Way Relative Frequency Tables

- Construct two-way relative frequency tables - Compare and make conjectures about data displayed in a two-way relative frequency table

M08.D-S.1.2.1

9.1 (HMH)

Measures of Center and Spread

- Use the mean and median to describe and compare the center of data sets* - Use the range, interquartile range, or standard deviate to describe and compare spreads of data sets*

*Note: These objectives are not part of PA 8th Grade Eligible Content and so are only assessed on the Keystone

A1.2.3.2.1 A1.2.3.2.2


Unit 6: Probability, Data Analysis and Displays

Suggested Dates

Topic- Lesson


9.3 (HMH)

Histograms and Box and Whisker Plots*

- Estimate statistics and compare distributions using histograms - Use box-and-whisker plots to represent and compare data sets **Note: Box and Whisker Plots were shifted to Grade 6 (from Grade 8) in the PA Core, so students may not have prior knowledge.

A1.2.3.1.1 A1.2.3.2.2

Probability (1 Day Supplementary / Review Lesson)

- Find probabilities of compound events - Find probability and represent it as a fraction, decimal or percent

A1.2.3.3.1

Benchmark 2 Window: 01/29 – 02/13




2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools.

M08.C-G.1.1.1 Identify and apply properties of rotations, reflections, and translations. Example: Angle measures are preserved in rotations, reflections, and translations.

8.G.1. Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines.

M08.C-G.1.1.2 Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.

8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

M08.C-G.1.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures, using coordinates.

8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

M08.C-G.1.1.4 Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.

8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

2.1.8.E.1 Distinguish between rational and irrational numbers using their properties.

M08.A-N.1.1.1 Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).

8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually,



M08.A-N.1.1.2 Convert a terminating or repeating decimal into a rational number (limit repeating decimals to thousandths).

and convert a decimal expansion which repeats eventually into a rational number.

2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers.

M08.A-N.1.1.3 Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: √5 is between 2 and 3 but closer to 2

8.NS.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

M08.A-N.1.1.4 Use rational approximations of irrational numbers to compare and order irrational numbers.

M08.A-N.1.1.5 Locate/identify rational and irrational numbers at their approximate locations on a number line.

2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.

M08.B-E.1.1.1 Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. Example: 312 × 3-15 = 33 = 1/33 = 1/27

8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

M08.B-E.1.1.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of perfect squares (up to and including 122) and cube roots of perfect cubes (up to and including 53) without a calculator. Example: If x2 = 25 then x = ±√25

8.EE.2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

M08.B-E.1.1.3 Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10, and express how many times larger or smaller one number is than another. Example: Estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that

8.EE.3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7



the world population is more than 20 times larger than the United States population.

times 109, and determine that the world population is more than 20 times larger.

2.3.8.A.3 Understand and apply the Pythagorean Theorem to solve problems.

M08.C-G.2.1.1 Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.

8.G.6. Explain a proof of the Pythagorean Theorem and its converse.

M08.C-G.2.1.2 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.)

8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

M08.C-G.2.1.3 Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.




A1.1.1.1.1 Compare and/or order any real numbers. Note: Rational and irrational may be mixed.

CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with

rational exponents.

CC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real-world or mathematical problems.

A1.1.1.1.2 Simplify square roots (e.g., √24 = 2√6).

A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or

absolute values to solve problems. Note: Exponents should be integers from –10 to 10.

C.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with

rational exponents.


A1.1.1.4.1 Use estimation to solve problems.

CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.

A1.1.1.5.1 Add, subtract, and/or multiply polynomial expressions (express answers in simplest

form).Note: Nothing larger than a binomial multiplied by a trinomial.

CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of

its context.

CC.2.2.HS.D.2Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to

polynomials.

CC.2.2.HS.D.5Use polynomial identities to solve problems. CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms.

A1.1.1.5.2 Factor algebraic expressions, including difference of squares and trinomials.

Note: Trinomials are limited to the formax2

+ bx + c

where a is equal to 1 after factoring out all monomial factors.

A1.1.1.5.3 Simplify/reduce a rational algebraic expression.



A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.

CC.2.1.6.E.3 Develop and/or apply number theory concepts to find common factors and

multiples.




