Chapter 3: Banking Services (approximately 15 days)



Algebra 1 Math Lab

COURSE PURPOSE

Algebra 1 Math Lab is a mathematical modeling course that is based on Common Core Learning Standards in Algebra. The Mathematical Modeling standards in Common Core will form a basis for which students are able to use mathematics as a tool to solve rigorous, real-life, non-routine problems. The course allows students to experience the interrelatedness of mathematical topics, find patterns, make conjectures, and extrapolate from known situations to unknown situations. . Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. The course offers students multiple opportunities to use, construct, question, model, and interpret real-world situations through symbolic algebraic representations, graphical representations, geometric representations, and verbal representations. It provides students a motivating context for understanding and applying the mathematics they are guaranteed to use in the future

The overarching purpose of the course is to develop the type of mathematically proficient students addressed in this excerpt from the Common Core State Standards for Mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Algebra 1 Math Lab builds strength in reasoning and number sense, because the real-world applications demand that solutions make sense. Through contextual problem solving and the mathematical modeling of real situations, the course gives the students the motivation to persevere through routine and non-routine problems, and as a result, develop strength and confidence in their mathematics ability. Students will attend every other day for 45 minutes, and earn ½ math credit. This course is not pass/fail and teachers must assign students a grade for each marking period.

Mathematical Modeling

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Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.

A model can be very simple, such as writing total cost as a product of unit price and number bought, or using a geometric shape to describe a physical object like a coin. Even such simple models involve making choices. It is up to us whether to model a coin as a three-dimensional cylinder, or whether a two-dimensional disk works well enough for our purposes. Other situations—modeling a delivery route, a production schedule, or a comparison of loan amortizations—need more elaborate models that use other tools from the mathematical sciences. Real-world situations are not organized and labeled for analysis; formulating tractable models, representing such models, and analyzing them is appropriately a creative process. Like every such process, this depends on acquired expertise as well as creativity.Some examples of such situations might include:

*Estimating how much water and food is needed for emergency relief in a devastated city of 3 million people, and how it might be distributed.

*Planning a table tennis tournament for 7 players at a club with 4 tables, where each player plays against each other player.

*Designing the layout of the stalls in a school fair so as to raise as much money as possible.

*Analyzing stopping distance for a car.

*Modeling savings account balance, bacterial colony growth, or investment growth.

*Engaging in critical path analysis, e.g., applied to turnaround of an aircraft at an airport.

*Analyzing risk in situations such as extreme sports, pandemics, and terrorism.

*Relating population statistics to individual predictions.

In situations like these, the models devised depend on a number of factors: How precise an answer do we want or need? What aspects of the situation do we most need to understand, control, or optimize? What resources of time and tools do we have? The range of models that we can create and analyze is also constrained by the limitations of our mathematical, statistical, and technical skills, and our ability to recognize significant variables and relationships among them. Diagrams of various kinds, spreadsheets and other technology, and algebra are powerful tools for understanding and solving problems drawn from different types of real-world situations.

One of the insights provided by mathematical modeling is that essentially the same mathematical or statistical structure can sometimes model seemingly different situations. Models can also shed light on the mathematical structures themselves, for example, as when a model of bacterial growth makes more vivid the explosive growth of the exponential function.

The basic modeling cycle is summarized in the diagram. It involves (1) identifying variables in the situation and selecting those that represent essential features; (2) formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables; (3) analyzing and performing operations on these relationships to draw conclusions; (4) interpreting the results of the mathematics in terms of the original situation; (5) validating the conclusions by comparing them with the situation and then either improving the model; (6) or if it is acceptable, reporting on the conclusions and the reasoning behind them. Choices, assumptions, and approximations are present throughout this cycle.

Algebra 1 Math Lab

COURSE OUTLINE

|Solving Linear Equations |September 7-30 |

|Interpreting Linear Equations and Functions |October 3- November 10 |

|Interpreting Exponential Functions |November 14-January 13 |

|Interpreting Quadratic Functions |January 16-March 24 |

|Descriptive Statistics |March 27-April 28 |

|Modeling Functions |May 1-June 13 |

Solving Linear Equations

Student Outcomes:

♣ Students extend the use of the properties of equality to solve linear equations having rational coefficients.

