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This task addresses many standards regarding the description and analysis of bivariate quantitative data, including regression and correlation. Students should recognize that the pattern shown is one of a strong, positive, linear association, and thus a correlation coefficient value near +1 is plausible. Students should also be able to interpret the slope of the least-squares line as an estimated increase in y per unit change in x (and thus for a 3 unit increase in x, students should expect an estimated increase in y that equals 3 times the model's slope value).

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
02/19/2013 Unrestricted Use
CC BY
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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: A seven-year-old boy has a favorite treat, Super Fruity Fruit Snax. These "Fruit Snax" come in pouches of 10 snack pieces per pouch, and the pouches ar...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/22/2013 Unrestricted Use
CC BY
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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: Ancient Egyptians used unit fractions, such as $\frac{1}{2}$ and $\frac{1}{3}$, to represent all other fractions. For example, they might express the n...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/24/2013 Unrestricted Use
CC BY
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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: When Marcus started high school, his grandmother opened a college savings account. On the first day of each school year she deposited money into the ac...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/13/2013 Unrestricted Use
CC BY
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The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even.

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/18/2013 Unrestricted Use
CC BY
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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: It takes Clea 60 seconds to walk down an escalator when it is not operating, and only 24 seconds to walk down the escalator when it is operating. How m...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/30/2013 Unrestricted Use
CC BY
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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: Sara's doctor tells her she needs between 400 and 800 milligrams of folate per day, with part coming from her diet and part coming from a multi-vitamin...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/27/2013 Unrestricted Use
CC BY
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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 product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the ...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
10/14/2013 Unrestricted Use
CC BY
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This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/21/2013 Unrestricted Use
CC BY
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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 each of the equations below, rewrite the equation, solving for the indicated variable If $F$ denotes a temperature in degrees Fahrenheit and $C$ is ...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/20/2014 Unrestricted Use
CC BY
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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 rectangle $ABCD$ with segment $\overline{MN}$ drawn where $M$ is the midpoint of $\overline{BC}$ and $N$ is the midpoint of \o... Subject: Secondary Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 08/20/2013 Unrestricted Use CC BY Rating This task provides a simple but interesting and realistic context in which students are led to set up a rational equation (and a rational inequality) in one variable, and then solve that equation/inequality for an unknown variable. Subject: Secondary Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 12/15/2012 Unrestricted Use CC BY Rating 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: Consider three points in the plane,P=(-4, 0), Q=(-1, 12)$and$R=(4, 32)$. Find the equation of the line through$P$and$Q. Use your equation in (a... Subject: Secondary Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 09/09/2013 Unrestricted Use CC BY Rating 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: Jason and Arianna are working on solving the equations \begin{align} 6x + 17y &= 100\\ 5x + 9y &= 86. \end{align} Rounding their answer to the nearest ... Subject: Secondary Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 03/20/2014 Unrestricted Use CC BY Rating 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: Without graphing, construct a system of two linear equations where(-2,3)is a solution to the first equation but not to the second equation, and whe... Subject: Secondary Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 05/26/2013 Unrestricted Use CC BY Rating 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 sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?... Subject: Secondary Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 03/27/2013 Unrestricted Use CC BY Rating 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: This task will investigate the intersection points of the circleC$of radius 1 centered at$(0,0)$and different lines passing through the point$(0,...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
09/11/2013 Unrestricted Use
CC BY
Rating

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 following is a student solution to the inequality \frac{5}{18} - \frac{x-2}{9} \leq \frac{x-4}{6}. \begin{align} \frac{5}{18} - \frac{x-2}{9} & \le...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
09/11/2013 Unrestricted Use
CC BY
Rating

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: Enrico has learned a geometric technique for ''completing the square'' to find the solutions of quadratic equations. To solve the equation \$x^2 + 6x + ...

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/20/2014 Unrestricted Use
CC BY
Rating

The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

Subject:
Secondary Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics