This case shows a teacher supporting groups of students using graphing calculators by asking probing questions, and students graphing the equations of polynomial functions, drawing sketches, recording observations, and determining rules.

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.

In this case the teacher is facilitating students comparing and contrasting the properties of roots and students are applying their understanding of root functions to solve problems and make conclusions about the transformation rules of the square function.

In this case the teacher is engaging the class in a discussion about sample randomization, subsamples, and methodology as they apply to presidential election polling and students are using mathematical reasoning to figure out the importance of each methodology, responding to their peers' arguments, and offering their own opinions based on what they had read, observed, or reasoned.

In this case a teacher expertly guides his algebra students through the process of factoring polynomials and students engage in mathematical discourse about the process of factoring at a level they have not seen before.

In this case the teacher is helping her students understand how to determine the distance between two points using an "Amazing Race" simulation and students are using coordinate peg boards to plot the points corresponding to the starting point and a specific location.

This case shows a teacher facilitating a discussion about linear functions using a real-life example and students discovering the difference between slope and y-intercept from tables, graphs, equations, and verbal expressions.

In this case the teacher is facilitating student understanding of quadratic inequalities analytically and graphically and students are working on a problem involving a moving baseball, graphing functions, comparing approaches and solutions with a partner and the whole class.

In this case the teacher is facilitating a discussion on a specific word problem by having students identify number patterns and students are recognizing, interpreting, and sharing their solutions using a graphic organizer to break down the problem while constructing viable arguments with their work as evidence.

This case shows a teacher using real-life scenarios to enable students to read and interpret line graphs and students reasoning, thinking mathematically, and communicating their thinking as they interpret the graphs.

In this case the teacher is facilitating groups working with graph and image cards having to do with volume and height and students collaboratively develop arguments as to why a specific graph card fits with a specific image card.

This case shows a teacher guiding student groups in an activity matching graph cards with function cards and students explaining how they grouped them, watching a YouTube video on discontinuities, and then re-sorting their cards if needed.

In this case the teacher is introducing how to solve and graph inequalities and the students are discussing their understanding and graphing at the whiteboard, exposing particular misconceptions they have about the topic.

In this case the teacher is guiding students in learning about exponential growth and developing algebraic expressions and students are creating these expressions with the help of graphing calculators, using a 'handshake problem' as the basis of their investigation.

In this case the teacher is facilitating small groups using manipulatives to find multiple representations of a growing pattern to write a function rule and students are using mathematical discourse to share, predict, and critique ideas while refining and redirecting their own thinking prior to whole class sharing.

This case shows a teacher facilitating small groups of students as they match function graphs to derivative graphs and students exploring and demonstrating their knowledge of rates of change graphically.

In this case the teacher is helping students move from concrete to abstract concepts in an activity and students are finding growth patterns, generalizing the patterns they find, writing rules, and justifying their findings with evidence in order to predict future and previous figures.

In this case the teacher is facilitating a student discussion about their choice of a specific technique for solving a system of linear equations and students are engaged in mathematical discourse about why they picked either the substitution, elimination, or graphing methods.

In this case the teacher is guiding students in an activity where they are sorting number cards trying to determine patterns and sequences, thinking mathematically and making connections to their prior knowledge while also writing a general rule that describes what they have found.

In this case the teacher is building students' abilities to solve word problems in algebra and the students are analyzing algebraic relations, making detailed graphs, answering questions, and preparing to present their findings to their classmates.