mathematics curriculum grade 11 - buenaschools.org€¦ · 2/1/2019 · mathematics curriculum...

Buena Regional High School SAT Math Curriculum

Common Core State Standards June 2012

Created for New Jersey school districts through a project of the New Jersey Department of Education, Office of Academic Standards, in partnership with the N.J Association for Supervision and Curriculum Development and the N.J. Principals and Supervisors Association.

Mathematics Curriculum

Grade 11

Buena Regional School District Buena, NJ




Board of Education

Debra Bell, President

James Abba, Vice-President Mark Beamer Jr.

John Cressey Syd D’Angelo

Valentina DiPrimio Lynda Gazzara

Al Gazzara Barbara Meyrick

Matt Walker Edward Zebedies

Superintendent

John Destefano

Supervisor

Brian Kern

Curriculum Committee

Curriculum Approval Date

2015




Content Area: Mathematics

Course Title: SAT Prep Math Grade Level: 11

Unit 1

Introduction to SAT

Arithmetic Skills & Concepts

Pacing Guide

(15) 40 minute class periods

Unit 2

Algebraic Methods

Pacing Guide


Unit 3 Geometric Concepts & Reasoning

Pacing Guide


Unit 4

Word Problems

Pacing Guide


Unit 5 Special Problem Types

Pacing Guide


Unit 6 Algebra II Methods

Pacing Guide


Date Created: June 2012

Author: Michelle Henning

Board Approved on: 9/18/2012




Unit 1 Overview


Unit Title: Introduction to SAT’s and Arithmetic Skills & Concepts

Target Course/Grade Level: SAT PREP MATH / Grade 11

Unit Summary

• All numbers that appear on the SAT are real numbers. Real numbers include all the different types of

numbers, both positive and negative, you encountered in arithmetic and beginning algebra classes.

• A variable is a symbol that serves as a placeholder for an unknown member of a given set of numbers. Letters of the alphabet such as a, b, and x are used as variables to help make general statements about how

numbers behave.

Primary interdisciplinary connections: language arts

21st century themes:

WORK.9-12.9.1.12 - [Standard] - All students will demonstrate creative, critical thinking,

collaboration and problem solving skills to function successfully as global citizens and

workers in diverse ethnic and organizational cultures.

WORK.9-12.9.1.12.1 - [Content Statement] - The ability to recognize a problem and apply

critical thinking and problem-solving skills to solve the problem is a lifelong skill that develops over

time.

WORK.9-12.9.1.12.A.1 - [Cumulative Progress Indicator] - Apply critical thinking and problem-solving

strategies during structured learning experiences.

Unit Rationale

Introduce the guidelines for the SAT and develop an understanding of the scoring. This unit will covers arithmetic principles and

computations including whole numbers, fractions, decimals, percents, measurement, graph interpretation, geometric forms, and

applications.

Learning Targets




Standards

MA.9-12.HSN-RN.A - [Cluster Statement] - Extend the properties of exponents to rational exponents. MA.9-12.HSN-RN.1 - [Standard] - 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.

MA.9-12.HSN-RN.2 - [Standard] - Rewrite expressions involving radicals and rational exponents using the properties of

exponents.

MA.9-12.HSN-RN.B - [Cluster Statement] - Use properties of rational and irrational numbers.

MA.9-12.HSN-RN.3 - [Standard] - 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.

MA.9-12.HSN-Q - [Domain] - Quantities

MA.9-12.HSN-Q.A - [Cluster Statement] - Reason quantitatively and use units to solve problems.

MA.9-12.HSN-Q.1 - [Standard] - 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.

MA.9-12.HSN-Q.2 - [Standard] - Define appropriate quantities for the purpose of descriptive modeling.

MA.9-12.HSN-Q.3 - [Standard] - Choose a level of accuracy appropriate to limitations on measurement when reporting

quantities.

Unit Essential Questions

• How does the knowledge of the general format

of the test better prepare you?

• How does the knowledge of weakness in

mathematics skills better prepare you?

Unit Enduring Understandings

• Student’s scores on standardized tests will be enhanced

through understanding of test format and strategies

• Student’s scores on standardized tests will be enhanced


• Students will identify weaknesses within their mathematics

skills

Unit Learning Targets

Students will ...

