Distinguish defining attributes of shapes (e.g. triangles are closed and three-sided) from non-defining attributes (e.g. colour, orientation, overall size)
Every triangle has 3 straight sides and 3 corners. That is what makes it a triangle. It does not matter what color it is, how big it is, or which way it is turned.
Mia draws a tiny green triangle on her paper. Then she draws a huge yellow triangle next to it. They look very different, but both have 3 straight sides that join up with no gaps, and 3 corners. So both are triangles.
To check if a shape is a triangle, do not look at the color or the size. Count the straight sides. If there are 3 sides and 3 corners, and the sides join up with no gaps, it is a triangle.
A triangle is a triangle because of its 3 sides and 3 corners, never because of its color, size, or direction.
A polygon is a shape made of straight lines that close up. The lines meet at points called vertices. The corners are called angles. Every polygon has the same number of sides and angles.
Here are some common polygons:
- Triangle: 3 sides - Quadrilateral: 4 sides, like a square, a rectangle, or a rhombus - Pentagon: 5 sides - Hexagon: 6 sides
When you draw a polygon, look at the number of sides. That number tells you the name. A shape with 3 straight sides is a triangle, even if it is big or small. A shape with 3 sides is still a triangle if it is red, blue, or green.
Try drawing your own. Pick a number of sides. Draw straight lines that connect end to end and close up. Count the sides to check the name of your new shape.
What is a polygon?
A polygon is a closed shape with at least 3 straight sides. Closed means there are no gaps. The lines join end to end all the way around.
Polygons get their names from how many sides they have:
3 sides is a triangle 4 sides is a quadrilateral 5 sides is a pentagon 6 sides is a hexagon 7 sides is a heptagon 8 sides is an octagon
Watch out for shapes that are not polygons. A shape with a gap in it is open, so it is not a polygon. A circle has no straight sides, so it is not a polygon either.
To check if a shape is a polygon, ask two questions. Is it closed? Are the sides straight? If you can say yes to both, you have a polygon. Then count the sides to learn its name.
A tangram is a set of seven flat pieces called tans. The tans include triangles, a square, and a parallelogram. You can slide and turn the pieces to make new shapes.
Each tangram piece keeps its own shape. But when you join pieces together, the new shape can change:
- The number of sides can grow or change. - Two short sides can join into one longer side. - The new shape can belong to a new family, like a new quadrilateral.
Try it yourself. Take two triangle tans and push them together along one side. Count the sides of the new shape. Is it still two triangles, or is it one big triangle or one quadrilateral now? Slide, turn, and join the pieces to build shapes with 3, 4, or 5 sides, and count the sides to name each one.
Shapes are all around you. A door is a rectangle. A road sign might be an octagon. A slice of pizza can look like a triangle.
Here is a fun game to play outside or at home. Pick a shape and look for it in the world around you. For each shape you find, tell two things about it.
First, tell its defining attributes. These are the parts that make the shape what it is. How many sides does it have? How many corners? Are the sides straight? Is the shape closed, with no gaps?
Next, tell its non-defining attributes. These are things that can change without changing the shape. How big is it? What colour is it? Which way is it turned?
Try it with a triangle. A yield sign is a triangle. A big red yield sign and a small blue one are both still triangles. They have 3 straight sides and 3 corners. That is what makes them triangles. The colour and size are just extra details.
You have counted sides and corners before. On the playground there are shapes painted on the ground, and today the game is: only stand on the triangles. Mia finds a tiny green one, with a huge yellow one right next to it.
Mia is not sure the huge yellow one counts. What should she check?
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14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.