Math Accuplacer Grade 12 · 2018. 5. 10. · Math Accuplacer Grade 12 Prepared by: Louis Cappello Salvatore Goncalves, Superintendent of Schools Jaynellen Behre Jenkins, Assistant

BLOOMFIELD PUBLIC SCHOOLS Bloomfield, New Jersey 07003

Curriculum Guide

Math Accuplacer Grade 12

Prepared by:

Louis Cappello

Salvatore Goncalves, Superintendent of Schools Jaynellen Behre Jenkins, Assistant Superintendent of Curriculum

Roger Marchegiano, Supervisor of Mathematics

Board Approved: July 28, 2015

Title of Unit Real Number System Grade Level 12

Curriculum Area Mathematics Time Frame 3 weeks Developed By Lou Cappello

Desired Results (Stage 1)Established Goals

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Primary Interdisciplinary Connections

8.1.12.A.3 Participate in online courses, learning communities, social networks, or virtual worlds and recognize them as resources for lifelong learning. 8.1.12.F.2 Analyze the capabilities and limitations of current and emerging technology resources and assess their potential to address educational, career, personal, and social needs. 9.1.12.A.1 Apply critical thinking and problem-solving strategies during structured learning experiences. 9.1.12.A.2 Participate in online strategy and planning sessions for course-based, school-based, or outside projects. 9.1.12.B.1 Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems, using multiple perspectives. 9.1.12.C.4 Demonstrate leadership and collaborative skills when participating in online learning communities and structured learning experiences. 9.1.12.C.5 Assume a leadership position by guiding the thinking of peers in a direction that leads to successful completion of a challenging task or project. 9.1.12.F.2 Demonstrate a positive work ethic in various settings, including the classroom and during structured learning experiences

Accuplacer – Math

21st Century Interdisciplinary Themes: __X__ Global Awareness __X__ Financial, economic, business, and entrepreneurial literacy _____ Civic Literacy _____ Health Literacy

TransferStudents will be able to independently use their learning to… T1. Analyze real life situations as a math problem T2. Become proficient in daily living skills involving math

MeaningUnderstandings Essential Questions

Students will understand that… Students will keep considering…

U1 - all numbers, rational and irrational, have a location on a number line. U2 - every number has a decimal expansion. U3 - every rational number has a decimal expansion that terminates or eventually repeats. U4 - a number in the form a/b means a is divided by b. U5 - every irrational square root can be estimated by its location between two rational square roots, e.g., √7 is between √4 and √9.

Q1 - Why does one need to distinguish between rational and irrational numbers? Q2 - How does one locate irrational numbers on a number line?

AcquisitionKnowledge Students will know…

SkillsStudents will be able to…

K1 - numbers that are not rational are called irrational. K2 - the process of dividing one number by another. K3 - how to truncate or round a decimal expansion to a specific number of places. K4 - how to compare decimal values. K5 - the perfect square numbers (if not memorized, students should know how to find the perfect square numbers by multiplying each whole number by itself).

S1 - show that the decimal expansion of a rational number terminates or repeats eventually. S2 - convert a decimal expansion which repeats eventually into a rational number. S3 - find rational approximations of irrational numbers. S4 - compare the size of approximations of irrational numbers. S5 - locate approximations of irrational numbers on a number line. S6 - estimate the value of expressions of irrational numbers.

Evidence (Stage 2) Checks for Alignment Evaluation Criteria

Performance is judged in terms of…

Assessment Evidence

T1,2, U1, Q1-7 Blooms Taxonomy

Remembering Understanding Applying Analyzing Evaluating Creating

Rubric

Transfer Task(s) Formative

o Book problems o Worksheets o Cooperative Activities o Problem Solving Activities o Worksheets o Do Now o Closure

Summative

o Quizzes o Test o Project

K1-5, S1-6 Blooms Taxonomy Remembering Understanding Applying Analyzing Evaluating Creating

Rubric

Other Evidence Formative

Essays Journals Rubrics Reports Other Assessments

Summative

Pre-Assessment Journals Informal Observations

Learning Plan (Stage 3)

Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals.

Required Activities Required Resources

Investigate the following: Integers and rational numbers. Comparing and scaling rates.

