2011-12 Algebra 1-2 syllabus - Portland Public Schools

Instructor:	Amy MacKinnon
School:	Access
School year:	2011-12

Course number:	2031
Course title:	Algebra 1-2
Subject:	Mathematics
Grade level(s):
Credits:	1
Course description:
In this first year course in algebra the representation of functions is used as a unifying theme. Students are introduced to linear and quadratic functions through graphical, numerical and symbolic representations. Students learn to solve linear equations, inequalities, systems of equations, and quadratic equations. They deepen their understanding of basic algebraic concepts using hands-on activities, TI-84 calculator lessons, and problem solving, and develop confidence in their ability to think mathematically as they work both individually and collaboratively. Homework is required in this course. The course is structured around problems and investigations that build the conceptual understanding of algebraic topics and an awareness of connections between these ideas. There are strong threads woven throughout the course on multiple representations and the meaning of a solution. Students will be asked to justify their thinking, generalize relationships, make connections between ideas and reverse thinking to solve problems. The course also works on skills such as organization, note taking, referencing, and group and independent problem solving through inquiry based lessons. A major focus of Algebra 1-2 is to develop multiple strategies to solve problems and to recognize multiple ways of understanding concepts. Remember the study of Algebra is a broad continuum whose applications bleed into all facets of mathematics.
Final Proficiencies Checklist
Solve linear equations with one or two variables. Given a situation, identify the variables, write a linear equation and use the equation to solve the problem. Given a linear relationship (pattern or situation, graph, table, equation), find the other three representations. Given a situation, identify the variables, write a system of linear equations and use the equations to solve the related problem symbolically and graphically. Interpret slope as rate. Given a system of equations, choose an algebraic strategy (equal values, substitution, or elimination), solve and check the answer. Given a point and slope, write a linear equation. Given two points, write a linear equation. Solve linear inequalities with one variable. Solve one and two variable linear inequalities by graphing. Find the solution to a given proportion with one variable. Given a proportional situation write then solve a proportion. Given a quadratic equation, make a table of values and a graph to represent it. Solve quadratic equations by factoring and using the quadratic formula. Given a quadratic equation, identify the x-intercepts (roots) and y-intercepts without graphing. Evaluate variable expressions with integer exponents. Simplify expressions with integer exponents using laws of exponents.
Prerequisites:
This class is open to students who have not yet earned 1.0 credit in Algebra I. Students must demonstrate mastery of skills from middle school mathematics and pre-algebra including a solid foundation of number sense, the order of operations, fractions, factors and multiples, and basic knowledge of equations variables.
Priority standards and final proficiencies:
H.1A.1. Compare, order, and locate real numbers on a number line. H.1A.2. Evaluate, compute with, and determine equivalent numeric and algebraic expressions with real numbers and variables that may also include absolute value, integer exponents, square roots, pi, and/or scientific notation. H.1A.3. Express square roots in equivalent radical form and their decimal approximations when appropriate. H.1A.4. Develop, identify, and/or justify equivalent algebraic expressions, equations, and inequalities using the properties of exponents, equality and inequality, as well as the commutative, associative, inverse, identity, and distributive properties. H.1A.5. Factor quadratic expressions limited to factoring common monomial terms, perfect-square trinomials, differences of squares, and quadratics of the form x2 + bx + c that factor over the integers. H.2A.1. Identify, construct, extend, and analyze linear patterns and functional relationships that are expressed contextually, numerically, algebraically, graphically, in tables, or using geometric figures. H.2A.2. Given a rule, a context, two points, a table of values, a graph, or a linear equation in either slope intercept or standard form, identify the slope of the line, determine the x and/or y intercept(s), and interpret the meaning of each. H.2A.3. Determine the equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, determine an equation of a new line, parallel or perpendicular to a given line, through a given point. H.2A.4. Fluently convert among representations of linear relationships given in the form of a graph of a line, a table of values, or an equation of a line in slope-intercept and standard form. H.2A.5. Given a linear function, interpret and analyze the relationship between the independent and dependent variables. Solve for x given f(x) or solve for f(x) given x. H.2A.6. Analyze how changing the parameters transforms the graph of f(x)=mx + b. H.2A.7. Write, use, and solve linear equations and inequalities using graphical and symbolic methods with one or two variables. Represent solutions on a coordinate graph or number line. H.2A.8. Solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically. H.3A.1. Given a quadratic or exponential function, identify or determine a corresponding table or graph. H.3A.2. Given a table or graph that represents a quadratic or exponential function, extend the pattern to make predictions. H.3A.4. Given a quadratic or exponential function, interpret and analyze the relationship between the independent and dependent variables, and evaluate the function for specific values of the domain. H.3A.5. Given a quadratic equation of the form x²+ bx + c = 0 with integral roots, determine and interpret the roots, the vertex of the parabola that is the graph of y = x² + bx +c, and an equation of its axis of symmetry graphically and algebraically.