♣ Students transform equations into simpler forms using the distributive property.

♣ Students learn that not every linear equation has a solution.

♣ Students rewrite and solve equations that are not obviously linear equations using properties of equality.

♣ Students use a table to find solutions to a given linear equation and plot the solutions on a coordinate plane.

STANDARDS

8.EE.B.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.

8.EE.C.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).

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

Teaching Resources

Grade 8 Module 4, Lesson 3 - Linear Equations in x

Demonstrate- Example 2, 3, 4, Exercise 1, 2

Exit Ticket, Problem Set 1-4

Grade 8 Module 4, Lesson 4 - Solving a Linear Equation

Demonstrate- Example 1, 2, 3, Exercise 1, 2

Exit Ticket, Problem Set 1-7

Grade 8 Module 4, Lesson 6 – Solutions of a Linear Equation

Demonstrate- Example 1, 2, 3

Exit Ticket, Problem Set 1-7

Grade 8 Module 4, Lesson 7 – Classification of Solutions

Demonstrate- Exercise 1- 3, Exercises 4-10

Exit Ticket, Problem Set 1-7

Grade 8 Module 4, Lesson 8 – Linear Equations in Disguise

Demonstrate- Example 4, Exercise 1, 2

Exit Ticket, Problem Set 1-10

Grade 8 Module 4, Lesson 9 – An Application of Linear Equations

Demonstrate- Selection from Exercises 3-11

Exit Ticket #2, Problem Set 2-9

Grade 8 Module 4, Lesson 12 – Linear Equation in Two Variables

Demonstrate-Opening Exercise , Exercise 3

Exit Ticket #2, Problem Set 1-5

Grade 8 Module 4, Lesson 21 – Some Facts About Graphs of Linear Equation in Two Variables

Demonstrate- Example1, 2, 3,

Exit Ticket #2, Problem Set 1-8

Interpreting Linear Equations and Functions

Student Outcomes:

♣ Students define appropriate quantities from a situation (a “graphing story”), choose and interpret the scale and the origin for the graph, and graph the piecewise linear function described in the video. They understand the relationship between physical measurements and their representation on a graph.

♣ Students develop the tools necessary to discern units for quantities in real-world situations and choose levels of accuracy appropriate to limitations on measurement. They refine their skills in interpreting the meaning of features appearing in graphs.

♣ Students interpret the meaning of the point of intersection of two graphs and use analytic tools to find its coordinates.

♣ Students recognize and identify solutions to two-variable equations. They represent the solution set graphically. They create two variable equations to represent a situation. They understand that the graph of the line ax + by = c is a visual representation of the solution set to the equation ax + by = c

♣ Students recognize and identify solutions to two-variable inequalities. They represent the solution set graphically. They create two variable inequalities to represent a situation.

♣ Students understand that a half-plane bounded by the line ������������ + ������������ = ������ is a visual representation of the solution set to a linear inequality such as ������������ + ������������ < ������. They interpret the inequality symbol correctly to determine which portion of the coordinate plane is shaded to represent the solution.

♣ Students identify solutions to simultaneous equations or inequalities; they solve systems of linear equations and inequalities either algebraically or graphically.

♣ Students use systems of equations or inequalities to solve contextual problems and interpret solutions within a particular context

* Students create equations and inequalities in one variable and use them to solve problems.

♣ Students create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales.

♣ Students represent constraints by inequalities and interpret solutions as viable or non-viable options in a modeling context.

STANDARDS

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.★

N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.★

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

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.★

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

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

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

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

A-REI.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.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.

