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: Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is 10%. She leaves a 15% tip on the price of her meal before the s...

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: If 100 dollars in one year gain $3\frac12$ dollars interest, what sum will gain \$38.50 cents in one year and a quarter?...

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: The taxi fare in Gotham City is \$2.40 for the first $\frac{1}{2}$ mile and additional mileage charged at the rate \$0.20 for each additional 0.1 mile....

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: Jamaican sprinter Usain Bolt won the 100 meter sprint gold medal in the 2012 Summer Olympics. He ran the 100 meter race in 9.63 seconds. There are abou...

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: Inflation is a term used to describe how prices rise over time. The rise in prices is in relation to the amount of money you have. The table below show...

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: There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4. There are 180 students at Winthrop Middle School, where the ra...

This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

Many students will not know that when comparing two quantities, the percent decrease between the larger and smaller value is not equal to the percent increase between the smaller and larger value. Students would benefit from exploring this phenomenon with a problem that uses smaller values before working on this one.

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 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.  Upon completion of this course students will have the ability to Analyze proportional relationships and use them to solve real-world and mathematical problems. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models.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 7EdGems Math Grade 7enVisions Grade 7Eureka Math Grade 7Fishtank Plus Math Grade 7HMH Into Math Grade 7Imagine Learning Illustrative Mathematics Grade 7i-Ready Math Grade 7MidSchoolMath Grade 7Open Up Resouces Math Grade 7Reveal Math Grade 7Additional Course Information:  Major work of Grade 7 mathematics focuses on ratios and proportional relationships and arithmetic of rational numbers. Habits 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 Ratios and Proportional Relationships and Expressions and Geometry. Learning this unit will enable students to: Analyze proportional relationships and use them to solve real-world and mathematical problems; and Draw, construct, and describe geometrical figures and describe the relationships between them. 

Engineering analysis distinguishes true engineering design from "tinkering." In this activity, students are guided through an example engineering analysis scenario for a scooter. Then they perform a similar analysis on the design solutions they brainstormed in the previous activity in this unit. At activity conclusion, students should be able to defend one most-promising possible solution to their design challenge. (Note: Conduct this activity in the context of a design project that students are working on; this activity is Step 4 in a series of six that guide students through the engineering design loop.)

This real world problem is appropriate for mental mathematics and students should be encouraged to think through the solution mentally.

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality.  Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions.  Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.

**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 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to “the whole” serves as a foundation for students.  Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations.  Material in early lessons is designed to reinforce students’ understanding by having them use mental math and basic computational skills. To develop a conceptual understanding, students use visual models and equations, building on their earlier work with these.  As the lessons and topics progress and students solve multi-step percent problems algebraically with numbers that are not as compatible, teachers may let students use calculators so that their computational work does not become a distraction.

**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 this activity, students gain first-hand experience with the mechanical advantage of pulleys. Students are given the challenge of helping save a whale by moving it from an aquarium back to its natural habitat into the ocean. They set up different pulley systems, compare the theoretical and actual mechanical advantage of each and discuss their recommendations as a class.

This goal of this task is to give students familiarity using the formula for the area of a circle while also addressing measurement error.