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 is facilitating discussion about the rules, meanings, and correct mathematical vocabulary behind adding mixed numbers and students are creating and defending their arguments concerning what two mixed numbers could be added to arrive at a sum of 10 7/8.
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.
In this case the teacher is discussing what a derivative is and what it means to analyze a graph of a function and students are brainstorming a minimum of four ways a derivative can be used and how to use the graph of the derivative to describe functions.
This case shows a teacher skillfully assisting students engaged in an activity on light and students using the scientific processes and communication skills to make sense of their data and the specific properties of light.
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 facilitating a discussion about the application of basic concepts to probability problems and students are using diagrams and models, exploring the concepts behind the solutions instead of just focusing on a set procedure.
This case shows a teacher in a discussion with students about derivatives and students giving information and answering questions about derivative properties.
This case shows a teacher working with students on applying derivatives to a group of individual graphs and students trying to determine the relationship among the graphs and the first and second derivatives.
In this case the teacher is facilitating the class's work on a motion design of their own while assessing their understanding of force and motion and students are collaborating with their partners as they begin to build and try to move their objects, re-designing them if necessary.
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.
This case shows a teacher working with small groups of students to apply their background knowledge to generalize patterns in data from the sum of measures of interior angles of different polygons.
This case shows a teacher leading a discussion on a geometry problem and students engaging in mathematical discourse about the properties of triangles.
In this case the teacher is assisting the class in identifying and correcting errors in their application of u-substitution and students are integrating definite and non-definite integrals, using generalized strategies for implementing the substitution process.
In this case the teacher is helping students recognize and understand the importance of variables, constants, and coefficients and students are doing an activity involving pattern blocks, visualizing actual changes, and formulating a rule as an equation for unknown terms based on the patterns they observe.
This case shows a teacher working with small groups on making connections between integral and differential calculus both analytically and graphically and students working collaboratively to make predictions based on the patterns in given functions.
This case shows a teacher helping students understand the relationship between the motion of their matchbox cars and the Laws of Motion and students engaged in an activity using cars and ramps, repeating trials, recording and analyzing their data.
This case shows a teacher working with small groups of students and students applying the properties of quadrilaterals to determine lengths of segments and measures of angles of parallelograms.
In this case the teacher is engaging her students in a discussion of the Pythagorean Theorem as applied to real-life situations and students are actively participating in collaborative problem solving using mathematical discourse and their prior knowledge.
In this case the teacher is assisting students in determining relationships among shapes and students are determining if specific statements about these shapes are 'sometimes', 'always', or 'never' true by moving to certain areas of the classroom, defending their choice by stating the applicable properties, and their own thought processes.