• Elementary Mathematics Grade 4 Unit 7

    Subject: Mathematics
    Grade: 4 
    Timeline: 10 days
    Unit 7 Title: Decimals

    Unit Overview: 
    This unit will give students the opportunity to review and develop decimal skills.  They have experience using decimals for money.  This unit will help them develop more experiences for using decimals in everyday life.  For example, thermometers, measuring distances, measuring times, and gasoline mileage can all be in decimal form.  Students will also have the opportunity to extend their place-value charts to include decimals.  Using the metric system of measurement, students will be converting one measurement to another.  

    Unit Objectives:
    At the end of this unit, students must be able to read and write decimals.  They will also be able to build decimals using Base-10 blocks.  Comparing and ordering decimals must also be mastered by the end of the unit.  Students must be able to convert measurements in the metric system.     

    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.3  Connect decimal notation to fractions, and compare decimal fractions (base
    10 denominator, e.g., 19/100). (4.NF.6, 4.NF.7)

    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: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. 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.
    #3 Construct viable arguments and critique the reasoning of others. 
    Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. 
    #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 consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course 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 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. In the elementary grades, students give carefully formulated explanations to each other. 

    Concepts - Students will know:
    • Decimals are parts of whole
    • Decimals are found in our everyday lives
    • Decimals can be used in place of fractions
    Competencies -Students will be able to:
    • Name the part of the whole in decimal form
    • Name decimals as measurement, money, and base-10 blocks
    • Convert decimals to fractions

    • Unit 7 Assessment
    • Daily RSA
    • Optional Quizzes (3)

    Elements of Instruction:
    Learners in 4th grade will extend their understanding of decimals from third grade involving money, to understanding how to compare, order, and use decimals to name fractional parts. They will also be able to convert decimals and fractions from one form to the other. 

    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:
    Student will play various games to enhance their abilities to construct and measure angles. These games include:
    • Decimal Top-It
    • Base-10 Exchange