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Algebra 1 Learning Progression

Page history last edited by Brenda Butz 6 years, 4 months ago

* Indicates an objective that is repeated in another unit or an objective that is partially taught in a unit and will be taught in its entirety in a later unit. The parts of the objective that will be taught in a later unit is indicated by the “strikethroughs.” Occasionally, new words are added to the objective to ensure the objective still makes sense considering the strikethroughs.

Unit

Unit Storyline

Full Objectives

Unit 1:

Expressions


Timing

1-2 weeks


Objectives

A1.N.1.1

A1.N.1.2

A1.A.3.2

A1.A.3.4

Students will evaluate and simplify expressions involving radical expressions and polynomial expressions.  Students will interpret the solutions in its original context. (See Unit 7 for multiplication of polynomial expressions.)

A1.N.1.1 Write square roots and cube roots of monomial algebraic expressions in simplest radical form.

A1.N.1.2 Add, subtract, multiply, and simplify square roots of monomial algebraic expressions and divide square roots of whole numbers, rationalizing the denominator when necessary.

A1.A.3.2 Simplify polynomial expressions by adding, subtracting, or multiplying.

A1.A.3.4 Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as .

Unit 2:

Solving Equations and Inequalities


Timing

2-3 weeks


Objectives

A1.A.1.1

A1.A.1.2

A1.A.2.2

A1.A.3.1

Students will solve equations for one variable involving absolute and rational values as well as interpret their solutions. They will also, solve one-variable inequalities while interpreting their solutions on a number line.

A1.A.1.1 Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context.

A1.A.1.2 Solve absolute value equations and interpret the solutions in the original context.

A1.A.2.2 Represent relationships in various contexts with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line.

A1.A.3.1 Solve equations involving several variables for one variable in terms of the others.

Unit 3:

Linear Functions and Relations

Timing

6-7 weeks


Objectives

A1.F.1.1

A1.F.1.2

A1.F.1.3*

A1.F.1.4

A1.F.2.1**

A1.F.2.2***

A1.F.3.1

A1.F.3.2ɫ

A1.F.3.3

Students will use linear functions to solve and graph mathematical and real-world situations. *(Students will use function notation and write linear functions which will associate with writing equations in Unit 4.)

**(Students will use the definition of linear with relations and functions and will approach nonlinear equations in depth in Unit 5.)

***(Unit 3 will introduce the linear function and Unit 5 will introduce the absolute value equation.)

ɫ (See Unit 5 for the focus on nonlinear.)

 

A1.F.1.1 Distinguish between relations and functions.

A1.F.1.2 Identify the dependent and independent variables as well as the domain and range given a function, equation, or graph. Identify restrictions on the domain and range in real-world contexts.

A1.F.1.3 Write linear functions, using function notation, to model real-world and mathematical situations.

A1.F.1.4 Given a graph modeling a real-world situation, read and interpret the linear piecewise function (excluding step functions).

A1.F.2.1 Distinguish between linear and nonlinear (including exponential) functions arising from real-world and mathematical situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal!intervals.

A1.F.2.2 Recognize the graph of the functions f(x)=x and  f(x)=x and predict the effects of transformations [  f(x+c) and f(x)+c, where c is a positive or negative constant] algebraically and graphically using various methods and tools that may include graphing calculators.

A1.F.3.1 Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations.

A1.F.3.2 Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of real-world and mathematical problems.

A1.F.3.3 Add, subtract, and multiply functions using function notation.

Unit 4:

Linear Equations


Timing

6-7 week


Objectives

A1.A.2.1

A1.A.3.5

A1.A.4.1

A1.A.4.2

A1.A.4.3

A1.A.4.4

A1.F.1.3*

A1.D.1.2**

Students will solve linear equations and inequalities of two variables and interpret their graphs when presented real-world situations.

* (See Unit 3-Students will connect linear functions and equations.

** (See Unit 8-Students will use graphing, regression, and predictions to determine lines and correlation coefficients.)

 

A1.A.2.1 Represent relationships in various contexts with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions.

A1.A.3.5 Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Use the pattern, find the next term.

A1.A.4.1 Calculate and interpret slope and the x- and y-intercepts of a line using a graph, an equation, two points, or a set of data points to solve real-world and mathematical problems.

A1.A.4.2 Solve mathematical and real-world problems involving lines that are parallel, perpendicular, horizontal, or vertical.

A1.A.4.3 Express linear equations in slope-intercept, point-slope, and standard forms and convert between these forms. Given sufficient information (slope and y-intercept, slope and one-point on the line, two points on the line, x- and y-intercept, or a set of data points), write the equation of a line.

A1.A.4.4 Translate between a graph and a situation described qualitatively.

A1.F.1.3 Write linear functions, using function notation, to model real-world and mathematical situations.

A1.D.1.2 Collect data and use scatterplots to analyze patterns and describe linear relationships between two variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.

 Unit 5:

Non-Linear Functions and Equations


Timing

2-3 weeks


Objectives

A1.F.2.1**

A1.F.2.2***

A1.F.3.2ɫ

A1.A.3.6*

 

Students will recognize, evaluate, and write non-linear functions and distinguish them from linear functions.

*(See Unit 7 on using the geometric sequence formula and defining its variables while finding terms of a sequence.)

**(See Unit 3 on using nonlinear and linear functions.)

***(See Unit 3 on using the linear function where Unit 5 will introduce the absolute value equation.)

ɫ (See Unit 3 introduces linear functions; whereas, Unit 5 is determining nonlinear functions.)

A1.F.2.1 Distinguish between linear and nonlinear (including exponential) functions arising from real-world and mathematical situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal intervals.

A1.F.2.2 Recognize the graph of the functions f(x)=x and f(x)=x and predict the effects of transformations [ f(x+c) and f(x)+c, where c is a positive or negative constant] algebraically and graphically using various methods and tools that may include graphing calculators.

A1.F.3.2 Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of real-world and mathematical problems.

A1.A.3.6 Recognize that geometric sequences are exponential using equations, tables, graphs and verbal descriptions. Given the formula f(x)=a(r)x, find the next term and define the meaning of a and r within the context of the problem.

Unit 6:

Solving Systems of Equations and Inequalities


Timing

2-3 weeks


Objectives

A1.A.1.3

A1.A.2.3

Students will solve systems of equations and inequalities using various methods and use graphing to show multiple solutions possible.

 

 

 

A1.A.1.3 Analyze and solve real-world and mathematical problems involving systems of linear equations with a maximum of two variables by graphing (may include graphing calculator or other appropriate technology), substitution, and elimination. Interpret the solutions in the original context.

A1.A.2.3 Solve systems of linear inequalities with a maximum of two variables; graph and interpret the solutions on a coordinate plane.

Unit 7: 

Polynomials


Timing

2-3 weeks


Objectives

A1.A.3.2*

A1.A.3.3

A1.A.3.6**

Students multiply and simplify polynomials. Students will factor simple polynomials of quadratic degree exponentially and recognize that geometric sequences are also exponential by using various representations (tables, graphs, equations, and verbal descriptions). *(See Unit 1 for addition and subtraction when simplifying polynomial expressions.)

**(See Unit 5 for the recognition of geometric sequences are exponential).

A1.A.3.2 Simplify polynomial expressions by adding, subtracting, or multiplying.

A1.A.3.3 Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.

A1.A.3.6 Recognize that geometric sequences are exponential using equations, tables, graphs and verbal descriptions. Given the formula f(x)=a(r)x, find the next term and define the meaning of a and r within the context of the problem.

 

Unit 8:

Collecting Data and Linear Predictions


Timing

2-3 weeks


Objectives

A1.D.1.1

A1.D.1.2*

A1.D.1.3

Students will use measures of central tendency.  They will gather data and derive the line of best fit by using the regression function of their calculator.  Finally they will analyze , and interpret their graphs.

*(See Unit 4-Students will use prior knowledge of linear data.)

A1.D.1.1 Describe a data set using data displays, describe and compare data sets using summary statistics, including measures of central tendency, location, and spread. Know how to use calculators, spreadsheets, or other appropriate technology to display data and calculate summary statistics.

A1.D.1.2 Collect data and use scatterplots to analyze patterns and describe linear relationships between two variables. Using graphing technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.

A1.D.1.3 Interpret graphs as being discrete or continuous.

Unit 9:

Probability


Timing

2-3 weeks


Objectives

A1.D.2.1

A1.D.2.2

A1.D.2.3

A1.D.2.4

Students will calculate probabilities, apply concepts, and perform experiments to model real-world situations.

 

 

 

A1.D.2.1 Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

A1.D.2.2 Describe the concepts of intersections, unions, and complements using Venn diagrams to evaluate probabilities. Understand the relationships between these concepts and the words AND, OR, and NOT.

A1.D.2.3 Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.

A1.D.2.4 Apply probability concepts to real-world situations to make informed decisions.

 


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