Algebra I Course Map

Course Overview for Algebra

In Algebra I, students focus on the key concepts of algebraic thinking: expressions, equations, and inequalities; linear, quadratic, and exponential functions; and manipulating variables. Students learn to represent these functions as verbal statements, equations, tables, and graphs. They become practitioners of algebraic thinking by applying their learning to real-world and mathematical problems. The course also teaches students to form coherent mathematical arguments, and to articulate these arguments in clear, precise writing.

Recommended Fluencies for Algebra I:

• Analytic geometry of lines, including modeling with equations
• Add, subtract, and multiply polynomials
• Transforming expressions and chunking (seeing the parts of an expression as a single object) as used in factoring, completing the square, and other algebraic calculations
• Graphing functions and interpreting key features of graphs and fitting a data set to a curve
• Understand quantities and their relationships - using appropriate units
• Understand effects of parameter changes and apply them to create a rule modeling a function

CCSS Emphasis Seeing Structure in Expressions · Reasoning with Equations and Inequalities · Creating Equations · Reasoning Quantitatively · Interpreting and Building Functions · Interpreting Categorical and Quantitative Data · Performing operations on Polynomials · Interpreting Linear,  Quadratic and Exponential Functions in terms of the situation they model

Course Competencies Students continue to interface with the Standards of Mathematical Practices that intend to guide students to the real-world, logical use of MAP. The course will also add the PARCC performance level descriptors for measuring student command of content and refer them to the sub-claims as they pertain to content, additional supporting content, apply reasoning, and exhibit accurate modeling.

Competency Sets:

Standards of Mathematical Practice

PARCC PLDs

Modules for this Course:

Module 1: Relationships Between Quantities and Reasoning with Equations

Module 2: Descriptive Statistics

Module 3: Linear and Exponential Relationships

Module 4: Polynomial and Quadratic Expressions and Equations

Module 5: Quadratic Functions and Modeling

Instructional Model and Implementation Strategies for Math

The WLA math course is a two-tiered approach to teaching on-grade level Algebra and customized learning for students based on their individual growth needs. Both courses will utilize curated learning materials compiled into learning activities called playlists. Using a block schedule, students will attend their Algebra course for 90-minutes on one day and then attend the Math Studio class. The Math Studio course is where students engage in custom made playlists based on their ability level.

Modular Playlists for Algebra: Playlists for Algebra will be made for each module written in this course map. The playlist will consist of learning materials that engage students in a conceptual, procedural, and applied understanding of each standard. A playlist might include:

• Direct instruction videos or tutoring sessions made to introduce a topic (conceptual understanding)
• List of practice problems (procedural practice)
• Performance tasks/word problem/real-world Scenarios (application)
• Small formative assessment (conceptual, procedural, and applied)

Personally Curated Playlists for Math Studio: Playlists made for students in the Math Studio courses are personally curated based on diagnostic assessments. Each student will take the Measures of Academic Progress (MAP) diagnostic test in addition to other diagnostic assessments to measure each students individual, standardized abilities. Playlists will be made that address student’s growth needs starting with the most delayed skills first (farthest back in grade level). Playlists will follow a similar format to the Algebra course playlists in that they will ensure conceptual, procedural, and applied understanding of a standard.

Personalized Tutoring and Flex Models of Instruction: Teachers will use a variety of methods to capture data from students as they progress through playlists. Teachers will use these measurements to aggregate students together who need to review a concept. The teacher will arrange time within a class period to review concepts to groups of students as needed through the completion of a playlist.  

Instructional Strategies Utilized in Algebra and Math Studio:

• Accountable video-based Instruction: videos used to introduce or review a  specific concept in Math that includes practice problems and scenarios within the video ensuring that students attention and time spent. Student usage data is tracked as well as their achievement data on video-associated assessments.

• Small Group Instruction: direct instruction or review of a concept with a teacher in groups ranging from 2-6 students.

• Flex Tutoring Sessions: as students progress through a playlist they made become stuck on a specific concept, using data and flexible scheduling a facilitating teacher may group students together for remediation, review, or further explanation.
• Adaptive Problem Sets: Programs like ALEKS math, IXL Math, or Kahn Academy allow students to attempt a problem set for a specific standard or skill. As students answer questions correctly the problems become more rigorous, as they answer them incorrectly the software reteaches the topic and provides lower level questions. If a student is stuck with a specific skill they may flag a teacher for Flex Tutoring, Small-group instruction, or in-the-moment help.

• Problem-based Discussions: Use of a real-world scenario that requires specific Math skills to solve where students must collaborate on how to go about solving the problem then attempt to solve the problem as a group.

• Multi-step Performance Tasks: a multi-step problem that uses an application of multiple Math skills or concepts to solve an outcome many times using real-world scenarios.

• Digital Formative Assessments: using digital hosting software within a Learning Management System (such as Canvas) or an formative assessment engine (Formative at goformative.com) students can take a digitally-based assessment and get results immediately.

• Project-based Learning: teaching method in which students gain knowledge and skills by working for an extended period of time to investigate and respond to an engaging and complex question, problem, or challenge.

Methods of Assessment in the Algebra Course

Students will be assessed in a variety of methods throughout the Algebra course with assessments ranging in length, depth, and style. Assessments in some cases will seek to emulate the PARCC assessment and in other instances assess students’ abilities to apply their skills in other environments. Below is a list of assessment types for the Algebra Course:

Digital Formative Assessments (Exit Tickets): students will take small digital assessments at the end of each playlist within a module. These assessments provide small, instantaneous feedback to students on their learning.

Performance-based Assessments for PARCC Performance Level Descriptors: students will be given multi-step problems to solve that integrate the standards prescribed in the PARCC Performance Level Descriptors.  Assessments will be given when each student has learned the concepts categorized within a sub-claim and use a single question stimulus with multiple steps for solving the problem. For example, as students complete all standards in the Expressions strand of Algebra I they will be given a Performance-based Assessment that addressed that sub-claim following the rubric set out in the Performance-Level Descriptors:

Modular Assessments: At the completion of a module students will take a Modular assessment that assesses the conceptual, procedural, and applied portions of a standard.

Interim Assessments: At the completion of every interim students will take interim assessments. These assessments emulate PARCC-styled assessments and assess all materials covered up to that point of the year.

Project Artifacts and Exhibitions: Throughout each interim students will be asked to investigate a challenge or problem aligned to the interim topic and complete a project that addresses the topic while also integrating skills learned in each course. Each project will have a course-specific artifact or exhibition that is assessed by the course teacher.

Standards Coverage

Module 1: Relationships Between Quantities and Reasoning with Equations

Module 2: Descriptive Statistics

Module 3: Linear and Exponential Functions

Module 4: Polynomial and Quadratic Expressions and Equations

Module 5: Quadratic Functions and Modeling