The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.

The accuracy and simplicity of this experiment are amazing. A wonderful project for students, which would necessarily involve team work with a different school and most likely a school in a different state or region of the country, would be to try to repeat Eratosthenes' experiment.

This Flash game for one or two players gives students practice in estimating the size of angles. A circle and a radius pointing in a random direction are given. The student activates a second sweeping radius, which can move in either direction, and tries to stop it at the specified measure. Three difficulty levels control the range of angle measures. Points are awarded based on closeness of the estimate. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support.

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

This series of problems requires students to apply their knowledge of area and perimeter to find the optimal area given a specified amount of fencing. The problems progress in difficulty as new elements are added to the situation, therefore changing the outcome. This page includes tips for getting started, solution, teachers resource page, and a printable problem page.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90_ and that angle measure is additive.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

In this Cyberchase video, Inez and Digit identify the location of the transformation using their knowledge of parallel and intersecting lines.

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

This activity gives students the chance to explore area and perimeter in a problem solving setting. Nine differently-sized squares need to be tiled into a rectangular frame of unknown proportions. Three prompts of solving strategies are provided. Ideas for implementation, extension and support are included along with a printable sheet of the problem.

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.

The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.

In this problem students study motion along a path and the properties of a parallelogram. Students must navigate back to a starting point after traveling three legs in cardinal directions on a compass. Ideas for implementation, extension and support are included.

This three-act math task utilizes videos and questioning to help students explore geometry and angles.

This problem helps develop an understanding of the relationship between the part and the whole. Given a square figure divided into smaller triangles, students are asked to use the pattern to divide the square into two halves, three thirds, six sixths, and nine ninths. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of of the problem.

This problem gives students practice in calculating with fractions, using factors and multiples, finding equivalent fractions, logical reasoning, and working systematically. Students use clues to determine the total number of discs in a game and the fraction represented by each color. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of the problem.

The goal of this task is to use ideas about linear functions in order to determine when certain angles are right angles. The key piece of knowledge implemented is that two lines (which are not vertical or horizontal) are perpendicular when their slopes are inverse reciprocals of one another.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.