Accentuate the Negative Investigation 1, 2, 3 and 4 Stretching and Shrinking Investigation 4 Filling and Wrapping Investigations 2 and 3

Suggested Activities Suggested Resources Illuminations lessons AN – Inv 1 – ACE 1-74; Inv 2 – ACE 1-60; Inv 3 – ACE 1-48; Inv 4 ACE 1-52 S&S – Inv 4 – ACE 1-39 FW – Inv 2 – ACE 1-25; Inv 3 ACE 1-40

http://illuminations.nctm.org http://nlvm.usu.edu

Strategies for DifferentiationStudents Below Target: Students Meeting or Exceeding Target:

Paired/Group Activity Role Play Guided practice SQ3R Role Play Cooperative Learning QAR Choice boards Cooperative Learning Independent Study Choice boards Interest Based Mini Lessons Tic - Tac - Toe menus Skill-Based Mini Lessons Learning Buddies Tiered Products /Activities Varied Rubrics Choice Menus Mentorships Advance notice of assignments Small Group Instruction Review with study skills and strategies training. Visual cues found on worksheets Teach organizational skills Chunking and grouping of material Test modifications Advance notice of assignments Time extensions Review with study skills and strategies training. Teach organizational skills Test modifications/time extensions

Accuplacer – Math

Title of Unit Foundations for Algebra Grade Level 12 Curriculum Area Mathematics Time Frame 3 weeks

Developed By Lou Cappello


A-SSE-1.a: Interpret parts of an expression such as terms, factors and coefficients. N-RN-3: 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.




TransferStudents will be able to independently use their learning to… T1. Communicate about ideas in Algebra in a standard and understandable manner T2. Relate the topics learned in Algebra to things that they do in their everyday lives T3. Analyze real life situations in a mathematical way T4. Become proficient in daily skills involving mathematics



U1. Algebra uses symbols to represent quantities that are unknown or that vary. U2. Mathematical phrases and real-world relationships can be represented using symbols and operations. U3. Equations are used to represent the relationship between two quantities that have the same value. U4. Sometimes, the value of one quantity can be found if the value of another is known. The relationship between the quantities can be represented in different ways, including tables, equations, and graphs. U5. When simplifying an expression operations must be performed in the correct order. U6. Mathematics involves the use of different types of numbers which can be represented in a hierarchical model. U7. Mathematical properties can be used to transform mathematical relationships.

Q1. How can you represent quantities, patterns, and relationships? Q2. How are properties related to algebra? Q3. How do you identify the correct mathematical relationship from the context of a real life situation? Q4. What are advantages and disadvantages of different mathematical relationships? Q5. What are different ways you can verify the correctness of your mathematical transformations??



K1. Variables and expressions K2. Order of operations and evaluating expressions K3. Real numbers and the number line K4. Properties of real numbers K5. Adding and subtracting real numbers

S1. To write algebraic expressions S2. To simplify expressions involving exponents S3. To use the order of operations to evaluate expressions S4. To classify, graph, and compare real numbers S5. To find and estimate square roots

K6. Multiplying and dividing real numbers K7. The distributive property K8. An introduction to equations K9. Patterns, equations, and graphs

S6. To identify and use properties of real numbers S7. To find sums and differences of real numbers S8. To find products and quotients of real numbers S9. To use the distributed property to simplify expressions S10. To solve equations using tables and mental math S11. To use tables, equations, and graphs to describe relationships



Assessment Evidence



Rubric



Summative o Quizzes o Test o Project


Rubric



Summative Pre-Assessment Journals Informal Observations




Student groups will be formed to examine the Challenge problems in the text.

Text: Algebra 1 Pearson

Suggested Activities Suggested Resources Think about a plan 1-1 PPSW Game 1-1: “Matching Expressions” OTRC Think about a plan 1-2 PPSW Puzzle 1-2: “Calc-words” OTRC Think about a plan 1-3 PPSW Activity 1-3: “Inequality Ski Trail” OTRC Think about a plan 1-4 PPSW Game 1-4: “You’ve Got my Property” OTRC Think about a plan 1-5 PPSW Concept Byte 1-5: “Always, Sometimes, or Never” (Pg. 37) Puzzle 1-5: “That’s Sum Puzzle!” OTRC Think about a plan 1-6 PPSW Concept Byte 1-6: “Closure” (Pg. 45) Activity 1-6: “A Class Divided” OTRC Think about a plan 1-7 PPSW Game 1-7: “Algebra Baseball” OTRC Think about a plan 1-8 PPSW

