Fractions: Dividing shapes into parts with equal area

Suggested Books
Book Cover
The Underachievers

Grade level:  3rd grade

Common Core Standards:  3.NF.3,3.G.1, 3.G.2, 3.MD.7d

Time for the lesson:  2 hours

Supplies:  Pattern blocks, The Underachievers by Holly Young, Dividing shapes handout

1)   Review working definition of fraction:  A whole cut into equal parts.

2)   Read Underachievers by Holly Young from pg. 15 to pg. 21.

3)   Divide Geometric shapes into parts with equal area: 

  • Looking at pattern blocks (all students receive access to many different blocks per table group), ask them to decide which ones could make 1 whole?  [all of them can]
  • Ask them to decide which blocks can be cut in ½ using another shape?  Model with the hexagon and trapezoid. 
  • Using the handout (page 1), ask students to work independently first and then share responses.  Look for misconceptions.  Encourage students to be creative with how they cut their shapes.
  • Looking at pattern blocks, ask students: Which blocks can be cut into thirds using another shape?  What do they have in common?  Can you divide the other shapes?  Why or why not?
  • Using the handout (page 2), ask students to work independently first and then share responses.  Look for misconceptions.  Encourage students to be creative with how they cut their shapes.
  • Looking at pattern blocks: What other fractions can any of the shapes be divided into using pattern block shapes?  Discuss?
  • How can we divide up any shape into a number of equal parts – discuss and look at strategies (cut and fold).  Prove and justify!  Using handout (page 3):  Irregular shapes – how to do it?  Use graph paper behind it, handout page 4 – how can that help?
  • Using handout (page 5):  Look at shapes that have parts shaded in – what is the fractional part that is shaded?  Ask students to share strategies.

4)   Exploration:  Ask students to use a pattern block repeatedly to create a larger version of itself.  For example – 9 squares can be placed to create a larger square.  Then ask what fraction each original piece represents.  In the square example, the fraction is 1/9.