1. What makes these shapes tricky for children to identify?
They don't look like the standard equilateral point-up triangle, and so they don't fit the mental image they have developed of what a triangle is. Some children develop an internal visualization of "triangle" that is restricted to just equilateral triangles.
2. What makes these shapes tricky for children to identify?
They have the general shape of an equilateral triangle, and you have to attend to the details of the triangle definition (and realize that the details are important) to understand that these are not actually triangles.
3. What are some things you can do when teaching what triangles are that will help children understand the definition of triangle better?
4. What are the defining characteristics of a triangle (that are usually used in the definition of a triangle)?
It must have 3 straight sides and 3 angles
5. What are the defining characteristics of a rectangle (that are usually used in the definition of a rectangle)?
It must have 4 straight sides and 4 right angles.
It's OK (also correct) to add that the opposite sides have to be the same length.
It's not OK to add that the length and width have to be different. (this is not a correct property of all rectangles)
6. What are the defining characteristics of a square (that are usually used in the definition of a square)?
It must have 4 straight sides that are all equal, and it must have 4 right angles.
7. Is this a rectangle? How do you know?
Yes, it is. The defining characteristics of a rectangle are that it has 4 straight sides and 4 right angles. This shape has 4 straight sides and 4 right angles, so it is a rectangle.
8. Is this a square? How do you know?
No. The defining characteristics of a square are that it has 4 equal length straight sides, and 4 right angles. This shape has 4 right angles, but its sides don't all have equal length, so this is not a square.
9. Are all squares special kinds of rectangles?
Yes (see #7)
10. Are all rectangles special kinds of squares?
No, some are not (see #8)
11. What is wrong with this rhyme? (What misconception does it reinforce? What does it not include?)
Ricky Rectangle is my name.
My four sides are not the same.
2 are short and 2 are long.
Count my sides, come right along.
1, 2, 3, 4.This rhyme reinforces the misconception that a square is not a rectangle.
It does not include that the angles have to be right angles (could be a parallelogram).
12. Other than color and position, what are some properties that some triangles have (and children might think of triangles as having), but that aren't defining characteristics (triangles don't have to have those properties)?
Children might think that triangles have to have a point on the top and a side on the bottom. They might think that the sides have to be all the same, or that two sides have to be the same. They might think that a triangle has to look like a witches hat or a tooth. They might think that triangles can't be too skinny or too fat.
13. Other than color and position, what are some properties that some rectangles have (and children might think of rectangles as having), but that aren't defining characteristics (rectangles don't have to have those properties)?
Children might think that rectangles have to have one long side and one short side (the length and width have to be different). They might think that a rectangle has to be shaped like a door, or that it has to be taller than it is wide, or that one side has to be twice as long as another side.