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. Here are the first few lines of the commentary for this task: Alysha really wants to ride her favorite ride at the amusement park one more time before her parents pick her up at 2:30 pm. There is a very long line ...

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 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.  Upon completion of this course students will have the ability to:Understand ratio concepts and use ratio reasoning to solve problems. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Multiply and divide multi-digit numbers and find common factors and multiples. Apply and extend previous understandings of numbers to the system of rational numbers. Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables. Solve real-world and mathematical problems involving area, surface area, and volume. Develop understanding of statistical variability. Summarize and describe distributions.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 6EdGems Math Grade 6enVisions Grade 6Eureka Math Grade 6Fishtank Plus Math Grade 6HMH Into Math Grade 6Imagine Learning Illustrative Mathematics Grade 6i-Ready Math Grade 6MidSchoolMath Grade 6Open Up Resouces Math Grade 6Reveal Math Grade 6Additional Course Information:  Major work of Grade 6 mathematics focuses on ratios and proportional relationships and early expressions and equations.  Fluencies required upon completion of grade 6 include multi-digit division and multi-digit decimal operations. 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  

This unit focuses on the Number Systems domain and provides an opportunity to apply number systems content within the context of geometry.  Learning in this unit will enable students to: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.Compute fluently with multi-digit numbers and find common factors and multiples Solve real-world and mathematical problems involving area, surface area, and volume.  

One common mistake students make when dividing fractions using visuals is the confusion between remainder and the fractional part of a mixed number answer.

The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division.

This task builds on a fifth grade fraction multiplication task and uses the identical context, but asks the corresponding ŇNumber of Groups UnknownÓ division problem.

This task builds on a fifth grade fraction multiplication task and uses the identical context, but asks the corresponding ŇNumber of Groups UnknownÓ division problem.

In Module 1, students used their existing understanding of multiplication and division as they began their study of ratios and rates.  In Module 2, students complete their understanding of the four operations as they study division of whole numbers, division by a fraction and operations on multi-digit decimals.  This expanded understanding serves to complete their study of the four operations with positive rational numbers, thereby preparing students for understanding, locating, and ordering negative rational numbers (Module 3) and algebraic expressions (Module 4).

**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.**

These two fraction division tasks use the same context and ask ŇHow much in one group?Ó but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.

These problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.

This is the first of two fraction division tasks that use similar contexts to highlight the difference between the ŇNumber of Groups UnknownÓ a.k.a. ŇHow many groups?Ó (Variation 1) and ŇGroup Size UnknownÓ a.k.a. ŇHow many in each group?Ó (Variation 2) division problems.

This is the second of two fraction division tasks that use similar contexts to highlight the difference between the ŇNumber of Groups UnknownÓ a.k.a. ŇHow many groups?Ó (Variation 1) and ŇGroup Size UnknownÓ a.k.a. ŇHow many in each group?Ó (Variation 2) division problems.

This task builds on a fifth grade fraction multiplication task, Ň5.NF Running to School, Variation 1.Ó This task uses the identical context, but asks the corresponding ŇNumber of Groups UnknownÓ division problem. See Ň6.NS Running to School, Variation 3Ó for the ŇGroup Size UnknownÓ version.

It is much easier to visualize division of fraction problems with contexts where the quantities involved are continuous. It makes sense to talk about a fraction of an hour. The context suggests a linear diagram, so this is a good opportunity for students to draw a number line or a double number line to solve the problem.

This task could be used in instructional activities designed to build understandings of fraction division. With teacher guidance, it could be used to develop knowledge of the common denominator approach and the underlying rationale.