miami-dade county public schools 2014 2015...

MIAMI-DADE COUNTY PUBLIC SCHOOLS 2014 – 2015 District Pacing Guide

ALGEBRA II Course Code: 120033001

Division of Academics-Department of Mathematics of 9 Topic II_First Nine Weeks

Topic II: Linear Systems

MATHEMATICS FLORIDA STANDARDS & MATHEMATICAL PRACTICE (MP)

MATHEMATICAL PRACTICE (MP)

ESSENTIAL CONTEXT OBJECTIVES

MAFS.912.A-CED.1.3: 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 food. (MP.1, MP.2, MP.4, MP.5) (Assessed with MAFS.912.A-CED.1.2) MAFS.912.A-REI.3.6: Solve systems of linear

equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (MP.2, MP.4, MP.5, MP.6, MP.7, MP.8) (Assessed with MAFS.912.A-CED.1.2) MAFS.912.F-BF.1.1a: Determine an explicit

expression, a recursive process, or steps for calculation from a context. (MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7, MP.8) (Assessed with MAFS.912.F-BF.1.2)

MAFS.K12.MP.1

Make sense of problems and persevere in solving them. MAFS.K12.MP.2

Reason abstractly and quantitatively. MAFS.K12.MP.3

Construct viable arguments and critique the reasoning of others. MAFS.K12.MP.4

Model with mathematics MAFS.K12.MP.5

Use appropriate tools strategically. MAFS.K12.MP.6

Attend to precision. MAFS.K12.MP.7

Look for and make use of structure. MAFS.K12.MP.8

Look for and express regularity in repeated reasoning.

A. Systems of Equations with Two

Variables

B. Systems of Inequalities C. Linear Programming

D. Solving Systems of Equations with

Three Variables

I can:

Solve linear systems using a graph or a table

Solve linear systems algebraically

Solve systems of linear inequalities

Solve problems using linear programming Identify the quantities in a real-world

situation that should be represented by distinct variables

Write a system of equations given a real-world situation

Graph a system of equations that represents a real-world context using appropriate axis labels and scale

Solve systems of linear equations

Write a system of equations for a modeling context that is best represented by a system of equations

Write a system of inequalities for a modeling context that is best represented by a system of inequalities

Interpret the solution of a real-world context as viable or not viable

Solve systems of linear inequalities in two variables using graphical methods

Solve systems in three variables using elimination, substitution, and graphically

Define a recursive process, or complete a table of calculations that can be used to mathematically define a real-world context

Pacing Date(s) Traditional 14 09/08/14-09/26/14

Block 07 09/08/14-09/26/14




INSTRUCTIONAL TOOLS

Core Text Book: Prentice Hall Algebra 2. Honors Gold Series Florida

Standard Suggested Lessons Teacher Notes

MAFS.912.A-CED.1.2 MAFS.912.A-REI.3.6 MAFS.912.F-BF.1.1a

3.1 – 3.5

p.163

Pearson Additional Lessons N/A

McGraw-Hill Supplemental Resources

N/A

Topic II Assessment: Linear Systems

EQuIP Rubric Dimensions

The EQuIP Rubric Dimensions provide criteria to determine the quality and alignment of lessons and units to the MAFS in order to: (1) Identify exemplars/ models for teachers’ use within and across states; (2) provide constructive criteria-based feedback to developers; and (3) review existing instructional materials to determine what revisions are needed. Here are the four areas of your lesson to review: (For ratings information, go to EQuIP Rubric)

I. Alignment to the Depth of the MAFS – The lesson/unit aligns with the letter and spirit of the MAFS. II. Key Shifts in the MAFS – The lesson/unit reflects evidence of key shifts that are reflected in MAFS: Focus, Coherence, and Rigor III. Instructional Supports – The lesson/unit is responsive to varied student learning needs. IV. Assessment – The lesson/unit regularly assesses whether students are mastering standards-based Context and skills.

Algebra 1 (NGSSS) – Opportunities for Remediation

Algebra Nation (NGSSS)

Section 1: Sets and Venn Diagrams Section 2: Relations and Functions

Section 3: Solving for X Section 4: Solving Real World Equations

Housed in: Learning Village/ Pacing Guides and Curriculum/ High School/ Mathematics/ Algebra 1 (NGSSS) – Opportunities for Remediation/ Topic II

