The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction.

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 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume. Upon completion of this course students will have the ability to: Write and interpret numerical expressions; Analyze patterns and relationships; Understand the place value system; Perform operations with multi-digit whole numbers and with decimals to hundredths; Use equivalent fractions as a strategy to add and subtract fractions; Apply and extend previous understandings of multiplication and division to multiply and divide fractions; Convert like measurement units within a given measurement system; Represent and interpret data; Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition; Graph points on the coordinate plane to solve real-world and mathematical problems; and Classify two-dimensional figures into categories based on their properties. Aligned Core Resources:  Core resources is a local control decision.  Ensuring alignment of resources to the standards is critical for success.  There are tools that are available to assist in evaluating alignment, such as CCSSO’s Mathematics Curriculum Analysis Project and Student Achievement Partner’s Instructional Materials Evaluation Tool.  In addition EdReports and Louisiana Believes are two sources of completed reviews for a variety of resources.  Connecticut is currently working on providing additional alignment guidance for the most frequently used resources across the state. 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.  Achievement First Math Grade 5enVisions Grade 5Eureka Grade 5Fishtank Plus Math Grade 5HMH into Math Grade 5Imagine Learning Illustrative Mathematics Grade 5i-Ready Math Grade 5MidSchoolMath Grade 5Reveal Math Grade 5Financial Literacy Connections:The State of Connecticut is committed to implementing high-quality Financial Literacy instruction at all grade levels beginning in kindergarten. Financial Literacy supports students’ academic performance in several subject areas. The K-5 Model Math Curricula embeds tasks that align the mathematical content and skill to the essential Financial Literacy concepts such as income, spending, saving, investing, credit and risk.  The concepts contained in the learning tasks are designed to be rich, hands-on activities with developmentally appropriate real-world connections.  The tasks are identified by grade level and embedded in the appropriate units so that students can demonstrate mastery of what they need to know and be able to do by the end of their K-5 school experience. In this way, elementary students will be prepared to build upon Financial Literacy knowledge as they advance through middle and high school.Additional Course Information:  Major work of Grade 5 mathematics focuses on multiplication and division of whole numbers and fractions including concepts, skills, and problem solving. Fluencies expected for Grade 5 include: Multi-digit multiplication 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 task requires students to recognize both "number of groups unknown" and "group size unknown" division problems in the context of a whole number divided by a unit fraction.

This hands-on activity explores five different forms of erosion (chemical, water, wind, glacier and temperature). Students rotate through stations and model each type of erosion on rocks, soils and minerals. The students record their observations and discuss the effects of erosion on the Earth's landscape. Students learn about how engineers are involved in the protection of landscapes and structures from erosion. Math problems are included to help students think about the effects of erosion in real-world scenarios.

Grade 5’s Module 4 extends student understanding of fraction operations to multiplication and division of both fractions and decimal fractions.  Work proceeds from interpretation of line plots which include fractional measurements to interpreting fractions as division and reasoning about finding fractions of sets through fraction by whole number multiplication.  The module proceeds to fraction by fraction multiplication in both fraction and decimal forms.  An understanding of multiplication as scaling and multiplication by n/n as multiplication by 1 allows students to reason about products and convert fractions to decimals and vice versa.  Students are introduced to the work of division with fractions and decimal fractions.  Division cases are limited to division of whole numbers by unit fractions and unit fractions by whole numbers.  Decimal fraction divisors are introduced and equivalent fraction and place value thinking allow student to reason about the size of quotients, calculate quotients and sensibly place decimals in quotients.  Throughout the module students are asked to reason about these important concepts by interpreting numerical expressions which include fraction and decimal operations and by persevering in solving real-world, multistep problems which include all fraction operations supported by the use of tape diagrams.

**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.**

This task provides a context for performing division of a whole number by a unit fraction. This problem is a "How many groups?'' example of division.

The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.

Students explore building a pyramid, learning about the simple machine called an inclined plane. They also learn about another simple machine, the screw, and how it is used as a lifting or fastening device. During a hands-on activity, students see how the angle of inclination and pull force can make it easier (or harder) to pull an object up an inclined plane.