• Elementary Mathematics Grade 4 Unit 4


    Subject: Mathematics
    Grade: 4 
    Timeline: 15 days
    Unit 4 Title: Fractions

    Unit Overview: 
     
    This unit will give students the opportunity to explore fractions--of a region, on a number line, and of a set.  Students will also be developing their understanding of mixed numbers and improper fractions. Students will generate multiple names for fractions (equivalent fractions), determine the simplest form of a fraction, and compare fractions. Finally, students will compute with fractions-addition, subtraction, and multiplication of fractions and whole numbers.

    Unit Objectives:
     
    At the end of this unit, students will have developed a deep understanding of concepts related to fractions, which will be built upon in future grades.

    Focus Standards:
     
    PA.CCSS.Math.Content.CC.2.1.4.C.1 Extend the understanding of fractions to show equivalence and ordering. (4.NF.1, 4.NF.2)
    PA.CCSS.Math.Content.CC.2.1.4.C.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3, 4.NF.4)

    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 simply jumping into a solution attempt. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they 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 complementary abilities to bear on problems involving quantitative relationships.  Quantitative reasoning entails habits of creating a 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. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
     
    #5 Use appropriate tools strategically.  
     
    Mathematically proficient students in First Grade have access to a variety of concrete (e.g. 3-dimensional solids, ten frames, number balances, number lines) and technological tools (e.g., virtual manipulatives, calculators, interactive websites) and use them to investigate mathematical concepts. They select tools that help them solve and/or illustrate solutions to a problem. They recognize that multiple tools can be used for the same problem- depending on the strategy used. For example, a child who is in the counting stage may choose connecting cubes to solve a problem. While, a student who understands parts of number, may solve the same problem using ten-frames to decompose numbers rather than using individual connecting cubes. As the teacher provides numerous opportunities for students to use educational materials, first grade students’ conceptual understanding and higher-order thinking skills are developed.
     
    #6 Attend to precision.  
     
    Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

    Concepts - Students will know:
    • Fractions of a region
    • Fractions of a set
    • Fractions on a number line
    • Fraction operations
    Competencies -Students will be able to:
    • Decompose fractions
    • Solve problems involving fractions in a set
    • Complete number lines using fractions
    • Add, Subtract, and Multiply fractions

    Assessments:
    • Unit 4 Progress Check
    • Daily RSA 
    • Optional Quizzes (3)

    Elements of Instruction:
     
    Learners in 4th grade will extend their understanding of fractions of a region from third grade to fractions of a set and fractions on number line.  Students will also use fractions to add, subtract, and multiply.  There will be opportunities to solve word problems with fractions.

    Differentiation:
     
    Each lesson has differentiation options for each portion of the lesson.  Additional differentiation options are listed with directions and student masters in the Teacher’s Guide to Games.

    Interdisciplinary Connections:
    • Mental Math and Math message routines

    Additional Resources / Games:
     
    Students will play a variety of games that directly support the content of the lesson and the overall goals for the unit. Games for unit four include:
    • Fraction Match
    • Fraction Top-It