POINT PLEASANT BEACH SCHOOL DISTRICT

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Content Area: Mathematics

Course Title: Integrated Mathematics 1 Grade Level: 9

Unit Plan 1

Foundations of Algebra:

Variables, Expressions, Integers

and the Coordinate Plane

Pacing Guide

3 weeks

Unit Plan 2

Equations and Inequalities

Pacing Guide

5 weeks

Unit Plan 3

Rational Numbers and Exponents

Pacing Guide

4 weeks

Unit Plan 4

Ratios, Proportions, and Percents

Pacing Guide

4 weeks

Unit Plan 5

Linear Equations and Functions

Pacing Guide

6 weeks

Unit Plan 6

Real Numbers, Right Triangles and

Coordinate Geometry

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Course Title: Integrated Mathematics 1 Grade Level: 9

Unit Plan 7

Polynomials

Pacing Guide

3 weeks

Unit Plan 8

Data Analysis and Probability

Pacing Guide

3 weeks

Date Created: July 2016 Written by: Maureen Caprio

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Standards for Mathematical Practices

The following standards for Mathematical Practice will be covered throughout various units of the curriculum.

MP.1 Make sense of problems and persevere in solving them

Find meaning in problems Look for entry points

Analyze conjecture and plan solution pathways

Monitor and adjust Verify answers

Ask themselves the question: “Does this make sense?”

MP.2 Reason abstractly and quantitatively Make sense of quantities and their relationships in problems

Learn to contextualize and decontextualize Create coherent representations of problems MP.3 Construct viable arguments and critique the

reasoning of others

Understand and use information to construct arguments

Make and explore the truth of conjectures Recognize and use counterexamples

Justify conclusions and respond to arguments of others

MP.4 Model with Mathematics Apply mathematics to problems in everyday life

Make assumptions and approximations Identify quantities in a practical situation Interpret results in the context of the situation and reflect on whether the results make sense MP.5 Use appropriate tools strategically Consider the available tools when solving

problems

Are familiar with tools appropriate for their grade or course

Make sound decisions of which of these tools might be helpful

MP.6 Attend to precision Communicate precisely to others

Use clear definitions, state the meaning of symbols and are careful about specifying units of measure and labeling axes

Calculate accurately and efficiently MP.7 Look for and make use of structure Discern patterns and structures

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See complicated things as single objects or as being composed of single objects

MP.8 Look for and express regularity in repeated reasoning

Notice if calculations are repeated and look both for general methods and shortcuts

In solving problems, maintain oversight of the process while attending to detail

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Career Ready Practices

The following Career Ready Practices will be developed throughout various units of the curriculum. CRP1 Act as a responsible and contributing citizen and employee.

CRP2 Apply appropriate academic and technical skills. CRP3 Attend to personal health and financial well-being. CRP4 Communicate clearly and effectively and with reason.

CRP5 Consider the environmental, social and economic impacts of decisions. CRP6 Demonstrate creativity and innovation.

CRP7 Employ valid and reliable research strategies.

CRP8 Utilize critical thinking to make sense of problems and persevere in solving them. CRP9 Model integrity, ethical leadership and effective management.

CRP10 Plan education and career paths aligned to personal goals. CRP11 Use technology to enhance productivity.

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Unit Overview

Unit Title: Foundations of Algebra: Variables, Expressions, Integers, and Coordinate Plane Target Course/Grade Level: 9

Unit Summary: Students will work with quantities and simple linear expressions. They will

perform operations with integers. Students will use units to represent problems. This unit provides the foundation for the study of equations, inequalities, and functions.

Primary interdisciplinary connections: Science, History, Political Science, Language Arts 21st_{century themes: Applying problem solving skills, critical thinking, and technology to form}

reasonable conclusions; developing financial literacy skills and career ready skills; applying mathematics to real world situations and 21st_{century challenges}

Learning Targets

Content Standards

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

N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context S.ID.A.1 Represent data with plots on the real number line

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

Review: 6.EE.A.1; 6.EE.A.2; 6.EE.A.3; 6.EE.B.6; 6.NS.C.5; 6.NS.C.6; 6.NS.C.6.a; 6.NS.C.6.c; 6.NS.C.7; 6.NS.C.7.a; 6.NS.C.7.b; 6.NS.C.7.c; 6.NS.C.7.d; 8.SP.A.1

Unit Essential Questions What is a variable?

