Students explore how pendulums work and why they are useful in everyday applications. In a hands-on activity, they experiment with string length, pendulum weight and angle of release. In an associated literacy activity, students explore the mechanical concept of rhythm, based on the principle of oscillation, in a broader biological and cultural context in dance and sports, poetry and other literary forms, and communication in general.

After geometric series, this Nrich problem is one of the simplest infinite series with finite sum, all of whose terms are positive. This geometric demonstration of the result requires students to continue a pattern and to use several steps of reasoning to deduce that the sum is bounded by 2. Summing infinite geometric series also play an important role in the this proof, so this could be used to show an application of them in a larger proof. (It would be useful for students to be able to sum 12+14+18+⋯ before tackling this problem.)

In Nrich's Twisting and Turning, the Conway Rope Trick was introduced. You'll need to take a look at the video on that page and do the rope trick for yourself before reading the rest of this article, since here we're going to take a good long look at the symmetries of the resulting tangles.

This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.

Doing this Nrich problem is an excellent way to work at problem solving with learners. The problem lends itself to small group work, and provides an engaging context for pupils to use the skills of trial and error, and working systematically.

This short video and interactive assessment activity is designed to teach fourth graders about telling the time - before and after.

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.   

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in composite figures.

This third grade math unit is composed of two parts that I created.  First, there are videos for the first six lessons of Math Expressions Unit 1 for Third Grade and their accompanying scripts.  These videos can be posted to a site like Google Classroom so that students can work at their own pace while the teacher helps those who need their attention the most.  Secondly, there is a formative assessment sheet for each lesson.

This Nrich problem encourages children to explain observations and to generalize. It requires a good understanding of multiplication. It may also introduce the idea that opposite faces of a dice add to seven, if that is something with which learners are not already familiar

This Nrich problem supports the development of the idea of generic proof with the children. This is a tricky concept to grasp but it draws attention to mathematical structures that are not often addressed at primary school level.

This short video and interactive assessment activity is designed to give fourth graders an overview of time conversion between words and numbers.

The course provides a survey of the theory and application of time series methods in econometrics.

This short video and interactive assessment activity is designed to give fourth graders an overview of telling time to quarter and hour.

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.

" This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc."

This lesson introduces students to the “Tragedy of the Commons,” an extended metaphor for problems of shared environmental or man-made resources that are overused and eventually depleted. In this metaphor, shared resources are compared to a common grazing pasture, or “commons,” on which any dairy farmer can graze as many cows as he/she wishes. If too many cows are added to the commons, they will overeat the grass in the pasture and the shared resource will become depleted – a disadvantage to everyone. In this lesson, students will be inspired to think about possible solutions to this problem. To get there, they will use basic math to frame the problem and will discover how useful this can be in considering consequences of various actions. Most importantly, they will become comfortable with the concept of problems of shared resources – and will learn to recognize, and seek out, examples all around them. An exposure to algebra 1 and basic functions is the only math prerequisite necessary. The lesson will take around 50 minutes to complete and the required materials for this lesson are paper and pens or pencils, as well as some sort of prize to provide the winning team with in the final activity. For all five activities, students are asked to work in groups of 4, but groups of 3 or 5 would also be okay. Students will work with their groups to discuss the logic behind the tragedy of the commons, to consider some options for preventing this tragedy and to examine examples of problems of shared resources that are relevant to them. They will also come up with functions that fit behavior described in the video, and be asked to think about the behavior of functions provided in the video and accompanying materials.

This short video and interactive assessment activity is designed to teach third graders an overview: sum of the angles of a triangle.

This short video and interactive assessment activity is designed to teach third graders about turning words into numbers using place value models.

This Nrich investigation is one that uses the very popular multilink cubes. It gives a wonderful opportunity for pupils to explore ways of recording. This activity is also designed to nurture children's curiosity by introducing mathematics into a familiar non-mathematical context. Children might end up pursuing different ideas from each other and this freedom to explore may well encourage learners to persevere more than they might usually. In this way, they will immerse themselves in the particular number sequence they have chosen to use, which will help them gain a deep understanding of its structure. This activity lends itself to pupils posing their own questions in the form “I wonder what would happen if...?”