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# High School Mathematics

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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:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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: Michelle, Hillary, and Cory created a YouTube video, and have a plan to get as many people to watch it as possible. They will each share the video with...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/11/2014
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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: Let $a$ and $b$ be real numbers with $a>b>0$ and $\frac{a^3-b^3}{(a-b)^3}=\frac{73}{3}$. What is $\frac{b}{a}$?...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/29/2013
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: For 70 years, Oseola McCarty earned a living washing and ironing other people’s clothing in Hattiesburg, Mississippi. Although she did not earn much mo...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
04/12/2013
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 company uses two different-sized trucks to deliver concrete blocks. The first truck can transport $x$ blocks per trip, and the second can transport ... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 04/01/2013 Unrestricted Use CC BY Rating 0.0 stars 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 profit,P$(in thousands of dollars), that a company makes selling an item is a quadratic function of the price,$x(in dollars), that they charg... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 08/08/2013 Unrestricted Use CC BY Rating 0.0 stars 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: Given the heighth$and volume$V\$ of a certain cylinder, Jill uses the formula r=\sqrt{\frac{V}{\pi h}} to compute its radius to be 20 meters. If a s...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/20/2013
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CC BY
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This task examines, from a mathematical and statistical point of view, how scientists measure the age of organic materials by measuring the ratio of Carbon 14 to Carbon 12. The focus here is on the statistical nature of such dating. This task addresses a very important issue about precision in reporting and understanding statements in a realistic scientific context.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
09/13/2012
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CC BY
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This task is a refinement of Carbon 14 dating'' which focuses on accuracy. Because radioactive decay is an atomic process modeled by the laws of quantum mechanics, it is not possible to know with certainty when half of a given quantity of Carbon 14 atoms will decay. This type of question is very important in science and it also provides an opportunity to study the very subtle question of how errors behave when applying a function: in some cases the errors can be magnified while in others they are lessened.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
09/13/2012
Unrestricted Use
CC BY
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This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.

Subject:
Algebra
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/15/2012
Unrestricted Use
CC BY
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This task is a somewhat more complicated version of "Accurately weighing pennies I'' as a third equation is needed in order to solve part (a) explicitly. Instead, students have to combine the algebraic techniques with some additional problem-solving (numerical reasoning, informed guess-and-check, etc.)

Subject:
Algebra
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/15/2012
Unrestricted Use
CC BY
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The problem statement describes a changing algae population as reported by the Maryland Department of Natural Resources. In part (a), students are expected to build an exponential function modeling algae concentration from the description given of the relationship between concentrations in cells/ml and days of rapid growth (F-LE.2).

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
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This task provides a construction of the angle bisector of an angle by reducing it to the bisection of an angle to finding the midpoint of a line segment. It is worth observing the symmetry -- for both finding midpoints and bisecting angles, the goal is to cut an object into two equal parts. The conclusion of this task is that they are, in a sense, of exactly equivalent difficulty -- bisecting a segment allows us to bisect and angle (part a) and, conversely, bisecting an angle allows us to bisect a segment (part b). In addition to seeing how these two constructions are related, the task also provides an opportunity for students to use two different triangle congruence criteria: SSS and SAS.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/11/2013
Unrestricted Use
CC BY
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In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Subject:
Algebra
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
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The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc) shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The problem combines the ideas of ratio and proportion within the context of density of matter.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/04/2013
Unrestricted Use
CC BY
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In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.

Subject:
Geometry
Mathematics
Trigonometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
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The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
Rating
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In this real world problem students solve questions based on the relationship between production costs and price.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
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This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
Rating
0.0 stars

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