Pilot Algebra Foundations
The primary purpose of the Algebra Foundations course is to promote opportunities for deep understanding of core algebraic concepts to develop algebraic thinkers. The course is composed of 5 topics: Operating with Rational Numbers, Expressions and Equations, Developing Function Foundations, Modeling Linear Equations, and Quadratics. Throughout these topics, students have the opportunity to develop foundational understandings and draw connections to key concepts.
This course is intended to strengthen foundational conceptual understandings from middle school math through Algebra I and is designed to be flexible in meeting the needs of students. Your individual course is created based solely on data that suggests which topics will best develop your students as algebraic thinkers. Each learning session is designed to further develop a skill, and together, these sessions connect skills and concepts to key algebraic understandings. The student learning experience of the Algebra Foundations course promotes conceptual understanding through a focus on active learning and making sense of the mathematics.
Determining Slopes from Equations, Graphs, and Tables
Given algebraic, tabular, and graphical representations of linear functions, the student will determine the slope of the relationship from each of the representations.
Demonstrating the Pythagorean Theorem
Given pictures or models that represent the Pythagorean Theorem, the student will demonstrate an understanding of the theorem.
Comparing and Contrasting Proportional and Non-Proportional Linear Relationships
Given problem solving situations, the student will solve the problems by comparing and contrasting proportional and non-proportional linear relationships.
Graphing Proportional Relationships
Given a proportional relationship, students will be able to graph a set of data from the relationship and interpret the unit rate as the slope of the line.
Analyzing Scatterplots
Given a set of data, the student will be able to generate a scatterplot, determine whether the data are linear or non-linear, describe an association between the two variables, and use a trend line to make predictions for data with a linear association.
Writing Geometric Relationships
Given information in a geometric context, students will be able to use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
Solutions of Simultaneous Equations
Given a graph of two simultaneous equations, students will be able to interpret the intersection of the graphs as the solution to the two equations.
Comparing and Explaining Transformations
Given rotations, reflections, translations, and dilations, students will be able to develop algebraic representations for rotations, and generalize and then compare and contrast the properties of congruence transformations and non-congruence transformations.
Mean Absolute Deviation
Given a set of data with no more than 10 data points, students will be able to determine and use the mean absolute deviation to describe the spread of the data.
Generalizing about Populations from Random Samples
Given a population with known characteristics, students will be able to use a variety of methods to generate random samples of the same size in order to understand how a random sample is representative of a population.
Evaluating Solutions for Reasonableness
Given problem situations, the student will determine if the solutions are reasonable.
Predicting, Finding, and Justifying Solutions to Problems
Given application problems, the student will use appropriate tables, graphs, and algebraic equations to find and justify solutions to problems.
Developing the Concept of Slope
Given multiple representations of linear functions, the student will develop the concept of slope as a rate of change.
Generating Different Representations of Relationships
Given problems that include data, the student will generate different representations, such as a table, graph, equation, or verbal description.
Predicting, Finding, and Justifying Data from a Graph
Given data in the form of a graph, the student will use the graph to interpret solutions to problems.
Approximating the Value of Irrational Numbers
Given problem situations that include pictorial representations of irrational numbers, the student will find the approximate value of the irrational numbers.
Expressing Numbers in Scientific Notation
Given problem situations, the student will express numbers in scientific notation.
Comparing and Ordering Rational Numbers
Given a problem situation, the student will compare and order integers, percents, positive and negative fractions and decimals with or without a calculator.
Determining if a Relationship is a Functional Relationship
The student is expected to gather and record data & use data sets to determine functional relationships between quantities.