MiniPractice MA.912.D.7.1 MiniPractice MA.912.D.7.2

MiniPractice MA.912.A.2.3 MiniPractice MA.912.A.2.4

MiniPractice MA.912.A.3.1 MiniPractice MA.912.A.3.3 & A.5.4

MiniPractice MA.912.A.3.4 MiniPractice MA.912.A.3.5

Pacing Date(s) Traditional 14 09/08/14-09/26/14

Block 07 09/08/14-09/26/14

Topic II Assessment Window 09/19/14-10/03/14




INSTRUCTIONAL TOOLS

Vocabulary: System of equations, linear system, solution of a system, inconsistent system, consistent system, independent system, dependent system, equivalent systems, system of inequalities, absolute–value system, constraint, linear programming, feasible region, objective function, Maximizing/minimizing the objective function, coordinate space, ordered triples, systems with three variables. Instructional Strategies: Provide examples of real-world problems that can be modeled by writing an equation or inequality. Begin with simple equations and inequalities and build up

to more complex equations in two or more variables that may involve quadratic, exponential or rational functions. Discuss the importance of using appropriate labels and scales on the axes when representing functions with graphs. Use a graphing calculator to

demonstrate how dramatically the shape of a curve can change when the scale of the graph is altered for one or both variables. Examine real-world graphs in terms of constraints that are necessary to balance a mathematical model with the real-world context. For example, a student

writing an equation to model the maximum area when the perimeter of a rectangle is 12 inches should recognize that y = x(6 – x) only makes sense when 0 < x < 6. This restriction on the domain is necessary because the side of a rectangle under these conditions cannot be less than or equal to 0, but must be less than 6. Students can discuss the difference between the parabola that models the problem and the portion of the parabola that applies to the context.

Systems of equations are classified into two groups, consistent or inconsistent, depending on whether or not solutions exist. The solution set of a system of equations is the intersection of the solution sets for the individual equations. Stress the benefit of making the appropriate selection of a method for solving systems (graphing vs. addition vs. substitution). This depends on the type of equations and combination of coefficients for corresponding variables, without giving a preference to either method.

The graphing method can be the first step in solving systems of equations. A set of points representing solutions of each equation is found by graphing these equations. Even though the graphing method is limited in finding exact solutions and often yields approximate values, the use of it helps to discover whether solutions exist and, if so, how many are there?

The next step is to turn to algebraic methods, elimination or substitution, to allow students to find exact solutions. For any method, stress the importance of having a well-organized format for writing solutions.

Provide a real-world example (e.g., a table showing how far a car has driven after a given number of minutes, traveling at a uniform speed), and examine the table by looking “down” the table to describe a recursive relationship, as well as “across” the table to determine an explicit formula to find the distance traveled if the number of minutes is known.

Remarks: The system solution methods can include but are not limited to graphical, elimination/linear combination, substitution, and modeling. Systems can be written

algebraically or can be represented in context. Students may use graphing calculators, programs, or applets to model and find approximate solutions for systems of equations.

Connections: Students use their experience in solving and analyzing systems of two linear equations as a foundation for solving and analyzing linear systems with more

than two linear equations and systems with non-linear equations.




MATHEMATICS FLORIDA STANDARDS

MATHEMATICAL PRACTICES

DESCRIPTION

MAFS.K12.MP.1 (back to top)

Make sense of problems and persevere in solving them.

Mathematically proficient students will be able to:

Explain the meaning of a problem and looking for entry points to its solution.

Analyze givens, constraints, relationships, and goals.

Make conjectures about the form and meaning of the solution and plan a solution pathway.

Consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.

Monitor and evaluate their progress and change course if necessary.

Explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.

Check answers to problems using a different method, and continually ask, “Does this make sense?”

Identify correspondences between different approaches.


Reason abstractly and quantitatively.


Make sense of quantities and their relationships in problem situations.

Decontextualize—to abstract a given situation and represent it symbolically.

Contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols

Create a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them.

Know and be flexible using different properties of operations and objects.


Construct viable arguments and critique the reasoning of

others.


Understand and use stated assumptions, definitions, and previously established results in constructing arguments.

Make conjectures and build a logical progression of statements to explore the truth of their conjectures.

Analyze situations by breaking them into cases, and can recognize and use counterexamples.

Justify their conclusions, communicate them to others, and respond to the arguments of others.

Reason inductively about data, making plausible arguments that take into account the context from which the data arose.

Compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.

Determine domains to which an argument applies.


Model with mathematics.


Apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

Use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.

Apply what they know and feel comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.

Identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.

Analyze relationships mathematically to draw conclusions.

Interpret 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.





MATHEMATICAL PRACTICES

DESCRIPTION


Use appropriate tools strategically.


Consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.

Make sound decisions about when each of the tools appropriate for their grade or course might be helpful, recognizing both the insight to be gained and their limitations. Example: High school students analyze graphs of functions and solutions using a graphing calculator.

Detect possible errors by strategically using estimation and other mathematical knowledge.

Know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data.

Identify relevant external mathematical resources, such as digital Context located on a website, and use them to pose or solve problems.

Use technological tools to explore and deepen their understanding of concepts

MAFS.K12.MP.6

(back to top)

Attend to precision.


Communicate precisely to others.

Use clear definitions in discussion with others and in their own reasoning.

