• Elementary Mathematics Grade 5 Unit 7


    Subject: Mathematics
    Grade: 5
    Timeline: 22 days
    Unit 7 Title: Bits and Pieces II

    Unit Overview: 
     
    This unit focuses on understanding and developing systematic ways to add, subtract, multiply, and divide fractions. While working on this unit, students will investigate interesting problem situations to help them develop algorithms for fraction computation.  In addition, students will use benchmarks and number and operation sense to estimate solutions for computations to help them decide if their answers are reasonable.

    Unit Objectives:
     
    At the end of this unit, all students must be able to add, subtract, multiply, and divide fractions.      

    Focus Standards:
     
    PA.CCSS.Math.Content.CC.2.1.5.C.1 Use the understanding of equivalency to add and subtract fractions. (5.NF.1, 5.NF.2) 
    PA.CCSS.Math.Content.CC.2.1.5.C.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (5.NF.3, 5.NF.4, 5.NF.5) 

    Mathematical Practice Standards:  
     

    #1 Make sense of problems and persevere in solving them.
     
    Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway, rather than jumping into a solution attempt. They monitor and evaluate their pathway and change course if necessary. Mathematically proficient students check their answers to problems using a different method and continually ask themselves, “Does this make sense?” 
     
    #2 Reason Abstractly and Quantitatively.
     
    Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complimentary abilities to bear on problems involving quantitative relationships: the ability to decontextualize and the ability to contextualize. Quantitative reasoning entails habits of creating coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 
     
    #4 Model with mathematics.  
     
    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation.  
     
    #5 Use appropriate tools strategically.
     
    Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, or a calculator. Proficient students are sufficiently familiar with tools appropriate for their grade to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.   
     
    #6 Attend to precision.
     
    Mathematically proficient students try to communicate precisely to others. They use clear definitions in discussion with others and in their own reasoning. They are careful about specifying units of measure, specifying axes and use careful calculations. 
     
    #7 Look for and make use of structure.  
     
    Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. 
     
    #8 Look for and express regularity and repeated reasoning.
     
    Mathematically proficient students notice if calculations are repeated and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11, that they are repeating the same calculations over and over again and conclude they have a repeating decimal. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.  

    Concepts - Students will know:
    • Benchmark fractions
    • How to add fractions
    • How to subtract fractions
    • How to multiply fractions
    • How to divide fractions
    Competencies -Students will be able to:
    • Add fractions
    • Subtract fractions
    • Multiply fractions
    • Divide fractions

    Assessments:
     
    Formative Assessments:
    • Informal assessments on learning targets
    • Exit Slips
    • Quizzes
    • Self-Assessment
    Summative Assessment:
    • Assessment- Bits and Pieces II

    Elements of Instruction:
     
    With the Grade 4 Common Core State Standards stating that students should be fluent with benchmark fractions and decimals, they should be able to use this knowledge to convert among decimals, percents, and fractions of all amounts. They will be able to develop a deeper understanding of the fractions in everyday life.

    Differentiation:
     
    Each lesson and/or unit offers a wide variety of ways to differentiation for all levels of learners.  These include:
    • Special Need Handbook (adapting instruction/lessons)
    • Unit Projects
    • Spanish Additional Practice and Skills guide
    • Strategies for English Language Learners Guide
    • “Extension” homework questions

    Interdisciplinary Connections:
    • Mathematical Reflections
    • “Did You Know?” sections
    • phschool.com and web codes
    • “Connections” homework questions
    • The real-world context embedded in lesson problems 

    Additional Resources / Games:
     
    CMP2 and/or the Erie School District provide the following additional resources to aid students in achieving mathematical success. 
    • Additional Practice worksheets per investigation
    • Skills Review worksheets to target key components of each investigation
    • Parent letter to be sent home prior to beginning the unit to share with parents the skills, goals, and 
    • expectations of the coming unit.
    • Assessment Resources workbook with extra test items (multiple choice, essay, open ended, 
    • question bank, etc)
    • Investigation specific pre-generated notebooks that include tables, graphs, problem numbers, and all 
    • other items students may need to complete the investigation and all its parts.  Students are provided
    • with one per unit. 
    • Reflection questions at the end of each investigation to assess students’ comprehension of key
    • concepts. 
    • phschool.com and web codes
    • Transparencies of models, graphs, etc used within lesson(s)