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Fraction Models

  • Fraction Models

    Grade: 3rd to 5th, 6th to 8th

    Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally, there are length, area, region, and set models. Adjust numerators and denominators to see how they alter the representations and models. Use the table to keep track of interesting fractions.

    This interactive is optimized for your desktop and tablet.

    Activity

    Instructions

    Modes

    Choose Length, Area, Region, or Set on the bottom right to show different representations of the fractions. Set also lets you choose from four different objects. 

    How to Use

    • Adjust the value of the numerator and denominator by: moving the slider, using the + or – on either side of the sliders, or entering the values directly in the boxes.
    • Change the possible denominator values using the Narrow Range, Limited, and Wide Range tabs at the top.
    • You can also change values on the model. Click on sections to add or remove them or use or click + or – at the bottom of the model space to add or remove whole units.
      Note: The squares button at the bottom left of the model space shows or hides the sections. To add or remove sections, they must be shown.
    • Record fractions to the table using the + button above the table. Click individual entries to bring up the model in the model space. Move entries by selecting them and clicking below in the empty table space. Delete entries using the – button above the table. Delete all entries using the × button.
    • On the upper right hand corner of the interactive, students can choose to save their work as a PNG, or print it.
     

    Exploration

    • Adjust the numerator and denominator at the bottom to change the fraction. What is the result? How does the result relate to the values shown for mixed number, decimal, and percent?
    • When the numerator is greater than the denominator, what do you notice? What does the picture look like if the numerator is greater than the denominator? What if the numerator is less than the denominator?
    • Using the set model, start with the fraction 7/4. Add the fraction to the table. What is the decimal equivalent? Change the denominator to 8 and add and remove sections until the decimal is the same as it was for 7/4. Add this result to the table. Try to find 3 more fractions equivalent to 7/4 and record these to the table. What do you notice about the values in the table? Change to the length model and look at each fraction's model. What do you notice?
     

    Objectives and Standards

    NCTM Standards and Expectations
    • 3-5
    • 6-8
    • Number and Operations