Elementary Algebra

Course Map

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*Last updated on February 22, 2005

Month

Core Standard

Learning Activity

Assessment

August-

September

1.2.1-Compare and find approximate locations of rational numbers on a number line

1.1.3, 1.3.2, 1.3.3-Apply properties and operations in simplifying rational numeric decimal, fraction, percent, and exponential expressions including integer exponents

1.3.3-Use physical models and calculators to review perfect squares and square roots, including variable expressions

1.3.1, 1.3.2-Introduce rational numbers using physical models, number lines, and patterns to develop a sense of “betweenness.”  Classify numbers as rational or irrational.

2.1.1-Write Algebra expressions to model and generalize visual patterns, manipulative patterns, numeric patterns, and data sets.

     A.  1.1.1, 1.1.2, 1.1.3-Extrapolate values using these algebraic expressions

     B.  1.2.2, 1.3.2-Simplify algebraic expressions using properties

2.2.7-Simplify simple algebraic exponential expressions including those with integer exponents

Problem Solving:  Use appropriate methods for computing, make a model, draw a diagram or picture, eliminate possibilities, estimate solutions to determine reasonableness, find a pattern.

Reasoning/Proof:  Examine various patterns, make conjectures, draw reasonable conclusions.

Communication:  Use precise language and notation, organize and consolidate mathematical thinking, clearly express ideas verbally and in writing, group discussion.

Connections:  Establish connections between physical models, diagrams and symbols, formulate real-world applications.

Representation:  Represent verbally, numerically, algebraically, use technological representations.

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Unit tests  (70% of grade)  

October

 

2.1.1-Use a variety of real-world or student-created data sets to write one variable equations

2.2.2-solve multi-step one variable equations including algebraic first degree proportions and absolute value equations using:  a)  guess and check, b)  manipulatives, c)  technology, d)  algebraically.

2.1.1-Represent real world situations using inequalities.

2.2.2-Solve multi-step one variable inequalities and graph solutions on a number line.

2.1.2, 2.3.4, 4.1.3, 5.1.1-Write Algebraic equations to represent and generalize linear relations derived from manipulatives, geometric, and other visual models and data sets.  Find appropriate domain and range.

Problem Solving:  Use manipulatives, guess and check, solve a simpler problem, choose appropriate operation, work backwards, use proportional reasoning, choose appropriate operations, make a model or simulation.

Reasoning/Proof:  Explain and justify problem solving procedures, link problem solving to the sequence of steps, draw reasonable conclusions.

Communication:  Employ precise language to justify reasoning, express ideas clearly.

Connections:  Formulate real-world situations, make a connection between models and mathematical expressions and procedures.

Representations:  Use physical models and appropriate symbolic notations, represent verbally, numerically, and algebraically.

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Unit tests  (70% of grade)   

November

2.2.2, 4.1.3-Solve real world problems involving constant rates of change

2.1.4, 4.1.1, 4.1.3-Review slope as a rate of change using

     A.  4.1.2-real world problems including manipulatives

     B.  Technology

     C.  2.3.11, 4.1.2-Direct variation

     D.  3.2.3, 4.1.2-Measurement and geometric ratios

2.3.1-Identify the slope of a line when given

     A.  A set of two ordered pairs

     B.  A table of values

     C.  The graph of a linear function

     D.  The equation of a linear function

2.3.3-Identify horizontal and vertical lines from given equations

2.3.10, 4.1.3-Determine and explain the meaning of intercepts using real world examples

Problem Solving:  Use manipulatives, use proportional reasoning, make a model or simulation, estimate to determine reasonableness, solve a simpler problem, ask questions like “where have we seen this before?”, “why do you think so?”, eliminate possibilities.

Reasoning/Proof:  Examine patterns, draw reasonable conclusions, make and investigate conjectures, note regularities and irregularities

Connections:  Use extended real world investigations, connect mathematical expressions and technological and physical models to other curricular areas and outside classroom.

Communication:  Clearly express mathematically ideas verbally and in writing, group discussion.

Representations:  Use technological representations, represent numerical, graphically, and algebraically with the correct symbolic notation.

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Daily assignments, homework, quizzes (30%)

Unit tests  (70% of grade)   

December

2.3.7-Determine X- and Y-intercepts

     A.  From a graph

     B.  From an equation

2.3.8-Graph linear functions using X- and Y-intercepts

2.1.2-Represent equations in slope-intercept form

2.3.8-Graph linear equations by

     A.  2.3.8, 5.1.1-Generating a table of values and plotting points

     B.  Using slope-intercept form of an equation

     C.  Using slope and any point on the line

2.3.6-Explore how changing the value of m and b affects the graphs of linear relations

Problem Solving:  Reflect and evaluate mathematical thinking processes, make a model or simulation, tables, graphs, develop clarification, determine reasonableness of an answer.

Reasoning/Proof:  Look at patterns and make conjectures, link problem solving to the steps.

Connections:  Explore historical and multicultural contributions, establish connection among mathematical expressions, models, pictorial, and real world situations

Communication:  Class and group discussions, use precise language and notation.

Representations:  Represent verbally, numerically, graphically, and algebraically use a variety of visual representations, graph paper, and technology.

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Daily assignments, homework, quizzes (30%)

Unit tests  (70% of grade)   

January

2.3.4-Identify the domain and range from a graph, equation, table, and set of ordered pairs and discuss appropriate domain and range for data

2.3.2-Write the equation of a line when given

     A.  The graph of a line

     B.  The slope and a point on the line

     C.  A set of ordered pairs

2.1.2-Represent linear equations in standard form

5.1.3-Interpret the correlation between two variables as being positive, negative, or having no correlation

5.1.4-Explore the line of best fit

     A.  4.1.3-Find the line of best fit by estimation, choosing two points, and using technology for given sets of data

     B.  5.1.5-Analyze the meaning of the slope and Y-intercept of a line of best fit as it relates to the data

     C.  5.1.6-Make predictions based on the line

Problem Solving:  Solve a related problem; look for a pattern; develop vocabulary; make a list, table, graph or equation; reflect and evaluate mathematical thinking processes.

Reasoning/Proof:  Note regularities and irregularities of patterns, explain and justify.

Connections:  Use real-world situations and connect to other curricular areas.

Communication:  Organize and consolidate mathematical thinking.

Representations:  Represent problem situations verbally, numerically, graphically, or algebraically using technology and appropriate symbolic notation.

Daily feedback on 
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Daily assignments, homework, quizzes (30%)

Unit tests  (70% of grade)   

February

2.2.6-Solve common linear formulas and literal equations for a specified variable

2.3.9-Graph linear inequalities and identify the boundary line and solution area

3.2.3, 5.1.1-Collect, record, organize, and display various sets of linear and nonlinear data including pi

5.1.2-Determine if the patter of the data is linear or nonlinear when given in a list, table, and graph

3.2.1, 4.1.1-Find the approximate midpoint by measuring

3.2.1-Find the coordinates of a midpoint given two points

2.2.5, 3.3.1, 4.1.1, 4.1.3-Explore the Pythagorean Theorem and solve problems using the Theorem

Problem Solving:  “How are these related?”  Look for a pattern; make a list, table, graph or equation.

Reasoning/Proof:  Examine patterns; make and investigate mathematical conjectures examining slope; justify eliminating possibilities.

Connections:  Find applications in other sources.

Communication:  Class discussion; use precise language and rotation in verbal and written explanations.

Representations:  Represent problem situations verbally and in writing; express numerically, graphically, and algebraically using technology.

Daily feedback on 
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Daily assignments, homework, quizzes (30%)

Unit tests  (70% of grade)   

March

2.2.5, 3.2.1-Find the distance between two points.

3.2.2, 4.1.1-Solve problems using the distance formula.

1.3.3-Simplify irrational numeric expressions.

1.3.2-Apply properties and operations in simplifying irrational expressions.

3.3.2, 2.2.5-Solve systems of two linear equations

     A.  Graphically, estimate solutions to determine reasonableness.

     B.  Technology, estimating solutions.

     C.  2.2.5-Numerically from a table and guess and check

     D.  Algebraically, computing solutions

Problem Solving:  Check reasonableness of answer; reflect and evaluate mathematical thinking processes.  Consider thinking strategies of others; use a model or simulation; make a list, tables, graphs, and evaluations.  How is this related to ideas before?

Reasoning/Proof:  Justify sequence of steps, realize that extrapolating isn’t proof.

Connections:  Use real world situations.

Communication:  Group discussions, oral presentations, written reports.

Representations:  Represent verbally, numerically, graphically, geometrically, and algebraically using technology, formulate conjectures, use physical models, visualizations, and appropriate symbolic notations.

Daily feedback on 
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Daily assignments, homework, quizzes (30%)

Unit tests  (70% of grade)   

April

2.2.3-Solve systems of two inequalities

     A.  Graphically, estimate solutions to determine reasonableness

     B.  Technology, estimating solutions

     C.  2.2.5-Numerically from a table and guess and check

     D.  Algebraically, computing solutions

3.3.3, 4.4.1-Illustrate multiplication of polynomials using area models

3.3.4-Use area models to factor polynomials

     A.  Identify the greatest common monomial factor

     B.  Find factors of the form when

5.1.2-Determine and express the probability of an event as a fraction, percent, ration, and decimal.

5.2.2-Identify the probability of an event as being between 0 and 1

5.2.3-Recognize the sum of probability of an event and its complement is equal to 1

Problem Solving:  Use proportional reasoning; look for patterns; make a model or simulations; make a list, table, graph, or equation; consider thinking strategies of others, multi-step problems, estimate to determine reasonableness, use counter examples.

Reasoning/Proof:  Make conjectures, identify conclusions as valid or invalid, justify sequence of steps.

Connections:  Use physical models, pictorial representations and real world situations, connect models to mathematical expressions.

Communication:  Use precise language and notation, written and group discussion.

Representations:  Represent verbally, numerically, graphically, geometrically, and algebraically, use a variety of visual representations.

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Daily assignments, homework, quizzes (30%)

Unit tests  (70% of grade)   

May-

June

5.2.4-Determine if a game or process is fair.

Review for CRT

Problem Solving:  Reflect and evaluate mathematical thinking processes, draw a picture or diagram, use a model or simulation, choose an appropriate operation, estimate solutions, consider the thinking of others.

Reasoning/Proof:  Explain patterns, explain regularities and irregularities, determine whether conclusions are valid or invalid, make and investigate conjectures.

Connections:  Use real world investigations, recognize and apply mathematical ideas and relationships in other curricular areas.

Communication:  Organize and consolidate mathematical thinking, group discussion, oral written reports using appropriate notation.

Representations:  Represent problem situations verbally, numerically, geometrically, or algebraically using technology; use visual representations; use correct notation.

Daily feedback on 
terms and usage

Daily assignments, homework, quizzes (30%)

Unit tests  (70% of grade)