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Algebra 1

2016 – 2017 Course Syllabus

Mathematics Prince George’s County Public Schools

Course Code: Prerequisites: Successful completion of Math 8 or Foundations for Algebra Credits: 1.0 Math, Merit The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. Because it is built on the middle grades standards, this is a more ambitious version of Algebra I than has generally been offered. The critical areas deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. In all mathematics courses, the Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

INTRODUCTION: Typically in a Math class, to understand the majority of the information it is necessary to continuously practice your skills. This requires a tremendous amount of effort on the student’s part. Each student should dedicate study time for his/her mathematics class. Some hints for success in a Math class include: attending class daily, asking questions in class, and thoroughly completing all homework problems with detailed solutions as soon as possible after each class session.

INSTRUCTOR INFORMATION: Name: E-Mail Address: Planning Time: Phone Number:

CLASS INFORMATION: COURSE NUMBER:

CLASS MEETS: ROOM: TEXT: Algebra 1, Glencoe - http://connected.mcgraw-hill.com

CALCULATORS: For Algebra 1, a TI-84 graphing calculator is required.

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GRADING: High School Mathematics

The goal of grading and reporting is to provide the students with feedback that reflects their progress towards the mastery of the content standards found in the Algebra 2 Curriculum Framework Progress Guide.

Factors Brief Description Grade Percentage

Per Quarter

Classwork

This includes all work completed in the classroom setting, including: Group Participation

Notebooks Warm-ups Vocabulary Written responses Journals/Portfolios Group discussions Active participation in math projects Assignments students complete via online

resources Completion of assignments

40%

Homework

This includes all work completed outside the classroom to be graded on its completion and student’s preparation for class (materials, supplies, etc.) Assignments can include, but are not limited to:

Assignments students complete via online resources

Performance Tasks Journals/Portfolios

Other Tasks as assigned

10%

Assessment

This category entails both traditional and alternative methods of assessing student learning:

Group discussions Performance Tasks Problem Based Assessments Exams Quizzes Portfolios Research/Unit Projects Oral Presentations Surveys

An instructional rubric should be created to outline the criteria for success and scoring for each alternative assessment.

50%

Your grade will be determined using the following scale: 90% - 100% A

80% - 89% B 70% - 79% C 60% - 69% D 59% and below E _________________________________ ______________________________________ _____________

Student’s Name Parent’s/Guardian’s Signature Date

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Algebra 1

Weekly Timeline 2016 - 2017

Week Dates # of

Days Unit Assessment Suggestion

1 August 23 – 26 4 Unit 1 Unit 1 Pre-Test / Expressions

2 August 29 – September 2 5 Unit 1 Equations / SLO Pre-Test

3 September 6 – 9 4 Unit 1 Equations / SLO Pre-Test

4 September 12 – 16 5 Unit 1 Literal Equations / SLO Pre-Test

5 September 19 – 23 5 Unit 1 Inequalities / SLO Pre-Test

6 September 26 – 29 4 Unit 1 Inequalities / Unit 1 Assessment

7 October 3 – 7 5 Unit 2 Unit 2 Pre-Test / Functions

8 October 10 – 14 4 Unit 2 Rate of Change

9 October 17 – 20 4 Unit 2 Linear Functions

10 October 24 – 28 5 Unit 2 Linear Functions

END OF 1ST QUARTER (45 days)

11 November 1 – 4 4 Unit 2 Line of Best Fit

12 November 7 – 11 3 Unit 2 Systems of Equations

13 November 14 – 18 5 Unit 2 Systems of Equations

14 November 21 – 22 2 Unit 2 Linear Inequalities / Unit 2 Assessment

15 November 28 – December 2 5 Unit 3 Unit 3 Pre-Test / Exponential Expressions

16 December 5 – 9 5 Unit 3 One-Variable Exponential Equations

17 December 12 – 16 5 Unit 3 Two-Variable Exponential Equations

18 December 19 – 22 4 Unit 3 Exponential Functions

19 January 3 – 6 4 Unit 3 Exponential Functions / SLO Post-Test

20 January 9 – 13 5 Unit 3 Systems of Equations / SLO Pre-Test

21 January 17 – 19 3 Unit 3 Line of Best Fit / Unit 3 Assessment / SLO Post-Test

END OF 2ND QUARTER (45 days)

