Educational tips and a printable template

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Tangrams for kids: A learning tool for building STEM skills

Like building blocks, tangrams can teach kids about spatial relationships. They may help kids learn geometric terms, and develop stronger problem solving abilities. They might even help children perform better on tests of basic arithmetic. But what is a tangram?

Invented in China approximately 200 years ago, a tangram is a two-dimensional re-arrangement puzzle created by cutting a square into seven pieces — seven geometric shapes called “tans” (Slocum et al 2003).

What are the seven shapes in a tangram? Each tangram puzzle contains the following:

• 2 large right triangles
• 1 medium-sized right triangle
• 2 small right triangles
• 1 small square
• 1 parallelogram

Arranged correctly, these tangram shapes can be fitted together as a large square, rectangle, or triangle. They can also be arranged in a variety of complex shapes, including fanciful ones.

There are many ways to play with tangrams. The simplest way is to let kids create their own complex shapes. But traditionally, tangrams are treated as puzzles, where players are challenged to reproduce specific designs. And there are rules.

The classic rules

The classic rules are pretty simple. To count as a standard solution, players must meet the following criteria:

• a completed design must use all of the tangram pieces;
• every piece must touch at least one other piece, even if it’s just the apex of a corner contacting another piece; and
• all of the pieces must lie flat, with none overlapping each other.

Also, in the standard, classic approach to the puzzle, the player is shown a target shape in outline only, so that the “seams” between the composite tans are concealed. Then the player attempts to recreate the shape using the seven pieces.

In essence, it’s an exercise similar to structured block play, where the challenge is to create an exact copy of a structure depicted in a diagram. But there’s a key difference.

In structured block play, the diagram provides you with explicit, visual information about where each piece goes. With a tangram puzzle, you’re left to figure that our for yourself.

As noted by Zhen Yuan and his colleagues, solving tangram puzzles appears to activate parts of the brain associated with creative thinking and trial-and-error problem-solving (Hu et al 2019).

What makes tangrams especially challenging?

The most difficult puzzles are called classic, “silhouette puzzles,” where players can’t see the internal lines defining the tans that make up a solution. In the image below, the middle row of tangrams are silhouette puzzles. The other rows provide players with explicit cues about the internal structure of each puzzle.

We can make things easier for players by providing them with lines or color cues as illustrated above. But even then, beginners — especially young children — may have difficulty matching the template. Puzzles often require the player to orient shapes in non-standard ways. You may need to turn or flip a piece to make it fit.

It’s not unusual for children to visualize certain shapes with a very particular orientation in mind. For example, students may think of a square not simply as a figure with four equal sides, but as a figure that “sits” flat along the horizontal plane (see image below). If the square is tilted from this orientation, kids might not interpret it as a square anymore. Now it’s a diamond (Clements and Sarama 2014).

This means that players may be slow to recognize the tan they need, even if the shape is right in front of them. If it’s not already oriented in a way that parallels the target orientation, they might not make the mental connection.

No wonder, then, that learning to turn and flip shapes is often a major breakthrough for players. It helps them reinterpret how pieces can fit together (Bofferding and Aqazade 2023).

What are the educational benefits of tangrams?

When we play with tans, we consider the shapes from a variety of angles and perspectives. How would the shapes look if we stuck them together? Rotated them? Slide them around into different positions?

Experiments suggest that thinking about such things — visualizing the spatial relationships between shapes in your “mind’s eye” — can boost our visual-spatial skills.

Research hints that it can boost arithmetic performance, too. When Yi Ling Cheng and Kelly Mix asked kids, aged 6-8, to perform a series of tangram-like spatial tasks, the practice session seemed to prime the brain for mathematics.

Kids who spent 40 minutes solving shape rotation puzzles performed better on a pencil-and-paper arithmetic test immediately thereafter.