State the meaning of the symbols they choose, including using the equal sign consistently and appropriately.

Be careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem.

Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

MAFS.K12.MP.7

(back to top)

Look for and make use of structure.


Discern a pattern or structure. Example: In the expression x2 + 9x + 14, students can see the 14 as 2 × 7 and the 9 as 2 + 7.

Recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. Step back for an overview and shift perspective.

See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. Example: They can see 5 – 3(x – y)2 as 5

minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.


Look for and express regularity in repeated

reasoning.


Notice if calculations are repeated, and look both for general methods and for shortcuts. Example: Noticing the regularity in the way terms cancel when expanding (x-1)(x+1),(x-1)(x2+x+1),and(x-1)(x3 +x2+x+1)might lead them to the general formula for the sum of a geometric series.

Maintain oversight of the process, while attending to the details as they work to solve a problem.

Continually evaluate the reasonableness of their intermediate results.





Domain: ALGEBRA: CREATING EQUATIONS

STANDARD CODE STANDARD DESCRIPTION

Cluster 1: Create equations that describe numbers or relationships

MAFS.912.A-CED.1.3

(Assessed with MAFS.912.A-CED.1.2)

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.

Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES


Cluster 3: Solve systems of equations

MAFS.912.A-REI.3.6

(Assessed with MAFS.912.A-CED.1.2)

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 food. Context Complexity: Level 1: Recall

Cluster 4: Represent and solve equations and inequalities graphically

Domain: FUNCTIONS: BUILDING FUNCTIONS


Cluster 1: Build a function that models a relationship between two quantities

MAFS.912.F-BF.1.1a

(Assessed with MAFS.912.F-BF.1.2)

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.

Context Complexity: Level 3: Strategic Thinking & Complex Reasoning




TECHNOLOGY TOOLS

CPALM RESOURCES

LESSON PLANS

Exploring Systems with Piggies, Pizzas and Phones

Feasible or Non-Feasible? - That is the Question (Graphing Systems of Linear Inequalities):

Bernardo and Sylvia Play a Game

VIRTUAL MANIPULATIVE

Data Flyer

PROBLEM-SOLVING TASK

Accurately weighing pennies I

Accurately weighing pennies II

GRAPHING CALCULATOR CORRELATION

TEXAS INSTRUMENT MATH ACTIVITY TITLE

Intersecting the Solution

Maximizing Your Efforts

GIZMO CORRELATION

GIZMO TITLE

Systems of Linear Equations - Activity A

Solving Linear Systems by Graphing

Linear Programming - Activity A

TOPIC II

VIDEO TITLE

IMAGE

TOPIC II DISCOVERY EDUCATION CORRELATION

VIDEO TITLE

Systems of Equations: Part 01



http://www.cpalms.org/Public/PreviewResource/Preview/38181

http://education.ti.com/en/timath/us/detail?id=42BF31B766E246DFBF80ED1693F0EE39&sa=291B0ACD31104D178C0EA77ABC7FB53A

http://education.ti.com/en/timath/us/detail?id=F147E752DCFE4A609CFC019FBF4A190D&sa=291B0ACD31104D178C0EA77ABC7FB53A

http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=161



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http://app.discoveryeducation.com/player/view/assetGuid/8D5302E5-2704-4CEB-B9B9-BB7866FAB0BB




TOPIC II DISCOVERY EDUCATION CORRELATION


Systems of Inequalities

Solving Systems of Inequalities: Linear Programming

MATH OVERVIEW

Algebra II: Linear Programming - Optimizing Real World Problems

MATH EXPLANATION TITLE

Algebra II: Solving Linear Systems by Graphing Method: Linear Systems of Equations

Algebra II: Systems of Three Linear Equations in Three Variables: Substitution for Systems of Equations in Three Variables

Algebra II: Graphing and Solving Systems of Linear Inequalities: Graphing Systems of Linear Inequalities

Algebra II: Solving Linear Inequalities: Solving Inequality Word Problems

Algebra II: Linear Programming - Optimizing Real World Problems: Linear Programming

Algebra II: Linear Programming - Optimizing Real World Problems: Finding Maximum and Minimum Values, Part One

Algebra II: Linear Programming - Optimizing Real World Problems: Finding Maximum and Minimum Values, Part Two

http://app.discoveryeducation.com/player/view/assetGuid/18BA283D-8DC2-4866-9C1A-F39F7982E533

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MIAMI-DADE COUNTY PUBLIC SCHOOLS Instructional Focus Template



Date Pacing Guide

Standards Data Driven Standard(s)

Activities Assessment(s) Strategies

Traditional 14

Block 07

09/08/14-09/26/14 (back to top)

MAFS.912.A-CED.1.3 MAFS.912.A-REI.3.6 MAFS.912.F-BF.1.1a

miami-dade county public schools 2014 2015...

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