Naming circles, triangles, squares and rectangles

When you reach for it

Young children often learn shape names from one picture each: a triangle that sits flat with its point up, a square that sits flat on a side. Then a triangle pointing down, or a square standing on its corner, gets a new name, or none. The aim of these four days is that a name belongs to the shape itself, so a triangle stays a triangle when it is huge, tiny, thin, or turned any way at all.

Each day takes ten to fifteen minutes. Talk about shapes the way the child sees them (“it’s pointy”, “it’s round all the way”) and add the name each time; careful counting of sides and corners comes in the next lesson.

Day 1: Circles and triangles

You need: a cup or jar lid, a sheet of paper, crayons, scissors.

Trace around the bottom of a cup and say, “This is a circle. It is round all the way around, with no straight parts and no points.” Trace a smaller lid and a bigger plate: all circles. Then fold a square of paper corner to corner and cut along the fold. Hold up one piece: “This is a triangle. It has three straight sides and three points.” Turn it around in your hands and ask, “What is it now?” It is still a triangle.

Show the picture below and ask about each shape, “Is it a circle, a triangle, or neither? How do you know?” Two of the shapes are traps. A pizza slice has a curved crust, so it is not a triangle; a triangle needs every side straight. A shape with a dent cut into it has an extra point, four instead of three, so it is not a triangle either.

Practice. Point to each shape and ask its name.

1. Shape A. Answer: a circle.
2. Shape B. Answer: a triangle, even though it is small and tipped.
3. Shape C. Answer: not a triangle. One side is curved, like a pizza crust.
4. Shape D. Answer: a triangle, even though it is tall and thin.
5. Shape E. Answer: not a triangle. The dent at the bottom gives it four points, not three.

Day 2: Squares and rectangles

You need: a sheet of printer paper, scissors, a book.

Hold up the sheet of paper: “This is a rectangle. It has four straight sides, and every corner is a square corner, like the corner of this book.” Fold one corner of the sheet down to meet the long side, cut off the strip that sticks out, and unfold. “This is a square. It is a rectangle with all four sides the same length.” A square is a special kind of rectangle, so it is never wrong to call it a rectangle too; at this stage, calling it a square is enough.

Now stand the square on one corner. Many children call this a “diamond”. Say, “Some people call it a diamond. Its shape name is still square. I only turned it.” Turn it back to show nothing changed.

Practice. Point to each shape and ask its name.

1. Shape A. Answer: a square.
2. Shape B. Answer: a square, turned onto its corner.
3. Shape C. Answer: a rectangle, long and flat.
4. Shape D. Answer: a rectangle, tall and thin.
5. Shape E. Answer: not a rectangle. It leans over, so its corners are not square corners.

Day 3: Any size, any turn

You need: paper shapes cut in two sizes (a big and a small circle, triangle, square and rectangle), a table.

Lay one shape on the table and have the child name it. Then turn it a little, and a little more, naming it each time. Ask, “Did it change? What is different?” Only the way it points has changed. Swap in the small one of the same shape: “Is this one a triangle too, even though it is little?” Yes. Then let the child turn a shape and ask you to name it.

Finish with a quick game. Hold a shape behind your back, bring it out turned an odd way, and the child names it as fast as possible. Fast is fine here because it shows the name comes from the shape and not from which way it sits.

Practice. Point to each shape and ask its name.

1. Shape A. Answer: a triangle, pointing down.
2. Shape B. Answer: a rectangle, tilted.
3. Shape C. Answer: a circle, a tiny one.
4. Shape D. Answer: a square, turned a little.
5. Shape E. Answer: a triangle, tiny and pointing sideways.

Day 4: Shapes in the room

You need: nothing but the room you are in.

Go on a shape hunt. Say, “I spy a circle,” and let the child look until they find one: a clock face, a plate, the top of a jar. Take turns spying. Ask the child to trace the shape in the air with a finger and name it. Point out that flat faces of real things carry the shape names: the door is a rectangle, even though the door itself is thick. (Naming the solid things, like a ball or a can, belongs to naming solid shapes.)

Look for shapes inside shapes too. A window may be one big square split into four small squares.

Practice. Use the picture of the wall.

1. The clock. Answer: a circle.
2. The door. Answer: a rectangle, tall and narrow.
3. The whole window. Answer: a square.
4. One small pane of the window. Answer: a square, and there are four of them.
5. The flag. Answer: a triangle, pointing to the right.

Exercises

1. Name each shape A to D in the picture. If a shape is none of circle, triangle, square or rectangle, say which one it is close to and why it is not that shape.
2. Without looking around, ask, “Tell me one thing at home shaped like a rectangle and one shaped like a circle. How do you know?”

Where this goes next

Once the names hold up in any size and turn, a child can look closely at what makes each shape: counting sides and corners and sorting by them, and later saying which features matter and which do not in Defining and non-defining attributes of shapes. Putting small shapes together into new ones is composing and decomposing shapes. Words for where a shape sits, like above or beside, come in Position words: above, below, beside, in front of, behind. The square being a special rectangle grows into Rhombuses, rectangles and squares, and the circle’s “same distance all the way around” becomes the exact definition in what a circle is.