Pilot Geometry
In this course, students will build understanding of the following modules: Reasoning with Shapes, Establishing Congruence, Investigating Proportionality, Connecting Geometric and Algebraic Descriptions, and Making Informed Decisions.
Each module is broken up into topics where you will find teacher materials to guide the instruction and the student materials both used in the classroom for learning together and learning individually.
The agency developed these learning resources as a contingency option for school districts during COVID. All resources are optional. Prior to publication, materials go through a rigorous third-party review. Review criteria include TEKS alignment, support for all learners, progress monitoring, implementation supports, and more. Products also are subject to a focus group of Texas educators.
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.
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.
Using Logical Reasoning to Prove Conjectures about Circles
Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.
Making and Verifying Conjectures about Three-Dimensional Figures
Students will explore volume conjectures and solve problems by applying the volume formulas to composite figures.
Constructing and Justifying Statements about Geometric Figures
Students will distinguish between undefined terms, definitions, postulates, conjectures, and theorems and investigate patterns to make conjectures about geometric relationships.
Using Counter Examples to Disprove Statements That Are False
Given statements about a geometric relationship, the student will use counter examples to disprove statements that are false.
Using Inductive Reasoning to Formulate Conjectures
Students will practice identifying the converse, inverse, and contrapositive of conditional statements.
Using Logical Reasoning to Prove Statements are True
Given statements about a geometric relationship, the student will distinguish between the undefined terms, definitions, postulates, conjectures, and theorems to prove the statements are true.
Using Properties of Transformations
Given examples of mathematics in the real world, the student will use properties of transformations and their composites to describe and perform transformations of figures in a plane.
Developing Algebraic Expressions to Represent Geometric Properties
The student will investigate patterns to make conjectures.