Shaping Up! Exploring 2D and 3D Shapes

I’m sure you’ve been there: you carefully select a gift for a toddler only to find he’s more interested in the box. As for toy wooden blocks, multicolor building construction bricksbabies, the gift wrap might as well be the gift. My son Charlie was no exception. He showed no interest whatsoever in his first Christmas gifts.

We returned from a shopping trip late in December to discover that all he wanted to play with were cans (we call them tins in England). He loved cans of soup, condensed milk, olives and soon developed a savvy eye for more specialist products like Thai coconut milk. To his absolute delight, Charlie discovered that if you lay a can on its curved surface, it will roll, everywhere! Puzzlingly, the can didn’t roll when placed on the two flat faces, but the flat parts provided other possibilities: they enabled the cans to be stacked and as long as you could get your hands on enough cans from the cupboard, you could build towers.

Soon we had unlocked the key to keeping our son entertained on shopping trips: unstacking and stacking shelves – for as long as we could get away with it. When we were just at the point of being kicked out of the store, we would smile at the security guard and hurry off to pay for our purchases.

At nine months of age, Charlie was doing what babies are naturally programmed to do: explore the properties of three-dimensional objects. The cylinder was his favorite shape, but high on his list was the ball or sphere, probably the simplest and most entertaining of solid shapes. Children are interested in solid shapes before they are ready to explore plane shapes, because you can feel, observe and play with solid shapes. Junk modeling encourages children to see how shapes fit or do not fit together. This encourages spatial reasoning and problem solving. Save food containers and empty packages for the purpose. I’m not saying you have to keep them forever, unless of course someone gives you a bar of Swiss Toblerone chocolate; triangular prisms are hard to come by.

Why is shape important?

Shape and Space (Geometry) is a huge area of the mathematics curriculum, but for some reason it’s not taken as seriously as Arithmetic. It’s as if you have to be abstract to be clever. When I was a teacher, the government was obsessed with getting calculations right, although Geometry is important for lots of reasons:

Spatial Awareness

The world is built of geometric shapes and Geometry is the language of shape. The ability to call up 3D shapes in your mind and reason with these images is important for developing spatial awareness.

Understanding Abstraction

You need experience with the concrete before you can comprehend the abstract. Understanding the relationship between shapes and sizes will help you do that. Classification lies at the heart of mathematics. If a child can classify shapes according to particular attributes, she’ll find classifying prime numbers less abstract.

Brain Capacity

Geometry helps you connect your more logical left-brain with the more visual right-brain and gets the two sides working together.


Most geniuses, such as Einstein, had the ability to think multi-dimensionally. He argued that we live in a four-dimensional world, yet often expect our children to learn in a two-dimensional way (verbally and through text books). Geometry gives us the opportunity to explore multi-dimensions.

The Language of Shape

As your child gets older, you can start to introduce the vocabulary of shape. Before using the names we give shapes (cylinder, sphere, cube) start with words for concepts: round, flat, edge, corner, straight, curved, face, surface.  “The ball rolls because it is round.” “The cans stack because they have a flat part”. Call me pedantic, but when you start using the language of shape with your child, it’s good to get it right. 2D shapes, such as squares, have straight edges or sides and circles have curved lines. 3D shapes, on the other hand, have faces and surfaces.  A sphere has one curved surface. A cube doesn’t have six sides; it has six faces, each of which is square. “Come on, that’s over the top with a young child,” you might be thinking. The shape police aren’t going to get you if you say a cube has sides. My point is that it’s never too early to introduce correct terminology and get your child thinking like a mathematician. This will help iron out misconceptions later on. Architects and designers will understand what I mean.

When I was a full-time teacher in England, I saw first-hand the positive benefits of encouraging young children to explore shape and use the correct language. I was about to embark on teaching shape with my new class of five-year-olds, only to discover that Maeve, the experienced teacher in-charge of the class the previous year, had taught the children everything I was supposed to teach them that year already. Forget squares and triangles, a particularly bright five-year-old boy asked me if I knew that a pyramid was a triangular-based prism, also known as a tetrahedron. We then looked at Egyptian and Mayan pyramids and discussed why a square base is more stable. If you treat children like experts and have high expectations of them, you’ll be amazed at what they can learn!

Once you get started on shape with your children, you may feel you need to do some homework to keep up with them. Not everyone knows the difference between a rhombus and a kite, or that a square is a kind of rhombus. Most of the basics can be found online. Incidentally, a kite does not always have four equal sides or two pairs of parallel sides like a rhombus. In my next two articles, I will be sharing more shape resources and looking at activities you can do with your preschooler at home.

For ideas and activities see my Pinterest Board, “Exploring Shape”.


Shape and Space in Geometry. Available at (Visited March 3, 2015)

Liebeck, Pamela. How Children Learn Mathematics. Penguin, London: 1984.


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