Multiplying and Dividing Fractions
North Carolina Department of Public Instruction
Overview The implementation of the Common Core State Standards in Mathematics (CCSSM) is both an exciting and anxious time for teachers around the country. Part of the excitement is the CCSS inclusion of both the Content Standards and the Standards for Mathematical Practice. The Standards for Mathematical Practice provide a foundation for the process skills that all K-12 students should be developing during every lesson. Overview of the Unit The purpose of this document is to provide teachers with a set of lessons that are standards-based and align with the CCSS Content Standards and Standards for Mathematical Practice. By standards-based, we mean that students are learning mathematics by exploring mathematically-rich tasks and sharing strategies, ideas, and approaches with one another. During these lessons, the teacher’s role is to truly facilitate learning by posing a task, asking questions that guide students’ understanding, and assess students’ mathematical understanding. The phases of each lesson are: • Engage- Students open the lesson by engaging in a brief activity to build upon students’ prior knowledge. • Explore- Students explore a mathematically rich task or activity that includes the main mathematical goals. During this phase, the teacher may model how to play a game or do an activity, but should not model or over teach strategies or procedures. • Explain- Students discuss strategies and mathematical ideas from the Explore phase. The teacher may teach content and emphasize concepts or strategies here. • Elaborate- Students complete a follow-up activity or task that extends their work from Explore and the discussion of concepts in Explain. • Evaluation of Students o Formative Assessment- How can the teacher assess students during the lesson? o Summative Assessment- How can the teacher assess students’ work after the lesson? Resources on the Common Core This document is only a starting resource as teachers begin implementing the CCSS and the Standards for Mathematical Practice. The North Carolina Department of Public Instruction has also written Unpacking Documents available at http://www.ncpublicschools.org/acre/standards/ support-tools/ . These unpacking documents provide specific descriptions of each standard as well as examples. This project was directed by Dr. Drew Polly at UNC Charlotte. Educators who collaborated to create these documents are Gail Cotton, Ryan Dougherty, Tricia Esseck, Marta Garcia, Tery Gunter, and Kayonna Pitchford along with the DPI staff.
Grade 5: Multiplying and Dividing Fractions
Unit Overview: Grade 5 Mathematical Goals In this unit, students will: • Apply and extend their understanding of whole number operations (specifically multiplication and division) to include fractional numbers. • Develop visual models for multiplying and dividing fractions (area models, arrays, bar and number line models) • Make use of benchmarks and other strategies to determine reasonableness of the solutions when operating with fractions • Explore the relationship between two numbers and their product • Interpret and create story contexts related to appropriate operations • Use knowledge of fractions, equivalences and the inverse relationship between multiplication and division to solve problems and develop strategies for operating on fractions. Lessons in Unit This lesson is intended to be taught in the second half of the year at the end of the unit on fractions. Lesson(s) Title and Description 1 Servings at the Fifth Grade Ice Cream Party: Students will solve story problems about ice cream cake servings at a fifth grade party and goal targets for a contest. 2 part: 1 and part: 2 3 Materials: student sheets, colored pencils, graph paper, fraction bars Collecting Recyclables: Students will solve story problems about collecting recyclables....