Text: Algebra 1: Pearson

Accuplacer – Math

Title of Unit Linear Equations, Inequalities, and Systems Grade Level 12 Curriculum Area Mathematics Time Frame 4 weeks



A-REI 1. 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 3. Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-REI 5. Represent and solve equations and inequalities graphically Solve systems of equations 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. 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Primary Interdisciplinary Connections8.1.12.A.3 Participate in online courses, learning communities, social networks, or virtual worlds and recognize them as resources for lifelong learning. 8.1.12.F.2 Analyze the capabilities and limitations of current and emerging technology resources and assess their potential to address educational, career, personal, and social needs. 9.1.12.A.1 Apply critical thinking and problem-solving strategies during structured learning experiences. 9.1.12.A.2 Participate in online strategy and planning sessions for course-based, school-based, or outside projects. 9.1.12.B.1 Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems, using multiple perspectives. 9.1.12.C.4 Demonstrate leadership and collaborative skills when participating in online learning communities and structured learning experiences. 9.1.12.C.5 Assume a leadership position by guiding the thinking of peers in a direction that leads to successful completion of a challenging task or project. 9.1.12.F.2 Demonstrate a positive work ethic in various settings, including the classroom and during structured learning experiences





U1. Manipulating symbols in order will help them solve algebraic equations in problem situations. U2. Algebraic concepts and the relationships among them will help them better understand the structure of algebra.

Q1. Why are the properties of equality important in the process of solving equations? Q2. Why is it important to check your answers when solving absolute value equations? Q3. How is solving an inequality similar to solving an equations? How is it different? Q4. What are the two types of compound inequalities? Q5. When does a system of equations have exactly one solution? No solution? An infinite number of solutions? Q6. When solving a system of equations algebraically, how do you decide whether to use the substitution method or elimination method? Q7. When does a system of inequalities have no solution? Inequality? Q8. What methods can you use to solve systems of equations?



K1. How to manipulate symbols in order to solve problems and use

algebraic skills to solve equations and inequalities in problem situation.

K2. How formulas are used in real-world problem.

K3. How properties of numbers are used to evaluate expressions.

K4. How solving equations use properties of equality.

K5. How solving inequalities are similar and different to solving

equations.

K6. How to graph systems of equations and inequalities.

K7. How to determine the solution from the graph of equations and

inequalities.

S1. Evaluate and simplify expressions.

S2. Solve equations.

S3. Solve and graph inequalities.

S4. Solve for a given variable in a formula

S5. Solve and checking absolute value equations.

S6. Solve inequalities

S7. Graph systems of equations.

S8. Graph systems of inequalities.

S9. Solve systems by substitution, elimination.



Assessment Evidence



Rubric



Summative



Rubric



Summative





Project A Good Sports Investigations and Project Masters Wkbk p.25

Text: Glencoe Algebra 2

Suggested Activities Suggested Resources

Project B Temperature Tendencies Investigations and Project Masters Wkbk p.27 Algebra 2 Teacher’s Edition Larsen, Kanold, Stiff Enrichment Activities p.8 Algebra 2 Teacher’s Edition Larsen, Kanold, Stiff Writing Problem p.15 Algebra 2 Teacher’s Edition Larsen, Kanold, Stiff Cooperative Learning p. 36

Internet Math Library Computer Lab Algebra Tiles



Accuplacer – Math

Title of Unit Polynomials and Factoring Grade Level 12 Curriculum Area Mathematics Time Frame 5 weeks



Algebra: A-APR- 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. A-SSE-3 a. Factor a quadratic expression to reveal the zeros of the function it defines. A-SSE-2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Functions: F-IF-8 a. 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.







U1. Monomials can be used to form larger expressions called polynomials. U2. Polynomials can be added and subtracted. U3. There are several ways to find the product of two binomials, including models, algebra, and tables. U4. The properties of real numbers (including multiplication and factoring) can be used to transform monomial and polynomial expressions.

Q1. How can two algebraic expressions that appear to be different be equivalent? Q2. How are the properties of real numbers related to polynomials? Q3. What patterns and characteristics can you observe in expressions when multiplying / factoring?



