Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Can you explain how this card trick works?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
These investigations require a supply of calendars that, at this
time of the year, should be easy to acquire. They are appropriate
investigations for the beginning of the new term as they provide an
opportunity to review foundation knowledge and basic skills in the
areas of numeration, operations and pattern.
Have the children bring in old calendars from home. It does not
matter which months are used. If the children work in groups but
have their own calendar page to investigate they will have plenty
to compare, predict, discuss and explain.
Before results are shared in the bigger group, the children
should be encouraged to look beyond the immediate answers they get
and see how the answer relates to the numbers on the calendar.
In investigating the square of nine numbers, do they identify
that the sum is three times the number in the centre?
Can any similarity be found between the three by three square and
the totals they get in the rows and columns for the four by four
Based on the results, what predictions can be made about the sum of
the right and left columns or the top and bottom rows?
Will it matter what month is chosen?
What if a different square of numbers is chosen?
What is the largest square that can be found in a month?
What would happen if they changed from investigating a square to
investigating a rectangle?
What if, for example, a 3x4 rather than a 4x3 rectangle is
How about changing the size of the rectangle?