In this case the teacher is facilitating small groups using manipulatives to create functions from data points based on the game Angry Birds and students are working together to determine which ordered pairs fit the graphs, creating equations that match a real-world scenario.

In this case the teacher is increasing student understanding of functions in preparation for their work with linear functions and students are communicating their understanding after doing a "growing dots" activity, discussing the tables, graphs, equations, and statements as they determine how to find the 100th term.

In this case the teacher is facilitating groups working on an activity using algebra tiles and students are collaborating on how to visually represent an equation by performing 'legal moves' to simplify the equation to find what x is equal to.

This case shows a teacher introducing the calculus method of approximation of functions through the use of power series and students working in groups to explore series concepts both algebraically, graphically, and finally with the associated calculus.

In this case the teacher is reinforcing and connecting the topics of slope, correlation, graphing, and functions by having students answer the question, "What contains more calories, fat or sugar?" and students are analyzing and discussing two graphs, ultimately choosing and applying the appropriate methods to find an answer to the essential question.

This case shows a teacher using real-world problems to make algebra more relevant to students and students working with salary problems collaboratively, using logic and reasoning, to determine which choice would pay more money over time.

In this case the teacher is using whole-class discussion to help students compare properties of quadratic equations and students are taking notes and answering questions while brainstorming ways these comparisions can be made through analysis of similarities and differences.

This case shows a teacher using written number sentences on the whiteboard to help her students understand what a function is, and students helping her with the placement of the sentence strips according to their growing understanding.

In this case the teacher is engaging her class in a discussion of angles formed by a pair of parallel lines cut by a transversal and students are applying inductive and deductive reasoning skills to find out the relationships between these, discovering patterns, and determining whether their conclusions are valid and logical.

This case shows a teacher working with small groups of students using mathematical discourse and reasoning to describe and discuss what they see. Students use manipulatives to move from verbal representation of patterns to rules or equations.

In this case the teacher is guiding students through the construction of conic sections and students are investigating the relationships among foci, ellipse shape, focal points, directrix, and parabola shape by writing their own definitions of a circle while describing how to construct one with string and pencil.

In this case the teacher is engaging students in discussion about the similarities between forms of equations and students are converting algebraically between multiple forms to solve a multi-step real-world problem, applying properties of operations and assessing the reasonableness of answers while sharing their results with the class.

This case shows a teacher facilitating an activity about logarithms and exponents as students investigate logarithms and how to use a calculator to show their relationship.

In this case the teacher is facilitating students working with perimeter and area, and students are modeling these measurements using manipulatives to create polynomial expressions.

This case shows a teacher helping his students determine how and when to use x and y-intercepts and students learning to use graphing calculators to facilitate their work while engaging in mathematical discourse.

This case shows a teacher leading small group discussions on linear relationships found in everyday life and students sharing and discussing their examples and thoughts.

In this case the teacher is facilitating a lesson involving undefined slopes and fractions and students are developing a conceptual understanding of these by trying to figure out what a 4/0 pizza would look like, sharing and discussing their ideas and solutions.

In this case the teacher is using a Socratic Seminar to assist students in reading graphs as comparisons of two sets of data and students are looking at a collection of graphs and constructing viable arguments about them and the real-life examples they represent while critiquing the reasoning of their peers.

This case shows a teacher working with small groups of students and students investigating the relationships between polynomials and zeroes.

In this case the teacher is assisting students in exploring and solving systems of equations on a worksheet and students are working through the problems in small groups, identifying systems that have no solution or infinitely many solutions using different strategies.