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Comparing Fractions and Decimals

Unit Plan

Comparing Fractions and Decimals

Objectives

In this unit, students are introduced to the relationship between fractions and decimals. Students will:

  • use benchmark fractions to compare fractions.
  • order fractions from least to greatest.
  • compare fractions.
  • solve “fair share” problems involving fractions.
  • represent models as both fractions and decimals.
  • write equivalent fractions and decimals.
  • add fractions.

Essential Questions

How are relationships represented mathematically?
How can mathematics support effective communication?
How is mathematics used to quantify, compare, represent, and model numbers?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
  • How is mathematics used to quantify, compare, represent, and model numbers?
  • How are relationships represented mathematically?
  • What does it mean to estimate or analyze numerical quantities?
  • What makes a tool and/or strategy appropriate for a given task?

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.


Formative Assessment

  • View

    Multiple-Choice Items:

     

    Use the fraction strip below to answer question 1.

     

     

    1. Which fraction is represented by the shaded section of the fraction strip?

     

            A    

            B    

            C    

            D    

     

     

     

    The number line below may be used to help answer questions 2 and 3.

     

     

    1. Which fraction is nearest to ?

            A    

            B    

            C    

            D    

    1. Which fraction is nearest to 1?

     

            A       

            B       

            C       

            D       

     

     

     

    Use the fractions below to answer question 4.

     

     

    1. Which series shows the fractions ordered from least to greatest?

     

            A       

     

            B       

     

            C       

     

            D       

     


    1. Choose the correct symbol (<, > or =) to complete the comparison below.

     

     

    Hint: Use the fraction strips to help you answer the question.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Which sign shows the correct comparison between the fractions?

     

            A        <

           

            B        >

           

            C        =

     

     

    Use the figure below to answer question 6.

     

     

    1. Which fraction represents the shaded portion of the square?

     

    A          

    B          

    C          

    D          


    Use the figure below to answer question 7.

     

     

    1. Choose the decimal equivalent of the shaded part.

     

    A         0.04

    B         0.4

    C         0.24

    D         0.42

     

     

    1. How is 0.63 written as a fraction?

     

            A       

            B       

            C       

            D       

     

     

     

     

     

     

     

    1. Which sum is less than 1?

    A          

    B          

    C          

                 D          

     

     

    Multiple-Choice Answer Key

    1. D

    2. A

    3. C

    4. D

    5. A

    6. B

    7. D

    8. B

    9. C

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Short-Answer Items:

     

    Use the fraction circles for help if needed.

     

    1. What is  ?

     

     

    1. What is  ?

     

     

    1. What is  ?

     

    Short-Answer Key and Scoring Rubric:

    1. What is  ?  

     

    1. What is  ?  

     

    1. What is  ?    or 1

     

    Points

    Description

    2

    Answers the question correctly.

    1

    Finds either the numerator or the denominator correctly.

    0

    Fails to answer any portion of the question correctly.

     

    Performance Assessment:

    Materials:

    • pencils
    • counters
    • crayons
    • copy of the muffin tray below for each student and one for display. (Task 1)
    • copy of the smiley faces shown below for each student and one for display. (Task 2)

     

    Task 1

    Present the following problem to students: “You have a pan with 12 muffins.” Give each student a copy of the muffin trays. “You want to divide the muffins equally among 8 people. Answer the following questions on your paper:

    1. How much will each person receive?
    2. Will the amount each receives be more than one muffin or less than one muffin?
    3. Write your answer on your paper. Then explain how you figured out the answer.
    4. Now draw a picture to show how much muffin each person receives.
    5. Write a number sentence that explains how the 8 people shared the pan of muffins.”

     

    You may allow students to use counters or fraction circles to help them solve this problem.

     

    Task 2

    Present the following problem to students: “You have the following smiley faces.” Give each student a copy of the smiley faces. “Label your paper Task 2. Write your answers to the following questions on your paper.

    1. What fraction of the characters is winking (showing only one eye)?
    2. Which is greater:  or the fraction of characters winking?
    3. What is the answer to question 1 written as a decimal?
    4. What decimal represents the number of smiley faces that have a mustache?
    5. Which is greater: the decimal in question 4 or the decimal 0.30?”

     

    If necessary, remind students how to turn a fraction to a decimal and remind them that the fraction bar is really a division symbol.

     

     

    Performance Assessment Answer Key:

    Task 1:

    1. How much will each person receive?

     or  or  or  muffins.

     

    Will the amount each receives be more than one muffin or less than one muffin?

    More.

     

    1. Write your answer on your paper. Then explain how you figured out the answer.

     

    Because each person can have a whole muffin with 4 left over. So everyone gets one plus some more.

     

    1. Now draw a picture to show how much muffin each person receives.

     

    1. Write a number sentence that explains how the 8 people shared the pan of muffins.   

     muffins

     

    Task 2:

    1. What fraction of the characters is winking (showing only one eye)?      
    2. Which is greater:  or the fraction of characters winking?            
    3. What is the answer to question 1 written as a decimal?    0.125
    4. What decimal represents the number of smiley faces that have a mustache?     0.5
    5. Which is greater: the decimal in question 4 or the decimal 0.30?             0.5

     

    Performance Assessment Scoring Rubric:

    Points

    Description

    4
    • Demonstrates understanding of the concepts of equal share from Task 1.
    • Demonstrates understanding of the concept of writing a fraction or a decimal.
    • Demonstrates understanding of how to compare fractions and decimals.
    • Completes all parts of Tasks 1 and 2 correctly.
    • Performs beyond the problem requirements. Possibly incorporates multiple methods/solutions.

    3
    • Completes questions 1 and 4 of Task 1 correctly.
    • Completes one of questions 2 and 3 of Task 1 correctly.
    • Completes two of questions 1, 3, and 4 of Task 2 correctly.
    • Completes one of questions 2 and 5 of Task 2 correctly.

    2
    • Completes questions 1 or 4 of Task 1 correctly.
    • Completes one of questions 2 and 3 of Task 1 correctly.
    • Completes one of questions 1, 3, and 4 of Task 2 correctly.
    • Attempts questions 2 or 5 of Task 2

    1
    • Completes or attempts any one question of Task 1 Correctly.
    • Completes any one question of Task 2 Correctly.

    0
    • Fails to demonstrate any understanding of how to write a fraction or decimal.
    • Fails to demonstrate any understanding of how to compare fractions or decimals.
    • Does not attempt to complete either task.
Final 05/16/2013
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