Addition makes a number bigger
Sometimes a question helps them broaden their understanding of math terminology:
Two identical triangles can be put together to make a parallelogram
I know some students will say 'Sometimes true' offering the case where two right-angled isosceles triangles join to make a square (in green below) which, they think, is not a parallelogram. Others might make what they think is a more obvious parallelogram (in blue below).
This gives us a great opportunity to learn why all squares are parallelograms (quadrilaterals with two pairs of parallel sides). This leads into an understanding of why the area of a triangle (½×base×height) is simply half the area of a parallelogram (base×height)
Perhaps my two favourite questions I got today were:
A solid that has a square shadow is a cube
A solid that has a circular shadow is a sphere
It immediately got me thinking about other solids that might have these shadows. Or what about if I reverse the order of each statement?:
A cube has a square shadow
A sphere has a circular shadow
So here, for your delight, are some other Always true/Sometimes true/ Never true questions:
- A rectangle is a square
- When you cut a piece off a shape, you reduce its area
- When you cut a piece off a shape, you reduce its perimeter
- Bigger objects are heavier than smaller ones
- The diagonals of a parallelogram are unequal in length
- Multiplication makes numbers bigger
- Division makes numbers smaller
- The sum of four consecutive numbers is a multiple of 4
- The sum of three consecutive numbers is a multiple of 3
- The more you roll a dice, the more likely you are to get a 6.
- The sum of two odd numbers is an odd number
- The product of an even number and an odd number is an odd number.