Marissa Secondary Mathematics Curriculum · 2017-11-02 · Marissa Community Unit School District...

Marissa Community Unit School District 40

November 2, 2017

Marissa Secondary

Mathematics

Curriculum

2014-2015


November 2, 2017

Table of Contents

Curriculum Authored by page 3

Curriculum Statement page 4

Symbols and Notations page 5

Mathematical Practices Synopsis page 6

Mathematical Practices Complete Definitions page 7

High School Modeling page 9

Course Sequence Chart page 10

Seventh Grade Curriculum page 11

Eighth Grade Curriculum page 27

Basic Skills Course page 42

Algebra I and Honors Algebra I page 44

Geometry page 63

Algebra II and Honors Algebra II page 78

Trigonometry and Statistics page 95

Calculus page 111

Appendices for PARCC page 120


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Created in 2013-2014 by

Darin Degenhart Mathematics Instructor

Gina Hamm Mathematics Instructor

Anne Trieb Mathematics Instructor

Karen Cannon Mathematics Consultant

Mark Heuring Principal

Dr. Kevin Codgill Superintendent


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Curriculum Statement

During the 2013-2014 school year, this mathematics curriculum document was created for Marissa

Junior High and Marissa Senior High School. The document is a compilation of the content the

secondary math faculty believes must be taught for students to be successful both in future math

courses and as they pursue their lives after graduation, whether they continue their education or they

enter the work force.

The curriculum is intended as a guide of what content to teach. How the content is delivered and when

the content is delivered are decisions to be made by the local math faculty as they work to best meet

the needs of their students. The content is also aligned with the Curriculum Frameworks of the Illinois

State Board of Education, the Common Core Standards for Mathematics and the needs of Marissa

students and is intended to help students be prepared for yearly assessments.

Curriculum documents are expected to be revised yearly as needed to best meet the needs of the

students, faculty and community.


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Symbols and Notations

1. Vocabulary words are typed in green.

2. The column titled “Common Core” shows notations that reference items in the Common Core

Standards for Mathematics. This information will be helpful when looking at state testing

results.

Example: SSE.A.1 in the Algebra I curriculum means the item is from the Seeing Structure

in Expressions (SSE) of the Algebra I curriculum. The notation A.1 means under Seeing Structure

in Expressions this item is in section A and it is the first item in section A.

3. The column titled “Correlation to the End of the Year Assessment” will have a blue asterisk, *,

in the column if the item is to be tested on state exams. Not all items will be tested as they are

content and skills that have been determined are needed to support mathematical knowledge.

4. In the Senior High School math courses, the column titled “PARCC Cluster Emphasis” will have

rectangular boxes and some boxes will have a black line under the box.

This indicates the content item will be tested in both Algebra I and in Algebra II. Please

see the appendices for an explanation of how the item will be tested at both levels.

Not all content in a course is equally emphasized in the standards. Some clusters of content

require greater emphasis and take greater time to master. They also have greater importance

to future math courses or for college or career readiness.

A green box indicates a major cluster and great importance.

A blue box indicates a supporting cluster.

A yellow box indicates additional clusters.


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Mathematical Practices per

Common Core Mathematics Standards

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.


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Mathematical Practices Definitions

Make sense of problems and persevere in solving them.

Mathematically proficiently students can understand and verbalize what the problem is asking them to

do. They conceptualize the problem and use appropriate tools to help them in finding the solution.

They use different methods to solve the problem and continually ask “Does this make sense?” They can

verbalize to others their work in a way that lets others understand the problem.

Reason abstractly and quantitatively.

Mathematically proficiently students can create a coherent representation of a problem. They are able

to represent a situation symbolically. As they compute they consider the units involved and understand

the size of the quantities. They use different properties of operations as they manipulate the symbols.

Construct viable arguments and critique the reasoning of others.

Mathematically proficiently students can understand and use definitions and assumptions as they

construct their arguments for the solution of a problem. They make conjectures, analyze their work and

make counterexamples. They justify their conclusions and can communicate them to others. They can

listen to the arguments of others and respond appropriately. Elementary students can construct

arguments using concrete objects, drawings, diagrams and actions.

Model with mathematics.

Mathematically proficient students can apply the math they know to solve problems in everyday life,

society and the workplace. This may be as simple as writing an equation to describe a situation or to

apply proportional reasoning to plan a school event. They are able to identify the important quantities

in a practical situation and show the relationships between the quantities by using a table, a graph, a

diagram, a flowchart or a formula.

Use appropriate tools strategically.

Mathematically proficient students know how to use a variety of tools to solve a math problem and can

utilize the appropriate tool for the job. These tools might include pencil and paper, concrete models, a

ruler, a protractor, a calculator, a spreadsheet or software. They use estimation as a tool to help them

detect errors and they can use the tools of technology to explore and deepen their understanding of

concepts.


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Attend to precision.

Mathematically proficient students try to communicate precisely to others. They understand and

communicate definitions clearly to others; specify units of measure and label axes appropriately. They

calculate accurately and efficiently and are able to carefully explain their work to each other.

Look for and make use of structure.

Mathematically proficient students look for patterns or structure. They will be able to use the

properties of algebra and mathematical strategies to help them solve problems. (Examples: 3 + 7 is the

same as 7 + 3. 7 x 8 is the same as 7 x 3 plus 7 x 5. 42 x 21 is the same as 42 x 20 plus 42 x 1 or (40 + 2)

(20 + 1)).

Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated and seek a general method or a

shortcut. As they work to solve the problem they not only see the details of the problem but the

overview of the problem; the bigger picture.


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High School: Modeling per Common Core Standards*

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 are 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.