22 January 23 – 27 5 Unit 4 Unit 4 Pre-Test / Real Numbers / SLO-Post Test

23 January 1 – February 3 5 Unit 4 Polynomials / SLO-Post Test

24 February 6 – 9 4 Unit 4 Multiplying & Factoring Polynomials / SLO-Post Test

25 February 13 – 17 5 Unit 4 One-Variable Quadratic Equations / SLO-Post Test

26 February 21 – 24 4 Unit 4 Two-Variable Quadratic Equations / SLO-Post Test

27 February 27 – March 3 5 Unit 4 Quadratic Functions

28 March 6 – 10 5 Unit 4 Systems of Equations

29 March 13 – 17 5 Unit 4 Line of Best Fit / Unit 4 Assessment

30 March 20 – 24 5 Unit 5 Unit 5 Pre-Test / Plots and Histograms

END OF 3RD QUARTER (43 days)

31 March 28 – 31 4 Unit 5 Measuring Data

32 April 3 – 7 5 Unit 5 Measuring Data

33 April 10 – 13 4 Unit 5 Two-Way Frequency Tables / PARCC

34 April 24 – 28 5 Unit 6 Unit 6 Pre-Test Square & Cube Root Functions / PARCC

35 May 1 – 5 5 Unit 6 Absolute Value Functions / PARCC

36 May 8 – 12 5 Unit 6 Step Functions / PARCC

37 May 15 – 19 5 Unit 6 Piece-wise Functions / PARCC

38 May 22 – 26 5 Unit 6 Compare Functions / PARCC /Unit 6 Assessment

39 May 30 – June 2 4 Final Exams Final Review / PARCC

40 June 5 – 9 5 Final Exams Final Exam

END OF 4TH QUARTER (47 days)

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Unit 1 – One-Variable Linear Equations

Linear Equations in One Variable

Interpreting the Structure

A.SSE.1 Interpret expressions that represent a quantity in terms of its context. ★

a. Interprets parts of an expression such as terms, factors, and coefficients (major)

b. Interpret complicated expressions by viewing one or more of their parts as a single entity★. (major) (fluency

Creating

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (major)(cross-cutting) A.CED.3 Represent constraints by equations or inequalities and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (major)

Solving

A.REI.1 Explain the steps in solving linear equations in one variable. (major) (cross-cutting) A.REI.3 Solve linear equations and inequalities in one, variable, including equations with coefficients represented by letters. A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

Linear Inequalities in One Variable

Creating

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (major)(cross-cutting) A.CED.3 Represent constraints by equations or inequalities and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (major)

Solving A.REI.1 Explain the steps in solving linear equations in one variable. (major) (cross-cutting) A.REI.3 Solve linear equations and inequalities in one, variable, including equations with coefficients represented by letters.

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Unit 2 – Linear Functions

Functions (2 days)

Understanding and Using

Function Notation

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. (major) F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (major)

Linear Functions (6 days)

Average Rate of Change

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

Arithmetic Sequence

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (supporting) (cross-cutting) (supporting)(cross-cutting) F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Graphing Linear Functions

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

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

a. Graph linear functions and show intercepts.(supporting)

A.REI.11★

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). F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (additional)(cross-cutting)

Writing Linear Functions

F.BF.1★

Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation from a context. ★ (supporting) (cross-cutting)

Interpreting Linear Functions

F.IF.4 For a function that models a relationship between two quantities, interpret key features of the graph and the table in terms of the quantities, and sketch the graph showing key features given a verbal description of the relationship. (major) F.LE.5

Interpret the parameters in a linear function in terms of a context. ★ (supporting)(cross-cutting)

Determining Linear Functions

F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential function

a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (supporting)

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

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Comparing Properties of

Functions

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

Scatter Plots, Line of Best Fit, Linear Regression (2 days)

Making Scatter Plots and

Determining Line of Best Fit

S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association.