K1. Adding and Subtracting Polynomials K2. Multiplying and Factoring K3. Multiplying Binomials K4. Multiplying Special Cases K5. Factoring x 2 + bx + c K6. Factoring ax 2 + bx + c K7. Factoring Special Cases K8. Factoring by Grouping

S1. To classify, add, and subtract polynomials. S2. To multiply a monomial by a polynomial. S3. To factor a monomial from a polynomial. S4. To multiply two binomials or a binomial by a trinomial. S5. To find the square of a binomial and to find the product of a sum and difference. S6. To factor trinomials of the form x 2 + bx + c. S7. To factor trinomials of the form ax 2 + bx + c. S8. To factor perfect-square trinomials and the differences of two squares. S9. To factor higher-degree polynomials by grouping.



Assessment Evidence



Rubric



Summative



Rubric



Summative







Suggested Activities Suggested Resources Think About a Plan 8-1 PPSW Puzzle 8-1; “Polynomial Search” OTRC Enrichment 8-2 AIORO Think About a Plan 8-2 PPSW Concept Byte: “Using Models to Multiply” (Pg.485) Think About a Plan 8-3 Puzzle 8-3: “The Binomial Code” OTRC Enrichment 8-4 AIORO Think About a Plan 8-4 PPSW Concept Byte 8-5: “Using Models to Factor” (Pg. 499) Think About a Plan 8-5 PPSW Game 8-5: “Factoring” OTRC Think About a Plan 8-6 PPSW Game 8-6: “One From Column A, One From Column B” OTRC Think About a Plan 8-7 PPSW


Accuplacer – Math

Title of Unit Quadratic Functions and Equations Grade Level 12 Curriculum Area Mathematics Time Frame 5 weeks



Functions: F-IF-7 a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F-IF-8 a. 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-LE-1 Distinguish between situations that can be modeled with linear functions and with exponential functions. Algebra: A-REI- b. 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. A-REI- 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.







U1. Quadratic equations can be solved by a variety of methods, including graphing, quadratic equation, factoring, and finding square roots. U2. You can use linear, quadratic, or exponential functions you have studied to model some sets of data. U3. You can solve systems of linear and quadratic equations graphically and algebraically. This type of system can have two solutions, one solution, or no solutions.

Q1. What are the characteristics of quadratic functions? Q2. How can you solve a quadratic equation? Q3. Why might you select one method of solving a quadratic function over another? Q4. How can you use functions to model real-world situations?



K1. Quadratic Graphs and Their Properties K2. Quadratic Functions K3. Solving Quadratic Equations K4. Factoring to Solve Quadratic Equations K5. Completing the Square K6. The Quadratic Formula and the Discriminant K7. Linear, Quadratic, and Exponential Models K8. Systems of Linear and Quadratic Equations

S1. To graph quadratic functions of the form y=ax^2 and y=ax^2+c S2. To graph quadratic functions of the form y=ax^2+bx+c S3. To solve quadratic equations by graphing and using square roots S4. To solve quadratic equations by factoring S5. To solve quadratic equations by completing the square S6. To solve quadratic equations by using the quadratic formula. S7. To find the number of solutions of a quadratic equation S8. To choose a linear, quadratic, or exponential model for data S9. To solve systems of linear and quadratic



Assessment Evidence



Rubric



Summative



Rubric



Summative







Suggested Activities Suggested Resources Think About a Plan 9-1 PPSW Puzzle 9-1; “Add ‘em Up” OTRC Enrichment 9-2 AIORO Think About a Plan 9-2 PPSW Concept Byte: “Finding Roots” (Pg.554) Think About a Plan 9-3 Activity 9-3: “Which is Which?” OTRC Enrichment 9-4 AIORO Think About a Plan 9-4 PPSW Think About a Plan 9-5 PPSW Activity 9-5: “Square Patterns” OTRC Think About a Plan 9-6 PPSW Game 9-6: “Start your Engines!” OTRC Think About a Plan 9-7 PPSW Think About a Plan 9-8 PPSW


Documents

Math Accuplacer Grade 12 · 2018. 5. 10. · Math Accuplacer Grade 12 Prepared by: Louis Cappello Salvatore Goncalves, Superintendent of Schools Jaynellen Behre Jenkins, Assistant