Teaching Resources

Piecewise Functions

Modules

Algebra 1 Module 1, Lesson 1 – Graphs of Piecewise Linear Functions

Demonstrate- Example 1, Example 2

Exit Ticket, Problem Set 1, 2

Algebra 1 Module 1, Lesson 5 – Two Graphing Stories

Demonstrate- Examples 1-2

Exit Ticket, Problem Set 1-6

Additional resources on emathinstruction

Lesson 3- Graphs of Functions

Algebra 1 Major Content Review

p. 41 Problem #2

p. 43 Problem #5

p. 44 Problem #4

p. 46 Problem #10

Systems of Equations and Inequalities

Modules

Algebra 1 Module 1, Lesson 20 – Solution Sets to Equations With Two Variables

Demonstrate- Exercise 1-5

Exit Ticket, Problem Set 1-3

Algebra 1 Module 1, Lesson 21 – Solution Sets to Inequalities With Two Variables

Demonstrate- Exercise 1, 2, Example 1

Exit Ticket, Problem Set 1, 2, 3

Algebra 1 Module 1, Lesson 23 – Solution Sets to Simultaneous Equations

Demonstrate- Exploratory Challenge

Exit Ticket, Problem Set 4, 5, 6

Algebra 1 Module 1, Lesson 24 – Applications to Systems of Equations and Inequalities

Demonstrate- Opening Exercise, Example 1,

Exploratory Challenge, Exit Ticket, Problem Set 2, 3, 4, 5

Algebra 1 Module 1, Lesson 28 – Federal Income Tax

Demonstrate- Example 1, Exercise 1-7

Exit Ticket, Problem Set 1, 2, 4, 5, 6, 7

Additional resources on emathinstruction

Lessons 1-5

1. Solutions to Systems and Solving By Graphing

2. Solving Systems by Substitution

3. Properties of Systems and Their Solutions

4. The Elimination Method

5. Modeling With Systems of Equations

Algebra 1 Major Content Review

p. 12 Problem #6

p. 13 Problem #9

p. 18 Problem #7

p. 17 Problem #6

p. 29 Problem #8

p. 31 Problem #9

p. 32 Problem #10

Analyzing Structure of Linear Functions

Additional resources on emathinstruction

Lessons 6,7

6. Modeling With Linear Functions

7. More Linear Modeling

Algebra 1 Major Content Review

p. 6 Problem #1

p. 7 Problem #6

p. 8 Problem #7

p. 8 Problem #8

p. 11 Problems #1-3

p. 13 Problems #7-8

p. 15 Problems #1-3

p. 16 Problem #4

p. 55 Problem #5-6

Interpreting Exponential Functions

Student Outcomes:

♣ Students compare the rate of change for simple and compound interest and recognize situations in which a quantity grows by a constant percent rate per unit interval.

♣ Students are able to model with and solve problems involving exponential formulas.

♣ Students compare linear and exponential models of population growth.

♣ Students describe and analyze exponential decay models; they recognize that in a formula that models exponential decay, the growth factor ������ is less than 1; or, equivalently, when ������ is greater than 1, exponential formulas with negative exponents could also be used to model decay.

♣ Students create tables and graphs of functions and interpret key features including intercepts, increasing and decreasing intervals, and positive and negative intervals.

♣ Students compare linear and exponential models by focusing on how the models change over intervals of equal length. Students observe from tables that a function that grows exponentially will eventually exceed a function that grows linearly.

♣ Students create models and understand the differences between linear and exponential models that are represented in different ways.

♣ Students apply knowledge of exponential functions and transformations of functions to a contextual situation.

STANDARDS

F-IF.B.46 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-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.★

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

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

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

F-LE.A.211 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).★

F-LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Teaching Resources

Modules

Algebra 1 Module 3, Lesson 4 – Why Do Banks Pay YOU to Provide Their Services?

Demonstrate- Example 1, Example 2

Example 3, Exit Ticket, Problem Set 1-3

Algebra 1 Module 3, Lesson 5 – The Power of Exponential Growth

Demonstrate- Opening Exercise, Example 1

Exit Ticket, Problem Set 1, 4, 5, 7

Algebra 1 Module 3, Lesson 6 – Exponential Growth-US Population and World Population

Demonstrate- Example 1.

