Comparing E

Compare fractions with unlike numerators and unlike denominators using models and symbols

Fraction Learning Pathway

Pretty Powerful Paper Folding



Students fold colourful paper strips into equal parts that represent unit fractions and label the folded regions using symbolic notation. These strips are powerful visual tools that allow students to see the relative size of fractional regions, which allows them to compare familiar fractional quantities.


Current educational and classroom research strongly highlights the importance of developing a sense of a fraction as a size as well as a quantity. Creating fraction strips through paper folding provides students with the opportunity to visualize fractional size, and once stacked, allows students to see equivalency as a way of naming the same area using a different number of units(e.g., the size of 24 is the same as the size of 12 but the units are different).

Curriculum Connections

Students will:

  • demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that 34 is equal to 912 )

Instructional Sequence

  5. Have some students stand side-by-side and hold different strips that show equivalency.

Highlights of Student Thinking

Students may:

  • fold in one direction or in two directions
  • use repeated halving by folding in half and then again in half
  • need to make several attempts at accurately folding the strips
  • fold without attention to equi-partitioning
  • label each partition as one of the unit they are writing (e.g. 13 , 13 , 13 ) or as a count (e.g. , 13 , 23 , 33 )

Key Questions

  5. Do you see any equivalent-sized folds (regions)?


  • Eight different coloured strips per student, with extras for errors

Pretty Powerful Paper Folding Video Transcript

Time Transcript
0:00 Student 1: I had to fold it into ninths so can I show you how I did it? Teacher: Sure. Student 1: I folded it into three and then I folded that into three so that is nine. Yeah. Teacher: What did you fold into three? Student 1: This. I don’t know I folded this piece of paper into three and then I took that length and I folded it into another three and I got nine.
0:29 Teacher: How are you folding your strip into ninths? What did you do? Student 2: I am folding them like a fan. Teacher: OK. How did you know where to start? Student 2: At the 22 mm and then I started folding back and forth cause if you fold like this they start getting bigger every time (showing a ‘roll’ fold). Teacher: So by going back and forth in a fan design, you keep them as accurate as possible? Student 2: Yeah. Teacher: I will be interested to see what it looks like at the end. Student 2: And it ends up (unfolding it). Teacher: Do you want to check to make sure? Student 2: (placing alongside ruler) One. Two. Three. Four. Five. Six. Seven. Eight. Nine. Ten.