Lesson 2 Representations of Fractions (Part 2)

    • Let’s name some other fractions and represent them with diagrams.

Warm-up Which One Doesn’t Belong: All Cut Up

Which one doesn’t belong?

  1. Shape. Square partitioned into 4 equal smaller squares.
  2. circle partitioned into 3 equal parts.
  3. square partitioned into 3 unequal parts.
  4. shape. hexagon partitioned into 3 equal parts. 1 part shaded.

Activity 1 A Diagram for Each Fraction

Work with a partner to match each fraction with a diagram. Two of the fractions have no matching diagrams. Use the blank diagrams to create representations for them.

  1. diagram. 8 equal parts, 4 part shaded.
  2. Diagram. Rectangle partitioned into 3 equal parts, 2 parts shaded. 
  3. Diagram. 5 equal parts, 3 parts shaded
  4. diagram. 8 equal parts, 7 parts shaded
  5. Diagram. 10 equal parts, 6 parts shaded
  6. diagram. 6 equal parts, 5 parts shaded.
  7. diagram. 8 equal parts, 3 parts shaded
  8. diagram. 6 equal parts, 4 parts shaded
  9. diagram. 5 equal parts, 2 parts shaded.
  10. Tape diagram. 4 equal parts. 3 parts shaded. 
  11. Diagram. Rectangle partitioned into 10 equal parts, 4 parts shaded. 
  12. diagram. 12 equal parts, 6 parts shaded.
  13. Diagram.  Rectangle partitioned into 12 equal parts, 5 parts shaded. 
  14. diagram. Rectangle, 1 whole.
  15. diagram. rectangle.

Activity 2 Diagrams for Some Other Fractions

Problem 1

What fraction do the shaded parts represent?

  1. 2 diagrams of equal length. Left diagram. 2 equal parts, 1 part shaded. Total length 1. Right diagram, 2 equal parts. Total length 1.
  2. Diagram. Rectangle partitioned into 4 equal parts. 3 parts shaded.
  3. Diagram. Rectangle partitioned into 6 equal parts. 4 parts shaded. 
  4. Diagram. Rectangle partitioned into 8 equal parts. 4 parts shaded. 
  5. Diagram. 8 equal parts, 6 parts shaded

Problem 2

Here are four fractions and four blank diagrams. Partition each diagram and shade the parts to represent the fraction.

  1. 2 diagrams of equal length. 1 part. total length, 1.

  2. Tape diagram. Two equal parts. 

  3. Tape diagram. Two equal parts. 

  4. Tape diagram. Two equal parts. 

Practice Problem

Problem 1

  1. The entire diagram represents 1 whole. What fraction does the shaded portion represent? Explain your reasoning.

    Diagram. 10 equal parts, 7 parts shaded.

  2. Shade this diagram to represent .

    Diagram. Rectangle partitioned into 10 equal parts.