Download Algebra IB 2016 - Pennsauken Public Schools

Pennsauken Public Schools
Pennsauken School District
Curriculum Guide
Algebra IB
(One Semester)
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Pennsauken Public Schools
Content Area: Mathematics
Course Title: Algebra IB
Grade Level: 8-9
Unit 1: Quadratic Expressions
17 days
Unit 2: Quadratic Equations and
Functions
26 days
Unit 3: Radical and Rational
Expressions and Equations
22 days
Unit 4: Modeling with Statistics
17 days
Date Created:
Aug 2016
Board Approved on:
August 2016
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Pennsauken Public Schools
Algebra IB Mathematics Pacing Guide for 2016-2017
NJSLO
A.APR.A.1: A.SSE.A.1:
A.SSE.A.1.A: A.SSE.A.1.B:
A.SSE.A.2:
F.IF.B.4: F.IF.B.5: F.IF.C.7:
F.IF.C.7.A: F.IF.C.8:
F.IF.C.8.A: F.BF.A.1:
F.BF.B.3; F.LE.A.1:
F.LE.A.2
A.SSE.B.3: A.SSE.B.3.A:
A.REI.B.4: A.REI.B.4.A:
A.REI.B.4.B: A.REI.B.4
G.SRT.C.8; N.RN.A.2;
A.REI.A.2
A.APR.D.6; A.APR.D.7;
N.RN.A.2: N.RN.B.3:
A.REI.A.2
S.ID.A.1: S.ID.A.2:
S.ID.A.3: S.ID.B.5:
N.Q.A.1: N.Q.A.2
Title
Instructional Period
Number
of Days
Quadratic Expressions
Jan 30 - Feb 21, 2017
15
Benchmark 1
Feb 22-23, 2017
2
Quadratic Functions
Feb 24 - Mar 14, 2017
13
Benchmark 2
March 15-16, 2017
2
Quadratic Equations
Mar 17-29, 2017
9
Benchmark 3
Mar 30-31, 2017
2
PARCC ADJUSTMENT
Apr 3-7, 2017
5
Radical Functions
Apr 10-25, 2017
9
Benchmark 4
April 26-27, 2017
2
Rational Functions
Apr 28 - May 10, 2017
9
Benchmark 5
May 11-12, 2017
2
Statistics
May 15 - June 6, 2017
15
Benchmark 6
June 7-8, 2017
2
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Pennsauken Public Schools
Pennsauken Public Schools
Content Area:
Mathematics-Algebra IB
Grade Cluster:
8-9
Course Description
Algebra I is a course that is required for high school graduation. Algebra IA in conjunction with Algebra IB
satisfies this requirement. The course is designed for a full semester block.
Overarching Understanding(s) for the Course
● Perform arithmetic operations on polynomials
● Understand the relationship between zeros and factors
● Interpret the structure of expressions
● Solve equations and inequalities in one variable
● Create equations that describe numbers or relationships
● Interpret functions that arise in applications in terms of the context
● Represent and solve equations and inequalities graphically
● Build a function that models a relationship between two quantities
● Construct & compare linear, quadratic, & exponential models
● Build new functions from existing functions
● Analyze functions using different representations
● Use properties of rational and irrational numbers
● Summarize, represent, and interpret data on a single count or
measurement variable
● Summarize, represent, and interpret data on two categorical and
quantitative variables
● Interpret functions that arise in applications in terms of the context
21st Century Theme(s), Interdisciplinary Opportunities
● Connecting the content knowledge to real-world applications and problem situations that enable students to
see how what they are learning connects with their lives and the world around them. The work that is asked
of students must be authentic work that is relevant and that mirrors real life.
● Emphasizing deep understanding of the learning by focusing on projects and problems that require students
to use the content knowledge in new ways and to extend their understanding through collaboration with
others.
● Helping students understand and monitor the thinking processes they are using by including metacognitive
activities that ask students to reflect on their use of thinking structures and the effectiveness of the thinking
strategies they employed.
● Using technology to help students access, analyze, organize and share what they are learning and allow
students to independently locate appropriate tools for the task.
● Engaging students in solving complex problems that require higher order thinking and application of
content and that result in new perspectives and solutions to problems.
● Providing opportunities for students to work collaboratively as they gather information, solve problems,
share ideas, and generate new ideas.
● Developing life and career skills by creating opportunities for students to become self-directed learners
who take responsibility for their own learning and who learn how to work effectively with others.
Technology Standards
● 8.1 Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize
information in order to solve problems individually and collaborate and to create and communicate
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knowledge.
● 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming: All
students will develop an understanding of the nature and impact of technology, engineering, technological
design, computational thinking and the designed world as they relate to the individual, global society, and
the environment.
