Paper Folding

“The ability to describe, use, and visualize the effects of putting together and taking apart shapes is important because the creating, composing, and decomposing units and higher-order units are fundamental to mathematics.

Further, there is transfer: Composition of shapes supports children’s ability to compose and decompose numbers”

 Clements and Sarama


Paper Folding

One simple way to approach composing and decomposing shape is to fold paper.

A task I suggested was simply to take a piece of paper and challenge students to fold it so as to have 2 shapes. Then describe the 2 shapes. Compare the possibilities across the class. (In the early grades just folding and seeing what shapes you can see it the task. I give out rulers and invite students to match them to the fold lines and then trace the line.)

  • What if I wanted one triangle and something else? Where would I fold?
  • What if I wanted no triangles, where would I fold?
  • What if I used 2 folds and wanted 3 shapes but only one triangle? where would I fold?
  • What if I used 2 folds and wanted 3 shapes two of them triangles? where would I fold?
  • What if I used 2 folds and wanted 3 shapes none of them triangles? where would I fold?
fold to make 5 sided shape
I folded to have one triangle. Do you know where it is? What shape is this?
Fold to make a 6 sided shape
I folded to have 2 triangles. What is the other shape

Label the shapesIMG_0226

Here is a paper folding power point that prepares students for the multiplicative reasoning that supports multiplication, division, fractions and decimals. Take a look:

Folding Tasks for Multiplicative Thinking

Here is another interesting folding power point. This screen-shot-2016-10-15-at-9-30-49-pmone is about interpreting folded diagrams. You might want to give it a try. I would suggest Grade 3 and up again.

Predict the Green Folds


Support ideas for using dot collections to build number properties are included in the power point I shared on Number Sense.


I am sharing some ppts that are dot collections. Preview them before using with class. I always create 3 slides to repeat each collection. I flash a collection 3 times before initiating a discussion.


 Lowrie et al. looked at the effects of a spatial intervention program for grade 8 students. The study involved 876 grade 8 students across 9 schools. The students received 20 hours of spatial interventions while other grade 8 students in the same schools did not. Both sets of students participated in a regular math class. The students who received the “spatial intervention” performed:

  • significantly better on spatial tasks (13% higher)
  • significantly better on Geometry – Measurement (problems included material not discussed in their intervention or in their math class
  • significantly better on Number – Algebra problems