High School Algebra I

Student Learnings: What students should know and be able to do

Mathematical Reasoning

Apply skills of mathematical representation, communication and reasoning throughout the remaining three content strands.

• Assess the reasonableness of a solution by comparing the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of solutions in a given context and rejecting extraneous solutions.
• Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.
• Support mathematical results by explaining why the steps in a solution are valid and why a particular solution method is appropriate.
• Determine whether or not relevant information is missing from a problem and if so, decide how to best express the results that can be obtained without that information.

Number Sense, Computation and Operations

Number Sense
Use real numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.

• Use real numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.

Computation and Operations
Appropriately use calculators and other technologies to solve algebraic, geometric, probabilistic and statistical problems.

• Apply the correct order of operations and grouping symbols when using calculators and other technologies.
• Know, use and translate calculator notational conventions to mathematical notation.
• Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.

Patterns, Functions, and Algebra

Patterns and Functions
Represent and analyze real-world and mathematical problems using numeric, graphic and symbolic methods for a variety of functions.

• Know the numeric, graphic and symbolic properties of linear, step, absolute value and quadratic functions. Graphic properties may include rates of change, intercepts, maxima and minima.
• Analyze the effects of coefficient changes on linear and quadratic functions and their graphs.
• Distinguish functions from other relations using graphic and symbolic methods.

Algebra (Algebraic Thinking)
Solve simple equations and inequalities numerically, graphically and symbolically. Use recursion to model and solve real-world and mathematical problems.

• Translate among equivalent forms of expressions, such as, simplify algebraic expressions involving nested pairs of parentheses and brackets, simplify rational expressions, factor a common term from an expression and apply associative, commutative and distributive laws.
• Understand the relationship between absolute value and distance on the number line and graph simple expressions involving absolute value such as, [x-3] = 6 or [x÷2] < 5.
• Find equations of a line given two points on the line, a point and the slope of the line or the slope and the y-intercept of the line.
• Translate among equivalent forms of linear equations and inequalities.
• Use a variety of models such as equations, inequalities, algebraic formulas, written statements, tables and graphs or spreadsheets to represent functions and patterns in real-world and mathematical problems.
• Apply the laws of exponents to perform operations on expressions with integer exponents.
• Solve linear equations and inequalities in one variable with numeric, graphic and symbolic methods.
• Find real solutions to quadratic equations in one variable with numeric, graphic and symbolic methods.
• Solve systems of two linear equations and inequalities with two variables using numeric, graphic and symbolic methods.
• Understand how slopes can be used to determine whether lines are parallel or perpendicular. Given a line and a point not on the line, find the equations for the lines passing through that point and parallel or perpendicular to the given line.

Data Analysis, Statistics and Probability

Data and Statistics
Represent data and use various measures associated with data to draw conclusions and identify trends. Understand the effects of display distortion and measurement error on the interpretation of data.

• Construct and analyze the circle graphs, bar graphs, histograms, box-and-whisker plots, scatter plots and tables, and demonstrate the strengths and weaknesses of each format by choosing appropriately among them for a given situation.
• Use measures of central tendency and variability, such as, mean, median, maximum, minimum, range, standard deviation, quartile and percentile, to describe, compare and draw conclusions about sets of data.
• Determine an approximate best-fit line from a given scatter plot and use the line to draw conclusions.
• Know the influence of outliers on various measures and representations of data about real-world and mathematical problems.

Spatial Sense, Geometry and Measurement

Geometry
Apply basic theorems of plane geometry, right triangle trigonometry, coordinate geometry and a variety of visualization tools to solve real-world and mathematical problems.

• Use coordinate geometry to represent and examine geometric concepts such as the distance between two points, the midpoint of a line segment, the slope of a line and the slopes of parallel and perpendicular lines.

Measurement
Use the interconnectedness of geometry, algebra and measurement to explore real-world mathematical problems.

• Use the interconnectedness of geometry, algebra and measurement to explore real-world mathematical problems.

Instructional resources used for this curriculum:

Copyright 2004, Holt Rinehart Winston Publishing
Algebra One