Desired Results
Unit: #
1
Unit Name: Quadratic Expressions
New Jersey Core Curriculum State Standards:
● CCSS.MATH.CONTENT.HSA.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.
● CCSS.MATH.CONTENT.HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its
context.
● CCSS.MATH.CONTENT.HSA.SSE.A.1.A: Interpret parts of an expression, such as terms, factors, and
coefficients.
● CCSS.MATH.CONTENT.HSA.SSE.A.1.B: Interpret complicated expressions by viewing one or more of
their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not
depending on P.
● CCSS.MATH.CONTENT.HSA.SSE.A.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).
Essential Question(s)
● Can two algebraic expressions that appear to be differnt be equivalent?
● How are the properties of real numbers related to polynomials?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
The Students will:
● Add, subtract, and multiply polynomials, relating these to arithmetic operations with integers.
● Factor to produce equivalent forms of quadratic expressions in one variable.
Assessment Evidence
Performance Task(s)
Summative:
● Unit 1 Assessment
● Topic Assessments
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● Homework
● Group Work
● Independant Work
● Center Activities
● Exploration and Extension Activities
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
This Unit will extend the learning from Algebra IA to include polynomials. Learning will include the use of
performing basic operations on polynomials. Factoring will be explored to begin the work of solving quadratic
equations in Unit 2.
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Resources:
● Glencoe Book - Chapter 8. Lessons are limited to factoring. Extensions to solving quadratic equations will
be covered in Unit 2. Lessons must include HOT Problems
● Pearson Book - Chapter 8. Lessons must include Concept Bytes and Challenge Questions
● A.APR.A.1 Powers of 11
● A.SSE.A.2 Equivalent Expressions
● A.REI.B.4 Visualizing Completing the Square
● http://betterlesson.com/lesson/486914/polynomial-puzzles-1-adding-and-subtracting-polynomials
● https://www.quantiles.com/tools/math-skills-database/
● http://map.mathshell.org/stds.php
Differentiation for high achieving, grade level, stuggling students and ELL can be found in the teachers editions of
Pearson and Glencoe.
Unit: #
2
Unit Name:
Quadratic Equations and Functions
New Jersey Core Curriculum State Standards:
● CCSS.MATH.CONTENT.HSA.SSE.B.3: Choose and produce an equivalent form of an expression to
reveal and explain properties of the quantity represented by the expression.*
● CCSS.MATH.CONTENT.HSA.SSE.B.3.A: Factor a quadratic expression to reveal the zeros of the
function it defines.
● CCSS.MATH.CONTENT.HSA.REI.B.4: Solve quadratic equations in one variable.
● CCSS.MATH.CONTENT.HSA.REI.B.4.A: Use the method of completing the square to transform any
quadratic equation in xinto an equation of the form (x - p)2 = q that has the same solutions. Derive the
quadratic formula from this form.
● CCSS.MATH.CONTENT.HSA.REI.B.4.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.
● CCSS.MATH.CONTENT.HSF.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. Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity.*
● CCSS.MATH.CONTENT.HSF.IF.B.5: Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the
number of person-hours it takes to assemble n engines in a factory, then the positive integers would
be an appropriate domain for the function.*
● CCSS.MATH.CONTENT.HSF.IF.C.7: Graph functions expressed symbolically and show key features
of the graph, by hand in simple cases and using technology for more complicated cases.*
● CCSS.MATH.CONTENT.HSF.IF.C.7.A: Graph linear and quadratic functions and show intercepts,
maxima, and minima.
● CCSS.MATH.CONTENT.HSF.IF.C.8: Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties of the function.
● CCSS.MATH.CONTENT.HSF.IF.C.8.A: Use the process of factoring and completing the square in
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a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these
in terms of a context.
● CCSS.MATH.CONTENT.HSF.BF.A.1: Write a function that describes a relationship between two
quantities.
● CCSS.MATH.CONTENT.HSF.BF.B.3 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.
● CCSS.MATH.CONTENT.HSA.REI.B.4: Solve quadratic equations in one variable.
● CCSS.MATH.CONTENT.HSF.LE.A.1: Distinguish between situations that can be modeled with linear
functions and with exponential functions.
● CCSS.MATH.CONTENT.HSF.LE.A.2: Construct linear and exponential functions, including
arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output
pairs (include reading these from a table).
Essential Question(s)
● What are the characteristics of quadratic functions?
● How can you solve a quadratic equation?
● How can you use functions to model real world situations?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
The Students will:
● Derive the quadratic formula by completing the square and recognize when there are no real solutions.
o use the method of completing the square to transform a quadratic equation in x into an equation
of the form (x - p)2 = q.
o derive the quadratic formula from (x - p)2 = q.