• Be able to register for the SAT

• Be able to understand the scoring of the SAT

• Be able to understand the general format of the SAT

• Be able to identify weaknesses in several areas of mathematics

• Be able to review general mathematical skills

Evidence of Learning




Formative Assessments:

• Teacher Observation

• Guided Practice

• Homework

• Basic Skills Diagnosis

• Strategy Diagnostic

• Discussions

Summative Assessments:

• SAT Question of the Day

• Practice SAT MATH Test

Equipment needed:

• Smart board

• Computer

Teacher Resources:

• Barron’s SAT Math Workbook 4th Edition

• McGraw Hill’s Conquering SAT Math 3rd Edition

Curriculum Development Resources:

Click the links below to access additional resources used to design this unit:

http://sat.collegeboard.org/

http://durlandsat.wikispaces.com/

http://www.majortests.com/sat/







Unit 2 Overview


Unit Title: Algebraic Methods

Target Course/Grade Level: SAT Math - Grade 11

Unit Summary

• A linear or first degree equation is an equation such as 2y+1=13 in which the exponent of the variable is 1.

To solve linear equation, do the same things to both sides of the equation until the resulting equation has the

form. Letter=number

• Factor quadratic equations by identifying GCF and difference between two squares

Primary interdisciplinary connections: Science, 21st Century Goals; business; social studies


WORK.9-12.9.1.12.1 - [Content Statement] - The ability to recognize a problem and apply critical thinking and

problem-solving skills to solve the problem is a lifelong skill that develops over time.

WORK.9-12.9.1.12.A.1 - [Cumulative Progress Indicator] - Apply critical thinking and problem-solving strategies

during structured learning experiences.

Unit Rationale

Instruction that is clearly relevant to today’s rapidly changing world is at the forefront of unit design. Content

knowledge cannot by itself lead all students to academic achievement. Classes and projects that spark student interest

and provide a rationale for why the content is worth learning, enable students to make connections between what they

read and learn in school, their lives, and their futures. An engaging and effective curriculum provides opportunities for exploration and exposure to new ideas. Real-world learning experiences provide students with opportunities to

transfer and apply knowledge in new diverse situations.

Learning Targets

Standards

MA.9-12.HSN-CN.C - [Cluster Statement] - Use complex numbers in polynomial identities and equations.

MA.9-12.HSN-CN.7 - [Standard] - Solve quadratic equations with real coefficients that have complex solutions.

MA.9-12.HSN-CN.8 - [Standard] - Extend polynomial identities to the complex numbers.

MA.9-12.HSA-SSE.1.a - Interpret parts of an expression, such as terms, factors, and coefficients.

MA.9-12.HSA-SSE.1.b - Interpret complicated expressions by viewing one or more of their parts as




a single entity.

MA.9-12.HSA-SSE.2 - [Standard] - Use the structure of an expression to identify ways to rewrite it.

MA.9-12.HSA-SSE.B - [Cluster Statement] - Write expressions in equivalent forms to solve problems

MA.9-12.HSA-SSE.3 - [Standard] - Choose and produce an equivalent form of an

expression to reveal and explain properties of the quantity represented by the expression.

MA.9-12.HSA-SSE.3.a - Factor a quadratic expression to reveal the zeros of the function it defines. MA.9-12.HSA-SSE.3.b - Complete the square in a quadratic expression to reveal the maximum or minimum

value of the function it defines. MA.9-12.HSA-SSE.3.c - Use the properties of exponents to transform expressions for exponential functions.

MA.9-12.HSA-SSE.4 - [Standard] - Derive the formula for the sum of a finite geometric series (when the

common ratio is not 1), and use the formula to solve problems. MA.9-12.HSA-APR - [Domain] - Arithmetic with Polynomials and Rational Expressions

MA.9-12.HSA-APR.A - [Cluster Statement] - Perform arithmetic operations on polynomials

MA.9-12.HSA-APR.1 - [Standard] - 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.

MA.9-12.HSA-APR.B - [Cluster Statement] - Understand the relationship between zeros and factors of

polynomials MA.9-12.HSA-APR.2 - [Standard] - Know and apply the Remainder Theorem: For a polynomial p(x) and a

number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

MA.9-12.HSA-APR.3 - [Standard] - 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.

MA.9-12.HSA-APR.C - [Cluster Statement] - Use polynomial identities to solve problems

Standards 9.4 Career and Technical Education All students who complete a career and technical education

program will acquire academic and technical skills for careers in emerging and established professions that lead to

technical skill proficiency, credentials, certificates, licenses, and/or degrees.