* per the Common Core Standards for Mathematics


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Course Sequence Chart

SEVENTH GRADE MATH

ALGEBRA I EIGHTH GRADE MATH

All

All

ADVANCED GEOMETRY GEOMETRY ALGEBRA I

ADVANCED ALGEBRA II ALGEBRA II GEOMETRY

TRIG AND STATS TRIG AND STATS ALGEBRA II

CALCULUS TRIG AND STATS

All students entering seventh grade are required to take a one quarter course, Basic

Skills, designed to assure all students are proficient in basic skills. If students are not

successful during 7th grade they will complete the course again in 8th grade. Please see

the Basic Skills Guidelines for more information.


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Seventh Grade Mathematics


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Seventh Grade Mathematics

Course Description

The primary goal of this course is to encourage students to learn mathematics by doing mathematics.

Topics include Real Numbers and Algebra, Proportional Reasoning, Geometry and Measurement,

Probability and Statistics, and Linear and Nonlinear Functions. When appropriate, calculators will be

permitted, but students will be encouraged to complete calculations both mentally and with paper and

pencil. The main objectives of this course are (1) developing understanding of and applying proportional

relationships; (2) developing understanding of operations with rational numbers and working with

expressions and linear equations; (3) solving problems involving scale drawings and informal geometric

constructions, and working with two- and three-dimensional shapes to solve problems involving area,

surface area, and volume; and (4) drawing inferences about populations based on samples. Successful

completion of this course will prepare students for the concepts found in Eighth Grade Mathematics and

future courses.


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Seventh Grade

Critical Areas

(1) Developing understanding of and applying proportional relationships;

(2) Developing understanding of operations with rational numbers and working with expressions and

linear equations;

(3) Solving problems involving scale drawings and informal geometric constructions, and working with

two- and three-dimensional shapes to solve problems involving area, surface area, and volume;

(4) Drawing inferences about populations based on samples.


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Mathematical Practices per Common Core Mathematics Standards










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High School: Modeling*





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.


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Seventh Grade

I. Ratio and Proportional Relationships Assessment Common Core

PARCC Cluster Emphasis

A. Analyze proportional relationships and use them to solve real-world and mathematical problems.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

7.RP.A.1

Recognize and represent proportional relationships between quantities.

7.RP.A.1

Decide whether two quantities are in a proportional relationship.

7.RP.A.2a

Identify the constant of proportionality

(unit rate) in tables, graphs, equations,

diagrams, and verbal descriptions of

proportional relationships.

7.RP.A.2b

Represent proportional relationships as equations.

7.RP.A.2c

Explain what a point on the graph of a proportional relationship means.

7.RP.A.2d

Use proportional relationships to solve multistep ratio and percent problems. (examples: simple interest, tax, discount, etc.)

7.RP.A.3

http://www.corestandards.org/Math/Content/7/RP/A/1

http://www.corestandards.org/Math/Content/7/RP/A/2/a

http://www.corestandards.org/Math/Content/7/RP/A/2/b

http://www.corestandards.org/Math/Content/7/RP/A/2/c

http://www.corestandards.org/Math/Content/7/RP/A/2/d

http://www.corestandards.org/Math/Content/7/RP/A/3


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Instructional Strategies

Activities/Websites/Games/Apps


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II. The Number System

Assessment Common Core


A. Apply and extend previous understandings of operations with fractions.

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers

7.NS.A.1

Represent addition and subtraction on a horizontal or vertical number line diagram.

Describe situations in which opposite quantities combine to make 0.

7.NS.A.1a

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses).

7.NS.A.1b

Understand subtraction as adding the inverse.

7.NS.A.1c

Apply properties of operations as

strategies to add and subtract rational

numbers.

o

o 7.NS.A.1d

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations.

7.NS.A.2a

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q).

7.NS.A.2b

Apply properties of operations as

strategies to multiply and divide rational

numbers.

7.NS.A.2c

Convert a rational number to decimal using long division.

7.NS.A.2d

http://www.corestandards.org/Math/Content/7/NS/A/1/a

http://www.corestandards.org/Math/Content/7/NS/A/1/b

http://www.corestandards.org/Math/Content/7/NS/A/1/c

http://www.corestandards.org/Math/Content/7/NS/A/1/d

http://www.corestandards.org/Math/Content/7/NS/A/2/a

http://www.corestandards.org/Math/Content/7/NS/A/2/b

http://www.corestandards.org/Math/Content/7/NS/A/2/c

http://www.corestandards.org/Math/Content/7/NS/A/2/d


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Solve real-world and mathematical problems involving the four operations with rational numbers.

7.NS.A.3



http://www.corestandards.org/Math/Content/7/NS/A/3


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III. Expressions and Equations


Quarter

A. Use properties of operations to generate equivalent expressions

Apply properties of operations as strategies

to add, subtract, factor, and expand linear

expressions (honors) with rational

coefficients.

7.EE.A.1

Rewrite expressions in different forms to help solve problems.

7.EE.A.2

B. Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Solve multi-step real word problems using positive and negative rational numbers.

7.EE.B.3

Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

7.EE.B.3

Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities

7.EE.4

Solve word problems using equations of the form px+r=q and p(x=r)=q

7.EE.B.4a

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

7.EE.B.4b

http://www.corestandards.org/Math/Content/7/EE/A/1

http://www.corestandards.org/Math/Content/7/EE/A/2

http://www.corestandards.org/Math/Content/7/EE/B/3


http://www.corestandards.org/Math/Content/7/EE/B/4/a

http://www.corestandards.org/Math/Content/7/EE/B/4/b


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IV. Geometry


Quarter

A. Draw construct, and describe geometrical figures and describe the relationships between them.

Solve problems involving scale drawings of

geometric figures, including computing actual

lengths and areas from a scale drawing and

reproducing a scale drawing at a different

scale.

7.G.A.1

Draw (freehand, with ruler and protractor,

and with technology) geometric shapes with

given conditions. Focus on constructing

triangles from three measures of angles or

sides, noticing when the conditions determine

a unique triangle, more than one triangle, or

no triangle.

7.G.A.2

Describe the two-dimensional figures that

result from slicing three-dimensional figures,

as in plane sections of right rectangular

prisms and right rectangular pyramids.

7.G.A.3

B. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.G.B.4

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

7.G.B.5

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

7.G.B.6

http://www.corestandards.org/Math/Content/7/G/A/1




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V. Statistics and Probability


Quarter

A. Use random samplings to draw inferences about a population

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.A.1

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

7.SP.A.2

B. Draw informal comparative references about two populations

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

7.SP.B.1

C. Investigate chance processes and develop, use, and evaluate probability models.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.C.5

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

7.SP.C.6

http://www.corestandards.org/Math/Content/7/SP/A/1

http://www.corestandards.org/Math/Content/7/SP/A/1

http://www.corestandards.org/Math/Content/7/SP/C/5



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Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7.SP.C.7

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

7.SP.C.7a

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process

7.SP.C.7b

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.C8

Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

7.SP.C8a

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

7.SP.C8b

Design and use a simulation to generate frequencies for compound events.

7.SP.C8c



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Eighth Grade Mathematics


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Course Description

The primary goal of this course is to encourage students to learn mathematics by doing mathematics.

Topics include Real Numbers and Algebra, Proportional Reasoning, Geometry and Measurement,

Probability and Statistics, and Linear and Nonlinear Functions. When appropriate, calculators will be

permitted, but students will be encouraged to complete calculations both mentally and with paper and

pencil. The main objectives of this course are (1) formulating and reasoning about expressions and

equations, including modeling an association in bivariate data with a linear equation, and solving linear

equations and systems of linear equations; (2) grasping the concept of a function and using functions to

describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using

distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

Successful completion of this course will prepare students for the concepts found in the Algebra I.


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Critical Areas for Eighth Grade Instruction

In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about

expressions and equations, including modeling an association in bivariate data with a linear equation,

and solving linear equations and systems of linear equations; (2) grasping the concept of a function and

using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space

and figures using distance, angle, similarity, and congruence, and understanding and applying the

Pythagorean Theorem.


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Mathematical Practices*










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High School: Modeling per Common Core Mathematics Standards












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.



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A. Know there are numbers that are not rational and approximate them by rational numbers.

Know that numbers that are not rational are called irrational. Understand decimal expansion, repeating decimals, and conversion of a decimal expansion into a rational number.

NS.A.1

Compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions

NS.A.2



II. Expressions and Equations


PARCC Cluster


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Emphasis

A. Work with radicals and integer exponents

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/2

8.EE.A.1

Use square root and cube root symbols, 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.

8.EE.A.2

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities. Express how many times as much one is than the other.

8.EE.A.3

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

Interpret scientific notation that has been generated by technology

8.EE.A.4

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

Graph proportional relationships, interpreting the unit rate as the slope of the graph.

8.EE.B.5

Compare two different proportional relationships represented in different ways.

8.EE.B.5

Use similar triangles to explain why the slope m is the same between any two distinct

8.EE.B.6





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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 atb.

8.EE.B.6

C. Analyze and solve linear equations and pairs of simultaneous linear equations.

Solve linear equations in one variable.

8.EE.C.7a

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

8.EE.C.7b

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

8.EE.C.7c

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

8.EE.C.7d

Analyze and solve pairs of simultaneous linear equations.

8.EE.C.8

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.

8.EE.C.8a

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

8.EE.C.8b

Solve real-world and mathematical problems leading to two linear equations in two variables.

8.EE.C.8c


http://www.corestandards.org/Math/Content/8/EE/C/7









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November 2, 2017

III. Functions

Assessment

Common Core


A. Define, evaluate and compare functions

Understand that a function is a rule that assigns to each input exactly one output and graph the function.

8.F.A.1

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

8.F.A.2

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.A.3

B. Use functions to model relationships between quantities.

Construct a function to model a linear relationship between two quantities.

8.F.B.4

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.

8.F.B.4

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.B.4

Describe qualitatively the functional relationship between two quantities by analyzing a graph

8.F.B.5

Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

8.F.B.5

http://www.corestandards.org/Math/Content/8/F/B/4






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November 2, 2017

IV. Geometry



A. Understand congruence and similarity using physical models, transparencies or geometry software.

Verify experimentally the properties of rotations, reflections, and translations

8.G.A.1

Lines are taken to lines, and line segments to line segments of the same length.

8.G.A.1a

Angles are taken to angles of the same measure.

8.G.A.1b

Parallel lines are taken to parallel lines.

8.G.A.1c

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.

8.G.A.2

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

8.G.A.3

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.

8.G.A.4

Establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

8.G.A.5


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B. Understand and apply the Pythagorean Theorem

Explain a proof of the Pythagorean Theorem and its converse.

8.G.B.6

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

8.G.B.7

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

8.G.B.8

3. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

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

8.G.C.9



http://www.corestandards.org/Math/Content/8/G/B/6



http://www.corestandards.org/Math/Content/8/G/C/9


November 2, 2017

V. Statistics and Probability

Assessment

Common Core


A. Investigate patterns of association in bivariate data

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.

8.SP.A.1

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.

8.SP.A.2

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

8.SP.A.3

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.

8.SP.A.4

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.

S-ID.A.2

http://www.corestandards.org/Math/Content/HSS/ID/A/2


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

S-ID.A.3




November 2, 2017

Basic Skills Mathematics Course


November 2, 2017

Basic Skills Quarter Course

Guidelines

All seventh grade students, without IEPs, will be placed in the Basic Skills class at the beginning of the quarter. Tests to determine the student’s proficiency will be administered at the beginning, middle, and end of each quarter. The course is structured in a highly individualized manner. Seventh grade students should expect to practice skills that are needed for all math classes. Technology will be utilized when appropriate and available. Although some problem solving and application problems will be included, a large portion of the course will focus on basic computation problems. When students reach a score of 90 percent or greater on one of the three proficiency tests, they will no longer need to attend the Basic Skills class.


