AgileMind is the curriculum that we will be using throughout the semester. This section will provide a description of what will be learned throughout the course, along with a link to blank notes.
To access AgileMind, click this link: crockett.agilemind.com | To access blank notes, click the topic header.
To access AgileMind, click this link: crockett.agilemind.com | To access blank notes, click the topic header.
Pre-Topic 1: Solidifying Fluency with Computation
Although the standards call for students' capabilities with positive rational number and signed number operations to be well developed in middle school, many teachers report that students come to high school with varying needs for review and repair of these key skills. In this topic, students can review and strengthen their fluency with rational number operations as they work with positive whole numbers, decimals, and fractions. This topic also contains resources for review of signed number operations. In addition to paper-and-pencil and online tasks, students engage with simulations and interactive animations that provide thousands of opportunities to build their knowledge and skills.
Pre-Topic 2: Solidifying Skills with Equations
Although the standards call for students' capabilities with solving equations to be well developed in middle school, many teachers report that students come to high school with varying needs for review and repair of these key skills. In this topic, students can review and strengthen their fluency with solving one-step and multi-step linear equations. In addition to paper-and-pencil and online tasks, students engage with simulations and interactive animations that provide thousands of opportunities to build their knowledge and skills.
Topic 1: Constructing Graphs
Students learned how to plot points in the Cartesian plane in early grades. Many students can create an accurate graph of given data but can't represent it in a manner that makes sense to them. Since this course focuses on functions and their graphs, it is crucial that students understand how to create and read graphs correctly. This topic, Constructing graphs, addresses principles for creating neutral, well-designed graphs. Through creating graphs, students review the distinction between independent and dependent variables in a functional relationship, learn conventions associated with this distinction, and are formally introduced to the concept of domain and range of a function.
Topic 2: Multiple Representations in the Real World
Creating multiple representations (concrete models, words, tables, graphs, and symbols) for relationships between two quantities is a strong theme throughout this course and subsequent mathematics courses. In this topic, students explore patterns arising from concrete models and contextual situations and then move from the concrete into increasingly more abstract representations. This topic sets the stage for students' work in the next topic, in which they will formalize the concept of a function.
Topic 3: Functions
In previous mathematics work, students have informally investigated the concept of a function as a systematic relationship between two variables, and this concept will be revisited throughout this course. The topic Functions builds on this previous work to formalize this concept for students and add to the tools they will use throughout the course to represent functional relationships. Students will learn how to use formal function notation, and they will connect sequences and functions.
Topic 4: Rate of Change
The topic Rate of change builds on students' work with rates and rate of change in previous grades to deepen their understanding of this central concept. Students build on previous work with constant rates as they investigate rates of change in a variety of situations, represented both numerically and graphically. Students learn that not all rates of change are constant, and they are introduced to patterns that can be modeled with inverse variation, quadratic functions, and exponential functions.
Topic 5: Moving Beyond Slope-Intercept
The topic Moving beyond slope-intercept builds on students' work in previous courses with recognizing constant rates of change and representing linear functions using slope-intercept form. Students deepen their understanding of slope-intercept form and begin work with transformations by investigating how different values of the slope and the y-intercept affect the graph. Students identify and interpret x-intercepts of linear functions, and they develop, graph, and apply the standard and point-slope forms for the equation of a line.
Topic 6: Creating Linear Models for Data
In the topic Creating linear models for data, students continue to deepen their understanding of linear functions as they fit linear models to approximately linear data. Students are introduced to the concept of correlation, and they learn that correlation does not imply causation. Without technology, they fit trend lines to data using what they know about rate of change and y-intercept, and make predictions using their trend lines. Students also explore transformations of functions by transforming the parent function y = x to create linear models. Finally, they are introduced to the concept of a line of best fit. They use technology to find the equation of the least-squares regression line, learn how the value of the correlation coefficient, r, indicates the strength and direction of a linear association between two variables and use residuals to informally assess the fit of a linear function.
Topic 7: Descriptive Statistics
Descriptive statistics, students build on their understanding of numerical univariate data that they developed in previous courses. Previously, students have learned how to compute measures of center and spread of numerical univariate data, including mean, median, mode, range, interquartile range, and mean absolute deviation. In this topic, students review those measures and learn about standard deviation and choose the most appropriate measures of center and spread to make comparisons between two or more data sets. Students also extend their knowledge of bivariate categorical data by creating two-way tables and calculating and interpreting relative frequencies to recognize associations between the variables.
Topic 8: Solving Linear Equations and Inequalities
The topic Solving linear equations and inequalities gives students time to explore and master solution techniques for solving linear equations and inequalities. This topic extends students' understanding of equations and inequalities from earlier grades by maintaining the use of multiple representations, solving equations and inequalities with algebraic techniques as well as checking solutions with graphs and tables. Using tabular and graphical representations side-by-side with algebraic methods helps students understand the solutions they are finding when they solve linear equations as well as the range of solutions they are finding when they solve an inequality. In addition to practice with equations and inequalities, this topic also includes explicit practice to solidify students' understanding of and automaticity with writing equations of lines and graphing linear functions.