Example 2, Exercise 2, Exit Ticket, Problem Set 2

Algebra 1 Module 3, Lesson 7 – Exponential Decay

Demonstrate- Example 1. 2

Exercise 6, Exit Ticket, Problem Set 2, 3, 5, 6

Algebra 1 Module 3, Lesson 13 – Interpreting Graphs of Functions

Demonstrate- Discussion

Exploratory Challenge, Exercises 1-12, Exit Ticket, Problem Set 1

Algebra 1 Module 3, Lesson 14 – Growth Rates

Demonstrate- Example 1

Example 2, Example 3, Exit Ticket, Problem Set 4

Algebra 1 Module 3, Lesson 21 – Comparing Linear and Exponential Functions Again

Demonstrate- Opening Exercise

Exit Ticket, Problem Set 8

Algebra 1 Module 3, Lesson 22 – Modeling an Invasive Species Population

Demonstrate- Lesson Notes, Classwork, Discussion

Mathematical Modeling Exercise, Exit Ticket

Additional resources on emathinstruction

Lessons 7,8

Lesson 7. Exponential Models Based on Percent Growth

Lesson 8. Linear Vs. Exponential

Algebra 1 Major Content Review

p. 7 Problem #4

p. 41 Problem #1

p. 50 Problem #1

p. 51 Problem #3

p. 52 Problems #5-6

p. 53 Problems #1

p. 54 Problems #4

p. 55 Problem #7

p. 56 Problem #8

p. 57 Problem #1

p. 57 Problem #3

Interpreting Quadratic Functions

Student Outcomes:

♣ Students interpret word problems to create equations in one-variable and solve them (i.e., determine the solution set) using factoring and the zero product property.

*Students examine quadratic equations in two variables represented graphically on a coordinate plane and recognize the symmetry of the graph. They explore key features of graphs of quadratic functions: ������-intercept and ������-intercepts, the vertex, the axis of symmetry, increasing and decreasing intervals, negative and positive intervals, and end behavior. They sketch graphs of quadratic functions as a symmetric curve with a highest or lowest point corresponding to its vertex and an axis of symmetry passing through the vertex.

♣ Students interpret quadratic functions from graphs and tables: zeros (������������-intercepts), ������������-intercept, the minimum or maximum value (vertex), the graph’s axis of symmetry, positive and negative values for the function, increasing and decreasing intervals, and the graph’s end behavior.

♣ Students determine an appropriate domain and range for a function’s graph and when given a quadratic function in a context, recognize restrictions on the domain. \

♣ Students write the quadratic function described verbally in a given context. They graph, interpret, analyze, check results, draw conclusions, and apply key features of a quadratic function to real-life applications in business and physics.

♣ Students create a quadratic function from a data set based on a contextual situation, sketch its graph, and interpret both the function and the graph in context. They answer questions and make predictions related to the data, the quadratic function, and graph.

.

STANDARDS

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

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and a factor not depending on P.

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

a. Factor a quadratic expression to reveal the zeros of the function it defines.

b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A-CED.A.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.★

4

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

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

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

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

Teaching Resources

Factoring

Modules

Algebra 1 Module 4, Lesson 1-2 – Multiplying and Factoring Polynomial Expressions

Various Examples and Exercises As Needed

Algebra 1 Module 4, Lesson 3-4 – Advanced Factoring Strategies for Quadratic Expressions

Various Examples and Exercises As Needed

Additional resources on emathinstruction

Lessons 3-6

Lesson 3. Factoring Polynomials

Lesson 4. Factoring Based on Conjugate Pairs

Lesson 5. Factoring Trinomials

Lesson 6. More Work Factoring Trinomials

Algebra 1 Major Content Review

p. 6 Problem #2-3

p. 8 Problem #9

Solving Quadratic Equations (By factoring, completing the square, Quadratic Formula) and Modeling

Modules

Algebra 1 Module 4, Lesson 7 – Creating and Solving Quadratic Equations in One Variable

Demonstrate- Example 2, Exercise 4, Exercise 5

Exit Ticket, Problem Set 2, 3, 4

Algebra 1 Module 4, Lesson 8 – Exploring the Symmetry in Graphs of Quadratic Functions

Demonstrate- Graph Vocabulary

Exploratory Challenge 2, Exit Ticket

Algebra 1 Module 4, Lesson 10 – Interpreting Quadratic Functions from Graphs and Tables

