Product and Quotient Properties of Exponents
This lesson helps students understand two foundational exponential properties: The Product and Quotient Properties of Exponents. Students will collaborate to formulate a rule for these properties. Ultimately, students should conclude that when the same bases are being multiplied, exponents will be added; and when the same bases are being divided, exponents will be subtracted. As the lesson progresses, students will apply these rules to simplify expressions of various difficulties.
Using Linear Equations to Count Pecans
Students will write linear equations in point-slope form given two points via a verbal description.
Teacher instructing
Working with Literal Equations
The lesson will provide a conceptual basis for illustrating the parallelism between solving multi-step equations and translating literal equations into solutions for specified variables.
Students working together
No Interest If Paid in Full: How Much Do I Owe?
Students will write a linear equation from a real-world situation, identify the components of the equation, and interpret their meanings in the problem’s context.
Students working on task
Can We Get There?
Students will calculate the rate of change and y-intercept from a real-world problem represented in a graph, a table, and/or an equation. They will then display and present their findings to the class.
Students working in their group
4 OnTRACK Grade 7 Math: Number and Operations
Students will learn how to apply mathematical process standards to represent and use real numbers in a variety of forms.
19 OnTRACK Grade 7 Math: Proportionality
Students will learn to use proportional relationships to describe dilations; to explain proportional and non-proportional relationships involving slope; and to use proportional and non-proportional relationships to develop foundational concepts of functions.
7 OnTRACK Grade 7 Math: Expressions, Equations, and Relationships
Students will learn to develop mathematical relationships and make connections to geometric formulas; use geometry to solve problems; use one-variable equations or inequalities in problem situations; and use multiple representations to develop foundational concepts of simultaneous linear equations.
4 OnTRACK Grade 8 Math: Number and Operations
Students will learn how to apply mathematical process standards to represent and use real numbers in a variety of forms.
11 OnTRACK Grade 8 Math: Proportionality
Students learn to to use proportional relationships to describe dilation; explain proportional and non-proportional relationships involving slope; and use proportional and non-proportional relationships to develop foundational concepts of functions.
9 OnTRACK Grade 8 Math: Expressions, Equations, and Relationships
Students will learn to develop mathematical relationships and make connections to geometric formulas; use geometry to solve problems; use one-variable equations or inequalities in problem situations; and use multiple representations to develop foundational concepts of simultaneous linear equations.
5 OnTRACK Grade 8 Math: Two-Dimensional Shapes, Measurement, and Data
Students will learn to develop transformational geometry concepts and to use statistical procedures to describe data.
6 OnTRACK Algebra I: Properties and Attributes of Functions
Students will learn how to use the properties and attributes of functions.
8 Chapter 5: Introduction to Trigonometry and Graphs
In this chapter, we will explore angle measures and the trigonometric ratios, including graphing and inverses.
5 Chapter 7: Sequences and Series
In this chapter, we introduce sequences and series, some of their applications, and the Binomial Theorem.
3 Chapter 4: Systems of Equations
In this chapter, we will explore the methods used to solve systems of equations, and real-world situations involving systems of equations.
6 Chapter 2: Polynomial and Rational Functions
In this chapter, we will explore beyond linear functions and learn about polynomial and rational functions.
8 Chapter 6: Trigonometric Identities and Applications
In this chapter, students will learn a robust list of trigonometric identities along with their applications. Students will also be introduced to vectors.
7 Chapter 8: Conic Sections, Parametric Equations, and Polar Coordinates
In this chapter, we introduce conic sections, parametric equations, and polar coordinates.
5 Chapter 1: Introduction to Functions and Graphs
In this chapter, students are introduced to lines, functions, and graphs of functions.