Unit 7: Geometric Transformations

Suggested Dates

Topic- Lesson


01

/29

– 0

2/2

3

2 D

ays

Per

Les

son

+ 4

.5 D

ays

6-1 Analyze Translations - Use coordinates to describe the rules of a translation - Translate a two-dimensional figure on a coordinate plane by mapping each of its vertices

M08.C-G.1.1.1 M08.C-G.1.1.3

6-2 Analyze Reflections

- Understand reflections as a type of transformation and how they differ from translations - Use coordinates to describe the image created by a reflection - Reflect a two-dimensional figure on a coordinate plane

M08.C-G.1.1.1 M08.C-G.1.1.3

6-3 Analyze Rotations - Identify and perform a rotation - Describe a rotation - Determine how a rotation affects a two-dimensional figure

M08.C-G.1.1.1 M08.C-G.1.1.3

6-4 Compose Transformations - Describe and perform a sequence of transformations - Apply their knowledge of transformations to solve problems

M08.C-G.1.1.1 M08.C-G.1.1.3

6-5 Understand Congruent Figures

- Use a sequence of transformations to justify the congruence of figures - Understand that reflections, rotations, and translations are actions that produce congruent geometric figures

M08.C-G.1.1.2 M08.C-G.1.1.3

6-6 Describe Dilations - Verify the properties of a dilation - Graph the image of a dilation given a fixed center and a common scale factor

M08.C-G.1.1.3 M08.C-G.1.1.4


Unit 8: Real Numbers and The Pythagorean Theorem

Suggested Dates

Topic- Lesson


02

/26

– 0

4/1

3

2 D

ays

per

Les

son

fo

r To

pic

1, 1

Day

per

Les

son

fo

r To

pic

7 a

nd

2 D

ays

fo

r 1

4.2

+ 2

Day

s an

d E

LA P

SSA

Wee

k

1-1 Rational Numbers as Decimals - Write repeating decimals as fractions M08.A-N.1.1.2

A1.1.1.1.1

1-2 Understand Irrational Numbers - Identify an irrational number M08.A-N.1.1.1

A1.1.1.1.1

1-3 Compare and Order Real Numbers

- Compare and order rational and irrational numbers M08.A-N.1.1.3 M08.A-N.1.1.4 M08.A-N.1.1.5

1-4 Evaluate Square Roots and Cube Roots

- Find square roots and cube roots of rational numbers M08.B-E.1.1.2

A1.1.1.1.2

1-5 Solve Equations Using Square Roots and Cube Roots

- Solve equations and problems, in real-world contexts involving square roots and cube roots* *Note: This would be an appropriate place to address volume formulas, if time allows

M08.B-E.1.1.2

1-6 Use Properties of Integer Exponents

- Understand the properties of exponents - Generate equivalent expressions with exponents

M08.B-E.1.1.1 A1.1.1.3.1

1-7 More Properties of Integer Exponents

- Simplify expressions with negative and zero exponents - Evaluate expressions with negative and zero exponents

M08.B-E.1.1.1 A1.1.1.3.1

1-8 Use Powers of 10 to Estimate Quantities

- Estimate very large and very small quantities by rounding and then writing that number as a single digit times a power of 10

M08.B-E.1.1.3 A1.1.1.4.1

1-9 Understand Scientific Notation

- Use scientific notation to write very large or very small quantities - Convert numbers written in scientific notation to standard form

Preparing for: M08.B-E.1.1.4

7-1 Understand the Pythagorean Theorem

- Understand a proof of the Pythagorean Theorem - Use the Pythagorean Theorem to find the length of the hypotenuse or a leg of a right triangle

Preparing for M08.C-G.2.1.1 M08.C-G.2.1.2

7-2 Understand the Converse of the Pythagorean Theorem

- Understand and apply the converse of the Pythagorean Theorem to identify right triangles. - Use the converse of the Pythagorean Theorem to analyze two-dimensional shapes

M08.C-G.2.1.1


Unit 8: Real Numbers and The Pythagorean Theorem

Suggested Dates

Topic- Lesson


(see

ab

ove

)

7-3 Apply the Pythagorean Theorem to Solve Problems

- Use the Pythagorean Theorem and its converse to solve problems

M08.C-G.2.1.2

7-4 Find Distance in the Coordinate Plane

- Apply the Pythagorean Theorem to find distance between two points in the coordinate plane - Use the Pythagorean Theorem to find the perimeter of a figure and to solve problems on the coordinate plane

M08.C-G.2.1.3

14.2 (HMH)

Simplifying Expressions with Rational Exponents and Radicals

- Use properties of exponents to simplify expressions *Note: Limited to integer exponents and index 2 radicals on the Keystone. Not assessed on the 8th Grade PSSA.