Interpreting Slope and Intercept of a

Linear Model

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

Correlation Coefficient

S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

Systems of Linear Equations (4 days)

Solving Linear Equations

Algebraically and Graphically

A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. (additional)

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (additional) (cross-cutting)

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A.REI.11★

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and g(x) are linear functions. (major)(cross-cutting)

Linear Inequalities and Systems of Linear Inequalities (2 days)

Graphing

A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.(major)

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Unit 3– Exponential Functions

Exponential Expressions (3 days) Rational

Exponents N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (5 1/3)3 must equal 5. N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Interpreting the Structure

A.SSE.1 Interpret expressions that represent a quantity in terms of its context. ★

a. Interprets parts of an expression such as terms, factors, and coefficients (major)

b. Interpret complicated expressions by viewing one or more of their parts as a single entity★. (major) (fluency

Equivalent Forms

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

c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be

rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Equations in One Variable (2 days) Creating A.CED.1 Create equations and inequalities in one variable and use them to solve problems (major)

Equations in Two Variables (2 days)

Creating

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales (major) A.CED.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

Exponential Functions (5 days)

Understanding and Using

Function Notation

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. (major) F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (major)

Average Rate of Change

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

Constructing and

Geometric Sequence

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (supporting) (cross-cutting) (supporting)(cross-cutting) F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

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Graphs and Tables

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(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.* F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (additional)(cross-cutting)

Writing Exponential Functions

F.BF.1★ Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation from a context. ★ (supporting) (cross-cutting)

Comparing Properties of

Functions

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

Constructing and Comparing Linear and Exponential

Functions

F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

System of Equations (2 days) Linear and

Exponential

A.REI.11★ Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the

solutions approximately, e.g., technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and g(x) are linear and exponential functions. (major)(cross-cutting)

Scatter Plots, Line of Best Fit, Linear Regression (2 days)

Making Scatter Plots and

Determining Line of Best Fit

S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a exponential function for a scatter plot that suggests a exponential association.

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Unit 4– Quadratic Functions

Properties of Rational and Irrational Numbers (2 days) Perform

Operations on Irrational Number

N.RN.3 Explain why the sum or product of two rational numbers is rational; the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational (additional)

Polynomials (2 days) Adding,

Subtracting and Multiplying

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction and multiplication; add, subtract, and multiply polynomials (major)

Expressions (3 days)

Interpret the Structure

A.SSE.1 Interpret expressions that represent a quantity in terms of its context★

a. Interpret parts of an expression, such as terms, factors, and coefficients (major). b. Interpret complicated expressions by viewing one or more of their parts as a single entity (major) A.SSE.2 Use the structure of an expression to identify ways to rewrite it (major)A.SSE.3 Choose and produce an equivalent form of an expression to reveal and

explain properties of the quantity represented by the expression★ (supporting)a. Factor a quadratic expression to reveal the zeros of the function it defines (supporting)

Equivalent Forms

A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression★(supporting a. Factor a quadratic expression to reveal the zeros of the function it defines (supporting b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines (supporting)

Equations in One Variable (3 days)

Creating and Solving

A.CED.1 Create equations and inequalities in one variable and use them to solve problems (major) A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (major) (cross-cutting) A.REI.4 Solve quadratic equations in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that

has the same solutions. Derive the quadratic formula from this form.(major)

b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula

and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions

and write them as a ± bi for real numbers a and b. (major)

Equations in Two Variables (2 days)

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Creating Quadratic Equations

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

Functions (3 days)

Understanding and Using

Function Notation

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. (major) F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (major)

Average Rate of Change

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

Writing Quadratic Functions

F.BF.1★ Write a function that describes a relationship between two quantities.