Students will ...

• Students will use variables to represent unknown

quantities in real world situation

• Students will identify the different kinds of


• A single quantity may be represented by many different

expressions

• Find a set of values that replace the variables in the equations

and make each equation true




transformations

• Students will solve a system of linear equations

by graphing the equation




• Guided Practice

• Homework



• Discussions




Teacher Resources:








Unit 3 Overview








Unit Title: Geometric Concepts & Reasoning


Unit Summary

Review the relationships among angles formed when two lines intersect, parallel lines, and triangles.

Review angle and side relationships in special types of triangles

The perimeter of a figure is the distance around the figure

The area of a polygon is the number of square units it encloses

Primary interdisciplinary connections: business; science, 21st century themes


WORK.9-12.9.1.12.1 - [Content Statement] - The ability to recognize a problem and apply critical thinking

and problem-solving skills to solve the problem is a lifelong skill that develops over time.



Unit Rationale

Instruction that is clearly relevant to today’s rapidly changing world is at the forefront of unit design.

Content knowledge cannot by itself lead all students to academic achievement. Classes and projects that

spark student interest and provide a rationale for why the content is worth learning enable students to make

connections between what they read and learn in school, their lives, and their futures. An engaging and

effective curriculum provides opportunities for exploration and exposure to new ideas. Real-world learning

experiences provide students with opportunities to transfer and apply knowledge in new, diverse situations.

Learning Targets




Standards

MA.9-12.HSG-GPE - [Domain] - Expressing Geometric Properties with Equations

MA.9-12.HSG-GPE.A - [Cluster Statement] - Translate between the geometric description and the equation for a conic section

MA.9-12.HSG-GPE.1 - [Standard] - 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. MA.9-12.HSG-GPE.2 - [Standard] - Derive the equation of a parabola given a focus and directrix.

MA.9-12.HSG-GPE.3 - [Standard] - Derive the equations of ellipses and hyperbolas given the foci, using the fact

that the sum or difference of distances from the foci is constant.

MA.9-12.HSG-GPE.B - [Cluster Statement] - Use coordinates to prove simple geometric theorems algebraically MA.9-12.HSG-GPE.4 - [Standard] - Use coordinates to prove simple geometric theorems algebraically.

MA.9-12.HSG-GPE.5 - [Standard] - Prove the slope criteria for parallel and perpendicular lines and use them to

solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

MA.9-12.HSG-GPE.6 - [Standard] - Find the point on a directed line segment between two given points that

partitions the segment in a given ratio.

MA.9-12.HSG-GPE.7 - [Standard] - Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

MA.9-12.HSG-GMD - [Domain] - Geometric Measurement and Dimension

MA.9-12.HSG-GMD.A - [Cluster Statement] - Explain volume formulas and use them to solve problems MA.9-12.HSG-GMD.1 - [Standard] - Give an informal argument for the formulas for the circumference of a

circle, area of a circle, volume of a cylinder, pyramid, and cone.

MA.9-12.HSG-GMD.2 - [Standard] - Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

MA.9-12.HSG-GMD.3 - [Standard] - Use volume formulas for cylinders, pyramids, cones, and spheres to solve

problems.

MA.9-12.HSG-GMD.B - [Cluster Statement] - Visualize relationships between two-dimensional and three-dimensional objects

MA.9-12.HSG-GMD.4 - [Standard] - Identify the shapes of two-dimensional cross-sections of three-dimensional

objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. MA.9-12.HSG-MG - [Domain] - Modeling with Geometry

MA.9-12.HSG-MG.A - [Cluster Statement] - Apply geometric concepts in modeling situations

MA.9-12.HSG-MG.1 - [Standard] - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

MA.9-12.HSG-MG.2 - [Standard] - Apply concepts of density based on area and volume in modeling situations

(e.g., persons per square mile, BTUs per cubic foot).








• How do the distance and midpoint formulas help us to solve real life problems?

• How do perimeter and area help us to solve real life problems?

• How do bisectors, medians, and altitudes help us to solve spatial problems?

• How do scale models help to solve real world problems?

• How are scale models used in everyday life?

• How does the Pythagorean theorem and the relationship of sides in special right triangles help us to solve real world problems?

• Where are transformations and symmetry present in everyday life?

