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: How do the values of the three functions $f(x) = 2x$, $g(x) = x^2$ and $h(x) = 2^x$ compare for large positive and negative values of $x$? Explain your...

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: According to ancient legend, Dido made a deal with a local ruler to obtain as much land as she could cover with an oxhide. Dido interpreted ''cover'' i...

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 are pictures of the first three triangular numbers: In general, the $n^{\text{th}}$ triangular number is the total number of dots in $n$ columns ...

This activity is an extension of the FOSS Variables Lifeboat investigation. Students choose a lifeboats variable to investigate, write up an experiment based on the variable to be tested, test the variable, and create a lifeboats investigation poster to share their results.

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 we will explore the effect that changing the parameters in a sinusoidal function has on the graph of the function. A general sinusoidal fu...

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 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 first create factor posters for a variety of different numbers that will be displayed in the classroom to be utilized as a resource throughout the school year. They make discoveries about factors using color tiles, represent their discoveries using graph paper, and display their information on poster board as find factors of an assigned number. The plan includes a list of materials, questions, assessment options, and extensions.

This is an interactive applet game exercises a student's factoring ability. A student can play against the computer or against a friend on grids containing the numbers 1-30, 1-49, or 1-100. Each player in turn chooses a number from the board, and then the opponent claims all of its remaining proper factors. A player's score is the sum of all the numbers and factors she/he has chosen. When there are no numbers remaining with unclaimed factors, the game ends and the player with the greater total is the winner.

An online, interactive, multimedia math investigation. The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.

In this math game, learners identify the factors of a number to earn points. Although practicing a mundane skill, learners enjoy the work because of the game scenario. Built into this game is cooperative learning--learners check one another's work before points are awarded. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

When students play the Factor Trail game, they have to identify the factors of a number to earn points. Built into this game is cooperative learning Š—” students check one another's work before points are awarded. The score sheet used for this game provides a built-in assessment tool that teachers can use to check their students' understanding.

This interactive applet allows a student to visually explore the concept of factors by creating different rectangular arrays for a number. The user constructs the array by clicking and dragging on a grid. The length and width of the array are factors of the number. A student can elect an option of a randomly selected number or the student selects his own number between 2 and 50. Exploration questions are included to promote student discovery of mathematical concepts with factors.