November 2, 2017

Algebra I and Honors Algebra I


November 2, 2017

Algebra I

Course Description

Algebra I is a bridge from the study of patterns and relationships in previous grades to the study of

functions. Topics include numerical and algebraic expressions, equations, a focus on linear equations

and graphing, inequalities, polynomial expressions, factoring, quadratic equations, and graphing

quadratics. The course is rich in applications and problem solving that connects math skills to life.

Technology is used as an instructional tool throughout the course. Calculators will be used, but students

are also expected to complete calculations mentally and with paper and pencil.

Honors Algebra I

Course Description

Algebra I is a bridge from the study of patterns and relationships in previous grades to the study of

functions. Topics include numerical and algebraic expressions, equations and inequalities, polynomial

expressions, factoring, radical functions, quadratic equations, graphing, and exponential functions. The

course is rich in applications and problem solving that connects math skills to life. This course will help

prepare today’s students for tomorrow’s world by involving students in exploring and discovering math

concepts that connect Algebra I with technology, engineering and science. Integrating technology as a

problem solving tool will be a strong instructional component. Calculators will be used, but students are

also expected to complete calculations mentally and with paper and pencil.


November 2, 2017

Mathematical Practices per the Common Core Mathematics Standards










November 2, 2017


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 are appropriately a creative process. Like every such process, this depends on acquired expertise as

well as creativity. Some examples of such situations might include:









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.






November 2, 2017

ALGEBRA

**Represents information for Honors or Advanced Algebra 1

I. The Real Number System Correlation to the End of Year Assessment

Common Core


A. Extend properties of exponents to rational

exponents

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

RN.A.1

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

RN.A.2

Explain why the sum or product of two rational numbers is rational; that 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

* RN.A.3

B. Reason quantitatively and use units to

solve problems

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

*

SN.Q.A.1

Define appropriate quantities for the purpose of descriptive modeling

* SN.Q.A.2

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities

* SN.Q.A.3

http://www.corestandards.org/Math/Content/HSN/RN/A/1



http://www.corestandards.org/Math/Content/HSN/Q/A/1




November 2, 2017

II. Seeing Structure in Expressions Assessment Common Core


A. Interpret the structure of expressions

Interpret expressions that represent a quantity in terms of its context

*

SSE.A.1

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

* SSE.A.1a

**Interpret complicated expressions by viewing one or more of their parts as a single entity.

* SSE.A.1b

**Use the structure of an expression to identify ways to rewrite it.

* SSE.A.2

Evaluate numerical expressions and algebraic expressions by using order of operations.

Solve open sentence equations and inequalities.


November 2, 2017

a) Recognize the properties of equality and identity and use them to evaluate problems using order of operations

b) Use the distributive, commutative

and associative properties to evaluate and simplify expressions

B. Write expressions in equivalent forms to solve problems

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression

SSE.B.3

a) Factor a quadratic expression to reveal the zeros of the function.

* SSE.B.3a

b) Complete the square in a quadratic equation and find the maximum and minimum values.

* SSE.B.3b

c) Use the properties of exponents to transform expressions for exponential functions.

* SSE.B.3c

** Derive the formula for the sum of a finite geometric series and use the formula to solve problems.

SSE.B.4


November 2, 2017


Use graphing calculator to emphasize what the zeros of a quadratic equation



November 2, 2017

III. Arithmetic with Polynomials and Rational Expression



A. Perform arithmetic operations on

polynomials

Understand that polynomials are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

* APR.A.1

B. Understand the relationship between zeros and factors of polynomials

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

* APR.B.3

C. Use polynomial identities to solve problems

Prove polynomial identities and use them to

describe numerical relationships

* APR.C.4

D. Rewrite rational expressions

Rewrite simple rational expressions in different forms

* APR.D.6

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions

APR.D.7

http://www.corestandards.org/Math/Content/HSA/APR/A/1

http://www.corestandards.org/Math/Content/HSA/APR/B/3

http://www.corestandards.org/Math/Content/HSA/APR/C/4

http://www.corestandards.org/Math/Content/HSA/APR/D/6

http://www.corestandards.org/Math/Content/HSA/APR/D/7


November 2, 2017




November 2, 2017

IV. Creating Equations Assessment Common Core


A. Create equations that describe numbers or relationships

Create equations and inequalities in one

variable and use them to solve problems

* HAS-CED.A.1

Create equations in two or more variables

to represent relationships between

quantities

* HAS-CED.A.2

Graph equations on coordinate axes with

labels and scales

* HAS-CED.A.2

Represent constraints by equations or

inequalities, and by systems of equations

and/or inequalities

* HAS-CED.A.3

Interpret solutions as viable or nonviable

options in a modeling context

* HAS-CED.A.3

Rearrange formulas to highlight a quantity

of interest, using the same reasoning as in

solving equations

* HAS-CED.A.4


November 2, 2017

B. Understand the Concept of Functions and

Use Function Notation

Understand that a function from one set

(called the domain) to another set (called

the range) assigns to each element of the

domain exactly one element of the range.

If f is a function and x is an element of its

domain, then f(x) denotes the output of f

corresponding to the input x. The graph

of f is the graph of the equation y = f(x).

* F-IF.A.1

Use function notation, evaluate functions

for inputs in their domains, and interpret

statements that use function notation in

terms of a context.

* F-IF.A.2

Recognize that sequences are functions,

sometimes defined recursively, whose

domain is a subset of the integers.

* F-IF.A.3

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.B.4

Relate the domain of a function to its graph

and, where applicable, to the quantitative

relationship it describes

* F-IF.B.5

http://www.corestandards.org/Math/Content/HSF/IF/A/1



http://www.corestandards.org/Math/Content/HSF/IF/B/4



November 2, 2017

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

F-IF.B.6

Graph linear and quadratic functions and

show intercepts, maxima and minima.

