Fold and Hole Sequence – A Math Activity

Fold and Hold Symmetry

Do you know the simplest way to teach kids symmetry mathematically is to do ‘Fold and Hole’ method. The one where you first fold the paper in a certain way and then punch a hole through it. Now without unfolding the paper, determine how many holes will be there and where each hole will be made. These strong spatial reasoning activities are said to develop problem solving and critical thinking skills among kids from early childhood. And, there are various ways we can teach this to our kids through art and mathematical activities.


In fact, kids start learning about symmetry through art from their preschool years. Remember the butterfly craft, the one where kids paint on one half of the paper, one of the wings of the butterfly and then fold the other half on top of it. As a result, the paint to get copied on the other side of the paper. And, when the paper is opened, two perfectly symmetrical butterfly wings are revealed. So, what exactly is symmetry ? Symmetry is when two parts of a whole are exactly identical. Something is symmetrical, if you can draw a line vertically down in the center and each side looks identical. This vertical line is called the line of symmetry.

How to do the activity

To do the Fold and Hold activity, all you need is a square piece of paper and a hole puncher. Fold the paper in different ways along the line of symmetry and punch a hole though the layers of paper. Without unfolding the paper, ask your kids where they expect the holes to be and how many holes would be there once you open the paper. Keep folding the paper in different ways and punching holes at separate spots. Slowly, your kids would start to understand the symmetry between the fold and each hole.

You can also work backward and show your kids a page with some holes. Ask them, how the page should be folded to get the above result by punching just one hole. The kids might use their imagery or analytical strategy to figure out the answer. Like, how many paper folds were punched through and therefore how many holes would be in the end.

Start by folding the paper into one fourth and punching a hole in the center. Ask your kids, how many holes would be there in the paper when it is opened.

Similarly, you can fold the paper in many different ways to reveal different patterns.

Can you guess how the paper is folded in the below patterns ?

A Big X- Pattern 1

A Circle – Pattern 2

Circle Within a Circle – Pattern 3

Two Ovals – Pattern 4

Two X’s – Pattern 5

It’s my goal to teach my kids math in a fun and interesting way. If you like my posts, please consider sharing it and liking my facebook page.

Here are some more interesting math activities.

Happy Learning !

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