M put a word problem on the board for homework towards the end of the period. I asked a boy for a rough estimate. He started thinking, but then the bell rang. We have to encourage and challenge the bright students. Our approach going step by step and giving attention to the weak students must not divert our attention from the very able students.

 

The homework was to do problems 16..32 even and 35. I asked them how many problems. The answer is (32-16 + 1)/2 + 1. The reason we have the +1 in the parenthesis can be understood if the assignment were to do 16..16 even. There is one problem assigned. When we take the last number – first number, we get 0 if the two are the same, 16..16, and so we have to add 1. After we calculated the result, I asked them to check by counting the problems. In general, if the assignment is a..b even, the number of problems is  (b-a + 1)/2.

 

This is an example of something to make them think. Mathematics is thinking. We can encourage thinking by asking them something relevant to their lives. How many problems they have for homework is very relevant.