Problem Description Sheet:       Putting the Pieces Together            

Introduction: When you share an orange or a chocolate bar, you have to break it into pieces and give those pieces to your friends. Each of the pieces is a part (or fraction) of the whole orange or whole chocolate bar. In this problem you will explore fractions.

Problem:

  1. Draw a square that is 6 cm by 6 cm. Using a ruler and pencil, measure and shade 1/3 of its area.
     

  2. Draw another square that is 6 cm by 6 cm. Using a ruler and pencil, measure and shade 5/8 of its area.
     
  3. If helpful, draw five more 6 cm by 6 cm squares. Divide, label, and cut out the first square as halves, the next as thirds, the next as fourths (quarters), the next as sixths, and the last as eighths. You can use these to help answer the following:

    a. How many sixths equal one-half?
    (1/2 = ?/6)

    c. How many thirds equal four-sixths?
    (4/6 = ?/3)

    b. How many eights equal three-quarters?
    (3/4 = ?/8)

    d. How many sixths equal one-quarter?
    (1/4 = ?/6)
     
  4. You can use the paper cut-outs to help you order the following fractions from smallest to largest: 1/2, 1/3, 3/8, 5/6, 1/10, 2/3
     
  5. Answer the following questions. Your paper cut-outs of the fractions might be helpful.

    a. What does 2/3 + 1/6 equal?

    b. What does 1/2 + 1/4 + 5/8 equal?
     
  6. Do you think 2/3 + 1/4 = 3/7? Explain or show your answer in detail.

Materials: pencil, paper, ruler, paper squares (fraction blocks)

Topic(s):

Fractions (N-92,94,97),
measurement, critical and creative thinking, communication

Activity Type:

  Group  Individual 

Assessment:

  Scale:      Levels 1-5        

  Self  Peer  Teacher 

  Include in your portfolio?
  Yes  No  Optional 

  Toward your marks?
  Yes  No  Optional 

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