This case shows a teacher working with a precalculus class about their knowledge of functions and students analyzing and predicting graphical representations of various functions.

In this case the teacher has given students sets of color-coded squares and students are matching the graphs and equations of various trigonometric transformations/translations by deciding and explaining their own strategies or plans, questioning each other, and sharing their answers.

This case shows a teacher leading a discussion and students engaged in translating quadratic equations drawn from a real-life example and explaining their work.

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.

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.

This case shows a teacher facilitating student discussion and students posing clarifying questions to their peers to understand how equations of periodic data were created.

This case shows a teacher guiding students as they work with functions and students using mathematical discourse as they construct exponential functions from graphs and then interpret the graph to create a word problem.

This case shows a teacher supporting small groups of students as they conduct science experiments and analyze real-world data, and students exploring slope-intercept, standard, and point-slope forms.

This case shows a teacher using social media to engage her class in determining which type of function should be paired with each scenario and the students analyzing each scenario within small groups and exercising higher critical thinking skills in a whole class discussion.

This case shows a teacher working with small groups of students on function transformations and students using mathematical discourse to analyze their data and graphs.

This case shows a teacher working with students using their prior knowledge of trigonometry and geometry to solve a pulley problem and students working collaboratively with a pulley system using hands-on manipulatives.

In this case the teacher is facilitating a group discussion about projectile motion simulations the students have investigated and students are working together to find the form of the equation, using mathematical discourse to discover patterns and solutions.

This case shows a teacher teaching about arithmetic sequences and linear equations and students developing their reasoning and mathematical confidence as they propose ideas and then support or dispute them.

In this case the teacher is helping students understand the concepts behind quadratic equations, discriminants, and how the function's graph changes as the discriminant does and students are working together to solve three different examples of quadratic equations, determining the discriminant, graphing each example and discussing with peers their ideas and solutions.

In this case the teacher is using real-life connections to help students calculate and graph components of quadratic functions with confidence and students are working in pairs to solve real-life scenarios and collaboratively creating a poster to summarize their learning.

In this case the teacher is assisting students in understanding what each segment of a distance and speed graph stands for and students are working together to create a story that is an accurate representation of each given graph, ultimately determining the differences between each.

This case shows a teacher working with students on how to identify a variety of patterns in different ways and students using cubes to determine the rules for the patterns they are working with by recalling prior knowledge of algebraic expressions.

In this case the teacher is using Socratic Seminar to help students use prior knowledge of solving linear systems and linear equations to figure out how to find the solution set of a linear quadratic system and students are discussing, presenting, and using their past experiences to reason their way through solving linear quadratic systems.

This case shows a teacher leading the class in solving a real-world calculus problem by guiding students to place events from a real-world context on a distance vs. time graph and engaging them in an active discussion about their answers.

In this case the teacher is using structured discussion to support students' development of content knowledge about quadratic functions and students are applying the information from the specific text they analyzed and collectively sharing ideas and problem solving techniques.