Schedule of topics/units covered:
Ch 1: Problem Solving Ch 2: Variables and Proportions Ch 3: Graphs and Equations Ch 4: Multiple Representations Ch 5: Multiplication and Proportions Ch 6: Systems of Equations Ch 7: Linear Relationships Ch 8: Quadratics Ch 9: Inequalities Ch 10: Simplifying and Solving; Exponents
Academic vocabulary:
Justify, generalize, apply, extend, reverse thinking, make connections Refer to the CPM Algebra Connections text and glossary.
District adopted materials:
College Preparatory Mathematics: Algebra Connections
Supplemental resources:
TI-84 graphing calculator (available in the classroom), http://www.cpm.org. http://www.hotmath.com, Algebra Connections: Parent Guide, Algebra Connections: Extra Practice (Skillbuilders)
Differentiation/accessibility strategies and support (TAG, ELL, SpEd, other):
The differentiation strategies used in this course are based on the evidence (data) received through multiple forms of pre, ongoing, and formative assessments. Described here are the types of assessments used and specific differentiation strategies in place to meet the needs of ALL learners (including TAG, ESL, Special Ed...) Students in this class are grouped by skill level as they have demonstrated readiness for algebra and are, thus, often accelerated as compared to their age peers. To differentiate based on learning rate, many strategies are employed and may include: Group work, individual work, tutoring, parent guides, literacy and accessibility strategies, a variety of assessment methods, projects, enrichment activities, calculator and technology activities, demonstrations, lectures, lesson compaction, and grading variations.
Career-related learning experiences (CRLEs):
Project-based Learning The Mathazine project and others.
Essential Skills and required Work Samples:
Apply mathematics Required Work Samples: 1 Algebra Work Sample Assessments used to assess this Essential Skill: Students will complete at least one work sample and will apply mathematics daily. Informal assessments and coaching will be used during units. Team and individual tests will be used to assess learning targets at the end of the unit. Personal management and teamwork Assessments used to assess this Essential Skill: Students will work on team problem solving and be assessed through team tests. As well, they will employ an assignement record sheet and parents can use this as assessment as well by checking it periodically and signing it at the end of each unit. Use technology Assessments used to assess this Essential Skill: Students will apply their knowledge of the TI-84 calculator in class and on tests. Problems will be designed so that calculator fluency will be built into the response.
Assessment/evaluation/grading policy:
Students must demonstrate proficiency on learning objectives through completion of homework, assignments, class work, projects and scores on quizzes and tests. Students can keep track of their own progress using our unit record sheets. As well, students can meet with their teacher to see their grade and assignment scores at anytime during the trimester. Progress reports are sent home at least once per trimester and can be requested by parents through phone or email: amackinn@pps.net Grades: determined based on a point system. Assignments are weighted with greater points for a greater importance. Absences: If you are absent, it is your responsibility to get the missing assignments, handouts, etc. Assignments are posted on the record sheets and displayed in the classroom. If a unit assessment is missed, talk with me about when you can make it up. Please note: informal and mid-unit assessments like homework quizzes cannot be made up.
Behavioral expectations:
Respectful listening is of the utmost importance and should be practiced daily. Students will be expected to work independently and collaboratively in study groups. Students are expected to participate in class discussions and ask questions. Homework is required in this class and is generally assigned nightly. Students are asked to assess their own performance on homework (review & preview) by checking their answers with an answer key provided. Students are asked to bring their notebook and a pencil to class everyday.
Safety issues and requirements:

Course number:

2031

Course title:

Algebra 1-2

Subject:

Mathematics

Grade level(s):

Credits:

Course description:

In this first year course in algebra the representation of functions is used as a unifying theme. Students are introduced to linear and quadratic functions through graphical, numerical and symbolic representations. Students learn to solve linear equations, inequalities, systems of equations, and quadratic equations. They deepen their understanding of basic algebraic concepts using hands-on activities, TI-84 calculator lessons, and problem solving, and develop confidence in their ability to think mathematically as they work both individually and collaboratively.

