The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

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 Expressions and Equations and Functions domain.  Learning this unit will enable students to: Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations  Define, evaluate, and compare functions. Use functions to model relationships between quantities. 

Students utilize data tables culled from the US DOE Energy Information Agency to create graphs that illustrate what types of energy we use and how we use it. An MS Excel workbook with several spreadsheets of data is provided. Students pick (or the teacher assigns) one of the data tables from which students create plots and interpret the information provided. Student groups share with the class their interpretations and new perspectives on energy resources and use.

Students experiment with an online virtual laboratory set at a skate park. They make predictions of graphs before they use the simulation to create graphs of energy vs. time under different conditions. This simulation experimentation strengths their comprehension of conservation of energy solely between gravitational potential energy and kinetic energy

In Grades 6 and 7, students worked with data involving a single variable.  Module 6 introduces students to bivariate data.  Students are introduced to a function as a rule that assigns exactly one value to each input.  In this module, students use their understanding of functions to model the possible relationships of bivariate data.  This module is important in setting a foundation for students’ work in algebra in Grade 9.

**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 primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Students will breed fruit flies through several generations and record their data using mathematical models in order to demonstrate the inheritance of trait variations.

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.

This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.

This task presents an opportunity to explore a more general and non-algebraic view of functions.

Students use authentic spectral data from the Cassini mission of Saturn and Saturn's moon, Titan, gathered by instrumentation developed by engineers. Taking these unknown data, and comparing it with known data, students determine the chemical composition of Saturn's rings and Titan's atmosphere.

In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.

Students are introduced to the similarities and differences in the behaviors of elastic solids and viscous fluids. Several types of fluid behaviors are described Bingham plastic, Newtonian, shear thinning and shear thickening along with their respective shear stress vs. rate of shearing strain diagrams. In addition, fluid material properties such as viscosity are introduced, along with the methods that engineers use to determine those physical properties.