F.IF. 7a

Write a function defined by an expression in

different but equivalent forms to reveal and

explain different properties of the function

F-IF.C.8

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.

* F-IF.C.8a

C. Analyze functions using different

representations

Graph linear and quadratic functions and show

intercepts, maxima, and minima.

* F-IF.C.7a

**Graph square root, cube root, and piecewise-

defined functions, including step functions and

absolute value functions.

* F-IF.C.7b

** 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.

* F-IF.C.8a


http://www.corestandards.org/Math/Content/HSF/IF/C/8


http://www.corestandards.org/Math/Content/HSF/IF/C/8/a


November 2, 2017

**Compare properties of two functions each

represented in a different way (algebraically,

graphically, numerically in tables, or by verbal

descriptions).

* F-IF.C.9

D. Construct and compare linear, quadratic,

and exponential models and solve problems

Distinguish between situations that can be

modeled with linear functions and with

exponential functions.

* F-LE.A.1

Prove that linear functions grow by equal

differences over equal intervals, and that

exponential functions grow by equal factors

over equal intervals.

* F-LE.A.1a

Construct linear and exponential functions,

including arithmetic and geometric sequences,

given a graph, a description of a relationship, or

two input-output pairs

* F-LE.A.2

Observe using graphs and tables that a quantity

increasing exponentially eventually exceeds a

quantity increasing linearly, quadratically, or

(more generally) as a polynomial function.

* F-LE.A.3

http://www.corestandards.org/Math/Content/HSF/LE/A/1





November 2, 2017


Mixture Picture

See-Saw Method

Chart Method

Utilize the graphing calculator to check a graphed equation.



November 2, 2017

V. Reasoning with Equations and Inequalities Assessment Common Core


A. Understand solving equations as a process of reasoning and explain the reasoning

Explain each step in solving a simple equation.

Construct a viable argument to justify a solution

method.

* REI.REI.A.1

Solve simple rational and radical equations in

one variable, and give examples showing how

extraneous solutions may arise.

* REI.A.2

Solve system of linear equations exactly and

approximately focusing on pairs of linear

equations in two variables.

REI.A.6

B. Solve equations and inequalities in one variable

Solve linear equations and inequalities in one

variable, including equations with coefficients

represented by letters.

* REI.B.3

Solve quadratic equations in one variable. * REI.B.4

**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.

* REI.B.4a

http://www.corestandards.org/Math/Content/HSA/REI/B/4/a


November 2, 2017

**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.

* REI.B.5

**Understand that the graph of an equation in

two variables is the set of all its solutions

plotted in the coordinate plane, often forming a

curve (which could be a line)

* REI.B.10

** 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.

* REI.B.12


Quadratic Formula Song



November 2, 2017

VI. Data Analysis and Probability Assessment Common Core


A. Summarize, represent and interpret data on a single count or measurement variable

Represent data with plots on the real number line (dot plots,

histograms, and box plots).

*

S-ID.A.1

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.

* S-ID.A.2

Interpret differences in shape, center, and spread in the context

of the data sets, accounting for possible effects of extreme data

points (outliers)

* S-ID.A.3

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

S-ID.A.4

**Summarize categorical data for two categories in two-way frequency tables. Recognize possible associations and trends in the data.

* S-ID.A.5

**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

* S-ID.A.6a

** Informally assess the fit of a function by plotting and analyzing residuals.

* S-ID.A.6b






November 2, 2017

**Fit a linear function for a scatter plot that suggests a linear association.

* S-ID.A.6c

B. Interpret linear models

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

* S-ID.A.7





November 2, 2017

Geometry


November 2, 2017

Geometry

Course Description

Geometry is designed to develop spatial concepts and insight into the relationships between plane figures such as points, lines, triangles, quadrilaterals, other polygons, and circles. Algebraic principles, including the use of coordinates, are applied to geometric problems. Measurement of two and three-dimensional figures will be explored. The use of a ruler, compass, protractor, and technology will be used when appropriate, throughout the course as instructional tools. Because development of precise mathematical language is stressed, reading and problem solving are emphasized throughout.

Course Description

Honors Geometry is designed to develop spatial concepts and insight into the relationships between plane figures such as points, lines, triangles, quadrilaterals, other polygons, and circles. Algebraic principles, including the use of coordinates, are applied to geometric problems. Measurement of two and three-dimensional figures will be explored. To appreciate the power of logic as a tool for understanding the world around you, the concept of a formal proof is a substantial focus of the course. The use of a ruler, protractor, compass and technology will be used throughout the course as an instructional tool. Because development of precise mathematical language is stressed, reading and problem solving are emphasized throughout.

NOTE: Students are expected to utilize the concepts of Algebra I throughout the Honors Geometry course. Therefore, to be successful in Honors Geometry, a grade of “B” or better is recommended in Algebra I if the student has just completed 8th grade Algebra I, or a grade of “A” is recommended if the student has just completed 9th grade Algebra I.


November 2, 2017











November 2, 2017

Geometry

I. Congruence



A. Experiment with transformations in the plane

*

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

* G-CO.A.1

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not

* G-CO.A.2

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

* G-CO.A.3

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

* G-CO.A.4

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

* G-CO.A.5

B. Use congruence in terms of rigid motion

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

* G-CO.B.6

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

* G-CO.B.7

http://www.corestandards.org/Math/Content/HSG/CO/A/1

http://www.corestandards.org/Math/Content/HSG/CO/C/9



November 2, 2017

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

* G-CO.B.8

C. Prove geometric theorems

Prove theorems about lines and angles. * G-CO.C.9

Prove theorems about triangles. * G-CO.C.10

Prove theorems about parallelograms. * G-CO.C.11

D. Make geometric constructions

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)

* G-CO.D.12

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

* G-CO.D.13


Activities, Websites, Games and Apps





http://www.corestandards.org/Math/Content/HSG/CO/D/12


November 2, 2017

II. Similarity, Right Triangles and Trigonometry



A. Use similarity in terms of similarity transformations

Verify experimentally the properties of dilations given by a center and a scale factor

* G-SRT.A.1

A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

G-SRT.A.1a

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G-SRT.A.1b

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

* G-SRT.A.2

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

* G-SRT.A.3

B. Prove theorems involving similarity

Prove theorems about triangles.

* G-SRT.B.4

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

* G-SRT.B.5

C. Define trigonometric ratios and solve problems involving right triangles

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

* G-SRT.C.6

Explain and use the relationship between the sine and cosine of complementary angles.

* G-SRT.C.7

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

* G-SRT.C.7

http://www.corestandards.org/Math/Content/HSG/SRT/A/1





http://www.corestandards.org/Math/Content/HSG/SRT/B/4

http://www.corestandards.org/Math/Content/HSG/SRT/B/4

http://www.corestandards.org/Math/Content/HSG/SRT/C/6

http://www.corestandards.org/Math/Content/HSG/SRT/C/6


November 2, 2017

D. Apply trigonometry to general triangles

Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

G-RT.D.9 (+)

Prove the Laws of Sines and Cosines and use them to solve problems.

G-RT.D.9 (+)

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

G-RT.D.9 (+)



http://www.corestandards.org/Math/Content/HSG/SRT/D/9




November 2, 2017

III. Circles



1. Understand and apply theorems about circles

Prove that all circles are similar.

* SG-C.A.1

Identify and describe relationships among inscribed angles, radii, and chords.

* SG-C.A.2

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

* SG-C.A.3

Construct a tangent line from a point outside a given circle to the circle.

* SG-C.A.4(+)

2. Find arc lengths and areas of sectors of circles

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

* SG-C.B.5


http://www.corestandards.org/Math/Content/HSG/C/A/1




http://www.corestandards.org/Math/Content/HSG/C/B/5


November 2, 2017



November 2, 2017

IV. Geometric Properties with Equations



A. Translate between the geometric description and the equation of a conic section

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

* G-GPE.A.1

Derive the equation of a parabola given a focus and directrix.

* G-GPE.A.2

B. Use coordinates to prove simple geometric theorems algebraically

Use coordinates to prove simple geometric theorems algebraically

* G-GPE.B.4

Find the equation of a line parallel or perpendicular to a given line that passes through a given point).

* G-GPE.B.5

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

* G-GPE.B.6

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula

* G-GPE.B.7


http://www.corestandards.org/Math/Content/HSG/GPE/A/1

http://www.corestandards.org/Math/Content/HSG/GPE/B/7





November 2, 2017



November 2, 2017

V. Geometric Measurement and Dimension

Assessment Common Core PARCC Cluster Emphasis

1. Explain volume formulas and use them to solve problems

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

* G-GMD.A.1

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

* G-GMD.A.3

2. Visualize relationships between two and three dimensional objects

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

* G-GMD.B.4


http://www.corestandards.org/Math/Content/HSG/GMD/A/1

http://www.corestandards.org/Math/Content/HSG/GMD/A/1

http://www.corestandards.org/Math/Content/HSG/GMD/B/4


November 2, 2017



November 2, 2017

VI. Modeling with Geometry Assessment Common Core PARCC Cluster Emphasis

1. Apply geometric concepts in modeling situations

Use geometric shapes, their measures, and their properties to describe objects

* G-MG.A.1

Apply concepts of density based on area and volume in modeling situations

* G-MG.A.2

Apply geometric methods to solve design problems

* G-MG.A.3



http://www.corestandards.org/Math/Content/HSG/MG/A/1




November 2, 2017

Algebra II


November 2, 2017

Algebra II

Course Description

In this course, the basic concepts from Algebra I are enriched. Topics studied include graphing,

analyzing, and interpreting functions including linear, polynomial (especially quadratics), rational, and

exponential functions; systems of linear equations and inequalities; conic sections; exponents and

radicals. Graphing calculators will be used when appropriate to enhance learning and as an instructional

tool. Students will be expected to think critically and apply their knowledge and skills to solve problems

that occur in life.

Honors Algebra II: Course Description

In this course, the basic concepts from Algebra I are enriched. Topics studied include graphing,

analyzing, and interpreting functions including linear, polynomial (especially quadratics), rational,

exponential, and logarithmic functions; systems of linear equations and inequalities; conic sections;

exponents and radicals. Graphing calculators will be used when appropriate to enhance learning and as

an instructional tool. Students will be expected to think critically and apply their knowledge and skills to

solve problems that occur in life. This course is designed for students wanting to move on to

Trigonometry and eventually Calculus.


November 2, 2017

Mathematical Practices per Common Core Mathematics Standards










November 2, 2017



















November 2, 2017

Algebra II

I. The Real Number System Correlation to the End of the Year Assessment

Common Core


A. Extend the properties of exponents to rational numbers

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

* N-RN.A.1

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

* N-RN.A.2

B. Use properties of rational and irrational numbers

Explain why the sum or product of two rational numbers is rational; that 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

* N-RN.B.3

C. Reason quantitatively and use units to solve problems

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.A.1

Define appropriate quantities for the purpose of descriptive modeling.

* N-Q.A.2

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities

* N-Q.A.3

D. Perform arithmetic operations with complex numbers

Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real

* N-CN.A.1

Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers

* N-CN.A.2

Solve quadratic equations with real coefficients that have complex solutions.

* N-CN.A.7



http://www.corestandards.org/Math/Content/HSN/RN/B/3




http://www.corestandards.org/Math/Content/HSN/CN/A/1



November 2, 2017




November 2, 2017

II. Reasoning with Equations and Inequalities Assessment Common Core


A. Understand solving equations as a process of reasoning and explain the reasoning

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.

* A-REI.B.1

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise

* A-REI.A.2

B. Solve equations and inequalities in one variable

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.