In what order should expressions be evaluated?

What are opposites?

What are the rules for adding, subtracting, multiplying, and dividing integers?

How is a point in the coordinate

Unit Enduring Understandings

Students will understand that…

A variable represents an unknown number or quantity. Expressions must be evaluated in a specific order (order of operations).

Integers include negative integers, zero, and positive integers.

There are rules for performing operations on the set of integers.

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plane represented? Unit Objectives

Students will know…

The definition of variable, numerical expression, variable expression. Words and phrases that indicate operations.

The order of operations. How to read and write powers (exponential notation).

The definition of absolute value and opposites.

The set of integers. The coordinate plane and

corresponding vocabulary (ordered pair, origin, x-axis, y-axis,

quadrants).

Unit Objectives

Students will be able to…

Evaluate variable expressions.

Simplify numeric and variable expressions. Write variable expressions to describe situations. Use powers to describe repeated multiplication. Compare and order integers.

Graph integers on a number line. Find the absolute value of integers.

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

Formative Assessments

Teacher questions and classroom discussion Exit questions Class warm-ups Quizzes Chapter Review Homework Tests

Chapter “Skills Preview” Class work

Summative Assessments

Midterm Exam Final Exam

SGO (if given in a particular year to this class)

Modifications (ELLs, Special Education, Gifted and Talented) Allow use of calculators or online calculators when applicable Supplement notes when applicable

Provide outline of formulas and procedures where applicable Collaboration in class

Peer and teacher tutoring

Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Textbook, Online Textbook, Calculators or online calculators, Whiteboard, Markers, MacBook Computers, Ipevo Ziggi Camera, Television, Kuta Software, Plastigraph coordinate grid

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Unit Overview

Unit Title: Equations and Inequalities Target Course/Grade Level: 9

Unit Summary: Students will learn how to solve equations and inequalities in one variable. Students will work with the vocabulary and properties associated with these processes. They will create an equation or inequality for a given situation and then solve that equation or inequality. Students will also convert between measurement systems.

Primary interdisciplinary connections: Science. Language Arts

21st_{century themes: Applying problem solving skills, critical thinking, and technology to form}

Learning Targets

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

A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems

A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations

A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution

A.REI.B.3 Solve linear equations and inequalities in one variable

A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it

Review: 6.EE.A.2; 6.EE.A.2.a; 6.EE.A.2.b; 6.EE.A.2.c; 6.EE.A.3; 6.EE.A.4; 6.EE.B.5; 6.EE.B.6; 6.NS.B.3; 6.G.A.1; 7.EE.A.1; 7.EE.B.3; 7.EE.B.4; 7.EE.B.4.a; 7.EE.B.4.b;

7.NS.A.1; 7.NS.A.1.c; 7.NS.A.1.d; 7.NS.A.2; 7.NS.A.2.a; 7.NS.A.2.b; 7.NS.A.2.c; 8.EE.C.7; 8.EE.C.7.b

Unit Essential Questions

What are some properties of addition and multiplication?

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What is the procedure for solving equations and inequalities in one variable and corresponding applications problems?

How are inequalities in one variable graphed on the number line?

What does the graph of an inequality represent?

Equations and inequalities are solved in a specific way. Solving equations and inequalities can be used to work out many application problems.

The graph of an inequality represents all possible solutions to that inequality.

Unit Objectives

The Commutative and Associative Properties of Addition and Multiplication.

The Identity Properties of Addition and Multiplication.

Common conversions within the U.S. and metric systems.

The Distributive Property.

The definition of terms, like terms, unlike terms, coefficient, constant.

The procedure for solving inequalities in one variable.

Unit Objectives

Use the properties of addition and multiplication. Convert within and between the Metric and U.S. measurement systems.