● Solve quadratic equations in one variable using a variety of methods (including inspection, taking
square roots, factoring, completing the square, and the quadratic formula) and write complex solutions
in a ± bi form.
o solve a quadratic equation in one variable by inspection.
o solve quadratic equations in one variable by taking square roots.
o solve a quadratic equation in one variable by completing the square.
o solve a quadratic equation in one variable using the quadratic formula.
o solve a quadratic equation in one variable by factoring.
o strategically select, as appropriate to the initial form of the equation, a method for solving a
quadratic equation in one variable.
o write complex solutions of the quadratic formula in a ± bi form.
● Create quadratic equations in one variable and use them to solve problems.
● Interpret key features of quadratic functions from graphs and tables. Given a verbal description of the
relationship, sketch the graph of a quadratic function, showing key features and relating the domain of
the function to its graph.
o interpret maximum/minimum and intercepts of quadratic functions from graphs and tables in the
context of the problem.
o sketch graphs of quadratic functions given a verbal description of the relationship between the
quantities.
o identify intercepts and intervals where function is increasing/decreasing
o determine the practical domain of a function.
● Use factoring and completing the square to produce equivalent forms of quadratic expressions in one
variable that highlight particular properties such as the zeros or the maximum or minimum value of the
function.
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●
●
●
●
●
o factor a quadratic expression for the purpose of revealing the zeros of a function.
o complete the square for the purpose of revealing the maximum or minimum of a function.
Given a context, write an explicit expression, a recursive process or steps for calculation for quadratic
relationships.
Graph quadratic functions by hand in simple cases and with technology in complex cases, showing
intercepts, extreme values and symmetry of the graph. Compare properties of two quadratic functions,
each represented in a different way.
o graph quadratic functions expressed symbolically.
o graph more complicated cases of quadratic functions using technology.
o identify and describe key features of the graphs of quadratic functions.
o given two quadratic functions, each represented in a different way, compare the properties of the
functions.
Calculate and interpret the average rate of change of a quadratic function presented symbolically or as a
table. Estimate and compare the rates of change from graphs of quadratic and exponential functions.
o calculate the rate of change of a quadratic function from a table of values or from a function
presented symbolically.
o estimate the rate of change from a graph of a quadratic function.
o analyze graphs and tables to compare rates of change of exponential and quadratic functions.
Identify the effects of transformations and combinations of transformations [f(x) + k, k f(x), f(kx),
and f(x + k)] on a function; find the value of k given the graph.
o perform transformations on graphs of linear and quadratic functions.
o 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).
o identify the effect on the graph of combinations of transformations.
o given the graph, find the value of k.
o illustrate an explanation of the effects on linear and quadratic graphs using technology.
o recognize even and odd functions from their graphs and from algebraic expressions for them.
Identify zeros of cubic functions when suitable factorizations are available and use the zeros to
construct a rough graph of the function. (*cubic functions are presented as the product of a linear and a
quadratic factor)
o find the zeros of a polynomial (quadratic and cubic).
o test domain intervals to determine where f(x) is greater than or less than zero.
o use zeros of a function to sketch a graph.
Assessment Evidence
Performance Task(s)
Summative:
● Unit 2 Assessment
● Topic Assessments
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● Homework
● Group Work
● Independant Work
● Center Activities
● Exploration and Extension Activities
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Pennsauken Public Schools
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
This Unit will extend the learning from Unit 1 to solve quadratic equations and model real world situations.
Resources:
● Glencoe Book - Chapter 8(extension of unit 1 to include solving), Chapter 9. Lessons must include
HOT Problems
● Pearson Book - Chapter 9. Lessons must include Concept Bytes and Challenge Questions
● A.REI.B.4 Braking Distance
● A.REI.B.4 Two Squares are Equal
● F.IF.B.4 Words – Tables - Graphs
● F.IF.B.5 The restaurant
● F.IF.C.8a Springboard Dive
● F.IF.C.8a Which Function?
● F.LE.A.3 Population and Food Supply
● F.BF.B.3 Identifying Even and Odd Functions
● F.BF.B.3 Transforming the graph of a function
● A.SSE.B.3 Profit of a company
● A.SSE.B.3 Rewriting a Quadratic Expression
● F.IF.C.7a Graphs of Quadratic Functions
● A.APR.B.3 Graphing from Factors 1
● https://www.quantiles.com/tools/math-skills-database/
● http://map.mathshell.org/stds.php
Differentiation for high achieving, grade level, stuggling students and ELL can be found in the teachers editions
of Pearson and Glencoe.
Unit: #
3
Unit Name:
Radical and RationalExpressions and Equations
New Jersey Core Curriculum State Standards:
● CCSS.MATH.CONTENT.HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to
solve right triangles in applied problems.(Use of Pythagorean Theorem only in Algebra I)
● CCSS.MATH.CONTENT.HSA.APR.D.6: Rewrite simple rational expressions in different forms; write
a(x)/b(x) in the form q(x) +r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of
r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples,
a computer algebra system.