REI.B.4a

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.

REI.B.4b

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.

REI.C.5

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

* REI.C.6

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

* REI.C.7

http://www.corestandards.org/Math/Content/HSA/REI/A/2


November 2, 2017

C. Represent and solve equations and inequalities graphically

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).

REI.C.10

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., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

REI.C.11

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.

REI.C.12



November 2, 2017



November 2, 2017

III. Functions Assessment Common Core


A. Interpret functions that arise in applications in terms of the context

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.

F-IF.B.4

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F-IF.B.5

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

F-IF.B.6

B. Analyze functions using different representations

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

F-IF.C.7b

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F-IF.C.7c

Graph exponential and logarithmic functions, showing intercepts and end behavior

F-IF.C.7e

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

F-IF.C.8

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.

F-IF.C.8a

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

F-IF.C.8b

Compare properties of two functions each represented in a different way.

F-IF.9F




http://www.corestandards.org/Math/Content/HSF/IF/C/7/b







November 2, 2017




November 2, 2017

III. Functions Assessment Common Core


C. Build a function that models a relationship between two quantities

Write a function that describes a relationship between two quantities.

F-BF.A.1

Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-BF.A.1a

Combine standard function types using arithmetic operations.

F-BF.A.1b

Composite functions

F-BF.A.1c

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

F-BF.3

D. Construct and compare linear, quadratic, and exponential models and solve problems

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

F-LE.A.1

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

F-LE.A.1a

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

F-LE.A.1c

E. Interpret expressions for functions in terms of the situation they model

Interpret the parameters in a linear or exponential function in terms of a context.

F-LE.B.5

F. Summarize, represent, and interpret data on two categorical and quantitative variables.

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.

S-ID.B.6a

Fit a linear function for a scatter plot that suggests a linear association.

S-ID.B.6c

http://www.corestandards.org/Math/Content/HSF/BF/A/1







http://www.corestandards.org/Math/Content/HSF/LE/B/5

http://www.corestandards.org/Math/Content/HSS/ID/B/6/a


November 2, 2017

G. Interpret linear models

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

Alg I? S-ID.C.7



http://www.corestandards.org/Math/Content/HSS/ID/C/7


November 2, 2017

IV. Complex Number System Assessment Common Core


A. Perform Operations with Complex Numbers

Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

HSN-CN.A.1

Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

HSN-CN.A.2

Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

HSN-CN.A.3

B. Represent complex numbers and their operations on the complex plane

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

HSN-CN.B.4

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

HSN-CN.B.5

Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

HSN-CN.B.6

C. Use complex numbers in polynomial identities and equations

Solve quadratic equations with real coefficients that have complex solutions.

HSN-CN.C.7

Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).

HSN-CN.C.8

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

HSN-CN.C.9




http://www.corestandards.org/Math/Content/HSN/CN/B/4



http://www.corestandards.org/Math/Content/HSN/CN/C/7




November 2, 2017




November 2, 2017

V. Matrices



1. Perform operations on matrices and use matrices in applications

Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

HSN-VM.C.6

Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

HSN-VM.C.7

Add, subtract, and multiply matrices of appropriate dimensions.

HSN-VM.C.8

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

HSN-VM.C.9

Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

HSN-VM.C.10

Work with 2 × 2 matrices as a transformation of the plane, and interpret the absolute value of the determinant in terms of area.

HSN-VM.C.12


http://www.corestandards.org/Math/Content/HSN/VM/C/6







November 2, 2017



November 2, 2017

Trigonometry and Statistics


November 2, 2017

Course Description


Trigonometry is a course where students study relations, functions, graphs, polar coordinates, complex

numbers, logarithms, and trigonometric functions and identities. This course is an in-depth look at right

triangles and their properties in relation to the unit circle and distance. Law of Sines and Law of Cosines

will be taught. Students will also graph logarithmic, exponential, and trigonometric functions. Vectors,

conics sections, and polynomial functions and their graphs will also be covered in addition to an

extensive unit on probability and statistics. This course will develop the students’ mathematical

concepts, improve logical thinking, and help to promote success. It is strongly recommended that

students who wish to continue their education beyond high school take trigonometry and then pursue

calculus.


November 2, 2017











November 2, 2017

High School: Modeling

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:









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.






November 2, 2017


I. Functions Assessment Common Core


A. Analyze trigonometric functions using different representations

Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior

F-F.C.7d

Graph trigonometric functions, showing period, midline and amplitude.

F-F.C.7e

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

F-IF.C.8

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.

F-IF.C.8a

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions

F-IF.C.8b

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)

F-IF.C.9






November 2, 2017

B. Build new functions from existing functions

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

F-BF.B.3

Find inverse functions F-BF.B.4

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse

F-BF.B.4a

Verify by composition that one function is the inverse of another.

F-BF.B.4b

Read values of an inverse function from a graph or a table, given that the function has an inverse

F-BF.B.4c

Produce an invertible function from a non-invertible function by restricting the domain.

F-BF.B.4d

Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents

F-BF.B.5

Find the inverse of a matrix if it exists and use

it to solve systems of linear equations (using

technology for matrices of dimension 3 × 3 or

greater).

REI.C.9

C. Construct and compare linear, quadratic, and exponential models and solve problems

http://www.corestandards.org/Math/Content/HSF/BF/B/3








November 2, 2017

For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

F-LE.A.4

Represent a system of linear equations as a single matrix equation in a vector variable.

