• Elementary Mathematics Grade 4 Unit 8

    Subject: Mathematics
    Grade: 4 
    Timeline: 13 days
    Unit 8 Title: Measurement

    Unit Overview: 
    In the first few lessons of this unit, students will have the opportunity to review the metric system of length and measure objects.  In previous grades, students studied the perimeter (distance around) and the area (amount of surface) of various geometric figures. This next unit will extend your students’ understanding of geometry by developing and applying formulas for the areas of figures such as rectangles.  The lessons on weight focus on grams and ounces. Students handle and weigh a variety of objects, trying to develop “weight sense” so that they can estimate weights effectively. Finally, we will consider familiar units of capacity (cups, pints, quarts, gallons) and the relationships among them.

    Unit Objectives:
    By the end of this unit, all students are expected to measure using the metric system of length.  Students must also find the area and perimeter of various shapes.  They also need to be able to estimate weights of objects effectively, and measure weight with grams and ounces.  Finally, students must be able to identify the relationships between cups, pints, quarts, and gallons.  

    Focus Standards:
    PA.CCSS.Math.Content.CC.2.4.4.A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit. (4.MD.1, 4.MD.2, 4.MD.3)

    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?” 
    #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.  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 calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

    Concepts - Students will know:
    • The metric system of length
    • Area
    • Perimeter
    • Estimate weights
    • Liquid Measurements
    Competencies -Students will be able to:
    • Explain and convert among the metric system
    • Find the area of various shapes
    • Find the perimeter of various shapes
    • Use their experiences to estimate weights
    • Use a graphic organizer to convert between liquid measurements

    • Unit 8 Progress Check
    • Daily RSA 
    • Optional Quizzes (3)

    Elements of Instruction:
    Learners in 4th grade will extend their understanding of measurement to the metric system.  They will also be able to work with liquid measurements and weights. 

    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 eight include:
    • Line Segment Limbo
    • Rugs and Fences
    • Number Top-It