Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.

This Nrich problem starts with a simple situation which can be analyzed quickly using mental methods, but which provides a starting point for tackling a more challenging problem. The challenge can be tackled at many different levels, using trial and improvement (perhaps using spreadsheets), looking for number patterns, or with a more formal algebraic approach.

All of us have felt sick at some point in our lives. Many times, we find ourselves asking, "What is the quickest way that I can start to feel better?" During this two-lesson unit, students study that question and determine which form of medicine delivery (pill, liquid, injection/shot) offers the fastest relief. This challenge question serves as a real-world context for learning all about flow rates. Students study how long various prescription methods take to introduce chemicals into our blood streams, as well as use flow rate to determine how increasing a person's heart rate can theoretically make medicines work more quickly. Students are introduced to engineering devices that simulate what occurs during the distribution of antibiotic cells in the body.

After the Great Depression struck, Ford especially wanted to support ailing farmers. For two years, Ford and his team researched ways to use farmers’ crops in his Ford Motor Company. They discovered that the soybean was the perfect answer. Soon, Ford’s cars contained many soybean plastic parts, and Ford incorporated soybeans into every part of his life. He ate soybeans, he wore clothes made of soybean fabric, and he wanted to drive soybeans, too. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Think about the people in your community and the challenges they face. List three challenges that affect their daily life. Consider something you use every day and brainstorm how it could be repurposed or modified to address this problem.

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

This lesson unit is intended to help teachers assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data; examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile; generalizing using numerical, geometrical or algebraic structure; and describing and explaining findings clearly and effectively.

This Nrich problem provides a fraction-based challenge for students who already possess a good understanding of fraction addition and subtraction, and it leads to algebraic manipulation of that same process.

This is course material published for a secondary Math 1 course. Authors of this work are: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius and updated from the original work in 2013 in partnership with the Utah State Office of Education.

In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, tables, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.

The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a non-standard point of view. Instead of giving a starting value and asking for subsequent values, it gives an end value and asks about what happened in the past. The simple first question can generate a surprisingly lively discussion as students often think that the algae will grow linearly.

Meg set out to climb up and investigate the rain forest tree canopies — and to be the first scientist to do so. But she encountered challenge after challenge. Male teachers would not let her into their classrooms, the high canopy was difficult to get to, and worst of all, people were logging and clearing the forests. Meg never gave up or gave in. She studied, invented, and persevered, not only creating a future for herself as a scientist, but making sure that the rainforests had a future as well. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Your community has many different areas to explore - it might be a park, a grocery store, a forest, or an alley. For some people, it might be difficult to explore these areas because they may have differing abilities. Select one area in your community, and come up with a plan to build a way for it to be more accessible to everyone.

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

This activity is a culmnating assessment of students' abilities to describe a linear function in words, in an equation, in a table, in a graph, identify a solution, and explain the solution.
Remix of: AEA Template for Building Lessons

Richard grew up in Kenya as a Maasai boy, herding his family’s cattle, which represented their wealth and livelihood. Richard’s challenge was to protect their cattle from the lions who prowled the night just outside the barrier of acacia branches that surrounded the farm’s boma, or stockade. Though not well-educated, 12-year-old Richard loved tinkering with electronics. Using salvaged components, spending $10, he surrounded the boma with blinking lights, and the system works; it keeps lions away. His invention, Lion Lights, is now used in Africa, Asia, and South America to protect farm animals from predators. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Your challenge is to use broken or old technology and other available resources to create a prototype that can be used to protect your home. This could involve tinkering, hacking, or redesigning the components of the technology to meet your needs.

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

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.

This resource was created by the Washington Office of Superintendent of Public Instruction.

Isatou Ceesay observed a growing problem in her community where people increasingly disposed of unwanted plastic bags, which accumulated into ugly heaps of trash. She found a way to be the agent of change by recycling the bags and transforming her community. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Use plastic bags to develop a new product (i.e. jump rope).

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

Recursos per al professorat de matemàtiques per introduir les matemàtiques interactives a l'aula. Es tracta d'un projecte impulsat pel Ministeri d'Educació, Cultura i Esport. Es pot trobar disponibles cursos de matemàtiques, recursos adaptables a l'aula així com informació tècnica per a la creació de recursos propis.

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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend's house with a full battery. The pictures below sho...