REI.C.8

D. Extend the domain of trigonometric functions using the unit circle

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle

F-TF.A.1

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle

F-TF.A.2

Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

F-TF.A.3

Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

F-TF.A.4

E. Model periodic phenomena with trigonometric functions

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline

F-TF.B.5

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed

F-TF.B.6


http://www.corestandards.org/Math/Content/HSF/TF/A/1




http://www.corestandards.org/Math/Content/HSF/TF/B/5

http://www.corestandards.org/Math/Content/HSF/TF/B/5


November 2, 2017

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

F-TF.B.7

F. Prove and apply trigonometric functions

Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle

F-TF.C.8

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems

F-TF.C.9



http://www.corestandards.org/Math/Content/HSF/TF/C/8

http://www.corestandards.org/Math/Content/HSF/TF/C/8


November 2, 2017

II. Statistics Assessment Common Core


A. Summarize, represent, and interpret data on a single count or measurement variable

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

S-ID.A.4

B. Summarize, represent, and interpret data on two categorical and quantitative variables

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

S-ID.B.5

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

S-ID.B.6

Informally assess the fit of a function by plotting and analyzing residuals.

S-ID.B.6b

C. Interpret linear models

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

S-ID.C.8

Distinguish between correlation and causation. S-ID.C.9

http://www.corestandards.org/Math/Content/HSS/ID/B/5






November 2, 2017

D. Understand and evaluate random processes underlying statistical experiments

Understand statistics as a process for making inferences about population parameters based on a random sample from that population

S-IC.A.1

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

S-IC.A.2

E. Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each

S-IC.B.3

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling

S-IC.B.4

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant

S-IC.B.5

Evaluate reports based on data

S-IC.B.6

http://www.corestandards.org/Math/Content/HSS/IC/A/1

http://www.corestandards.org/Math/Content/HSS/IC/B/3





November 2, 2017




November 2, 2017

III. Probability Assessment Common Core


A. Understand independence and conditional probability and use them to interpret data

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S-CP.A.1

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent

S-CP.A.2

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S-CP.A.3

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities

S-CP.A.4

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations

S-CP.A.5

B. Use the rules of probability to compute probabilities of compound events

Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

S-CP.B.6

http://www.corestandards.org/Math/Content/HSS/CP/A/1





http://www.corestandards.org/Math/Content/HSS/CP/B/6


November 2, 2017

Apply the Addition Rule and interpret the answer in terms of the model

S-CP.B.7

Apply the general Multiplication Rule in a uniform probability model and interpret the answer in terms of the model

S-CP.B.8

Use permutations and combinations to compute probabilities of compound events and solve problems.

S-CP.B.9

C. Calculate expected values and use them to solve problems

Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions

S-MD.A.1

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution

S-MD.A.2

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value

S-MD.A.3

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value

S-MD.A.4

D. Use probability to evaluate outcomes of decisions

Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values

S-MD.B.5

Find the expected payoff for a game of chance S-MD.B.5a

Evaluate and compare strategies on the basis of expected values

S-MD.B.5b




http://www.corestandards.org/Math/Content/HSS/MD/A/1




http://www.corestandards.org/Math/Content/HSS/MD/B/5




November 2, 2017

Use probabilities to make fair decisions S-MD.B.6

Analyze decisions and strategies using probability concepts

S-MD.B.7






November 2, 2017

IV. Vectors



I. Represent and model with vector quantities

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

HSN-VM.A.1

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

HSN-VM.A.2

Solve problems involving velocity and other quantities that can be represented by vectors.

HSN-VM.A.3

II. Perform operations on vectors

Add and subtract vectors. HSN-VM.B.4

Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

HSN-VM.B.4a

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

HSN-VM.B.4b

Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

HSN-VM.B.4c

Multiply a vector by a scalar.

HSN-VM.B.5

Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

HSN-VM.B.5 a

Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

HSN-VM.B.5 b

http://www.corestandards.org/Math/Content/HSN/VM/A/1



http://www.corestandards.org/Math/Content/HSN/VM/B/4












November 2, 2017

Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

HSN-VM.C.11






November 2, 2017

Calculus


November 2, 2017

Calculus

Course Description

Calculus will address limits, derivatives, and integrals of polynomial, exponential,

logarithmic and trigonometric functions, and applications of differentiation and

integration. This course prepares the student to take Calculus I at the college

level. Graphing calculators and computers will be integrated throughout the

course.


November 2, 2017











November 2, 2017



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:
















November 2, 2017

Calculus

I. Limits

Develop an intuitive interpretation of limits

Interpret limits geometrically/graphically

Evaluate one-sided limits

Apply properties of limits

Determine limits of polynomials

Investigate limits of rational functions

Analyze limits of infinity

Interpret the limit definition of continuity

Evaluate limits of trigonometric functions




November 2, 2017

II. Differentiation

Demonstrate the use of the limit definition of derivative

Interpret the geometric definition of a derivative

Calculate the derivative at a point

Determine the derivatives of the following functions:

1. Polynomial 2. Rational 3. Composite 4. Inverse 5. Exponential 6. Trigonometric 7. Logarithmic 8. Implicit

Analyze higher order derivatives

Apply the appropriate method to compute the following derivatives:

1. Power Rule 2. Product Rule 3. Quotient Tule 4. Chain Rule 5. Implicit Differentiation 6. Logarithmic Differentiation

Demonstrate the following applications of derivatives:

1. Analysis of curves, including monotonicity and concavity

2. Optimization 3. Rates of change and related rates

Know and apply the Mean Value Theorem

Know and apply the Extreme Value Theorem

Know and apply Rolle’s Theorem

Know and apply Newton’s Method


November 2, 2017




November 2, 2017

III. Integration

Calculate numerical approximations of the area under a curve

Apply the Fundamental Theorem of Calculus

Interpret the Second Fundamental Theorem of Calculus

Apply the appropriate method to compute the following anti-derivatives:

1. By power rule 2. By substitution 3. Of the form du/u 4. Inverse trigonometric functions 5. By parts 6. Volume of solids 7. Physical, biological or economic

situations

Use the integral to compute work and fluid pressure

Use and apply L’Hospital’s /Rule

Be able to solve basic differential equations.



November 2, 2017



November 2, 2017

Appendices from PARCC


November 2, 2017

Marissa Secondary Mathematics Curriculum · 2017-11-02 · Marissa Community Unit School District...

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