Determine an explicit expression, a recursive process, or steps for calculation from a context. ★ (supporting) (cross-cutting)

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

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

Graphing Quadratic Functions

F.IF.4 For a function that models a relationship between two quantities, interpret key features of the graph and the table in terms of the quantities, and sketch the graph showing key features given a verbal description of the relationship. (major) F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (major)

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

a. Graph linear and quadratic functions and show intercepts, maxima and minima.(supporting)

F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (additional)(cross-cutting)

Graphing Polynomials

A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Compare and Contrast Linear, Exponential and

Quadratic Functions

F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (supporting) F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (supporting)(cross-cutting)

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System of Equations (2 days)

Linear and Quadratic Equations

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A.REI.11★ Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) =

g(x); find the solutions approximately, e.g., technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and g(x) are linear and quadraticfunctions. (major)(cross-cutting)

Scatter Plots, Line of Best Fit, Linear Regression (2 days)

Making Scatter Plots and

Determining Line of Best Fit

S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a quadratic function for a scatter plot that suggests a quadratic association.

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Unit 5 – Descriptive Statistics

Data Represented by Single Count or Measurement Variables (7 days) Representing Data

on Dot Plots, Histograms and

Box Plots

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

Comparing Different Data Sets

S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Interpreting Differences in

Shapes, Center and Spread

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

Two Categorical and Quantitative Variables (3 days) Two-Way

Frequency Table S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Unit 6 – Other Functions

Square Root, Cube Root, Piecewise, Step and Absolute Value Functions (12 days)

Understanding and Using

Function Notation

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. (major) F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (major)

Interpreting Special Non-Linear

Functions and Graphing

F.IF.5★ Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(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.*

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

Average Rate of Change

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

graph.*

Comparing Properties

F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

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Standards for Mathematical

Practice

Student Friendly

Language

1. Make sense of problems and

persevere in solving them.

I can try many times to

understand and solve a

math problem.

2. Reason abstractly

and quantitatively.

I can think about the math

problem in my head, first.

3. Construct viable arguments

and critique the reasoning

of others.

I can make a plan, called a

strategy, to solve the

problem and discuss other

students’ strategies too.

4. Model with mathematics.

I can use math symbols and

numbers to solve the

problem.

5. Use appropriate tools

strategically.

I can use math tools,

pictures, drawings, and

objects to solve the problem.

6. Attend to precision.

I can check to see if my

strategy and calculations

are correct.

7. Look for and make use

of structure.

I can use what I already

know about math to solve

the problem.

8. Look for and express regularity

in repeated reasoning.

I can use a strategy that I

used to solve another math

problem.

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Standards for Mathematical Practice

Parents’ Guide

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. As your son or daughter works through homework exercises, you can help him or her develop skills with these Standards for Mathematical Practice by asking some of these questions: 1. Make sense of problems and persevere in solving them.

What are you solving for in the problem? Can you think of a problem that you have solved before that is like this one? How will you go about solving it? What’s your plan? Are you making progress toward solving it? Should you try a different plan? How can you check your answer? Can you check using a different method?

2. Reason abstractly and quantitatively. Can you write or recall an expression or equation to match the problem situation? What do the numbers or variables in the equation refer to? What’s the connection among the numbers and the variables in the equation?

3. Construct viable arguments and critique the reasoning of others. Tell me what your answer means. How do you know that your answer is correct? If I told you I think the answer should be (offer a wrong answer), how would you explain to me

why I’m wrong?

4. Model with mathematics. Do you know a formula or relationship that fits this problem situation? What’s the connection among the numbers in the problem? Is your answer reasonable? How do you know? What does the number(s) in your solution refer to?

5. Use appropriate tools strategically. What tools could you use to solve this problem? How can each one help you? Which tool is more useful for this problem? Explain your choice. Why is this tool (the one selected) better to use than (another tool mentioned)? Before you solve the problem, can you estimate the answer?

6. Attend to precision. What do the symbols that you used mean? What units of measure are you using? (for measurement problems) Explain to me (a term from the lesson).

7. Look for and make use of structure. What do you notice about the answers to the exercises you’ve just completed? What do different parts of the expression or equation you are using tell you about possible

correct answers?

8. Look for and express regularity in repeated reasoning. What shortcut can you think of that will always work for these kinds of problems? What pattern(s) do you see? Can you make a rule or generalization?