Simplify expressions and solve equations using the distributive property.

Identify and distinguish between coefficients and constants.

Translate simple sentences into simple equations and inequalities.

Solve one and two-step equations.

Solve equations that involve like terms and parentheses. Solve equations with variables on both sides.

Solve basic word problems with one or two unknown variables.

Rewrite literal equations and formulas (solve for a specified variable).

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

Teacher questions and classroom discussion Class warm-ups Exit questions Quizzes Chapter Review Homework Tests

Modifications (ELLs, Special Education, Gifted and Talented) Allow use of calculators or online calculators when applicable Supplement notes when applicable

Provide outline of formulas and procedures when applicable Collaboration in class

Provide manipulatives or models where applicable

Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Textbook, Online Textbook, Calculators or online calculators, Whiteboard, Markers, MacBook Computers, Ipevo Ziggi Camera, Television, Kuta Software

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Unit Overview

Unit Title: Rational Numbers and Exponents Target Course/Grade Level: 9

Unit Summary: This unit reviews the vocabulary associated with rational numbers and fractions. It introduces monomials and the basic rules of exponents, including zero and negative exponents. Students will simplify and evaluate expressions containing exponents, solve equations containing rational numbers, and solve real world problems that involve rational numbers and scientific notation.

Primary interdisciplinary connections: Science, Language Arts

Learning Targets

A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems

A.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise

A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters

A.APR.D.6 Rewrite simple rational expressions in different forms

Review: 6.EE.A.2; 6.EE.A.2.a; 6.EE.A.2.b; 6.EE.A.3; 6.EE.B.6; 6.EE.C.9; 6.NS.B.4; 6.NS.C.7; 6.NS.C.7.a; 6.NS.C.7.b; 7.EE.A.1; 7.EE.B.4; 7.EE.B.4.a; 7.EE.B.4.b; 7.NS.A.1; 7.NS.A.1.c; 7.NS.A.1.d; 7.NS.A.2; 7.NS.A.2.a; 7.NS.A.2.c; 7.NS.A.2.d; 7.NS.A.3; 8.EE.A.1; 8.EE.A.3; 8.EE.A.4; 8.NS.A.1

Unit Essential Questions What is a rational number?

How are rational numbers written? What operations can be performed on rational numbers?

A rational number is a number that can be written as the quotient of two integers, and this set of numbers is a part of the real number system.

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How are equations and inequalities that contain rational numbers solved?

What is meant by a factor? How can problems be solved by using factors or multiples?

How can expressions be simplified using the rules of exponents? Is there a shorter way to write very large or very small numbers?

numbers.

Equations and inequalities containing rational numbers are solved in a certain way.

Problems can be solved using factors and multiples. There are rules to be followed when working with exponents and expressions must be simplified by using the rules of exponents.

Very large and very small numbers can be written using powers of ten.

Unit Objectives

The definition of rational number and the parts of the real number system.

How to perform operations on, compare, and order rational numbers.

The definition of prime and

composite numbers, factor, greatest common factor, least common multiple.

The definition of monomial.

The Product and Quotient Rules of exponents.

The zero and negative exponent rules.

The Power Rule of exponents. How to write numbers in standard form.

How to write numbers in scientific notation.

Unit Objectives

Classify numbers in the real number system.

Compare, order, add, subtract, multiply, and divide rational numbers.

Solve equations and inequalities that contain rational numbers.

Identify whether a number is prime or composite. List the factors of a given number.

Find the greatest common factor of given numbers and monomials.

Find equivalent fractions and reduce fractions. Simplify rational expressions by reducing.

Find the least common multiple of given numbers. Solve application problems that involve finding the GCF (Greatest Common Factor) or LCM (Least Common Multiple).

Simplify expressions by using the rules of exponents. Write numbers in standard form and in scientific notation.

Perform operations with numbers written in scientific notation.

Convert temperatures between degrees Celsius and degrees Fahrenheit.

