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Algebra 1 Learning Progression (v2)

Page history last edited by Christine Koerner 2 years, 9 months ago

Welcome to the new progression for Algebra 1. This progression builds upon Math Framework Project Phase 1 work (see Progression v1 here), taking many of the best features and building in an Overarching Question, Essential Questions, and Big Ideas for each unit. This new model takes the work of bundling standards to the next level by grouping together grade level concepts under Big Ideas. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner we believe to be more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are not a replacement for the objectives. 

 

Click on the unit numbers below to see essential understandings, student activities, and suggested sequencing.

 

The use of an asterisk (*) indicates an objective 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

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0: 

Growth Mindset

How does improving student attitudes toward math affect their learning?  

1. Math is about learning not performing.

2.  Math is about making sense.

3.  Math is filled with conjectures, creativity, and uncertainty.

4.  Mistakes are beautiful things. 

  1. Students will understand the importance of a growth mindset (e.g., that math is not about talent or natural ability but is about thoughtful practice) and what it means to talk and listen. Students will also understand that class is where students practice thinking and doing math.

  2. Students will learn the value of taking time to think about math and listen to how others make sense of their work to arrive at a common understanding.

  3. Students will build the habits of using precise language, practicing, and sharing their thoughts.


 

Unit 1:

Expressions, Equations and Inequalities


Timing

~4 weeks 

 


Objectives

A1.A.3.2

A1.A.3.4

A1.A.3.3

A1.N.1.1

A1.N.1.2

A1.A.1.1

A1.A.1.2

A1.A.3.1

A1.A.2.2

 

 

How can we manipulate information to help us solve real-world problems?

  1. How can we represent information symbolically?

  2. How do we develop mathematical arguments/proofs for solving real-world situations?

  3. How can we use related, but different representations to solve real-world problems?

 

  • Polynomial expressions can be simplified and evaluated.

  • Polynomial expressions can be written as factors.

  • Square and cube roots can be added, subtracted, multiplied, divided, and simplified

  • Equations and inequalities can be solved in both algebraic and real-world contexts

 

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 .

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

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

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.

 

Unit 2:

Data


Timing

1-2 weeks


Objectives

A1.D.1.1

A1.D.1.2 (except regression)

A1.D.1.3


 

 

 

 

How does data help us interpret real-world situations?

  1. How do we use evidence to support arguments?

  2. How do we interpret evidence in order to support arguments?

  3. What can we learn from patterns within data sets?

 
  •  Data sets can be described with various models, both mathematical and graphical.
  • When displayed in a scatter plot, data often takes on a recognizable, definable, pattern.

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 3:

Functions

Timing

4-6 weeks


Objectives

A1.F.1.1

A1.F.1.2

A1.F.1.3

A1.F.3.3

A1.F.1.4

A1.F.3.2

A1.F.2.1

A1.F.2.2


How can we use data to determine patterns and relationships from real-world situations?

  1. How do we measure change?

  2. How do we quantify the relationships between quantities?

  3. Howcan different representations show relationships?

  4. What patterns exist among quantities?

 
  •  A function is a rule that describes a set of data for which each input has one and only one output
  • Functions are written and manipulated using function notation.

  • Functions can be evaluated and interpreted both algebraically and graphically.

  • Function families share similar graphs, behaviors, and properties.

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

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

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.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. 

 

 

 

 

Unit 4:

Linear Functions


Timing

4-6 weeks


Objectives

A1.D.1.2

A1.A.4.4

A1.A.3.5

A1.A.4.1

A1.A.4.3

A1.F.1.3

A1.F.3.1

A1.A.4.2

A1.A.2.1


How can patterns that exist in data help us make predictions to solve real-world problems?

  1. How do we measure change?

  2. How do we quantify the relationships between quantities?

  3. How can relationships between quantities be represented?

 
  • Linear functions describe data sets that have a direct correlation.

  • Linear functions can be represented in multiple equivalent ways.

  • Linear Functions can be used to to solve real world problems and make predictions.

  • Linear inequalities represent relationships with multiple solutions.

 

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

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

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

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

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.

 

 

 

 

 

Unit 5:

Systems


Timing

2-3 weeks


Objectives 

A1.A.1.3

A1.A.2.3


 

How can representing real-world problems in many ways help us understand them well?

1.  How can we apply our knowledge to model real-world situations  with more than one variable?

 

2. How can we represent and analyze our solutions to problems?

 

 

3. How can we represent the same thing in multiple different ways?

 

  • Systems of linear equations (and inequalities) contain functions that share the same set of variables.

  • A solution to a system makes each function rule true.

 

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 6:

Probability


Timing

~2 weeks


Objectives

A1.D.2.1

A1.D.2.2

A1.D.2.4

A1.D.2.3


How can we use probability to make predictions about real-world problems?

 

 

  1. How can data help us make decisions?

  2. How do we use the data gathered from experimentation?

 
  • Probability is calculated with multiplication or additional principles.

  • Probability is used to predict possible outcomes.

  • Experiments can model real-world probability 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.2.4 Apply probability concepts to real-world situations to make informed decisions.

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

 

 

 

 

 

 

Culminating Unit


Timing

~2 weeks

 

How can students show evidence of understanding?
  Algebra 1 Showcase  
Distance Learning Resources/
Supplemental Activities
How can students develop and show evidence of understanding?     Multiple objectives are covered in this material. These math tasks are designed to enhance current curriculum and support distance learning.

 


Introduction to the OKMath Framework

Algebra 1 Grade Introduction

 

 

 

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