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: Below is a picture of a right triangle with $a$ the measure of angle $A$: Joyce knows that the sine of $a$ is the length of the side opposite $A$ divid...

Studying the Fibonacci Sequence is our entry point for studying Heredity: Inheritance and variation of traits.

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 short video and interactive assessment activity is designed to teach second graders about counting vertices and sides in various shapes.

This short video and interactive assessment activity is designed to teach third graders an overview of flat surfaces of 3d shapes.

This short video and interactive assessment activity is designed to teach second graders about fact families (numbers to 1,000).

This short video and interactive assessment activity is designed to teach third graders about fact families (numbers to 1,000).

Based on what they have already learned about friction, students formulate hypotheses concerning the effects of weight and contact area on the amount of friction between two surfaces. In the Associated Activities (Does Weight Matter? and Does Area Matter?), students design and conduct simple experiments to test their hypotheses, using procedures similar to those used in the previous lesson (Discovering Friction). An analysis of their data will reveal the importance of weight to normal friction (the friction that occurs as a result of surface roughness) and the importance of surface area to the friction that occurs between smooth surfaces due to molecular attraction. Based on their data, students will also be able to calculate coefficients of friction for the materials tested, and compare these to published values for various materials.

This short video and interactive assessment activity is designed to teach fourth graders about completing the number patterns based on the multiplication table.

This problem uses the same numbers and asks essentially the same mathematical questions as "6.NS Bake Sale," but that task requires students to apply the concepts of factors and common factors in a context.

Students are introduced to the five fundamental loads: compression, tension, shear, bending and torsion. They learn about the different kinds of stress each force exerts on objects.

As some of the foundational texts for beginning readers, fairy tales are a staple of many classrooms. This lesson allows students to engage with fairy tales from different regions around the world and compare important cultural elements of these stories.

Using an Arduino microprocessor, students will build an automated fish food feeder so fish can be fed when no one is at school?

This project involves learning how to do simple wiring of an LED, a buzzer, and a servo (motor) to a simple-to-use Arduino microprocessor.

A collection of digitized primary sources exploring four different instances of intentionally misleading information through time: The Winsted Wild Man, Tobacco and Feminism, Smallpox Vaccines, and the Cottingley Fairies.

Alternative facts, fake news, and post-truth have become common terms in the contemporary news industry. Today, social media platforms allow sensational news to “go viral,” crowdsourced news from ordinary people to compete with professional reporting, and public figures in offices as high as the US presidency to bypass established media outlets when sharing news. However, dramatic reporting in daily news coverage predates the smartphone and tablet by over a century. In the late nineteenth century, the news media war between Joseph Pulitzer’s New York World and William Randolph Hearst’s New York Journal resulted in the rise of yellow journalism, as each newspaper used sensationalism and manipulated facts to increase sales and attract readers.

Using both families and schools as a lens for study, 1st grade students learn about geography, history, economics, and civics with strong connections to the literacy block!

Students use the engineering design process to solve a real-world problem shoe engineering! Working in small teams, they design, build and test a pair of wearable platform or high-heeled shoes, taking into consideration the stress and strain forces that it will encounter from the shoe wearer. They conclude the activity with a "walk-off" to test the shoe designs and discuss the design process.

Students design, build and test shoes to develop new styles and improve existing designs.

This collection uses primary sources to explore Fannie Lou Hamer and the civil rights movement in rural Mississippi. Digital Public Library of America Primary Source Sets are designed to help students develop their critical thinking skills and draw diverse material from libraries, archives, and museums across the United States. Each set includes an overview, ten to fifteen primary sources, links to related resources, and a teaching guide. These sets were created and reviewed by the teachers on the DPLA's Education Advisory Committee.

The aim of this video lesson is to introduce the concept of factorials, and to show students that everyday events in their lives have so much to do with factorials - even if they do not realize it! During this video, students will learn about the large number of ways to arrange people and objects using the mathematical concept of factorials. This video lesson will begin with a story of a family vacation to Pulau Pinang, an island located 330 km from the city of Kuala Lumpur in Malaysia. In this video, lessons about using factorials are demonstrated through several challenges this family encounters during their vacation. A prerequisite for this lesson is knowledge of the multiplication rule of counting. During the classroom activities, students are asked to carry out collaborative learning challenges in groups of 6. These activities require students to arrange cards to show different factorial arrangements that can be made. The materials needed for this activity are very simple. We only need to provide a few pieces of blank or colored paper for each student. The lesson will take about 40 – 50 minutes to complete.