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: Sketch graphs of $f(x) = \cos{x}$ and $g(x) = \sin{x}$. Find a translation of the plane which maps the graph of $f(x)$ to itself. Find a reflection of ...

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 an angle $\theta$ in the $x$-$y$ plane with the unit circle sketched in purple: Explain why $\sin{(-\theta)} = -\sin{\theta}$ and...

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: Use the unit circle and indicated triangle below to find the exact value of the sine and cosine of the special angle $\pi/4.$...

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: In this task, you will show how all of the sum and difference angle formulas can be derived from a single formula when combined with relations you have...

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: The points on the graphs and the unit circle below were chosen so that there is a relationship between them. Explain the relationship between the coord...

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: In the triangle pictured above show that \left(\frac{|AB|}{|AC|}\right)^2 + \left(\frac{|BC|}{|AC|}\right)^2 = 1 Deduce that $\sin^2{\theta} + \cos^2{\...

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...

Research physical scientist, Dr. Dalia Kirschbaum, is featured in this short (~3 min.) video. Dr. Kirschbaum explains how the integration of her initial interest in math and her subsequent interest in the science of natural disasters lead to her career focus of landslide modeling. Now part of the NASA Global Precipitation Measurement (GPM) team, she communicates about the GPM mission and data to the public and to others who use it in their work and/or research.

Imagine being the size of an ant. Be careful - a face-to-face encounter with an ant would be scary and potentially life-threatening! But, if you avoided being eaten, you could learn a lot about ant anatomy from a close-up view. Ants have many body parts that are normally hard to see without a magnifying glass or microscope. And each structure has its own special function.

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.

This activity teaches students how to formulate research questions and perform empirical analysis. Students analyse family budgets from late 19th-century industrial workers.

This lesson is a presentation of famous scientist throughout history where the students will learn and take notes about the contributions and discoveries made in science.

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.

Students use wood, wax paper and oil to investigate the importance of lubrication between materials and to understand the concept of friction. Using wax paper and oil placed between pieces of wood, the function of lubricants between materials is illustrated. Students extend their understanding of friction to bones and joints in the skeletal system and become aware of what engineers can do to help reduce friction in the human body as well as in machines.

In this activity, students are introduced to faults. They will learn about different kinds of faults and understand their relationship to earthquakes. The students will build cardboard models of the three different types of faults as they learn about how earthquakes are formed.

Students have the opportunity to create and interpret data from simple daily questions.

Almost everyone has wished at one time or another to be able to fly like a bird. Just the thought of soaring above your city or town without any mechanical device gives us a reason to envy these feathered animals. Also in: French | Spanish

This task provides students the opportunity to make use of units to find the gas need (N-Q.1). The key point is for them to explain their choices. This task provides an opportunity for students to practice MP2, Reason abstractly and quantitatively, and MP3, Construct viable arguments and critique the reasoning of others.

This task allows students to relate addition and subtraction problems to money in a context that introduces the concept of scarcity.