CurriculumandInstruction –Mathematics
Quarter 2Bridge Math
In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,
- 80% of our students will graduate from high school college or career ready
- 90% of students will graduate on time
- 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity
In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readinessis rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.
The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.
This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.
Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:
The TN Mathematics StandardsThe Tennessee Mathematics Standards:
/ Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.
Standards for Mathematical Practice
Mathematical Practice Standards
/ Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.
Purpose of the Mathematics Curriculum Maps
This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.
The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgement aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.
Additional Instructional Support
Shelby County Schools adopted our current math textbooks for grades 9-12 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards; therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials.
The additional materials purposefully address the identified gaps in alignmentto meet the expectations of the CCR standards and related instructional shifts while stillincorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., EngageNY), have been evaluated by district staff to ensure that they meet the IMET criteria.
How to Use the Mathematics Curriculum Maps
Overview
An overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.
Tennessee State Standards
The TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.
Content
Teachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.
Instructional Support and Resources
District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.
Topics Addressed in Quarter
- Polynomials
- Quadratic Functions and Equations
Overview
The content at the beginning of this quarter introduces students to polynomial expressions and how to add, subtract, and multiply polynomials.Studentswill understand factoring as the reverse process of multiplication and this understanding is extended and connected to factoring polynomial expressions and solving basic polynomial equations. The ability to manipulate expressions is critical to students’ understanding, particularly in solving quadratic equations. Students work extensively with factoring quadratics using various factoring techniques. Students will find and estimate roots, solve quadratics using the Quadratic Formula, completing the square, taking square roots, and by factoring using the Zero Product Property. Students will understand what it means to solve a quadratic equation. Building on previous units and prior courses that explored linear equations and expressions, students will begin to explore radicals and rational functions.
Fluency
The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.
References:
TN STATE STANDARDS / CONTENT / INSTRUCTIONAL SUPPORT & RESOURCES
Unit 4 - Chapter 11: Polynomials (McGraw-Hill Bridge Math)
Chapter 8: Polynomials & Factoring (Prentice Hall Algebra 1)
(Allow approximately 4weeks for instruction, review, and assessment)
Conceptual Category: Ways of Looking: Revisiting Concepts
Domain: Symbolic Mathematics (W-SM)
W-SM7 Perform polynomial arithmetic, including adding, subtracting, multiplying, dividing, factoring, and simplifying results. / Enduring Understanding(s):
The properties of integers apply to polynomials.
Essential Question(s):
Why is it important to know the operations of integers to understand the properties of polynomials?
Objective(s):
- Students will write polynomials in standard form.
- Students will add & subtract polynomials.
- Students will multiply polynomials by monomials.
- Students will factor polynomials into a monomial factor and a polynomials factor.
11-1 Add and Subtract Polynomials
11-2 Multiply by a Monomial
11-3 Divide and Find Factors
Prentice Hall Algebra 1
8-1 Adding and Subtracting Polynomials
8-2 Multiplying and Factoring
Concept Byte: Using Models to Multiply
Task(s):
Illustrative: Powers of 11
Polynomial Web Quest Tasks
Polynomial Farm Task
Additional Resources:
Khan Academy Videos: Intro to Polynomials
Khan Academy Videos: Adding & Subtracting Polynomials
Khan Academy Videos: Intro to factorization
Khan Academy Videos: Factoring monomials
Khan Academy Videos: Common monomial factors
Khan Academy Videos: Factoring polynomials by taking common factors
Better Lesson: Adding and Subtracting Polynomials
Lesson 5-Adding and Subtracting Polynomials
Lesson 6 - Multiplying Polynomials by Monomials
Math Planet Lesson: Monomials and Polynomials / Vocabulary:
Polynomial, monomial, coefficient, constant, binomial, trinomial, like terms, simplify, standard form, extracting factors, greatest common factor (GCF)
Writing in Math:
Tell whether you prefer to group terms or use columns to add or subtract polynomials. Explain why you prefer that method.
Explain how subtraction of polynomials is related to addition of polynomials.
How is algebraic multiplication of a monomial and a polynomial similar to arithmetic multiplication of a single-digit number and a multi-digit number?
Conceptual Category: Ways of Looking: Revisiting Concepts
Domain: Symbolic Mathematics (W-SM)
W-SM7 Perform polynomial arithmetic, including adding, subtracting, multiplying, dividing, factoring, and simplifying results. / Enduring Understanding(s):
The properties of integers apply to polynomials.
Essential Question(s):
How are the properties of real numbers related to polynomials?
Objective(s):
- Students will multiply a binomial by a binomial.
- Students will write polynomials in standard form.
- Students will expand a product of two binomials.