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

Modifications (ELLs, Special Education, Gifted and Talented) Allow use of calculators or online calculators when applicable Supplement notes or provide graphic organizers when applicable Provide outline of formulas and procedures when applicable Collaboration in class

Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Textbook, Online textbook, Calculators or online calculators, Whiteboard, Markers, MacBook Computers, Ipevo Ziggi Camera, Television, Kuta Software, graph paper

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Unit Overview

Unit Title: Ratios, Proportions, and Percents Target Course/Grade Level: 9

Unit Summary: This unit involves many application problems involving ratios, proportions, and percents. These problems involve similar figures, congruent figures, and scale drawings from geometry. The students also solve proportions using algebra including markup, discount, sales tax, and simple interest problems. These are all skills used in every day life.

Primary interdisciplinary connections: Science, Economics

Learning Targets

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

G.CO.B.7 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.D.12 Make formal geometric constructions with a variety of tools and methods

G.SRT.A.2 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.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures

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9.1.12.C.2 Compare and compute interest and compound interest

Review: 6.RP.A.1; 6.RP.A.2; 6.RP.A.3.b; 6.RP.A.3.c; 6.RP.A.3.d; 7.RP.A.1; 7.RP.A.2; 7.RP.A.2.c; 7.RP.A.3; 7.EE.A.2; 7.EE.B.3; 7.G.A.1; 8.G.A.2; 8.G.A.4;

Unit Essential Questions What is a ratio? What is a proportion? What are similar figures? What are congruent figures?

What does percent mean and how is it calculated?

What is simple interest?

Ratios and proportions can be used to solve problems. Percents can be calculated using certain methods and problems can be solved that involve percents.

Simple interest can be calculated using formulas.

Unit Objectives

The definition of a ratio.

How to write a ratio three different ways.

The definition of unit rate. Basic conversion factors. The definition of a proportion. The definition of congruent figures. The definition of similar figures. The definition of percent. The formula to calculate simple interest.

Unit Objectives

Find and write ratios. Find unit rates.

Convert between systems of measurement. Write and solve proportions.

Identify similar and congruent figures by using ratios. Find unknown side lengths of similar figures by using ratios.

Use fractions to find percents of numbers. Use proportions to solve percent problems. Use decimals to solve percent problems. Use equations to solve percent problems.

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Textbook, Online textbook, Calculators or online calculators, Whiteboard, Markers, MacBook Computers, Ipevo Ziggi Camera, Television, Kuta Software, graph paper, rulers, construction paper, protractors, plastigraph coordinate grid

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Unit Overview

Unit Title: Linear Equations and Functions Target Course/Grade Level: 9

Unit Summary: This unit introduces functions and function notation. The students will explore the nature of functions and will focus on linear functions, linear relationships, and models. This unit also discusses equations of lines, slope, systems of linear equations, and inequalities in two variables. The goal is that students will have a solid understanding of linear relationships.

Primary interdisciplinary connections: Science, Business, Economics

Learning Targets

A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients

A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems A.CED.A.2 Create equations in two or more variables to represent relationships between quantities;

graph equations on coordinate axes with labels and scales

A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in

solving equations

A.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions A.REI.C.6 Solve systems of linear equations exactly and approximately, focusing on pairs of linear

equations in two variables

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

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

statements that use function notation in terms of a context

F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship

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

F.IF.B.6 Calculate and interpret the average rate of change of a function over a specified interval F.IF.B.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima

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

F.BF.A.1.a Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context F.LE.A.1 Distinguish between situations that can be modeled with linear functions and with

exponential functions

G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and distance along a line, and distance around a circular arc

G.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

Review: 8.F.A.1; 8.F.A.2; 8.F.A.3; 8.F.B.4; 8.F.B.5; 8.EE.B.5; 8.EE.B.6; 8.EE.8.a; 8.EE.8.b; 8.EE.8.c; 8.SP.A.1; 8.SP.A.2; 8.SP.A.3

Unit Essential Questions What is a relation? What is a function?

What is the domain of a function? What is the range of a function? How do I know if a relation is a function?

How are solutions to equations in two variables found?

How are equations of lines written? What is slope?

How are systems of equations solved?

How are linear inequalities solved and graphed?

What are some real world applications of linear equations, functions, and inequalities?

A linear function is a function whose graph is a nonvertical line.

There are ways to find solutions to equations in two variables.

There are different forms of an equation of a line. The concept of slope can be related to real world situations.

There are methods to solve and graph a system of linear equations.

There are methods to solve and graph linear inequalities.

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Unit Objectives

The definition of a relation. The definition of a function.

The definition of domain of a function. The definition of range of a function. The Vertical Line Test.

The graph of a linear equation is a line.

The definition of a linear function. The definition of x and y intercepts. How to identify x and y intercepts. The definition and formula for slope. The slope intercept form of the equation of a line.

The definition of parallel, perpendicular, and skew lines. Positive, negative, and zero linear correlation.

The definition and how to identify outliers.

Function notation.

A system of linear equations can be solved algebraically or graphically.

Unit Objectives

Distinguish between relations and functions. Identify the domain and range of a relation and function.

Use graphs to identify relations and functions. Tell whether a given relation is a function. Find solutions of equations in two variables.

Graph equations in two variables (linear equations). Graph horizontal and vertical lines.

Write linear equations in function form (solve for y). Distinguish between linear and nonlinear functions. Graph a given function and determine whether it is increasing or decreasing.

Find the x and y intercepts of a linear equation. Graph linear equations using the x and y intercepts. Calculate and interpret slopes of lines.

Interpret and create graphs representing real world situations.

Graph equations of lines in slope intercept form. Find the slope of a line that is either parallel or perpendicular to the given line.

Write equations for real world scenarios.

Use the equation of a linear model to solve problems n the context of bivariate measurement data (fit lines to data).

Write linear equations using slope and y intercept. Write linear equations of parallel or perpendicular lines.

Analyze the domain and range of linear functions and classify functions as discrete or continuous.

Create and interpret scatter plots. Evaluate linear functions.

Graph linear functions. Compare functions.

Solve systems of linear equations graphically and algebraically.

Graph inequalities in two variables.

POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

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Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Textbook, Calculators or online calculators, Graphing calculators, Whiteboard, Markers, MacBook Computers, Ipevo Ziggi Camera, Television, Kuta Software, graph paper, rulers, plastigraph coordinate plane

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Unit Overview

Unit Title: Real Numbers, Right Triangles, Measurement, and Coordinate Geometry Target Course/Grade Level: 9

Unit Summary: Students will perform operations on real numbers, in particular, finding square roots of numbers. They will solve problems involving the Pythagorean Theorem, right triangle formulas, Distance formula, and trigonometry. This unit also covers basic geometry concepts such as classifying triangles and quadrilaterals, areas of polygons and circles, volumes, and surface area of solids. The concept of slope will be visited again as the students use it to solve coordinate geometry problems.

Primary interdisciplinary connections: Science, Geography, Art, Architecture

Learning Targets

A.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise

G.CO.A.1 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.C.9 Prove theorems about lines and angles

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G.SRT.C.6 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.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

G.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically

G.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

G.GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles G.GMD.A.1 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.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems G.GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects G.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects

Review: 7.RP.A.1; 7.G.A.3; 7.G.A.4; 7.G.A.6; 8.NS.A.1; 8.NS.A.2; 8.EE.A.2; 8.G.A.5; 8.G.B.6; 8.G.B.7; 8.G.B.8; 8.G.C.9;

What is meant by finding the square root of a number?

What is the Pythagorean Theorem? When and how can the Pythagorean Theorem be used to solve problems? What is the distance formula and how is it used?

How are polygons classified? What is area?

What is volume?

What are the three basic trigonometric ratios?

How can the trig ratios be used to solve problems?

Finding the square root of a number means finding one of its two equal factors.

The Pythagorean Theorem can be used to solve right triangle problems.

The distance formula can be used to find the distance between two points on a coordinate grid.

Polygons can be classified according to the number of sides they have.

The area and volume of figures can be found by using formulas.