Demonstrate- Example 2

Exit Ticket

Modeling

Modules

Algebra 1 Module 4, Lesson 23 – Modeling With Quadratic Functions

Demonstrate-Opening, Mathematical Modeling Exercise 2, Exercise 1

Exit Ticket, Problem Set 2, 4

Algebra 1 Module 4, Lesson 24 – Modeling With Quadratic Functions

Demonstrate- Exercise 2

Exit Ticket

Additional resources on emathinstruction

Lessons 6-8

Lesson 6. The Zeroes of a Quadratic

Lesson 7. More Zero Product Work

Lesson 8. Quadratic Word Problems

Algebra 1 Major Content Review

p. 21 Problem #1-3

p. 22 Problem #4-7

p. 23 Problem #8-10

p. 24 Problem #11-12

p. 38 Problem #3-5

p. 39 Problem #7

Descriptive Statistics

Student Outcomes:

.

♣ Students distinguish between scatter plots that display a relationship that can be reasonably modeled by a linear equation and those that should be modeled by a nonlinear equation.

♣ Students use an equation given as a model for a nonlinear relationship to answer questions based on an understanding of the specific equation and the context of the data.

.

*Students use the least-squares line to predict values for a given data set.

♣ Students use residuals to evaluate the accuracy of predictions based on the least-squares line.

STANDARDS

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.

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

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

S-ID.9 Distinguish between correlation and causation.

Teaching Resources

Algebra 1 Module 2, Lesson 12 – Relationships Between Two Numerical Variables

Demonstrate-Exercise 8-13

Exit Ticket

Algebra 1 Module 2, Lesson 13 – Relationships Between Two Numerical Variables

Demonstrate-Problem Set 1-3

Exit Ticket

Algebra 1 Module 2, Lesson 14 –Modeling Relationships With Lines

Demonstrate-Problem Set 1-13

Exit Ticket

Algebra 1 Module 2, Lesson 16 –Modeling Relationships With Lines

Demonstrate-Problem Set 1-13

Exit Ticket

Exploring Linear Data-NCTM Illuminations

Algebra 1 Major Content Review

p. 61 Problem #1-2

p. 62 Problem #3-4

p. 63 Problem #5-6

p. 64 Problem #7

Modeling Functions

Student Outcomes:

♣ Students create a two-variable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. They interpret the graph and function and answer questions related to the model, choosing an appropriate level of precision in reporting their results.

♣ Students write equations to model data from tables, which can be represented with linear, quadratic, or exponential functions, including several from Lessons 4 and 5. They recognize when a set of data can be modeled with a linear, exponential, or quadratic function and create the equation that models the data.

♣ Students interpret the function in terms of the context in which it is presented, make predictions based on the model, and use an appropriate level of precision for reporting results and solutions.

♣ Students use linear, quadratic, and exponential functions to model data from tables, and choose the regression most appropriate to a given context. They use the correlation coefficient to determine the accuracy of a regression model and then interpret the function in context. They then make predictions based on their model, and use an appropriate level of precision for reporting results and solutions.

♣Students model functions described verbally in a given context using graphs, tables, or algebraic representations.

STANDARDS

F-IF.B.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-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.★

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

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

Teaching Resources

Modules

Algebra 1 Module 5, Lesson 4 – Modeling A Context From A Graph

Demonstrate-Entire Lesson

Exit Ticket, Problem Set 1, 2

Algebra 1 Module 5, Lesson 6 – Modeling A Context From Data

Demonstrate-Opening, Example 1, Exercise 2

Exit Ticket

Algebra 1 Module 5, Lesson 7 – Modeling A Context From Data

Demonstrate-Entire Lesson

Exit Ticket, Problem Set 1, 2

Algebra 1 Module 5, Lesson 8 – Modeling A Context From a Verbal Description

Demonstrate-Entire Lesson

Exit Ticket, Problem Set 1, 2, 3

Additional resources on emathinstruction

Lessons 1. Function Transformations

Lesson 2. Horizontal Stretching of Functions

Lesson 4. Another Look at Linear and Exponential Models

Lesson 5. Step Functions

Lesson 6. Piecewise Linear Functions

Lesson 7. Quadratic Models

Lesson 8 Limits on the Accuracy of Models

Shrinking Candles, Running Water, Folding Boxes-NCTM Illuminations

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