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 two triangles pictured below $m(\angle A) = m(\angle D)$ and $m(\angle B) = m(\angle E)$: Using a sequence of translations, rotations, reflectio...

This geometry lesson shows that that an inscribed angle is half of a central angle that subtends the same arc. [Geometry playlist: Lesson 24 of 31]

This 12-minute video lesson gives the first example of solving an exact differential equation. [Differential Equations playlist: Lesson 6 of 45]

This 15-minute video lesson looks at covariance, variance, and the slope of the regression line. [Statistics playlist: Lesson 71 of 85]

This 12-minute video lesson looks at the T-Statistic Confidence Interval (for small sample sizes). [Statistics playlist: Lesson 52 of 85]

This 10-minute video lesson looks at what happens when the characteristic equations has complex roots. [Differential Equations playlist: Lesson 17 of 45]

This 11-minute video lesson shows how to use the variance of a sample to estimate the variance of a population. [Statistics playlist: Lesson 14 of 85]

This 10-minute video lesson looks at using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. [Differential Equations playlist: Lesson 22 of 45]

This 9-minute video lesson give a Rregression line example. [Statistics playlist: Lesson 67 of 85]

This 8-minute video lesson provides analysis of variance 1: Calculating SST (Total Sum of Squares). [Statistics playlist: Lesson 75 of 85]

This 11-minute video lesson looks at the the central limit theorem and the sampling distribution of the sample mean. [Statistics playlist: Lesson 36 of 85]

This 13-minute video lesson provides analysis of variance 2: Calculating SSW and SSB (total sum of squares within and between). [Statistics playlist: Lesson 76 of 85]

This 15-minute video lesson shows how to find the eigenvectors and eigenspaces of a 2x2 matrix. [Linear Algebra playlist: Lesson 136 of 143]

This site teaches Building Functions to High Schoolers through a series of 1355 questions and interactive activities aligned to 13 Common Core mathematics skills.

This site teaches The Real Number System to High Schoolers through a series of 1090 questions and interactive activities aligned to 8 Common Core mathematics skills.

Module 2 extends the concept of matrices introduced in Module 1.  Students look at incidence relationships in networks and encode information about them via high-dimensional matrices.  Matrix properties are studied as well as the role of the zero and identity matrices.  Students then use matrices to study and solve higher order systems of equations.  Vectors are introduced, and students study the arithmetic of vectors and vector magnitude.  The module ends as students program video games using matrices and vectors.

In this module, students explore and experience the utility of analyzing algebra and geometry challenges through the framework of coordinates. The module opens with a modeling challenge, one that reoccurs throughout the lessons, to use coordinate geometry to program the motion of a robot that is bound within a certain polygonal region of the plane—the room in which it sits. To set the stage for complex work in analytic geometry (computing coordinates of points of intersection of lines and line segments or the coordinates of points that divide given segments in specific length ratios, and so on), students will describe the region via systems of algebraic inequalities and work to constrain the robot motion along line segments within the region.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the role transformations play in defining congruence. The topic of transformations is introduced in a primarily experiential manner in Grade 8 and is formalized in Grade 10 with the use of precise language. The need for clear use of language is emphasized through vocabulary, the process of writing steps to perform constructions, and ultimately as part of the proof-writing process.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

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 aspects of the task and its potential use.