Introduction to discrete and computational geometry. Topics covered: planar graphs, geometric graphs, the theory of crossings, extremal graph theory, arrangements of curves and points in the plane (mainly pseudolines and pseudocircles), problems involving distances, Gallai-Sylvester-type problems, Davenport-Schinzel sequences. Emphasis on teaching methods in combinatorial geometry. Many results presented are recent, and include open problems.

Images of construction of copying an angle, with descriptive text and hotspots of key points on images.

In this unit, children learn about attributes of shapes, compose and decompose composite shapes.

This video lesson uses the technique of induction to show students how to analyze a seemingly random occurrence in order to understand it through the development of a mathematical model. Using the medium of a simple game, Dr. Lodhi demonstrates how students can first apply the 'rules' to small examples of the game and then, through careful observation, can begin to see the emergence of a possible pattern. Students will learn that they can move from observing a pattern to proving that their observation is correct by the development of a mathematical model. Dr. Lodhi provides a second game for students in the Teacher Guide downloadable on this page. There are no prerequisites for this lesson and needed materials include only a blackboard and objects of two different varieties - such as plain and striped balls, apples and oranges, etc. The lesson can be completed in a 50-minute class period.

Students will create and compare dot and box plots that show the percentages of single-mother and single-father households in different regions of the United States.

With this activity, students use a globe to learn how a position on Earth can be described. They investigate how latitude can be found using the stars. Students learn what latitude and longitude are and how to use them to indicate a position on Earth. They investigate how in some locations on Earth, the direction of the midday sun can change over the year.

This lesson is about the estimation of the value of Pi. Based on previous knowledge, the students try to estimate Pi value using different methods, such as: direct physical measurements; a geometric probability model; and computer technology. This lesson is designed to stimulate the learning interests of students, to enrich their experience of solving practical problems, and to develop their critical thinking ability. To understand this lesson, students should have some mathematic knowledge about circles, coordinate systems, and geometric probability. They may also need to know something about Excel. To estimate Pi value by direct physical measurements, the students can use any round or cylindrical shaped objects around them, such as round cups or water bottles. When estimating Pi value by a geometric probability model, a dartboard and darts should be prepared before the class. You can also use other games to substitute the dart throwing game. For example, you can throw marbles to the target drawn on the floor. This lesson is about 45-50 minutes. If the students know little about Excel, the teacher may need one more lesson to explain and demonstrate how to use the computer to estimate Pi value. Downloadable from the website is a video demonstration about how to use Excel for estimating Pi.

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.

The Illustrative Mathematics Project provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.

This is an activity that makes math real. The students complete some activities that show the length of a wheelchair ramp is determined using American Disabilities Act.

Reimagining mathematics instruction can be a heavy lift. Most teachers have years of traditional mathematics instruction under their belts by the time they enter their professional careers. Chapter 4 of  EL Education’s book Learning that Lasts explores two critical strategies for improving mathematics instruction—changing mindsets about mathematics; and remodeling the basic lesson structure for mathematics. This reimagination leads to mathematics instruction that is more challenging, engaging, and empowering for students as well as teachers.

In this instructional task students are given two inequalities, one as a formula and one in words, and a set of possible solutions. They have to decide which of the given numbers actually solve the inequalities.

Students sort and classify triangles based on similarities. Students are asked to discuss their decisions in this Nrich activity.

This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.

Mathematically Productive Instructional Routines (MPIR) are short (10ish minutes), daily exercises aimed at building number sense. These six different MPIR are part of the Mathematically Productive Instructional Routines collection from the Washington Office of Public Instruction and the Washington Association of Educational Service Districts.

This course was originally developed for the Open Course Library project.  The text used is Math in Society, edited by David Lippman, Pierce College Ft Steilacoom.  Development of this book was supported, in part, by the Transition Math Project and the Open Course Library Project. Topics covered in the course include problem solving, voting theory, graph theory, growth models, finance, data collection and description, and probability.

Students experience data collection, analysis and inquiry in this LEGO® MINDSTORMS® NXT -based activity. They measure the position of an oscillating platform using a ultrasonic sensor and perform statistical analysis to determine the mean, mode, median, percent difference and percent error for the collected data.

CK-12 Foundation's Middle School Math € Grade 6 Flexbook covers the fundamentals of fractions, decimals, and geometry. Also explored are units of measurement, graphing concepts, and strategies for utilizing the book's content in practical situations.

A work in progress, CK-12's Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.