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.

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.

This case shows a teacher discussing with her class how to find the area of a section of farmland using Google Earth and students engaged in mathematical discourse to see how each student determined the area.

In this case the teacher is facilitating the understanding of students with regards to properties of special quadrilaterals and students are classifying different types of polygons and quadrilaterals, analyzing why each one is a particular shape and applying these properties to different shapes.

In this case the teacher is assisting students in understanding the differences between theoretical and experimental probabilities and students are engaged in working with the two types of probabilities by performing trials using a game board and a die.

In this case the teacher is facilitating students working cooperatively to find the areas of all surfaces of two cylinders and students are working in groups to come up with a conjecture explaining the effect changing the dimensions of these cylinders has on surface area.

This case shows a teacher working with students on a graphing activity involving perpendicular bisectors and students communicating mathematically to explore and discover geometric concepts through manipulations on their calculators.

In this case the teacher is introducing volume of rectangles and students are using manipulatives to build different 3D shapes, developing and defending their own strategy for discovering the formula for volume.

In this case the teacher is facilitating mathematical reasoning about geometric terms and relationships involving circles and students are discussing their understanding with each other, using discourse to explain their thinking and to ask questions of each other for clarification.

This case shows a teacher using gender-specific examples of various cylinders to hook students and students using their prior knowledge to discover the volumes of the cylinders.

In this case the teacher is striving to help students improve critical mathematical reasoning skills and students are reasoning through different volume formulas to derive a new volume formula for a cone, deciding which tools would be most appropriate to help solve their problem and communicating mathematically with their classmates.

In this case the teacher is working with students to help them determine how to find the formula of a circle and students are manipulating a paper circle, cutting it into pieces, folding it or writing on it, brainstorming with each other to figure out the formula of the area of a circle using prior knowledge of the area of other shapes.

In this case the teacher is facilitating a discussion on lines of symmetry prior to investigating polygons and students are using mathematical discourse to accurately find lines of symmetry while dispelling common misconceptions they have about the topic.

In this case the teacher is using Socratic Seminar to help students understand the characteristics of 3D figures and students are engaged in mathematical discourse to determine what mathematical concepts and skills will be needed to solve a "painted cube" problem, then discussing the methods used to solve the problem.

This case shows a teacher working with students on trigonometric functions for the first time and students determining the relationship between sine, cosines and tangents of complimentary angles, predicting how a trig ratio reacts when the angle degrees are changed.

In this case the teacher is guiding students in using prior knowledge to construct viable arguments about different similar triangles and the students are engaged in an activity where they create their own triangles using manipulatives and determine how and why they are similar.