11-4 Multiply Two Binomials
Prentice Hall Algebra 1
8-3 Multiplying Binomials
Task(s):
Multiplying Binomials Task
Multiplying Polynomials Formative Assessment Task
Additional Resources:
EngageNY Lesson: Multiplying Polynomials
Khan Academy: Multiplying Binomials by Binomials
Regents Prep: Multiplying Binomials
Virtual Nerd Video
Learnzillion: Dividing Polynomials Using Long Division / Vocabulary: binomial, distributive property, product, terms, expanding, sum and difference of two squares,
Writing in Math:
Have students create multiple representations of binomial multiplication.
Have students write a response to the following: Can the product of two binomials ever have more than three terms? Explain your thinking.
Chapter 12: Quadratic Equations (McGraw-Hill Bridge Math)
Chapter 9: Quadratic Functions & Equations (Prentice Hall Algebra 1)
Chapter 4: Quadratic Functions and Equations (Prentice Hall Algebra 2)
(Allow approximately 5weeks for instruction, review, and assessment)
Conceptual Category: Ways of Looking: Revisiting Concepts
Domain: Graphic Mathematics (W-GM)
W-GM2Graph quadratic equations and identify key characteristics of the graph. / Enduring Understanding(s):
- Functions give us the power to organize, compare, and make sense of relationships around us.
- The graph of any quadratic function is a transformation of the graph of the parent quadratic function.
- The characteristics of quadratic functions and their representations are useful in solving real-world problems.
- How can we determine which way the parabola will be facing before you graph it?
- How do we find the vertex when an equation is given? A graph?
- How does a quadratic equation transform on a coordinate plane?
- How can we recognize solutions on a parabola?
- Students will graph quadratic functions.
- Students will identify key features of a quadratic equation.
12-1 Graph Parabolas
Prentice Hall Algebra 1
9-1 Quadratic Graphs and Their Properties
Prentice Hall Algebra 2
4-1 Quadratic Functions and Transformations
Khan Academy: Graphing Quadratic Functions
3-lesson unit on Quadratics
Learnzillion: Describe the graph of a given quadratic function in vertex form by using knowledge of transformations
Learnzillion: Understand characteristics of a quadratic equation by graphing transformations of the parent function f(x) = ax2
/ Vocabulary: quadratic, quadratic equation, function, parabola, vertex, axis of symmetryWriting in Math:
What are some of the real-life applications of quadratic equations?
What do you notice about the location of the vertex and axis of symmetry of the parabola you obtain when you graph an equation in the form y= ax2 + c?
Conceptual Category: Ways of Looking: Revisiting Concepts
Domain: Graphic Mathematics (W-GM)
W-GM2Graph quadratic equations and identify key characteristics of the graph. / Enduring Understanding(s):
- Quadratic functions have characteristics different than linear functions.
- For any quadratic function in standard form, y= ax2 + bx + c, the values of a, b, and c provide key information about its graph.
- What are the advantages of a quadratic function in vertex form? In standard form?
- How is any quadratic function related to the parent quadratic function?
- How are the real solutions of a quadratic equation related to the graph of the related quadratic function?
- Students will graph functions defined by the general quadratic equation (standard form).
- Students will solve quadratic equations by graphing
12-2 The General Quadratic Function
Prentice Hall Algebra 1
9-2 Quadratic Functions
Prentice Hall Algebra 2
4-2Standard Form of a Quadratic Function
Task(s):
Illustrative: Identifying Quadratic Functions (Vertex Form)
Illustrative: Identifying Quadratic Functions (Standard Form)
Additional Resources:
Khan Academy: Graphing Quadratic Functions
Learnzillion: Write a quadratic equation in vertex form by solving for the vertex and another point
3-lesson unit on Quadratics
EngageNY Lesson: Algebra I Module 4, Topic A, Lesson 8
EngageNY Lesson: Algebra I Module 4, Topic A, Lesson 10 / Vocabulary: quadratic equation, (standard form of a quadratic equation
Writing in Math:
Summarize the relationship between │a│ and the width of the graph of y= ax2 + bx + c.
Compare standard form with vertex form using an actual function. Compare the steps needed to find the vertex.
Explain how you can use the y-intercept, vertex, and axis of symmetry to graph a quadratic function. Assume the vertex is not on the y axis.
Conceptual Category: Ways of Looking: Revisiting Concepts
Domain: Graphic Mathematics (W-GM)
W-GM3 Find the solution of a quadratic equation and/or zeros of a quadratic function. / Enduring Understanding(s):
Quadratic equations can be solved by a variety of methods, including graphing, completing the square, using the quadratic formula, and using the Zero Pproduct Property.
Essential Question(s):
How can features of quadratic functions such as the equation, solutions, axis of symmetry, vertex, etc. be represented in tables, equations, and in “real world” contexts?
Objective(s):
- Students will solve quadratic equations by graphing and using square roots.
- Students will use factoring to solve quadratic equations.
12-3 Factor and Graph
Prentice Hall Algebra 1