Homework is required in this course.

The course is structured around problems and investigations that build the conceptual understanding of algebraic topics and an awareness of connections between these ideas. There are strong threads woven throughout the course on multiple representations and the meaning of a solution. Students will be asked to justify their thinking, generalize relationships, make connections between ideas and reverse thinking to solve problems. The course also works on skills such as organization, note taking, referencing, and group and independent problem solving through inquiry based lessons. A major focus of Algebra 1-2 is to develop multiple strategies to solve problems and to recognize multiple ways of understanding concepts. Remember the study of Algebra is a broad continuum whose applications bleed into all facets of mathematics.

Final Proficiencies Checklist

Solve linear equations with one or two variables.
Given a situation, identify the variables, write a linear equation and use the equation to solve the problem.
Given a linear relationship (pattern or situation, graph, table, equation), find the other three representations.
Given a situation, identify the variables, write a system of linear equations and use the equations to solve the related problem symbolically and graphically.
Interpret slope as rate.
Given a system of equations, choose an algebraic strategy (equal values, substitution, or elimination), solve and check the answer.
Given a point and slope, write a linear equation.
Given two points, write a linear equation.
Solve linear inequalities with one variable.
Solve one and two variable linear inequalities by graphing.
Find the solution to a given proportion with one variable.
Given a proportional situation write then solve a proportion.
Given a quadratic equation, make a table of values and a graph to represent it.
Solve quadratic equations by factoring and using the quadratic formula.
Given a quadratic equation, identify the x-intercepts (roots) and y-intercepts without graphing.
Evaluate variable expressions with integer exponents.
Simplify expressions with integer exponents using laws of exponents.

Prerequisites:

This class is open to students who have not yet earned 1.0 credit in Algebra I. Students must demonstrate mastery of skills from middle school mathematics and pre-algebra including a solid foundation of number sense, the order of operations, fractions, factors and multiples, and basic knowledge of equations variables.

Priority standards and final proficiencies:

H.1A.1. Compare, order, and locate real numbers on a number line.
H.1A.2. Evaluate, compute with, and determine equivalent numeric and algebraic expressions with real numbers and variables that may also include absolute value, integer exponents, square roots, pi, and/or scientific notation.
H.1A.3. Express square roots in equivalent radical form and their decimal approximations when appropriate.
H.1A.4. Develop, identify, and/or justify equivalent algebraic expressions, equations, and inequalities using the properties of exponents, equality and inequality, as well as the commutative, associative, inverse, identity, and distributive properties.
H.1A.5. Factor quadratic expressions limited to factoring common monomial terms, perfect-square trinomials, differences of squares, and quadratics of the form x2 + bx + c that factor over the integers.
H.2A.1. Identify, construct, extend, and analyze linear patterns and functional relationships that are expressed contextually, numerically, algebraically, graphically, in tables, or using geometric figures.
H.2A.2. Given a rule, a context, two points, a table of values, a graph, or a linear equation in either slope intercept or standard form, identify the slope of the line, determine the x and/or y intercept(s), and interpret the meaning of each.
H.2A.3. Determine the equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, determine an equation of a new line, parallel or perpendicular to a given line, through a given point.
H.2A.4. Fluently convert among representations of linear relationships given in the form of a graph of a line, a table of values, or an equation of a line in slope-intercept and standard form.
H.2A.5. Given a linear function, interpret and analyze the relationship between the independent and dependent variables. Solve for x given f(x) or solve for f(x) given x.
H.2A.6. Analyze how changing the parameters transforms the graph of f(x)=mx + b.
H.2A.7. Write, use, and solve linear equations and inequalities using graphical and symbolic methods with one or two variables. Represent solutions on a coordinate graph or number line.
H.2A.8. Solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically.
H.3A.1. Given a quadratic or exponential function, identify or determine a corresponding table or graph.
H.3A.2. Given a table or graph that represents a quadratic or exponential function, extend the pattern to make predictions.
H.3A.4. Given a quadratic or exponential function, interpret and analyze the relationship between the independent and dependent variables, and evaluate the function for specific values of the domain.
H.3A.5. Given a quadratic equation of the form x²+ bx + c = 0 with integral roots, determine and interpret the roots, the vertex of the parabola that is the graph of y = x² + bx +c, and an equation of its axis of symmetry graphically and algebraically.

