Welcome to the learning progression for Algebra 1. This progression incorporates the overall topics of this grade-level's mathematics and is formatted with Overarching Questions, Essential Questions, and Big Ideas for each unit. This progression model takes the work of bundling standards to the next level by grouping together grade-level concepts in the Big Ideas sections. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner that is more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are for progression and planning and are not a replacement for the OAS-M objectives.
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 |
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. |
|
||
Expressions, Equations and Inequalities Timing ~4 weeks
Objectives
|
How can we manipulate information to help us solve real-world problems? |
|
|
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 x ⨀ y=2x+y. 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 constants and monomial algebraic expressions in simplest radical form. A1.N.1.2 Add, subtract, multiply, divide, and simplify square roots of constants, rationalizing the denominator when necessary. A1.A.1.1 Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, 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 using mathematical models with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line. |
Timing 1-2 weeks Objectives
|
How does data help us interpret real-world situations? |
|
|
A1.D.1.1 Display, describe, and compare data sets using summary statistics (central tendency and spread (range)). Utilize technology (e.g., spreadsheets, calculators) to display data and calculate summary statistics. A1.D.1.2 Collect data and analyze scatter plots for patterns, linearity, and outliers. A1.D.1.3 Make predictions based upon the linear regression, and use the correlation coefficient to assess the reliability of those predictions using graphing technology.
|
Functions Timing 4-6 weeks Objectives |
How can we use data to determine patterns and relationships from real-world situations? |
|
|
A1.F.1.1 Distinguish between relations and functions. A1.F.1.2 Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models. A1.F.1.3 Write linear functions, using function notation, to represent mathematical models. A1.F.3.3 Add, subtract, and multiply functions using function notation. A1.F.1.4 Read and interpret the linear piecewise function, given a graph modeling a situation. A1.F.1.5 Interpret graphs as being discrete or continuous. A1.F.3.2 Recognize the parent functions f(x) = x and f(x) = |x|. Predict the effects of vertical and horizontal transformations f(x+c) and f(x) +c, algebraically and graphically. A1.F.2.1 Distinguish between linear and nonlinear (including exponential) functions. Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric). A1.F.2.2 Recognize the parent functions f(x) = x and f(x) = |x|. Predict the effects of vertical and horizontal transformations f(x+c) and f(x) +c, algebraically and graphically.
|
Timing 4-6 weeks Objectives |
How can patterns that exist in data help us make predictions to solve real-world problems? |
|
|
A1.D.1.2 Collect data and analyze scatter plots for patterns, linearity, and outliers. A1.A.4.4 Express linear equations in slope-intercept, point-slope, and standard forms. Convert between these forms. A1.A.4.5 Analyze and interpret associations between graphical representations and written scenarios. A1.A.4.1 Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret slope and the x- and y-intercepts of a line. A1.A.4.3 Write the equation of the line given its slope and y-intercept, slope and one point, two points, x- and y-intercepts, or a set of data points. A1.F.1.3 Write linear functions, using function notation, to represent mathematical models. A1.F.3.1 Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations. A1.A.4.2 Analyze and interpret mathematical models involving lines that are parallel, perpendicular, horizontal, and vertical. A1.A.2.1 Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions.
|
Timing 2-3 weeks Objectives
|
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?
|
|
A1.A.1.3 Analyze, use and apply mathematical models to solve problems involving systems of linear equations with a maximum of two variables by graphing, substitution, and elimination. Graphing calculators or other appropriate technology may be utilized. Interpret the solutions in the original context.
|
Timing ~2 weeks Objectives |
How can we use probability to make predictions about real-world problems?
|
|
|
A1.D.2.1 Apply simple counting procedures (factorials, permutations, combinations, and tree diagrams) to determine sample size, sample space, and calculate probabilities. A1.D.2.2 Given a Venn diagram, determine the probability of the union of events, the intersection of events, and the complement of an event. 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 Use simulations and experiments to calculate experimental probabilities.
|
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