A1.1.1.1.2 A1.1.1.3.1 A1.1.1.5.3

Math PSSA 4/16 – 4/20


Unit 9: Polynomials and Factoring

Suggested Date

Topic- Lesson


04

/23

– 0

5/1

1

2 D

ays

Per

Les

son

+ 2

Day

s

(do

es n

ot

incl

ud

e Sc

ien

ce P

SSA

day

s; d

oe

s

incl

ud

e h

alf

day

s)

17.1 (HMH)

Understanding Polynomial Expressions

- Distinguish between monomials and polynomials - Classify polynomials

A1.1.1.5.1

17.2 (HMH)

Adding Polynomial Expressions - Add polynomials A1.1.1.5.1

17.3 (HMH)

Subtraction Polynomial Expressions

- Subtract polynomials A1.1.1.5.1

18.1 (HMH)

Multiplying Polynomials by Monomials

- Multiply binomials by monomials A1.1.1.5.1

18.2 (HMH)

Multiplying Polynomial Expressions

- Multiply binomials A1.1.1.5.1

18.3 (HMH)

Special Products of Binomials - Use the square of a binomial pattern - Use the sum and difference pattern

A1.1.1.5.1

21.1 (HMH)

Factoring x2 + bx + c - Factor x2 + bx + c A1.1.1.5.2

GCF and LCM of Monomials (1 Day Supplementary Lesson)

A1.1.1.2.1

Keystone Exam Window 5/14 – 5/25


Cycle 4 Standards (8th Grade)


2.3.8.A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.

M08.C-G.3.1.1 Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.

8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.

M08.B-E.1.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g., interpret 4.7EE9 displayed on a calculator as 4.7 × 109).

8.EE.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.


Cycle 4 Scope and Sequence

Unit 10: Surface Area, Volume and Similarity

Suggested Dates

Topic- Lesson

Lesson Title Lesson Objective Eligible Content

5/1

6 –

6/1

2

2 D

ays

Per

Les

son

8-1 Find Surface Area of Three-Dimensional Figures

- Calculate the surface area of cylinders, cones and spheres Preparing for

M08.C-G.3.1.1

8-2 Find Volume of Cylinders

- Identify and use the correct formula to find the volume of cylinders - Recognize the relationship between the formulas for volume of a rectangular prism and the volume of a cylinder

M08.C-G.3.1.1

8-3 Find Volume of Cones - Find the volume of a cone - Recognize the relationship between volume of a cylinder and volume of a cone

M08.C-G.3.1.1

8-4 Find Volume of Spheres - Calculate the volume of a sphere - Recognize the relationship between the formula for the volume of a cone and the volume of a sphere

M08.C-G.3.1.1

6-7 Understand Similar Figures - Perform a sequence of transformations to identify similar figures

M08.C-G.1.1.3 M08.C-G.1.1.4

6-8 Angles, Lines, and Transversals

- Identify relationships between angles formed by parallel lines and a transversal - Determine the measures of angles formed by parallel lines and a transversal - Reason about parallel lines

M07.C-G.2.1.2

6-9 Interior and Exterior Angles of Triangles

- Determine unknown measures of interior and exterior angles in triangles - Write and solve algebraic equations to find angle measures

Not assessed in PA

6-10 Angle-Angle Triangle Similarity - Determine triangle similarity by comparing the angle measures of triangles - Solve algebraic problems involving similar triangles

M07.C-G.1.1.2

1-10 Operations with Numbers in Scientific Notation

- Apply number properties to calculations with numbers in scientific notation

M08.B-E.1.1.4


8th Grade Standards and Eligible Content by Quarter

PA Core Standard PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4

CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties.

M08.A-N.1.1.1 Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).

X

M08.A-N.1.1.2 Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths). X

CC.2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers

M08.A-N.1.1.3 Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144).

X

M08.A-N.1.1.4 Use rational approximations of irrational numbers to compare and order irrational numbers.

X

M08.A-N.1.1.5 Locate/identify rational and irrational numbers at their approximate locations on a number line.

X

CC.2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.

M08.B-E.1.1.1 Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided.

X

M08.B-E.1.1.2 Use square root and cube root symbols to represent solutions to

equations of the form x2 = p and x3

= p, where p is a positive rational number.

Evaluate square roots of perfect squares (up to and including 122) and cube

roots of perfect cubes (up to and including 53) without a calculator.

X

M08.B-E.1.1.1 Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided.

X

CC.2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations.

M08.B-E.2.1.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

X

M08.B-E.2.1.2 Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.

X



1 Cycle

2 Cycle

3 Cycle

4

M08.B-E.2.1.3 Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

X

CC.2.2.8.B.3 Analyze and solve linear equations and pairs of simultaneous linear equations.

M08.B-E.3.1.1 Write and identify linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

X

M08.B-E.3.1.2 Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

X

M08.B-E.3.1.3 Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously.

X

M08.B-E.3.1.4 Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection.

X

M08.B-E.3.1.5 Solve real-world and mathematical problems leading to two linear equations in two variables.

X

CC.2.2.8.C.1 Define, evaluate, and compare functions.

M08.B-F.1.1.1 Determine whether a relation is a function. X

M08.B-F.1.1.2 Compare properties of two functions, each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions).

X

M08.B-F.1.1.3 Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear.

X

CC.2.2.8.C.2 Use concepts of functions to model relationships between quantities.


X


X



1 Cycle

2 Cycle

3 Cycle

4

CC.2.3.8.A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve real world and mathematical problems.

M08.C-G.3.1.1 Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.

X

CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools.

M08.C-G.1.1.1 Identify and apply properties of rotations, reflections, and translations.

X

M08.C-G.1.1.2 Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.

X

M08.C-G.1.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

X

M08.C-G.1.1.4 Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.

X X

CC.2.3.8.A.3 Understand and apply the Pythagorean Theorem to solve problems.

M08.C-G.2.1.1 Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.

X

M08.C-G.2.1.2 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.)

X

M08.C-G.2.1.3 Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

X

CC.2.4.8.B.1 Analyze and/or interpret bivariate data displayed in multiple representations.

M08.D-S.1.1.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative correlation, linear association, and nonlinear association.

X

M08.D-S.1.1.2 For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line.

X

M08.D-S.1.1.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

X



1 Cycle

2 Cycle

3 Cycle

4

CC.2.4.8.B.2 Understand that patterns of association can be seen in bivariate data utilizing frequencies.

M08.D-S.1.2.1 Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible associations between the two variables.

X


Algebra Eligible Content by Quarter

PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4

A1.1.1.1.1 Compare and/or order any real numbers. Note: Rational and irrational may be mixed. X

A1.1.1.1.2 Simplify square roots (e.g., √24 = 2√6). X

A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. X

A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values

to solve problems.Note: Exponents should be integers from –10 to 10. X

A1.1.1.4.1 Use estimation to solve problems. X

A1.1.1.5.1 Add, subtract, and/or multiply polynomial expressions (express answers in simplest form).Note: Nothing larger than a binomial multiplied by a trinomial. X

A1.1.1.5.2 Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are

limited to the formax2 + bx + c where a is equal to 1 after factoring out all monomial factors. X

A1.1.1.5.3 Simplify/reduce a rational algebraic expression. X

A1.1.2.1.1 Write, solve, and/or apply a linear equation (including problem situations). X

A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: Linear equations only. X

A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation.Note: Linear equations only. X X

A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations. X

A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations. X


A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). X

A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line. X

A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation. Note: Linear inequalities only. X

A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. X

A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities. X

A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. X X

A1.2.1.1.2 Determine whether a relation is a function, given a set of points or a graph. X

A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). X

A1.2.1.2.1 Create, interpret, and/or use the equation, graph, or table of a linear function. X

A1.2.1.2.2 Translate from one representation of a linear function to another (i.e., graph, table, and equation). X

A1.2.2.1.1 Identify, describe, and/or use constant rates of change. X

A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems. X

A1.2.2.1.3 Write or identify a linear equation when given: the graph of the line, two points on the line, or the

slope and a point on the line.Note: Linear equation may be in point-slope, standard, and/or slope-intercept

form. X

A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph. X

A1.2.2.2.1 Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot. X

A1.2.3.1.1 Calculate and/or interpret the range, quartiles, and interquartile range of data. X


A1.2.3.2.1 Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation. X

A1.2.3.2.2 Analyze data, make predictions, and/or answer questions based on displayed data (box-and- whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations). X

A1.2.3.2.3 Make predictions using the equations or graphs of best-fit lines of scatter plots. X

A1.2.3.3.1 Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent. X


Document Information Page

Overview of Contents of Document The Cover Page lays out the Topics taught within each Cycle as well as the corresponding dates. The Benchmark Cycle X Standards pages that precede each cycle outline all of the standards that are taught within that cycle. These are, therefore, all of the standards that may be on that Cycle’s Benchmark. This document contains both 8th Grade Standards and the High School Standards aligned to the Keystone Eligible Content. The Benchmark Cycle X Scope and Sequence pages provide suggested pacing that allows for 1 day per lesson plus some flex days. We recommend proactively using the flex days for: reviewing pre-requisite content, splitting lessons over multiple days, assessing, re-teaching, and doing projects. Of course, some of these will also be taken by field trips and other school activities. The PA Core Standards and Eligible Content by Cycle page lists all of the standards and indicates in which cycle(s) they are taught.

What is a Cycle?

We want to offer clarity on what appears on each benchmark. Additionally, there should be sufficient time to teach that content before it is tested. Because each school administers the benchmark on a different day, not necessarily corresponding with the last day of the Term, we have created Cycles. Each Cycle contains the content that is to be taught and tested on a given benchmark. Please refer to the dates on the Cover Page to ensure you are aware of the beginning and ending dates for each Cycle.

What If I Fall Behind?

We trust you to make decisions about what is best for your students. This pacing will prepare you for the Benchmarks and PSSA, but it is a suggested, not mandated, pacing. You may also wish to move at a faster pace. Do not feel you should slow down to match this guide.

If you are concerned about content that you may not reach before the PSSA, consider implementing number talks and other short routines and games. For example, a lot of Geometry vocabulary and concepts could be taught through Which Once Doesn’t Belong. Rather than pushing to “cover” content, or using test prep resources, content can be infused through short but meaningful structures.

The table below is purely for informational purposes. We used the PSSA Mathematics Blueprint to calculate what percent of tested content you will cover, based on how much of the book you teach before the test. Again, we recommend depth and understanding over coverage, but we wanted to provide this information for your planning purposes.

Percent of 8th Grade PSSA Eligible Content if Topics 1-8 Are Taught

Percent of 8th Grade PSSA Eligible Content if Topics 1-7 Are Taught

Percent of PSSA Eligible Content if Topics 1-6 Are Taught

Percent of PSSA Eligible Content if Topics 1-5 Are Taught

100% 96% 88.2% 79.5%

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Additional Key Considerations in Mathematics

The Standards for Mathematical Practice are:

1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 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

You should try to infuse these Standards into your lessons regularly. Rather than thinking of them as a box to check, think about how you are providing students with opportunities to develop as mathematical thinkers and doers.

The following Common Core Standards have been identified as the major clusters for Grade 8:

8.EE.A Work with radicals and integer exponents. 8.EE.B Understand the connections between proportional relationships, lines, and linear equations. 8.EE.C Analyze and solve linear equations and pairs of simultaneous linear equations. 8.F.A Define, evaluate, and compare functions. 8.F.B Use functions to model relationships between quantities. 8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.B Understand and apply the Pythagorean Theorem.

These do not necessarily reflect what is most tested on the PSSA, but it is the content that is most essential as you prepare students for 9th grade.

The School District of Philadelphia’s Vision for Mathematics Teaching and Learning:

All students think mathematically, and they will be empowered to own, share, and do mathematics.

Our Guiding Principles: Equitable Discourse Rich + Meaningful Tasks Purpose-Driven Work

Questioning and Curiosity Valuing Diverse Thinking

If you have any questions or would like more information, please contact us at [email protected].

Documents

Grade 8 enVisionmath2.0 HMH Algebra 1 2017-2018 SY · PDF fileA1.1.2.1.2 2-4 Equations with No Solutions or Infinitely Many Solutions ... Creating and Solving Compound Inequalities