Trigonometric formulas can be used to solve right triangle problems.

Unit Objectives

The definition of square root. The Product and Quotient Properties of square roots. The Pythagorean Theorem.

The definition of irrational number. How to describe a point, line, line segment, and plane.

The definition of parallel and perpendicular lines.

Unit Objectives

Find and approximate square roots of numbers. Simplify radical expressions.

Use the Pythagorean Theorem to solve problems. Distinguish between rational and irrational numbers. Order real numbers.

Calculate the distance between two points by using the distance formula.

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The distance, midpoint, and slope formulas.

The definition of diagonal. The Sine, Cosine, and Tangent ratios.

The types of triangles.

That the sum of the interior angles of a triangle is 180 degrees.

The definition of polygon. The definition of quadrilateral. The definition of perimeter. The formulas to find the area of a square, rectangle, triangle, parallelogram, and trapezoid.

The formulas for circumference and area of a circle.

The meaning of vertices, faces, and edges in solids.

The formula for the volume of a rectangular prism and cylinder.

The formula for the volume of a sphere.

Calculate the slope of a line given two points.

Prove certain figures by using the slope, midpoint, and distance formulas.

Use the Sine, Cosine, and Tangent ratios to find the side lengths of triangles.

Classify triangles according to their sides and angles. Solve problems involving triangles.

Classify quadrilaterals.

Calculate the perimeter of polygons.

Calculate the area of a square, rectangle, triangle, parallelogram, and trapezoid.

Calculate the circumference and area of a circle. Calculate the area of irregular shapes.

Classify and name solids – prisms, pyramids, cones, and cylinders.

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

Teacher questions and classroom discussion Class warm-ups Exit questions Quizzes Chapter review Homework Tests

Midterm exam Final exam

Modifications (ELLs, Special Education, Gifted and Talented) Allow use of calculators or online calculators when applicable Supplement notes or provide graphic organizers when applicable Provide outlines of formulas and procedures when applicable Collaboration in class

Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Textbook, Online Textbook, Calculators or online calculators, Whiteboard, Markers, MacBook Computers, Ipevo Ziggi camera, Television, Kuta Software, plastigraph coordinate plane, graph paper, rulers, plastic solid models

Teacher Notes: Students will need a calculator with trig functions.

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CURRICULUM

Unit Overview

Unit Title: Polynomials and Introduction to Factoring Target Course/Grade Level: 9

Unit Summary: This unit lays the foundation for working with polynomials and introduces the students to factoring. Students will add and subtract polynomials. They will multiply monomials, divide by monomials, and multiply polynomials by monomials. The students will also multiply binomials, and factor using the GCF and the sum product method.

Primary interdisciplinary connections: Physics

Learning Targets

A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients

A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it

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

Review: 8.EE.A.1; 8.EE.C.7.b

What is a polynomial, monomial, binomial, trinomial?

How do I add, subtract, and multiply polynomials?

How do I divide polynomials by monomials?

What does it mean to factor a polynomial?

Polynomials should be written in standard form. Only like terms can be combined.

The rules of exponents must be followed when multiplying and dividing.

Different methods of factoring can be used depending on the polynomial.

Unit Objectives

Definition of polynomial, monomial, binomial, and trinomial.

Definition of standard form.

Unit Objectives

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Rules of exponents. Basic factoring methods.

Use the rules of exponents to multiply polynomials. Divide polynomials and monomials by monomials. Multiply polynomials by monomials.

Multiply binomials.

Factor polynomials by extracting the GCF (Greatest Common Factor).

Factor perfect square trinomials and the difference of perfect squares.

