Hollow Squares
Here is a hollow square.
- How many pegs form the square on the outside?
- How many pegs are there in the hollow?
- Draw some more hollow squares.
- Investigate.
Examples drawn from Hollow Squares.
Pupils can draw and make some hollow squares and count the dots in the middle (or on the sides).
- Example 1 - 16 pegs on outside
- Example 1 - 36 pegs on outside
- Example 1 - 18 pegs on outside
- Example 1 - 8 pegs on outside
Probing questions
Can you give me some other examples that match this statement? Can you give me some examples that don't match it?
What if pupils find this a barrier?
Line Crossings
- Draw three straight lines (line segments) so that some cross over each other.
- How many crossings are there?
- Try different arrangements of the lines. What is the maximum number of possible crossings?
- Try using more lines.
- Is there a rule for the maximum for any number of lines? If so, write it down.
Use the problem Line Crossings.
- Can you draw a different arrangement?
- How many crossings are there?
- Now try another arrangement and explain how many crossings.
- How would you write this down?
"How many crossings? There are one, two, three, four, five crossings"
"Four lines, four crossings"
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