● CCSS.MATH.CONTENT.HSA.APR.D.7: (+) 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.
● CCSS.MATH.CONTENT.HSN.RN.A.2: Rewrite expressions involving radicals and rational exponents
using the properties of exponents.
● CCSS.MATH.CONTENT.HSN.RN.B.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.
● CCSS.MATH.CONTENT.HSA.REI.A.2: Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may arise.
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Pennsauken Public Schools
Essential Question(s)
● How are radical and rational expressions represented?
● How can you solve a radical and rational equation?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
The Students will:
● Solve real world problems involoving right triangles using the Pythagorean Theorem
● Solve real world problems involving radicals.
● Explain and justify conclusions about sums and products of rational and irrational numbers.
Assessment Evidence
Performance Task(s)
Summative:
● Unit 3 Assessment
● Topic Assessments
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● Homework
● Group Work
● Independant Work
● Center Activities
● Exploration and Extension Activities
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
This Unit will lay a foundation for the more intricate algebraic content that will be developed and expanded in
Algebra II.
Resources:
● Glencoe Book - Chapter 10-2 thorugh 10-5, 11-3, 11-4, 11-5, 11-6. Lessons must include HOT
Problems
● Pearson Book - Chapter 10-1 through 10-4, 11-1 through 11-4. Lessons must include Concept Bytes
and Challenge Questions
● https://www.illustrativemathematics.org/content-standards/HSA/APR/D/6/tasks/1346
● https://www.illustrativemathematics.org/content-standards/HSA/REI/A/2/tasks/391
● https://www.illustrativemathematics.org/content-standards/HSA/REI/A/2/tasks/1915
● https://www.quantiles.com/tools/math-skills-database/
● http://map.mathshell.org/stds.php
Differentiation for high achieving, grade level, stuggling students and ELL can be found in the teachers editions
of Pearson and Glencoe.
Unit: #
4
Unit Name:
Modeling with Statistics
New Jersey Core Curriculum State Standards:
● CCSS.MATH.CONTENT.HSS.ID.A.1: Represent data with plots on the real number line (dot plots,
histograms, and box plots).
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Pennsauken Public Schools
● CCSS.MATH.CONTENT.HSS.ID.A.2: 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.
● CCSS.MATH.CONTENT.HSS.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).
● CCSS.MATH.CONTENT.HSS.ID.B.5: 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.
● CCSS.MATH.CONTENT.HSN.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.
● CCSS.MATH.CONTENT.HSN.Q.A.2: Define appropriate quantities for the purpose of descriptive
modeling.
Essential Question(s)
● How can collecting and analyzing data help you make decisions or predictions?
● How can you make and interpre differnt representations of data?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
The Students will:
● Represent data with plots (dot plots, histograms, and box plots) on the real number line.
● Compare center and spread of two or more data sets, interpreting differences in shape, center, and
spread in the context of the data, taking into account the effects of outliers.
o represent two or more data sets with plots and use appropriate statistics to compare their center
and spread.
o interpret differences in shape, center, and spread in context.
o explain possible effects of extreme data points (outliers) when summarizing data and
interpreting shape, center and spread.
● Summarize and interpret categorical data for two categories in two-way frequency tables; explain
possible associations and trends in the data.
o construct two-way frequency tables for categorical data.
o interpret joint, marginal and conditional relative frequencies in context.
o explain possible associations between categorical data in two-way tables.
o identify and describe trends in the data.
Assessment Evidence
Performance Task(s)
Summative:
● Unit 4 Assessment
● Topic Assessments
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● Homework
● Group Work
● Independant Work
● Center Activities
● Exploration and Extension Activities
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
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Pennsauken Public Schools
for high achieving, grade level, struggling students, and special needs/ELL
This Unit will engage the students in which statistics to compare, which plots to use, and what the results of
a comparison might mean. The students will investigate the real-life actions to be taken based on this
investigation. .
Resources:
● Glencoe Book - Chapter 12-1 through 12-6. Lessons must include HOT Problems
● Pearson Book - Chapter 12-2 through 12-6. Lessons must include Concept Bytes and Challenge
Questions
● S.ID.A.1-3 Haircut Costs
● S.ID.A.1-3 Speed Trap
● S.ID.A.2-3 Measuring Variability in a Data Set
● S.ID.A.3 Identifying Outliers
● S.ID.B.5 Support for a Longer School Day?
● https://www.quantiles.com/tools/math-skills-database/
● http://map.mathshell.org/stds.php
Differentiation for high achieving, grade level, stuggling students and ELL can be found in the teachers editions
of Pearson and Glencoe.
Board Approved Course Textbook
Glencoe Algebra I Common Core, McGraw Hill, 2015
Algebra I Common Core, Pearson, 2012
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