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

Teacher questions and classroom discussion Class warm-ups Exit questions Quizzes Chapter Review Homework Tests Class work Summative Assessments Midterm exam Final exam

Modifications (ELLs, Special Education, Gifted and Talented) Allow use of calculators or online calculators when applicable Supplement notes or provide graphic organizers when applicable Provide outlines of procedures when applicable

Collaboration in class Peer and teacher tutoring

Provide models where applicable

Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Whiteboard, Markers, Ipevo Ziggi Camera, Television, Calculators or online calculators, MacBook Computers, Kuta Software

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Unit Overview

Unit Title: Data Analysis and Probability Target Course/Grade Level: 9

Unit Summary: Students will calculate simple and compound probabilities in this unit. They will calculate measures of center and variation for a given data set. The unit introduces ways to organize and display data and how to interpret graphs. It also focuses on how linear models are used in various disciplines to model relationships between two quantities, and how a function may be fit to a data set. The unit also explores using permutations and combinations to solve problems. Primary interdisciplinary connections: Science, Political Science, Economics, Statistics

Learning Targets

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

S.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets

S.ID.A.3 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.5 Summarize categorical data for two categories in two-way frequency tables

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

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

S.ID.A.8 Compute (using technology) and interpret the correlation coefficient of a linear fit S.ID.A.9 Distinguish between correlation and causation

S.IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population

S.IC.A.2 Decide if a specified model is consistent with results from a given data-generating process S.IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and

observational studies; explain how randomization relates to each

S.CP.A.1 Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events

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are independent

S.CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified

S.CP.B.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model

S.CP.B.8 Apply the general Multiplication Rule in a uniform probability model P(A and B) = P(A)P(B/A) = P(B)P(A/B), and interpret the answer in terms of the model

S.CP.B.9 Use permutations and combinations to compute probabilities of compound events and solve problems

Review: 7.SP.A.1; 7.SP.A.2; 7.SP.B.3; 7.SP.B.4; 7.SP.C.5; 7.SP.C.6; 7.SP.C.7; 7.SP.C.8; 8.SP.A.1; 8.SP.A.2; 8.SP.A.3; 8.SP.A.4

Unit Essential Questions What is probability?

How can I collect and use data to find probabilities?

What are measures of center and how are they calculated for a given data set?

What are measures of variation? What conclusions/interpretations can be made using measures of center and variation for a data set? How are straight lines used to interpret a data set?

How do I find experimental and theoretical probabilities?

What is a compound event? What are independent and dependent events?

How can probabilities be calculated using permutations and

combinations?

Probability is a number between 0 and 1 that measures the likelihood that an event can occur.

There are methods used to calculate probability.

Measures of center and measures of variation for a data set can be used to draw conclusions about a data set. Data can be displayed in various ways and some graphs are better than others to display certain data.

Straight lines are widely used to model relationships between two quantities, and functions may be fit to the data.

Permutations can be used to solve problems involving probability.

Unit Objectives

The definition of probability.

How to calculate probabilities using the Addition and Multiplication Principles.

The definition of mean, median, mode, range, interquartile range, spread, and standard deviation. The difference between correlation and causation.

Unit Objectives

Calculate simple and compound probabilities.

Calculate mean, median, mode, and range for a data set. Create stem-and-leaf plots, frequency tables, two-way frequency tables, histograms, dot plots, line graphs, and scatter plots for given data sets and interpret results based on center and variation (spread).

Interpret scatter plots, clustering, outliers, correlation, and line of best fit.

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POINT PLEASANT BEACH SCHOOL DISTRICT

CURRICULUM

Evidence of Learning

Teacher questions and classroom discussion Class warm-ups Exit questions Quizzes Chapter Review Homework Tests Class work Summative Assessments Midterm exam Final exam

SGO (if given in a particular year to this class0

Modifications (ELLs, Special Education, Gifted and Talented) Allow use of calculators or online calculators when applicable Supplement notes or provide graphic organizers when applicable Provide outlines of procedures when applicable

Collaboration in class Peer and teacher tutoring

Provides manipulative and models where applicable

Follow all IEP modifications/504 plan

Gifted and Talented N/A

Curriculum development Resources/Instructional Materials/Equipment Needed Teacher Resources: Textbook, Online textbook, Whiteboard, Markers, Ipevo Ziggi Camera, Television, Calculators or online calculators, MacBook Computers, Kuta Software, Graph paper, Rulers, Different color pencils, Coins, Playing Cards, Dice, Construction paper