This activity asks students to visualize and construct three-dimensional objects from the two-dimensional drawings. Students are shown four solids composed of cubes, and they must reproduce the objects with manipulatives or sketch them on isometric dot paper. Ideas for implementation, extension and support are included along with a printable sheet of dot paper.

This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.

This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.

This problem helps children begin to understand the various properties of common geometric solid shapes. It also promotes naming, discussion and experimentation concerning their features, and requires them to justify their ideas. It asks students to judge the stability of nine configurations made from six common solids. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable sheets.

This Geometry Concept Collection is a rigorous presentation of high school geometry. It is fully correlated with the Common Core State Standards.

Code.org has partnered with Bootstrap to develop a curriculum which teaches algebraic and geometric concepts through computer programming. The two ten hour courses from Code.org focus on concepts like order of operations, the Cartesian plane, function composition and definition, and solving word problems. Or visit Bootstrap to explore their longer Bootstrap:1 and Bootstrap:2 courses which teach more mathematical and programming concepts. By shifting classwork from abstract pencil-and-paper problems to a series of relevant programming problems, Code.org's CS in Algebra demonstrates how algebra applies in the real world, using an exciting, hands-on approach to create something cool.

This course is an introduction to the calculus of functions of several variables. It begins with studying the basic objects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces, and various coordinate systems. It continues with the elementary differential geometry of vector functions and space curves. After this, it extends the basic tools of differential calculus - limits, continuity, derivatives, linearization, and optimization - to multidimensional problems. The course will conclude with a study of integration in higher dimensions, culminating in a multidimensional version of the substitution rule.

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.

The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).

This activity gives students practice naming and using shape and color attributes to create patterned sequences. The first challenge asks students to use attribute differences to extend a sequence. A second, more open-ended challenge asks students to maximize the length of their sequences under a further constraint. An interactive applet is provided as an alternative to physical manipulatives. The Teachers' Notes page includes suggestions for implementation and discussion questions.

This activity gives students a chance to relate some common three-dimensional solids to their polygonal faces. The object is to put solids in a sequence in which adjacent solids have a polygonal face in common. Ideas for implementation, extension, hints and support are included along with printable cards of the polyhedra.

This hands-on activity helps students develop spatial sense and scaling concepts. Students use interlocking cubes to build first a chair and then a table of appropriate size for the chair. The student goes on to build two other sets of chairs and tables to make three different sizes in all. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension.

This task is primarily about volume and surface area, although it also gives students an early look at converting between measurements in scale models and the real objects they correspond to.

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment. The point so constructed is called the circumcenter of the triangle.

This problem is an investigation into combinations of a number of cubes. It is a practical activity which involves working systematically, and visualizing and relating 3D shapes to their representation on paper. Children are asked how many different towers are possible using seven cubes on a base of two of them. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable handouts (word/pdf).

This activity allows students to explore reflective symmetry. They are asked to color a given arrangement of triangles in symmetric patterns using specific numbers of colors. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable sheets

Students must calculate the volume of a cone in this real world task.

This short video and interactive assessment activity is designed to give fourth graders an overview of forming figures with cutouts.

The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. The purpose of this first task is to see the relationship between the side-lengths of a cube and its volume.

The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. In this iteration, we do away with the lines that delineate individual unit cubes (which makes it more abstract) and generalize from cubes to rectangular prisms.