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...

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 $\frac{b}{a}$?...

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...

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 $...

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...

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 height $h$ 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...

This is a lesson plan created to assist in teaching integers and absolute value.  Here is an overview of this lesson:  (1) Hook: number line game to introduce absolute value.. (2) Teach: student notes, practice, and video to build knowledge.  (3) Apply/Assess: game using a deck a cards per partnership with teach observation.  Absolute Value of Integers © 2022 by Laura Zwahlen is licensed under CC BY-NC-SA 4.0 

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.

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.

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.

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.)

This is a 7th Grade Math Lesson on Adding & Subtracting Positive & Negative Integers. It is designed to be a 45-50 minute face-to-face lesson, however, some materials could be adapted for an online modality. Includes materials, and interactive activities for students to participate in. 

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).

This unit was created as an introductory/review unit for Algebra II to allow for a review of main concepts needed to progress in Algebra II. However, it could also be used in Algebra I to introduce for the first time real numbers; number operations; and equations, expressions, and inequalities.

This lesson will incorporate the use of the Keynote app on the iPad. Students will need to demonstrate their understanding of multiple representations of an arithmetic sequence. Students will spend a class period creating the presentation.

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.

This lesson plan was created to introduce Angles and Equations for 7th-grade math.

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.

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.

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.