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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: Given that $\overleftrightarrow{DE}\parallel\overleftrightarrow{AC}$ in the diagram below, prove that $a + b + c = 180.$ Explain why this result holds ...

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.

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 $\ell$ and $m$ are parallel lines with $Q$ a point on $\ell$ and $P$ a point on $m$ as pictured below: Also labelled in the picture is the midp...

CSDE Model Curricula Quick Start GuideEquitable and Inclusive Curriculum  The CSDE believes in providing a set of conditions where learners are repositioned at the center of curricula planning and design. Curricula, from a culturally responsive perspective, require intentional planning for diversity, equity, and inclusion in the development of units and implementation of lessons. It is critical to develop a learning environment that is relevant to and reflective of students’ social, cultural, and linguistic experiences to effectively connect their culturally and community-based knowledge to the class. Begin by connecting what is known about students’ cognitive and interdisciplinary diversity to the learning of the unit. Opposed to starting instructional planning with gaps in students’ knowledge, plan from an asset-based perspective by starting from students’ strengths. In doing so, curricula’s implementation will be grounded in instruction that engages, motivates, and supports the intellectual capacity of all students.Course Description:  In Grade 8, insructional time should focus on three critical areas: (1) formulating and resoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3)  analyzing two-and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. Upon completion of this course students will have the ability to:Know that there are numbers that are not rational, and approximate them by rational numbers;Work with radicals and integer exponents in expressions and equations;Understand the connections between proportional relationships, lines, and linear equations;Define, evaluate, and compare functions;Use functions to model relationships between quantities;Understand congruence and similarity using physical models, transparencies, or geometry software;Undestand and apply the Phthagorean Theorem;Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres; Aligned Core Resources:  It is critical that curriculum be implemented using high quality instructional materials to ensure all students meet Connecticut’s standards. Ensuring alignment of resources to the standards is critical for success. There are tools that are available to districts to assist in evaluating alignment of resources, such as CCSSO’s Mathematics Curriculum Analysis Project and Student Achievement Partner’s Instructional Materials Evaluation Tool.   In addition, there exist compilations of completed reviews from a variety of resources. Some of these include but are not limited to EdReports, Louisiana Believes, CURATE, and Oregon Adopted Instructional Materials.Aligned Core Programs:  The CSDE in partnership with SERC has engaged with providers of high-quality vetted resources to provide additional alignment guidance to the CSDE model curriculum.  High-quality instructional resources are critical for improving student outcomes. The alignment guidance is intended to clarify content and support understanding for clear implementation and coherence. Materials selection is a local control decision and these documents have been provided from participating publishers to assist districts in implementation. Use of the materials from these publishers is not required. These aligned core programs meet expectations as reported by EdReports. If your resource is not listed below, you are encouraged to review EdReports to ensure the alignment of your resource to the Connecticut Core Standards. Strong alignment of curricula and instructional materials have the potential to support student engagement of meaningful grade level content daily and teacher growth.  Carnegie Learning Math Grade 8EdGems Math Grade 8enVisions Grade 8Eureka Math Grade 8Fishtank Plus Math Grade 8HMH Into Math Grade 8Imagine Learning Illustrative Mathematics Grade 8i-Ready Math Grade 8MidSchoolMath Grade 8Open Up Resouces Math Grade 8Reveal Math Grade 8Additional Course Information:  Major work of Grade 8 mathematics focuses on linear equations and linear functionsHabits of Mind/SEIH/Transferable Skills Addressed in the Course:   The Standards for Mathematical Practice describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics. They describe student behaviors, ensure an understanding of math, and focus on developing reasoning and building mathematical communication. Therefore, the following should be addressed throughout the course: Make sense of problems & persevere in solving them Reason abstractly & quantitatively Construct viable arguments & critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for & make use of structure Look for & express regularity in repeated reasoning   

Unit Overview/Summary - FOCUS: This unit focuses on the Geometry domain.  Learning this unit will enable students to: Understand congruence and similarity using physical models, transparencies, or geometry software. 

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions. In the case of reflecting a rectangle over a diagonal, the reflected image is still a rectangle and it shares two vertices with the original rectangle.

ile patterns will be familiar with students both from working with geometry tiles and from the many tiles they encounter in the world. Here one of the most important examples of a tiling, with regular hexagons, is studied in detail. This provides students an opportunity to use what they know about the sum of the angles in a triangle and also the sum of angles which make a line.

This task aims at explaining why four regular octagons can be placed around a central square, applying student knowledge of triangles and sums of angles in both triangles and more general polygons.