Why do this problem?
is a great example of how patterns and numbers may be investigated in everyday contexts. If you are looking for opportunities that give your pupils chance to follow things up themselves, then this may be your answer!
This investigation would work well with the children in pairs, each pair with their own copy of the December calendar section. It might be helpful to supply them with a paper frame to isolate the set of four numbers. This can easily be slid around the calendar to find new sets of four.
The problem begins with the lowest set of numbers simply to make the addition tasks easy. Later in the investigation encourage the children to move to the largest numbers they can cope with. Depending on children's experiences, encourage them to try and explain any patterns that they find.
Tell me about the numbers you've found.
What have you done to get these answers?
If appropriate, guide the children to try multiplying the numbers and looking for patterns. If the children understand the basic concept of multiplication but can't readily manage the calculations, using calculators would be appropriate. This investigation could be revisited several times, trying different approaches each time. Encourage the children to discuss discoveries and suggest new
things to try. For example, what happens if the square box is enlarged to include nine numbers, or a rectangular frame of six numbers? Test discoveries on other months. What would happen if we lived somewhere where a week consisted of 6, 5, or just 4 days?
Those who struggle a little may need some help to focus on which numbers they are dealing with at each moment - an adult helper would be good.