Schedule of topics/units covered:

Ch 1: Problem Solving
Ch 2: Variables and Proportions
Ch 3: Graphs and Equations
Ch 4: Multiple Representations
Ch 5: Multiplication and Proportions
Ch 6: Systems of Equations
Ch 7: Linear Relationships
Ch 8: Quadratics
Ch 9: Inequalities
Ch 10: Simplifying and Solving; Exponents

Academic vocabulary:

Justify, generalize, apply, extend, reverse thinking, make connections

Refer to the CPM Algebra Connections text and glossary.

District adopted materials:

College Preparatory Mathematics: Algebra Connections

Supplemental resources:

TI-84 graphing calculator (available in the classroom), http://www.cpm.org. http://www.hotmath.com, Algebra Connections: Parent Guide, Algebra Connections: Extra Practice (Skillbuilders)

Differentiation/accessibility strategies and support (TAG, ELL, SpEd, other):

The differentiation strategies used in this course are based on the evidence (data) received through multiple forms of pre, ongoing, and formative assessments. Described here are the types of assessments used and specific differentiation strategies in place to meet the needs of ALL learners (including TAG, ESL, Special Ed...)

Students in this class are grouped by skill level as they have demonstrated readiness for algebra and are, thus, often accelerated as compared to their age peers. To differentiate based on learning rate, many strategies are employed and may include: Group work, individual work, tutoring, parent guides, literacy and accessibility strategies, a variety of assessment methods, projects, enrichment activities, calculator and technology activities, demonstrations, lectures, lesson compaction, and grading variations.

Career-related learning experiences (CRLEs):

Project-based Learning

The Mathazine project and others.

Essential Skills and required Work Samples:

Apply mathematics

Required Work Samples: 1 Algebra Work Sample

Assessments used to assess this Essential Skill:

Students will complete at least one work sample and will apply mathematics daily. Informal assessments and coaching will be used during units. Team and individual tests will be used to assess learning targets at the end of the unit.
Personal management and teamwork

Assessments used to assess this Essential Skill:

Students will work on team problem solving and be assessed through team tests. As well, they will employ an assignement record sheet and parents can use this as assessment as well by checking it periodically and signing it at the end of each unit.
Use technology

Assessments used to assess this Essential Skill:

Students will apply their knowledge of the TI-84 calculator in class and on tests. Problems will be designed so that calculator fluency will be built into the response.

Assessment/evaluation/grading policy:

Students must demonstrate proficiency on learning objectives through completion of homework, assignments, class work, projects and scores on quizzes and tests. Students can keep track of their own progress using our unit record sheets. As well, students can meet with their teacher to see their grade and assignment scores at anytime during the trimester. Progress reports are sent home at least once per trimester and can be requested by parents through phone or email: amackinn@pps.net
Grades: determined based on a point system. Assignments are weighted with greater points for a greater importance.
Absences: If you are absent, it is your responsibility to get the missing assignments, handouts, etc. Assignments are posted on the record sheets and displayed in the classroom. If a unit assessment is missed, talk with me about when you can make it up. Please note: informal and mid-unit assessments like homework quizzes cannot be made up.

Behavioral expectations:

Respectful listening is of the utmost importance and should be practiced daily.
Students will be expected to work independently and collaboratively in study groups.
Students are expected to participate in class discussions and ask questions.
Homework is required in this class and is generally assigned nightly.
Students are asked to assess their own performance on homework (review & preview) by checking their answers with an answer key provided.
Students are asked to bring their notebook and a pencil to class everyday.

Safety issues and requirements: