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...

In this lesson, students model their current conception of computers using a variety of self-selected media. They explain why they believe something is a computer.

In this lesson, students reimagine an everyday object as a computer, identify what problem the computer helps to solve, and decide how it receives input, and how it outputs. They earn their first badge: Impacts of Computing!

In this lesson, students develop their own secret handshake sequences using three or more moves. They record their sequences with symbols, revise them based on challenge criteria, and socially compare them with their classmates.

In this lesson, students identify visual patterns in everyday school settings and decide how to use them for problem solving. Later, students create and analyze playful patterns of their own to solve simple problems.

In this lesson, students practice decomposition by breaking a song and a dance into parts. Students creatively express themselves by choreographing their own "Funky Robot" dance, then decomposing it to teach classmates their sequence.

In this lesson, students practice algorithms by following step-by-step origami directions. Later, students choose an origami algorithm to add-on to, to create an original new shape. Students use inspiration from the character Joey, from More-igami, to persevere.

In this lesson, students will take turns using the Four Button Protocol to retell popular nursery rhymes by sequencing either three or four events. The lesson is flexible enough to accommodate any narrative, such as More-igami, and others students are studying during their Reading and Writing Workshop!

In this lesson, students will take turns using the Four Button Protocol to retell popular fairy tales by sequencing four to six events. The lesson is flexible enough to accommodate any narrative, such as More-igami, and others students are studying during their Reading and Writing Workshop!

In this lesson, students will take turns using the Four Button Protocol to retell their own stories from Writing Workshop!

In this introductory lesson, students build on one another's discoveries to articulate the functions of each button and switch on a Bee-Bot. Students then apply this knowledge to program a dance or game for their group-mates to actively engage with.

Using The Very Hungry Caterpillar as an anchor, students create fantasy stories of what Bee-Bot will eat on its way from one point to another on their Color Shape Mats. Students use a flat paper Bee-Bot to rehearse multiple paths before selecting one and recording it on a sheet. As a group, each child follows the Three Button Protocol to help the Very Hungry Bee-Bot eat its way to the finish!