• How do transformations and symmetry help us to develop our spatial abilities?


• There are various computational methods, including mental math, pencil and paper techniques and use of

calculators to find the solution.

• Coordinate geometry can be used to represent and verify

geometric/algebraic relationships.

• Reasoning proof s can be used to verify or refute

conjectures or theorems in geometry.

• Geometry can be learned through problem solving,

inquiry, and discovery.


Students will ...

• Be able to use the distance formula and Pythagorean theorem to find the length of a segment

• Be able to solve real word problems by using geometric theorems

• Be able to transform, rotate, and reflect objects







• Guided Practice

• Homework



• Discussions




Teacher Resources:

• Barron’s SAT Math Workbook 4th

Edition

• McGraw Hill’s Conquering SAT Math 3rd

Edition












Unit 4 Overview


Unit Title: Word Problems


Unit Summary

• Graph and tables can be used to summarize information in a way that is easy to read.

• Translate and English sentence into an Algebraic sentence

Primary interdisciplinary connections: Language Arts; Business; Science


WORK.9-12.9.1.12 - [Standard] - All students will demonstrate creative, critical thinking,

collaboration and problem solving skills to function successfully as global citizens and

workers in diverse ethnic and organizational cultures.

WORK.9-12.9.1.12.1 - [Content Statement] - The ability to recognize a problem and apply

critical thinking and problem-solving skills to solve the problem is a lifelong skill that develops over

time.



Unit Rationale

Current testing has shown that students generally do well in computation, but do poorly on items involving

reading a word problem and solving it. The student must learn to translate the verbal into mathematical

language using often times a formula or equation. A guided plan for students in order to solve problems is

of utmost importance in the teaching of word problems. With repeated practice, students improve when they

learn and use the terminology needed to decipher what operation(s) to use when solving. Students need to

discover relationships between problems to gain familiarity in solving them. Real world problems and

multi-tasks involving finding and writing your solution, will allow students to become more comfortable

and familiar with the terminology and strategies needed to succeed.

Learning Targets




Standards

MA.9-12. - With each extension of number, the meanings of addition, subtraction, multiplication, and

division are extended. In each new number system-integers, rational numbers, real numbers, and complex

numbers-the four operations stay the same in two important ways: They have the commutative, associative, and distributive properties and their new meanings are consistent with their previous meanings.

MA.9-12. - Extending the properties of whole-number exponents leads to new and productive notation.

For example, properties of whole-number exponents suggest that (5 to the 1/3 power should be 5 to the

(1/3) power = 5 = 5 and that 5 to the 1/3 power should be the cube root of 5. MA.9-12. - Calculators, spreadsheets, and computer algebra systems can provide ways for students to

become better acquainted with these new number systems and their notation. They can be used to

generate data for numerical experiments, to help understand the workings of matrix, vector, and complex number algebra, and to experiment with non-integer exponents.


• How does the knowledge of the format of multiple choice

questions and strategies to answer math questions better

prepare you for a test?

• How does the knowledge of the format of grid in questions and

strategies to answer math questions better prepare you for a

test?


• Students’ scores on standardized tests

will be enhanced through understanding

of test format and strategies

• Students’ scores on standardized tests

will be enhanced through understanding

of test format and strategies


Students will ...

• Be able to cancel quantities to make a problem simpler

• Be able to use specific examples to prove or disprove an answer

• Be able to identify and use simpler methods of solving problems

• Be able to eliminate certain choices

• Be able to ignore irrelevant information

• Be able to properly format answers to grid in questions







• Guided Practice

• Homework

• Quiz

• Test



• Practice SAT Tests

Equipment needed:

• Smart board

• Computer

• Calculator

Teacher Resources:



Curriculum Development Resources











Unit 5 Overview


Unit Title: Special Problem Types


Unit Summary

• Some problems can be solved by compiling a list and then adding up the number of items on the list.

• The probability of an event is a number from 0 to 1 that represents the likelihood that the event will occur.

Primary interdisciplinary connections: science, 21st century themes






Unit Rationale

Current testing has shown that students generally do well in computation, but do poorly on items involving

reading a word problem and solving it. The student must learn to translate the verbal into mathematical

language using often times a formula or equation. A guided plan for students in order to solve problems is

of utmost importance in the teaching of word problems. With repeated practice, students improve when they

learn and use the terminology needed to decipher what operation(s) to use when solving. Students need to

discover relationships between problems to gain familiarity in solving them. Real world problems and

multi-tasks involving finding and writing your solution, will allow students to become more comfortable

and familiar with the terminology and strategies needed to succeed.




Learning Targets

MA.9-12. - With each extension of number, the meanings of addition, subtraction, multiplication, and division are extended. In each new number system-integers, rational numbers, real numbers, and complex numbers-the four

operations stay the same in two important ways: They have the commutative, associative, and distributive properties

and their new meanings are consistent with their previous meanings.

MA.9-12. - Extending the properties of whole-number exponents leads to new and productive notation. For example,

properties of whole-number exponents suggest that (5 to the 1/3 power should be 5 to the (1/3) power = 5 = 5 and

that 5 to the 1/3 power should be the cube root of 5. MA.9-12. - Calculators, spreadsheets, and computer algebra systems can provide ways for students to become better

acquainted with these new number systems and their notation. They can be used to

generate data for numerical experiments, to help understand the workings of matrix, vector, and complex number algebra, and to experiment with non-integer exponents.


• How does the knowledge of the national

format of tests and strategies to answer

questions better prepare you for a test?


• Students’ score on standardized tests will be enhanced


• Students will understand the national formats and

strategies for standardized tests


Students will ...

• Be able to understand the scoring of the SAT

• Be able to understand the general format of the SAT

• Be able to measure understanding and growth in weak areas

• Be able to identify types of questions and use corresponding strategies







• Guided Practice

• Homework

• Quiz

• Test




Equipment needed:

• Smart board

• Computer

• Calculator

Teacher Resources:








Unit 6 Overview








Unit Title: Algebra II Methods


Unit Summary

• The rules that apply to positive integer exponents also word for negative integer and fractional exponents

• The variable in an equation may be underneath a radical, have a fractional exponent, or be part of an exponent

• The absolute value of x refers to the number x without regard to its sign

• A function is a rule or formula that tells how to pair the elements of on set, called the domain, with exactly one

element of another set, called the range.

Primary interdisciplinary connections: science, business, 21st century themes






Unit Rationale

Instruction that is clearly relevant to today’s rapidly changing world is at the forefront of unit design.

Content knowledge cannot by itself lead all students to academic achievement. Classes and projects that

spark student interest and provide a rationale for why the content is worth learning, enable students to make

connections between what they read and learn in school, their lives, and their futures. An engaging and

effective curriculum provides opportunities for exploration and exposure to new ideas. Real-world learning

experiences provide students with opportunities to transfer and apply knowledge in new diverse situations.

Learning Targets

Standards




MA.9-12.HSA-REI.4 - [Standard] - Solve quadratic equations in one variable.

MA.9-12.HSA-REI.4.a - Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p) = q that has the same solutions. Derive the quadratic formula from this form.

MA.9-12.HSA-REI.4.b - Solve quadratic equations by inspection (e.g., for x = 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.

MA.9-12.HSA-REI.C - [Cluster Statement] - Solve systems of equations

MA.9-12.HSA-REI.5 - [Standard] - 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. MA.9-12.HSA-REI.6 - [Standard] - Solve systems of linear equations exactly and approximately (e.g., with

graphs), focusing on pairs of linear equations in two variables.

MA.9-12.HSA-REI.7 - [Standard] - Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

MA.9-12.HSA-REI.8 - [Standard] - Represent a system of linear equations as a single matrix equation in a vector

variable. MA.9-12.HSA-REI.9 - [Standard] - 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).

MA.9-12.HSA-REI.D - [Cluster Statement] - Represent and solve equations and inequalities graphically

MA.9-12.HSA-REI.10 - [Standard] - 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).

MA.9-12.HSA-REI.11 - [Standard] - 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.





• How do you use variables to help you model real

world situations?

• Does it matter which form of a linear equation

you use?

• How does representing functions graphically

help you solve a system of equations?


• A single quantity may be represented by many different

expressions

• Find a set of values that replace the variables in the equations

and make each equation true


Students will ...

• Students will use variables to represent unknown quantities in real world situation




• Students will identify the different kinds of transformations

• Students will solve a system of linear equations by graphing the equation




• Guided Practice

• Homework

• Quiz

• Test




Teacher Resources:











mathematics curriculum grade 11 - buenaschools.org€¦ · 2/1/2019 · mathematics curriculum...

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