Label this plum tree graph to make it totally magic!
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
The Hints section contains additional direction for students
engaging with this task.
Students often possess the method but without any sense of why
it's valid. Hopefully this activity will not only help them to
explore this method's validity but will also encourage in them a
questioning attitude and a desire to establish the validity of
other common methods as they meet them.
There are a large number of values displayed on the sheet called
'Patterns with differences' (see the tab at the bottom of the work
area on Interactive Number Patterns 2). Students need to be given
the time to understand all parts of the display.
Below the formula box are three rows. These display the values
of the quadratic, linear and constant terms respectively. Change
the terms in the formula box to help students grasp what each row
shows, and verify that the three values added together match the
blue values. In the two rows of differences above the formula box
and verify that the data showing is the correct difference for the
blue values, and use the slider to change the red values, allowing
students to verify the new values displayed within the sheet.
The constant term contributes nothing to the first difference,
the linear term contributes to the first difference but not the
second, and the coefficient, or multiple, of the quadratic term is
the only coefficient which influences the second difference.