Topic 9: Absolute Value Equations and Piece-wise Functions
This topic, Absolute value equations and piecewise functions, builds on students' understanding of the absolute value of a number and of the absolute value of a difference of two numbers as a distance on the number line to develop the absolute value function. Students model distance constraints using the absolute value function and use multiple representations of the function to solve associated equations and inequalities.
Topic 10: Systems of Linear Equations and Inequalities
The topic Systems of linear equations and inequalities builds on and extends previous work on equation solving, graphing equations and inequalities, and modeling. Students start their work with systems of equations by setting up a system of linear equations and solving the system using graphs and tables. Solving by graphs and tables before addressing the analytic techniques for solving systems develops students' conceptual understanding of what a solution to a system of equations means, and makes the algebraic methods covered in the next topic easier to comprehend.
Topic 11: Other Methods for Solving Systems
The topic Other methods for solving systems builds on the previous topic, Systems of linear equations and inequalities. In this topic, the analytic methods of solving systems of linear equations, substitution and linear combination, are considered. Students also connect the algebraic solution methods to the graph of a system of equations and consider what it means when a true or false statement results from the analytic solution methods.
Topic 12: Other Nonlinear Relationships
The topic Other nonlinear relationships builds on students' work with linear patterns and functions as well as their work with patterning in previous grades to help them begin to recognize patterns that can be modeled with quadratic and exponential functions. This topic also introduces students to simple square root, cubic, and cube root functions. It is extremely important that students be given time to work with concrete objects as they continue to connect the various representations of functions (concrete, verbal, algebraic, graphical).
Topic 13: Laws of Exponents
In the topic Laws of exponents, students will revisit the laws of exponents previously learned in prior courses, including the meaning of zero and negative exponents, and apply these laws to algebraic expressions and numbers expressed in scientific notation. Students will also be introduced to fractional exponents.
Topic 14: Exponential Functions and Equations
The topic Exponential functions and equations introduces students to situations that can be modeled using exponential functions and provides opportunities to explore graphs of exponential functions. Students build on their understanding of recognizing patterns and linear functions to build intuition for exponential functions. By requiring students to constantly connect the different representations (concrete, verbal, numeric, algebraic, graphical) and to verbalize these connections, students will draw parallels between building linear functions with repeated addition and building exponential functions with repeated multiplication.
Topic 15: Graphs of Quadratic Functions
The topic Graphs of quadratic functions continues the study of transformations on parent functions that began with linear functions. Students build on their previous exposure to quadratic functions as they review the key features of the graph of the parent function y = x2. Students then explore how changing the values of the constants a and c affect the graph of the function y = ax2 + c.
Topic 16: Operations on Polynomials
The topic Operations on polynomials addresses polynomial multiplication, addition, and factoring, as well as polynomial division. Students are also introduced to the concept of a rational expression and its connection to polynomial division, foreshadowing future work with the arithmetic of rational expressions. Division of polynomials is included in this topic to address the idea that polynomials are only closed under multiplication, addition, and subtraction, not division. The knowledge and skills presented are important in the routine manipulation of many algebraic expressions.
Topic 17: Modeling with Quadratic Functions
The topic Modeling with quadratic functions builds on students' knowledge from the topic Graphs of quadratic functions. Now that students are familiar with graph of quadratic functions and the types of situations they can represent, they build off that knowledge to model more complex situations using quadratic functions. Students are introduced to horizontal shifts and are able to describe how a, h, and k in the rule y = a(x − h)2 + k affect the shape of a parabola. Students use this form to create function rules to fit data and they identify this form as vertex form. Students also complete the square on quadratic function rules to write the rules in vertex form, graph from this form, and use this form to identify key features. They are also able to compare functions represented in two different ways and use quadratic regression to find a function rule that models approximately quadratic data.
Topic 18: Solving Quadratic Equations
In the topic Solving quadratic equations, students extend what they know about solving linear equations to solving quadratic equations, using both graphical and algebraic solution techniques. Students solve quadratic equations by graphing, factoring, and completing the square. By providing ample time for questions and practice with the three different methods and discussing the various outcomes, students will begin to see the connections among the factors of the quadratic expression, the x-intercepts of the graph of the quadratic function, the roots of the associated quadratic equation, and the zeros of the associated quadratic function. This topic also includes explicit practice to solidify students' understanding of important skills related to working with quadratic expressions, equations, and functions.
Topic 19: The Quadratic Formula
The purpose of this topic, The quadratic formula, is to provide students a method by which to solve quadratic equations with irrational number solutions. The development in this topic builds toward the quadratic formula by first exposing students to irrational numbers that they might encounter in their work with the quadratic formula: those that can be expressed as square roots. Students then connect geometric representations of square roots to algebraic simplification methods, and finally learn to apply the quadratic formula to solve quadratic equations.