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.

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 picture below, the purple circle is the set of points in the plane whose distance from the origin (marked as $A$) is 1, often called the unit ci...

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: Suppose that $\cos\theta = \frac{2}{5}$ and that $\theta$ is in the 4th quadrant. Find $\sin\theta$ and $\tan\theta$ exactly....

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 aspects of the task and its potential use.

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...

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

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.

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

This task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator.